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Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. U n iv ersity M icrofilm s I n te rn a tio n a l A Bell & H o w e l l I n f o r m a t i o n C o m p a n y 3 0 0 N o r t h Z e e b R o a d . A n n A r b o r, Ml 4 8 1 0 6 - 1 3 4 6 U S A 3 1 3 -761-4700 80 0 /5 2 1 -0 6 0 0 O rd er N u m b e r 9 3 1 4 7 0 4 O p tim al a d o p tio n stra teg ies for con servation tilla g e tech n ology in M ichigan Krause, Mark A., Ph.D. Michigan State University, 1992 UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 OPTIMAL ADOPTION STRATEGIES FOR CONSERVATION TILLAGE TECHNOLOGY IN MICHIGAN By Mark A. Krause A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics ABSTRACT OPTIMAL ADOPTION STRATEGIES FOR CONSERVATION TILLAGE TECHNOLOGY IN MICHIGAN By Mark A. Krause Adoption of the no-till system of conservation tillage has been slower than many proponents expected, even though for many soils it appears to be more profitable than conventional tillage. This study evaluates whether dynamic adjustment costs due to machinery replacement and learning curves may delay no-till adoption. The effect of risk aversion on no-till adoption also is examined. The study determines optimal adoption strategies for two representative corn and soybean producers using a dynamic programming model. One of the representative farmers maximizes expected profit. The other representative farmer is risk-averse, and maximizes an expected utility function of net income. Crop yield parameters were estimated using crop growth simulation models. The mean estimated crop yields are slightly higher for the no­ till system than for conventional tillage, but only the differences for soybean yields are statistically significant. Estimated mean revenues net of variable costs also are slightly higher for the no-till system. Based on the estimated crop yields, the optimal adoption strategy for the profit-maximizing farmer is to immediately adopt the no-till system. If equal crop yields for the alternative tillage systems are assumed, the profit-maximizing farmer often delays adoption until currently-owned machinery has aged several years. A substantial learning curve also delays no-till adoption in this case. Based on the estimated crop yields, the risk-averse, expected utility-maximizing farmer often delays no-till adoption until currently owned machinery has aged several years. If equal mean crop yields are assumed, the expected utility-maximizing farmer never adopts no-till unless there is little or no learning curve. The results suggest that machinery replacement issues and learning curves affect the timing of no-till adoption by the profit-maximizing farmer and the risk-averse, expected utility-maximizing farmer. The machinery replacement issues and learning curves are particularly important to the risk-averse farmer. Both representative farmers would prefer to reduce learning costs by renting a no-till planter on a limited acreage. Technical support and opportunities to rent no-till planters appear to be critical components of no-till promotion programs. ACKNOWLEDGEMENTS Many people at Michigan State University helped me complete this dissertation. First, I thank J. Roy Black, my adviser, for his strong support and sage advice, which helped me over some hurdles and made the work more intellectually rewarding. I greatly appreciate the many helpful suggestions from my other dissertation committee members, Steve Hanson, Jack Meyer and Scott Swinton. Robert Myers and Lindon Robision also served on the committee in the early stages of this research and helped get me started. Frederic Dadoun, Brian Baer, and Joe Ritchie of the Michigan State Crop and Soils Department provided important help and moral support in modifying and using the CERES-MAIZE and SOYGRO crop growth simulation models for this research. In particular, Dadoun graciously provided modified source code for CERES-MAIZE that served as the foundation for these modifications, as is documented in the technical appendices. I greatly appreciate the financial support of the Agricultural Experiment Station at Michigan State University, which funded all of this research. Finally, I wish to thank my many friends among the graduate students and faculty of the Department of Agricultural Economics for helping me through the P h .D program and making my stay at Michigan State a happy one. TABLE OF CONTENTS Page LIST OF TABLES ............................................... viii LIST OF FIGURES .............................................. x Chapter 1 - EXPLANATION OF TECHNOLOGY ADOPTION LAGS........... 1 Introduction ........................................... Conservation Tillage and No-Till Technology ......... Problem Statement ...................................... Objectives ............................................. Hypotheses ............................................. Organization of the Dissertation ....................... 1 4 8 9 10 12 Chapter 2 - THEORETICAL FOUNDATIONS FOR THE ANALYSIS ......... 13 The Expected Utility Model for Risk Analysis ........... Input Demands under Uncertainty in a Static Model .... Dynamic Issues for Production Durables ................. Dynamic Programming .................................... 15 19 22 34 Chapter 3 - THE ANALYTICAL MODEL ............................. 40 State Variables and Control Variables .................. Modeling of Learning Curve Effects ..................... Length of the Planning Horizon ......................... Formulation of the Deterministic Model ................. Formulation of the Stochastic Model .................... 53 53 55 57 59 Chapter 4 - METHODOLOGY ...................................... 66 Crop Yields Climate and Soils in S.W. Michigan .................. Agronomic Studies of Crop Yields for Conservation Tillage Systems .................................... Effects of Soil Temperature on Corn and Soybean Growth Estimation of Crop Yields ........................... Input Data for the Estimation of Crop Yields ........ Determination of Operation Dates .................... v 67 69 71 73 78 83 TABLE OF CONTENTS (Continued) Page Chapter 4 (Continued) Production Costs The Machinery Sets .................................. Machinery Repair Costs and Trade-In Values .......... Variable Input Costs ................................ Determination of Crop Prices ........................... Computer Implementation ................................ 88 89 93 97 100 Chapter 5 - RESULTS FOR OPERATION DATES, CROP YIELDS AND NET REVENUES ......................................... 102 Good Field Day Results ................................. Scheduling of Crop Operations .......................... Crop Yields ............................................ Comparative Budget Results ............................. Variation in Net Revenue and Stochastic Dominance Results ............................................... Summary of Crop Yield and Static EconomicResults ....... 103 107 109 119 Chapter 6 - OPTIMAL ADOPTION STRATEGY RESULTS ................ 132 Results for the Deterministic Model .................... Limited Renting Options and Estimated Yields ...... Limited Renting Options and Equal Yields .......... Multiple Renting Options and EstimatedCrop Yields ... Multiple Renting Options and Equal CropYields ....... Results for the Stochastic Model ....................... Limited Renting Options and Estimated Yields ...... Limited Renting Options and Equal Yields .......... Multiple Renting Options ............................ Differences between Optimal and Second-Best Policies.. Review of the Research Hypotheses ...................... 134 134 136 142 146 149 149 165 165 167 168 Chapter 7 - SUMMARY AND CONCLUSIONS .......................... 172 Summary ................................................ Conclusions ............................................ Crop Yield Estimates for No-Till and Conventional Tillage ............................................ Economic Analyses of No-Till Adoption ............... Limitations of the Analysis ................. Suggestions for Further Research .................... 172 180 vi 122 130 179 183 189 193 TABLE OF CONTENTS (Continued) Page APPENDICES Appendix A -PROOF OF THE OPTIMAL REPLACEMENT RULES .... Appendix B - DETERMINATION OF DISCOUNT RATE AND CROP PRICES .................................... Appendix C - MODIFICATIONS OF THE CERES-MAIZE AND SOYCRO SIMULATION MODELS ................. Appendix D -TRACTOR REMAINING VALUE CALCULATIONS ...... Appendix E -MACHINERY COST ESTIMATES .................. Appendix F - DETAILED OPERATION DATE AND CROP YIELD RESULTS .................................. Appendix G - FORTRAN CODE FOR THE DETERMINISTIC DYNAMIC PROGRAMMING MODEL ........................ Appendix H - FORTRAN CODE FOR THE STOCHASTIC DYNAMIC PROGRAMMING MODEL ........................ Appendix I - MODIFICATIONS TO THE FORTRAN CODE FOR CERES -MAIZE .............................. Appendix J - MODIFICATIONS TO THE FORTRAN CODE FOR SOYGRO ................................... 196 BIBLIOGRAPHY ................................................. 307 vii 199 208 223 227 233 255 275 292 300 LIST OF TABLES Page Table 3.1 Control Options When a Large Tractor but No Planter is Owned ......................................... Table 3.2 Control Options When a Small Tractor but No Planter is Owned ......................................... Table 3.3 Control Options when a Large Tractor and Conventional Planter are Owned and Renting Options are Limited.. Table 3.4 Additional Renting Options when a Large Tractor and Conventional Planter are Owned ................... Table 3.5 Control Options when a Large Tractor and No-Till Planter are Owned................................. Table 3.6 Control Options when a Small Tractor and No-Till Planter are Owned................................. Table 3.7 Markovian Matrix of Price State Probabilities, Corresponding to the Historical Mean Prices ...... Table 4.1 Average Monthly Temperature and Precipitation, 1951-1980 at Kalamazoo, Michigan ................. Table 4.2 No-Till minus Plowed Corn Yields (kg/ha), 5-year Averages on Wooster and Hoytville Soils in Ohio ... Table 4.3 No-Till minus Plowed Soybean Yields (kg/ha), 5-year Averages on Wooster and Hoytville Soils in Ohio ... Table 4.4 Soil Nitrogen Inputs, Oshtemo sandy loam .......... Table 4.5 Soil Moisture Inputs, Oshtemo sandy loam .......... Table 4.6 Corn and Soybean Residue Inputs .................... Table 4.7 Tillage and Planting Machinery Implements .......... Table 4.8 Repair Cost and Trade-In Values for Planters ...... Table 4.9 Repair Cost and Trade-In Values for Tractors ...... Table 4.10 Variable Costs for MB Plow and No-Till Systems (excluding planter and tractor costs) ............ Table 4.11 Herbicides Applied by Crop and Tillage System ..... Table 4.12 Adjusted Corn and Soybean Prices ($/bu.), 1955-90 .. Table 5.1 Total Good Field Days by Specified Dates, MB Plow System ........................................... Table 5.2 Average Operation Dates, by Tillage System ........ Table 5.3 Mean Estimated Crop Yields (BU/A) for 70% Fall Plowing and No-Till, with July and August rainfall (inches) ................................ Table 5.4 Mean Estimated Crop Yields (BU/A) for 100%, 70%, and 45% Completion of Plowing in the Fall ........ Table 5.5 Revenues Net of Variable Costs, MB Plow and No-Till viii 43 44 45 46 47 48 62 67 70 70 79 80 80 90 91 92 95 96 99 106 108 110 116 120 LIST OF TABLES (Continued) Page Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table 6.7 Optimal Adoption Strategies based on Estimated Yields, Limited Renting Options, and a 6% Discount Rate .................................... Optimal Adoption Strategies for Current Prices, Limited Renting Options, a 20°/ Learning Curve, and a 9% Discount Rate ........................... Optimal Adoption Strategies for Median Prices, Multiple Renting Options, a 20% Learning Curve, and a 3% Discount Rate ........................... Optimal Adoption Strategies for Median Prices, Multiple Renting Options, a 20% Learning Curve, and a 6% Discount Rate ........................... Optimal Adoption Strategies for Current Prices, Multiple Renting Options, a 20% Learning Curve, and a 6% Discount Rate ........................... Optimal Adoption Strategies for Equal Yields, Median Prices, Multiple Renting Options, a 20% Learning Curve, and a 6% Discount Rate ........... Conditions for which the Optimal Risk-Averse Policy is to Adopt No-Till, Assuming Equal Yields and Limited Renting Options .......................... ix 135 137 143 144 145 147 166 LIST OF FIGURES Page Figure 2.1 Figure 2.2 Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Short-Run and Long-Run Flexibility in Type of Output Relative Short-Run Flexibility in Type of Output ... Good Field Days Probability, MB Plow System, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 .. Good Field Days Probability, No-Till System, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 .. Estimated Corn Yields, MB Plow and No-Till on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 .. Estimated Soybean Yields, MB Plow and No-Till on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 .. Estimated Corn Yields, No-Till minus MB Plow, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 .. Estimated Soybean Yields, No-Till minus MB Plow, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 Revenue Net of Variable Costs, No-Till minus 100% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 ................................. Revenue Net of Variable Costs, No-Till minus 70% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 ................................. Revenue Net of Variable Costs, No-Till minus 45% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 ................................. Net Revenue CDF's, No-Till and 100% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 Net Revenue CDF's, No-Till and 70% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 Net Revenue CDF's, No-Till and 45% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90 Profit-Maximizing Policies for Equal Yields, a 3% Discount Rate, a 20% Learning Curve, and Various Machinery Ages ................................... Profit-Maximizing Policies for Equal Yields, a 6% Discount Rate, a 20% Learning Curve, and Various Machinery Ages ................................... Profit-Maximizing Policies for Equal Yields, a 3% Discount Rate, No Learning Curve, and Various Machinery Ages .......................... Optimal Policies for Moderate Risk Aversion, a 6% Discount Rate, Estimated Yields, andPrice State 1 Optimal Policies for Moderate Risk Aversion, a 6% Discount Rate, Estimated Yields, andPrice State 3 x 26 26 104 105 Ill 112 114 115 123 124 125 126 127 128 138 140 141 150 151 LIST OF FIGURES (Continued) Page Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.10 Figure 6.11 Figure 6.12 Figure 6.13 Figure 6.14 Figure 6.15 Figure 6.16 Figure 6.17 Optimal Policies for Slight Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 1 Optimal Policies for Slight Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 3 Optimal Policies for Moderate Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 1 Optimal Policies for Moderate Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 3 Optimal Policies for Slight Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 1 Optimal Policies for Slight Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 3 Optimal Policies for Moderate Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 1.. ................................... Optimal Policies for Moderate Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 3 .................................... Optimal Policies for Slight Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 1 .................................... Optimal Policies for Slight Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 3 .................................... Penalty for Adoption with Various Planter Ages, a 1600 Hr. Tractor, and Profit-Maximization ........ Penalty for Adoption with Various Planter Ages, a 1600 Hr. Tractor, and Exp. Utility Maximization ... xi 153 154 156 157 158 159 160 161 162 163 169 169 Chapter 1 EXPLANATION OF TECHNOLOGY ADOPTION LAGS Introduction Agricultural technologies that were largely developed and promoted by public research and extension institutions have provided the United States with an abundance of inexpensive food and fiber. Examples of these technologies include hybrid seed, pesticides, artificial insemination, and various innovations in farm machinery. The adoption of these productivity-increasing technologies in the U.S. has usually been very rapid. Public agricultural research and extension institutions in the U.S. now emphasize the development and promotion of agricultural technologies which minimize adverse environmental impacts. Examples include integrated pest management (IPM) systems and conservation tillage systems. But adoption of the environmentally oriented technologies has been relatively slow, causing some to doubt whether they are profitable and whether the money allocated to the development and promotion of these technologies has been well spent. Greater understanding of farmers' adoption decisions is needed in order to answer these questions and design more effective programs to promote new technology. Agricultural technology adoption has been intensively studied by agricultural economists and rural sociologists for at least 50 years, and many factors affecting adoption rates have been examined. Rural sociologists such as Ryan and Gross (1943) and Rogers (1962) have usually examined the influence of rural communication networks and characteristics of farmers on the rate at which different farmers adopt 2 innovations. More recent sociological work has evaluated the effect of innovation characteristics, including compatiblity, complexity, divisibility, and communicability, on rates of adoption (Fliegel and Kivlin, 1966; Rogers, 1983). Griliches established the need to analyse the profitability of new technology when explaining adoption rates in his 1957 study of hybrid corn. Subsequent empirical analyses confirmed that economic variables influence adoption rates, but usually have not identified mechanisms for this influence. Another group of economists, including O'Mara (1971, 1983) and Stoneman (1983), have proposed theoretical models for adoption lags which are based on Bayesian updating of subjective probability distributions. However, empirical support for these Bayesian learning models is scarce and subject to alternative explanations (Lindner and Gibbs, 1990). A few economic analyses (Byerlee and Polanco, 1986; Szmedra et al., 1990) have examined the optimal sequence for adopting interrelated agricultural innovations. An important but generally neglected topic is the relationship between technology adoption decisions and investment decisions. In the highly mechanized agriculture of the U.S., investment and replacement decisions for farm machinery have critical impacts on the profitability and financial viability of farm operations. First, the costs associated with obtaining and operating agricultural machinery usually account for a major share of fixed and variable production costs. Second, the choice of agricultural machinery imposes constraints and design parameters on annual choices of technology and levels of production inputs. Third, agricultural machinery decisions can greatly increase or reduce farm-level financial and business (production) risks1. The risks associated with machinery investments increase greatly when the machinery embodies new technology. The performance of new technology is almost always more uncertain than that of familiar old technology. New technology often is difficult to learn how to use effectively and often must be adapted to the specific soil and other resource conditions of an individual farm. Hence, new technology is often described as exhibiting a "learning curve" (Mahd and Pindyck, 1989) , an increase in productivity that occurs during the initial years of use by learning how to best adapt the technology and use it most efficiently. When farmers consider using machinery which embodies new technology they also must consider how to acquire that technology. Purchasing new machinery exposes the farmer to potentially large financial losses. Machinery values fall dramatically in the first and second years of use. The technology may also be rendered obsolete by improved, new technology (Balcer and Lippman, 1984; Stefanou, 1987), in which case the resale value may drop to near the value of scrap metal. The machine's owner is responsible for all repair costs, whereas a short-term renter of machinery is usually responsible only for minor repairs. The combination of high or possibly very high costs and uncertain benefits discourages many farmers from purchasing machinery 1 Business risks are defined as the risks of operating a business that would be present with 100% equity financing. Financial risks are the additional risks that a business faces as a result of debt financing (Boehlje and Eidman, 1984). 4 that embodies new technology. However, purchased machinery is always available when needed to complete operations in a timely manner, which is necessary to obtain maximum crop yields. Rented machinery often may not be available during the optimal periods to perform necessary operations. Furthermore, renting machinery is generally more costly in the long run than purchasing machinery because rents include profits for the machine's owner and returns for risk-taking. Therefore, U.S. farmers usually own most of the machinery they operate2, but ownership of machinery which embodies new technology is risky. Conservation Tillage and No-Till Technology Conservation-tillage systems are an example of new technology that is largely embodied in farm machinery and has been heavily promoted during the last 25 years. These systems are designed to leave more crop residue on the soil surface in order to reduce soil erosion. Conservation-tillage systems may be divided into three types: no-till systems in which no tillage is performed before planting; ridge-till systems in which only the tops of ridges are tilled before planting; and reduced-tillage systems in which a chisel or disk plow is substituted for the moldboard plow and secondary tillage operations are reduced. The no-till system often reduces soil erosion by 85% or more compared to conventional tillage (Griffith et al., 1986). The no-till system also has been promoted because it greatly reduces labor requirements, machinery operating costs (fuel, oil, 2 Frequent exceptions are fertilizer applicators, pesticide sprayers, and harvesting equipment. 5 repairs), and machinery fixed costs compared to both conventional tillage and other conservation tillage systems. Furthermore, by conserving more soil moisture, the no-till system can provide crop yields that are equal to or greater than those for conventional tillage on many important soils in the U.S. corn belt (Mannering and Amemiya, 1987). Although the no-till system usually increases herbicide costs, most budget comparisons (e.g. Siemens and Oschwald, 1978; Klemme, 1983; Doster et al., 1983) have indicated that if crop yields for no-till are equal to or greater than those for conventional tillage, the no-till system provides higher net revenues than conventional tillage. However, adoption of the no-till system of conservation tillage has been slow, even on soils for which agronomic trials have shown greater or equal crop yields for no-till than for other tillage systems. A 1975 study by the U.S. Dept, of Agriculture reported that 2.2 million acres, or 1.5% of U.S. cropland was planted with the no-till system in 1974 and predicted that 65% would be planted with no-till by the year 2000 (Phillips et al., 1980). However, only 5.3% of U.S. cropland was planted with no-till in 1990 (Economic Research Service, 1992). No-till adoption also has been slow in Michigan, where relatively cool temperatures in May and June slow early crop growth. The crop residues left on the surface by no-till further reduce soil temperatures and early crop growth, and most agronomic trials have not demonstrated a statistically significant increase in crop yields for the no-till system (Hesterman et al., 1988). Yet, the no-till system generally provides crop yields on well-drained, sandy soils in southern Michigan that are approximately equal to crop yields for conventional tillage. 6 The slow rate of adoption has frustrated Soil Conservation Service (SCS) staff and other no-till proponents, who wonder why farmers are not paying attention to budget analyses indicating that no-till is more profitable than other tillage systems. Some agricultural economists have used stochastic dominance techniques to examine whether risk aversion discourages farmers from adopting conservation tillage systems, including no-till. Klemme's (1985) analysis was based on Indiana data showing higher crop yields for conventional tillage than for conservation tillage systems. He found that if a per-acre soil loss value that approximately equalled the difference in returns to labor and management between conventional tillage and chisel plow or no-till systems were subtracted from the returns for conventional tillage, the chisel plow or no-till systems would exhibit second-degree stochastic dominance. Where net returns to management are higher for conservation tillage than for conventional tillage, Williams (1988) found that risk averse farmers would prefer the conservation tillage systems. These stochastic dominance results do not suggest that risk aversion is responsible for slow adoption of conservation tillage systems. Budgets and stochastic dominance provide static comparisons of alternative technologies. They assume that the mean productivity of the alternative technologies does not change over time as a result of technological improvement or experience. They also ignore the possibility that the farmer may already own machinery that is welladapted for one technology but is ill-suited for other technologies. Budgets and stochastic dominance either assume that the farmer can costlessly exchange the current machinery for whatever machinery is 7 optimal for the alternative technologies or that no machinery is owned initially. However, conservation tillage systems, especially no-till, must be adapted to the unique soil conditions of individual farms (Nowak, 1983). Such adaptation often requires years of trial and error (Lockwood, 1987). Nowak and Korsching (1985) documented that conservation tillage adopters find it difficult to manage large amounts of surface crop residue until they have accumulated several years of experience with those systems. Production costs tend to be higher and crop yields tend to be lower during the initial years of conservation tillage adoption than in the long-run as farmers learn what adjustments they need to make. Epplin et al. (1982) suggested that optimal machinery replacement strategies would delay the adoption of a conservation tillage system for wheat production in Oklahoma. Cost budgets suggested that a two-till conservation tillage system had slightly lower costs than the conventional tillage sytem. However, Epplin et al. found that if the conventional tillage machinery complement was more than three years old, the profit-maximizing replacement strategy was to keep it until the end of its useful life. Shrestha et al. (1987) and Smith and Hallam (1990) analyzed alternative tillage systems with multiperiod linear programming models in order to consider investment, replacement, and financing issues. Like Epplin et al. (1982), Smith and Hallam (1990) found that it often is more profitable to wait until conventional tillage equipment is worn out before changing to conservation tillage equipment. Epplin et al. (1982) suggested that machinery leasing possibilities should be considered in economic analyses of alternative tillage systems. A survey of Ohio farmers (Ladewig and Garibay, 1983) also found that an inability to rent planters and drills was an important explanatory variable for not using conservation tillage. The economic studies that have examined dynamic issues relating to conservation tillage adoption suggest that dynamic adjustment problems and machinery replacement have important effects on adoption decisions. A major limitation of these studies of dynamic issues for no-till adoption is that the effect of risk aversion on dynamic adoption decisions was not considered. Knowing what effect machinery replacement decisions, learning curves, planter rental opportunities, and risk aversion have on optimal adoption strategies for the no-till technology could help accelerate its adoption, and thereby reduce soil erosion. Problem Statement In a dynamic perspective, farmers' choice of technology cannot be separated from their choice of durable machinery. This is especially true when farmers are choosing between a conventional tillage system and the no-till system of conservation tillage, which requires a different planter. The choice of durable equipment alters the costs and returns for all subsequent variable input use decisions. The choice of durable equipment also exposes the farm to more risk than variable input decisions because the durables are expensive and costly to change. The purpose of this study is to evaluate optimal dynamic strategies for durable selection and acquisition, then illustrate how the riskiness of 9 durable choices influences the adoption of new technology. Strategies for adopting the no-till system of conservation tillage in southern Michigan are examined in this illustration. Obi ectives 1. Determine the optimal dynamic strategies for choosing between conventional tillage and no-till technology and acquiring the necessary machinery for two representative farmers. Both representative farmers currently grow 400 acres of corn and 200 acres of soybeans with conventional tillage in southern Michigan. maximizes expected profit. One representative farmer The other farmer is risk-averse, and maximizes an expected utility function of net profit. 2. Evaluate the effect of the age of currently owned machinery on the optimal technology selection and machinery acquisition strategies3 of the profit-maximizing farmer and the expected utility-maximizing farmer. Assess whether current disincentives (if they exist) for profitmaximizing farmers and expected utility-maximizing farmers to adopt conservation tillage systems will be overcome in the normal course of machinery replacement. 3. Evaluate the effect of initially higher costs due to learning curves on the optimal adoption strategies of the profit-maximizing farmer and the expected utility-maximizing farmer. 3 Together, these will be called the optimal adoption strategies. 10 4. Evaluate the effects of uncertain crop yields and crop prices on the optimal adoption strategies of the profit-maximizing farmer and the expected utility-maximizing farmer. 5. Evaluate the effect of planter rental policies by the Soil Conservation Service and agricultural equipment dealers on the optimal adoption strategies of the profit-maximizing farmer and the expected utility-maximizing farmer. Hypotheses 1. The profit-maximizing farmer and the risk-averse, expected utilitymaximizing farmer will adopt the no-till system, but the timing of this adoption will depend on the age of currently-owned machinery, the magnitude of learning curves, and whether opportunities to rent no-till planters on a limited acreage exist. 2. The profit-maximizing farmer and the risk-averse, expected utilitymaximizing farmer will more often adopt the no-till system (as other factors are varied) when their machinery has accumulated several years of use than when their machinery is one or two years old. 3. The profit-maximizing farmer and the risk-averse, expected utilitymaximizing farmer will more often adopt the no-till system when they expect little or no learning curve effect on production costs than when they expect a large learning curve effect. 11 4. Even a slight level of risk aversion will make the risk-averse, expected utility-maximizing farmer adopt the no-till system less often than the profit-maximizing farmer. Furthermore, the expected utility- maximizing farmer will adopt the no-till system less often as the magnitude of risk aversion is increased. 5. Both the profit-maximizing farmer and the risk-averse, expected utility-maximizing farmer will choose to rent a no-till planter on a limited acreage if this opportunity is available. It is further hypothesized that the profit-maximizing farmer and the risk-averse, expected utility-maximizing farmer will more often rent a no-till planter on a limited acreage when learning curves have strong effects on production costs than when there are little or no learning curve effects. This hypothesis implies that the profit-maximizing and risk- averse, expected utility-maximizing farmers choose to rent a no-till planter on a limited acreage in order to reduce learning costs. If the profit-maximizing farmer and expected-utility maximizing farmer more often adopt the no-till system when their existing machinery is old than when it is new (Hypothesis 2), the other hypotheses have an important implication for the timing of adoption. Since the ages of the existing planter and tractor increase each year, any variable that makes the two representative farmers more likely to adopt the no-till system will accelerate adoption. Similarly, any variable that makes them less likely to adopt the no-till system will delay adoption. Furthermore, if the profit-maximizing farmer and the risk-averse, expected utility- 12 maximizing farmer are truly representative of large groups of farmers, then variables which make them more likely to adopt the no-till technology will accelerate no-till adoption by the general population of farmers. Organization of the Dissertation The remaining chapters are organized as follows. Chapter 2 presents the economic theory that underlies the analysis. Chapter 3 presents the analytical model for the determination of optimal adoption strategies. Chapter 4 explains how the model parameters were estimated. Chapter 5 presents results for the crop yield estimates, comparative budget analysis, and stochastic dominance analysis. Chapter 6 presents the optimal adoption strategies for the profit-maximizing and riskaverse, expected utility-maximizing farmers. These results are determined by the deterministic and stochastic dynamic programming models, respectively. Finally, Chapter 7 summarizes the earlier chapters and presents conclusions. Chapter 2 THEORETICAL FOUNDATIONS FOR THE ANALYSIS The neoclassical theory of the firm starts with a production function, input prices, and output prices, then proceeds to derive optimality conditions in static equilibrium for choice of output, output level, choice of inputs, and input levels. The standard objectives for the optimization are profit maximization (constrained or unconstrained) or cost minimization subject to a minimal production level. In the static theory of the firm, time is only considered as the short-run, when some inputs are held fixed, or the long-run, when all inputs are allowed to change (Beattie and Taylor, 1985; Varian, 1984). This view of short-run decisions is mathematically convenient, because it allows optimality conditions to be derived through simple constrained optimization, but has been soundly criticized for its lack of realism (Stigler, 1939; Johnson, 1956; Lucas, 1967; De Alessi, 1967; GeorgescuRoegen, 1970; Treadway, 1970; Antle, 1983). An intertemporal theory of the firm is required to analyze the demand for production durables such as agricultural machinery that provide services over time, are costly to adjust or exchange, and are often lumpy and indivisible1. Production durables are stocks which provide flows of services in more than one production period (i.e. a crop season). The flows of services are similar to variable inputs such as seed and fertilizer in that they are consumed within a production period. In the case of machinery, the service flows are usually variable. Thus, a crop 1 A few texts (Hicks, 1946; Henderson and Quandt, 1980; Doll and Orazem, 1984) present both atemporal and temporal theories of the firm. 14 production function is a function of variable inputs and variable service flows from production durables2. The set of production durables is often called the "plant" of the firm. The cost of changing some of the inputs in the short run may vastly exceed the expected benefits. In this sense, some of the inputs may be regarded as being fixed in the short run (De Alessi, 1967). Individual demand for a production durable is determined through investment analysis because expenditures and received services occur in multiple periods and must be dated and discounted to a common time period in order to be comparable. The dating and discounting are necessary because of the time value of money (Aplin et al., 1977). The investment analysis may utilize a multiperiod or continuous time present value model or it may be based on a dynamic optimization model, such as dynamic programming. These techniques are discussed below. Both static and dynamic models of production decisions often need to consider the effect of uncertain outcomes and the decision maker's risk preferences on optimal choices. The expected utility model is used to analyze these risk effects on production decisions. 2 Placing durable stocks in the production function as inputs is sometimes acceptable for econometric estimation (Griliches, 1960; Day, 1967), although it may lead to biased estimates (Yotopoulos, 1967). However, this often causes major problems for analyses of production technology. First, it ignores the possibility of renting durable services. Second, it prevents substitution possibilities from being considered. For example, farmers substitute herbicide treatments for the hours of tractor and cultivator services required to obtain similar weed control. Third, it ignores the fact that most machinery durables are transformed by use such that they are able to provide less services or services at higher cost in subsequent periods. Thus, the quantity of service to demand from a production durable in each period may be a choice variable, but cannot be considered when the production function contains durable stocks rather than durable service flows. 15 Risk Analysis Using the Expected Utility Model The expected utility model for ordering action choices that have uncertain outcomes3 provides a useful framework to model the selection of optimal dynamic strategies for risk-averse farmers. The expected utility model is based on a set of axioms regarding human behavior in choosing among risky alternatives. The most essential of these axioms are (Robison and Barry, 1987): (1) Ordering of Choices. For any two choices A3 and A2, the decision maker either prefers Ax to A2, prefers A2 to A 1 or is indifferent. (2) Transitivity of Choices. If Ax is preferred to A2, and A2 is preferred to A3, then Ax must be preferred to A3. (3) Substitution or Independence among Choices. If A 1 is preferred to A2,and A3 is some other choice, then therisky choice p®Ax + (l-p)®A3 is preferred to the risky choice p®A2 + (1 -p )•A3, where p is the probability that A: or A2 occurs. (4) Certainty Equivalence among Choices. If A 1 is preferred to A2, and A2 is preferred to A3, then some probability p exists that the decision maker is indifferent to having A2 for certain or receiving Ax with probability p and A3 with probability (1-p). A2 is called the certainty equivalent of P* Ax + (1 -p )®A3. If these axioms are satisfied, then a utility function can be formed which represents the decision maker's preferences regarding the risky 3 This is only a bare outline of expected utility theory. See Robison et al. (1984) or Robison and Barry (1987) for excellent, more comprehensive presentations. 16 action choices. The optimal choice then is the one which maximizes the expected value of this utility function. It is assumed that the decision maker has subjective estimates of the probability of occurrence for every possible outcome. These subjective probability estimates are the weights used to calculate the value of the expected utility function. Estimating an individual's utility function for risky action choices is extremely difficult (Robison et al., 1984; Alderfer, 1990). One way to rank preferences over risky action choices that avoids trying to estimate utility functions is to use stochastic dominance or other risk efficiency criteria (King and Robison, 1984). The easiest of the risk efficiency criteria to use is first-degree stochastic dominance (Hadar and Russell (1969) . Suppose the y outcomes for two risky action choices are described by the cumulative distribution functions F(y) and G(y). The risky action choice defined by F(y) is said to exhibit first degree stochastic dominance over the risky action choice defined by G(y) if F(y) s G(y) for all possible values of y and the inequality is strict for at least one value of y. First-degree stochastic dominance implies that all decision makers for whom y has a positive marginal value will prefer the action choice defined by F(y) to the action choice defined by G(y). First-degree stochastic dominance thus imposes a very weak restriction on preferences. The primary difficulty with first-degree stochastic dominance is that it cannot rank many risky action choices. Second-degree stochastic dominance (Hadar and Russell, 1969) is a more useful risk efficiency criterion because it is able to rank more risky action choices than does first-degree stochastic dominance. The 17 risky choice defined by cumulative distribution function (CDF) F(y) is said to exhibit second-degree stochastic dominance over the risky choice defined by CDF G(y) if: X J X F(y) dy s J G(y) dy, for all values of x and the inequality is strict of x. for at least one value Second-degree stochastic dominance implies that all risk-averse decision makers who derive a positive marginal utility from y will prefer the risky choice defined by F(y) to the risky choice defined by G(y). Again, second-degree stochastic dominance imposes a rather weak assumption on decision maker preferences, but is unable to rank many risky action choices. be ranked if bounds canbe More risky choices can imposed on the decision-maker's risk preferences by using the method of stochastic dominance with respect to a function (Meyer, 1977). However, even stochastic dominance with respect to a function cannot order all risky choices. Furthermore, all stochastic dominance comparisons are only valid for multiperiod analyses under very restrictive assumptions. The other method often used to rank preferences over risky action choices is to use a parametric approximation of the expected utility function (Lambert and McCarl, 1985). This entails: (1) choosing a functional form from a set of possible utility functions that are both mathematically tractable and somewhat consistent with empirical evidence; (2) determining an appropriate risk-aversion parameter for the utility function; (3) determining objective or subjective probabilities for the possible outcomes of each risky action choice; and (4) calculating the expected value of this function for each risky action 18 choice. Properties of several popular functional forms are summarized by Lins et al. (1981) and Selley. This approach is always able to rank risky action choices, but the ranking is conditional on very restrictive assumptions about risk preferences that often have little empirical foundation. Most empirical research regarding risk preferences has attempted to estimate levels of risk-avers ion for various groups of decision makers. One can determine whether an individual is risk-averse, risk- neutral (indifferent to risk), or risk-loving by examining whether the second derivative of the individual's utility function is negative, zero, or positive, respectively. However, since the utility function is only unique up to a positive linear transformation, Arrow (1974) and Pratt (1964) independently suggested dividing the second derivative of the utility function by the first derivative in order to measure the magnitude of risk aversion. Two widely-used measures of risk aversion are therefore the absolute risk aversion coefficient: Rara = -U"(y)/U' (y) , and the relative risk aversion coefficient: Rrra = -y*U"(y)/U'(y), which are measured at a specified monetary outcome, y. Because these risk aversion coefficients are functions of the monetary outcome levels, it is difficult to compare risk-aversion estimates from one empirical study based on one set of monetary outcomes with risk aversion estimates based on a different set of monetary outcomes. If decision makers are assumed to have constant relative risk aversion (CRRA), or constant partial relative risk aversion (CPRRA), 19 then the relative risk aversion coefficient measured at one monetary outcome level can be applied to a wide range of outcome levels. CRRA implies that relative risk aversion stays constant as wealth changes (Pratt, 1964). CPRRA implies that relative risk aversion stays constant as income changes (Menezes and Hanson, 1970). The assumption of CRRA or CPRRA is consistent with empirical observations that absolute riskaversion measures generally decline as income and wealth increase (Alderfer, 1990; Chavas and Holt, 1990; Pope and Just, 1991). However, the Chavas and Holt (1990) study suggests that relative risk aversion may not be constant either. Input Demands under Uncertainty in a Static Model Risk-averse, expected utility-maximizing farmers generally make different production decisions than expected profit-maximizing farmers. Some clear results have been obtained regarding the effects of price uncertainty on production decisions by expected utility-maximizing farmers. Sandmo (1971) shows that an increase in the spread of price outcomes around a constant mean price reduces input demand by riskaverse, expected utility maximizers. Sandmo (1971) also shows that if the decision maker's risk preferences exhibit decreasing absolute risk aversion (DARA) and prices are uncertain, an increase in fixed costs reduces variable input demand. However, when analyzing technology adoption decisions it is appropriate to examine the effects of uncertainty in the production function, which are not as clear as the price uncertainty effects. All crop production is uncertain due to unpredictable weather and agricultural pests, but when unfamiliar new 20 technology is being considered, the production function becomes especially uncertain. Pope and Kramer (1979) show that the effect of production function uncertainty depends on: (1) whether the stochastic component of the production function has a multiplicative or additive effect on output; and (2) whether the input is risk-increasing or risk-reducing. Examples of risk-reducing inputs are many herbicides and insecticides, if applied correctly'1. Consider an expected-utility maximizing farmer who is risk averse (U' (ji) > 0, U' '(n) < 0, where U( ji) is the utility of profit and U' (it) and U' '(n) are first and second derivatives) . The production function is: q <= F(X,e), where X is a vector of input levels Xj, j = 1 ... M, and e is a random disturbance. The first order conditions for profit maximization can be written as: E[U' (tc )» (P°Fj(X,e) - cj) ] = 0, j = 1 ... M, or P* E [Fj (X,e ) ] - cj = -P»Cov[U' (it) ,Fj(X,0] / (E[U' (m) ]) , (1) where P is the output price, Fj is the marginal product of the jth input, and Cj is the price of the jth input. First order conditions for profit maximization are assumed to be sufficient. An input is said to be risk increasing if under risk aversion the expected value of the marginal product is greater than the factor price at the optimum. Using this definition and equation (1), Xj is marginally risk increasing if 4 Herbicides and insecticides are not always risk-reducing. Excessive applications of some herbicides may harm crops, particularly crops which follow the treated crop in a rotation. Careless herbicide application may harm crops in adjacent fields. Insecticide applications often kill natural predators of insect pests, and may lead to an eventual increase in the population of the target pest or secondary pests. 21 Cov[U'(n),Fj(X,e)] < 0. If the production function is written in its multiplicative form: q = f (X) •g (e ) ; fj > 0, fjj < 0 at the optimum, (2) Cov[U' (it) ,Fj(X,e) ] = fj» Cov [TJ'(it) ,g(e ) ] . As g'(e) > 0, Cov[U'(it) ,g(e ) ] < 0. Therefore, the multiplicative form of the production function (2) implies that all inputs are marginally risk increasing (Pope and Kramer, 1979) . Also, given (2), the variance of q, V(q), is given by: V (q) = f2(X)•V(g(e )), and the marginal change in variance is given by: dV(q)/dxj - 2.f(X).fj(X).V(g(e)) > 0. Now if the production function is written in an additive form: q = f(X) + h(X) •e ; fj > 0, fjj < 0, E(e) = 0, and h(X) is assumed to be positive. Cov[U'(it) ,Fj(X,e) ] = hj»Cov[U'(it) ,€ ]. For this function, The covariance term is negative for a risk averter and E(P»fj) > Cj if and only if hj > 0. Therefore, an input is marginally risk increasing only if hj is positive. Also, for this production function, V(q) = h2(X)•V(e), and dV(q)/dxj) = 2»h(x)»hj(X)*V(e) > 0 if and only if hj > 0. An input only increases variance if hj is positive. All other things equal, a risk averter uses less of a risk increasing input than a person who is risk neutral (Pope and Kramer, 1979). Whether an input is risk increasing or risk reducing has been shown to depend on the functional form of the production function. In 22 summary, the effect of uncertainty in the production function on input demands depends on how the uncertainty enters the production function. Dynamic Issues for Production Durables In addition to providing input services in more than one production period, an essential difference between production durables and variable inputs is that durables usually are costly to change. Costly changes include increasing the durable stock through investment, decreasing the durable stock through disinvestment, modifying the durable, and exchanging the durable for another. In the economic investment literature, the costs of such changes are called adjustment costs (Lucas, 1967; Gould, 1968; Treadway, 1970). Many agricultural economists have been primarily concerned with the cost of disinvestment and Johnson (1956) developed a theory of asset fixity to explain its effects. Asset fixity results when not owning a durable would increase profits but the resale value of the durable is less than its use value. Hsu and Chang (1990) recently showed that asset fixity is a special case of adjustment cost effects on investment and disinvestment. Adjustment cost theory was developed by macroeconomists primarily in order to justify using distributed lags in econometric studies of investment behavior (Rothschild, 1971). Lucas (1967) also used adjustment costs to reconcile "U-shaped" long-run average cost curves with empirical evidence that rates of firm growth are independent of firm size (except for very small firms). Investment theorists proposed that two types of adjustment costs exist; (1) external costs due to rising short-run supply curves in the industry that supplies durable 23 investment goods; and (2) internal costs due to reorganizing production lines, training new workers, etc. (Eisner and Strotz, 1968)5. Lucas (1967) also proposed that new technology is a key stimulus for investment but the new technology often is not fully effective until after a learning period, and the costs of this learning are an example of internal adjustment costs. The investment economists generally assume a symmetric, continuous, and convex cost function for investment and disinvestment (for I>0: C(I)>0, C'(I)>0, C"(I)>0, and C(0)=0, where C(I) is investment cost and I is gross investment). This functional form implies that investment always responds to changes in prices or costs, but the rate of response may be slow. The quadratic form of the investment cost function is mathematically convenient and the most often used (Gould, 1968). However, Rothschild (1971) argues that non-convex adjustment cost functions are just as likely and often cause no response to small changes in prices or costs. Likewise, Hsu and Chang (1990) argue that adjustment costs in agriculture probably are not symmetric. Also, when the cost of investment is not smooth, but kinked at 1=0, Johnson's asset fixity trap results (Hsu and Chang, 1990). One way to avoid adjustment costs is to design production durables to be flexible. Several types of durable flexibility can be distinguished, including: flexibility in efficiency (cost flexibility), flexibility in output level, flexibility in types of output, and flexibility in the types and levels of inputs with which the durable is 5 Lichtenberg (1988) estimates that average internal adjustment costs to expansion and replacement investment in U.S. industries equal 35% and 21%, respectively, of the investment amounts. 24 combined in production. A general economic definition of flexibility is that "one position is more flexible than another if it leaves available a larger set of future positions at any given level of cost" (Jones and Ostroy, 1984)6. Stigler (1939) and Lev (1984) define durable flexibility as having relatively constant average costs of operation across a wide range of output levels rather than having lower average costs at an optimal output level but sharply increasing average costs at higher or lower output levels. This flexibility can be called flexibility in efficiency or cost efficiency (as Heady, 1950, referred to it). Robison and Barry (1987) suggest another type of flexibility which is defined according to whether the capacity of the durable to provide services changes with time and use. Durables are called inflexible in output when their capacity to provide services is fixed and declines with time, not use. One can extract more total services over the lifetime of such durables by using more of this capacity. a barn. An example is Durables are called completely flexible in output when they provide the same total amount of services over their lifetime, independently of the service extraction rate. durables declines only with use, not with time. stored gasoline and fertilizer. The capacity of these Extreme examples are Agricultural machinery, if kept clean, lubricated, and protected from the weather, comes close to being completely flexible in output, because its capacity declines mostly with use and relatively few parts deteriorate with age. 6 Marschak and Nelson (1962) propose a similar definition (their Measure III) that is both more general but less intuitive. Lev (1984) discusses the deficiencies of both general definitions. 25 Heady (1950) defines flexibility in terms of the costs of producing alternative outputs with the same durable. This type of flexibility is referred to here as flexibility in type of output, and is easily illustrated with product transformation (production possibility) curves (Figures 2.1 and 2.2)7. The product transformation curve maps the maximum amounts of one product that can be produced for given levels of production for another product and a given input set. In Figure 2.1, the long-run product transformation function between products X and Y is represented by the curve (MN). In the same figure, the short-run product transformation function is represented by the more concave curve (mn). If the firm initially produces Y2 units of Y and units of X, but wants to reduce production of Y to Y x and shift resources to production of X, in the long run the firm can produce (X3, Y":) along curve (MN). However, some of the production durables may be designed more for the production of Y than for the production of X and in the short run it may be costly to change those durables. Thus, the short- run product transformation curve (mn) indicates that only (X2, Yx) can be produced until the specialized production durables are changed. A durable that is relatively flexible in types of output can be represented by a relatively flat short-run product transformation curve (mn in Figure 2.2). A relatively Inflexible durable is represented by the product transformation curve (m'n') in Figure 2.2. The inflexible durable is commonly able to produce more within a narrow range of (X, Y) combinations (the arc AB in Figure 2.2) than the flexible durable, but the flexible durable produces more if a more uneven combination of 7 These are equivalent to Figures 2 and 5 in Heady (1950). 26 Figure 2.1 Short-Run and Long-Run Flexibility in Type of Output Y output X x X2 X3 Figure 2.2 X output Relative Short-Run Flexibility in Type of Output Y output Y Xi X2 X output 27 products is desired (arcs mA and Bn) in Figure 2.2). If a durable is completely inflexible in the production of two or more products, they would be called "joint products" (Debertin, 1986, Doll and Orazem, 1984). Stigler (1939) discusses the "adaptability" of durables to changing quantities of variable inputs. This could be called flexibility in the production function. For example, farm machinery is usually designed to be operated by just one person. Putting another laborer on a tractor or combine does not increase the amount of productive services that can be extracted from the tractor or combine. Stigler also notes that having one kind of flexibility in a durable makes other kinds of flexibility less valuable. In a dynamic perspective, flexibility is valuable because it allows the firm to respond to new information. When there is complete flexibility, a firm can ignore the possibility that prices and technology may change tomorrow and base investment decisions purely on today's prices and technology because adjustment to future prices and technology is costless. Less durable flexibility results in greater uncertainty regarding future net returns, hence more need for risk analysis. Costly adjustment but some flexibility to respond to price and technology changes increases the need for dynamic analysis. A firm can obtain the most flexibility by postponing investments in durable assets while learning more about which investment will provide the greatest discounted future returns. This is especially true if the durable investment can only be reversed at a large economic loss, in which case the investment is said to be economically irreversible 28 (McDonald and Siegel, 1986; Jones and Ostroy, 1984; Pindyck, 1988). Some investments, especially those involving natural resources may effectively be permanently irreversible (Arrow and Fisher, 1974). However, most investments are reversible after a period of time. A machinery investment is reversible once the net present value of investing in a replacement machine (including whatever salvage value can be obtained for the old machine) exceeds the opportunity cost of the value of lost production from the old machine (Baldwin and Meyer, 1979). When investment is irreversible and future demand or cost conditions are uncertain, an investment expenditure kills the option to invest those resources in the future. The possibility of waiting for new information that might affect the desirability or timing of the expenditure is forfeited (Pindyck, 1988). "This lost option value must be included as part of the investment. the cost of As a result, the Net Present Value (NPV) rule 'Invest when the value of a unit of capital is at least as large as the purchase and installation cost of the unit' is not valid. Instead the value of the unit must exceed the purchase and installation cost, by an amount equal to the value of keeping the firm's option to invest these resources elswhere alive - - a n opportunity cost of investing" (Pindyck, 1988, p. 969), Calculations by McDonald and Siegel (1986) show that even for moderate levels of uncertainty, in many cases the value of this, opportunity cost can be so large that projects should be undertaken only when their present value is at least double the purchase and installation cost. 29 Several analytical results have been obtained for the value of waiting to make irreversible investments when returns are uncertain. The value of waiting to invest increases with uncertainty about future returns and decreases with the discount rate for future returns (Jones and Ostroy, 1984; McDonald and Siegel, 1986). The value of waiting to invest also increases with the length of time an irreversible investment will continue to be productive and the slower the depreciation rate (Baldwin and Meyer, 1979; McDonald and Siegel, 1986). For example, the value of waiting to invest is much greater for buildings that will last at least 30 years than for machine tools that will last only 1-2 years. The value of waiting to invest does not depend on risk aversion (Jones and Ostroy, 1984; Baldwin and Meyer, 1979; Cukierman, 1980; Bernanke, 1983) . The value of waiting to invest also counteracts one of the important results of dynamic analyses of learning by doing; namely that firms using new technology should initially produce at levels at which marginal cost exceeds marginal revenue (Rosen, 1972; Brueckner and Raymon, 1983). The rationale for producing more than the optimal level determined by static analysis is that learning increases with the level of production, so current production provides an additional, shadow value of reducing future costs. However, these analyses ignore that the extra production is an irreversible investment in reduced future costs. Majd and Pindyck (1989) show that uncertainty regarding future prices reduces the shadow value of cumulative output and increases the option value of waiting for additional information about prices before producing with the new technology. The net result of the opposing 30 learning by"doing effect and option value effect on the optimal level of production is ambiguous, depending on the relative levels of future cost reductions and future price uncertainty. Another kind of uncertainty which may delay investment in a production durable is the possibility that a new technology may soon be introduced which makes the current technology obsolete. Rosenberg (1972) describes how the introduction of several important industrial technologies was followed by a long period during which important improvements to the technology were introduced. The value of waiting for possible new technology is another kind of option value. Balcer and Lippman (1984) analyze a model in which technology improves exogenously over time, but the timing and impact of future improvements on profits are uncertain. When a new technology is introduced, the firm decides whether to incur a fixed charge and adopt the technology immediately or defer adoption until either: (1) the technology is further improved, or (2) it appears unlikely that a new technology will be discovered soon. They find that adoption decisions depend on how the elapsed time since the last technological improvement and the pace of new discoveries affect expectations regarding future discoveries. Increased uncertainty about when new technology will appear may either speed or retard adoption, depending on what form of expectations are assumed. Not surprisingly, increases in the fixed charge for adopting a technology delay adoption. Another dynamic aspect of nearly all durable equipment is that it eventually deteriorates or fails to work and must be replaced. Replacement problems fall into two categories: (1) replacement of 31 equipment that deteriorates, becomes obsolete, or otherwise becomes less efficient than newer equipment; and (2) replacement of equipment that does not deteriorate but is subject to stochastic failure. Light bulbs are the standard example of equipment subject to failure, although it should be noted that much of the research on optimal replacement policies for equipment subject to failure has concerned equipment as vital as airplane parts, electric power plants, and military weapons systems. However, most agricultural machinery falls into the category of equipment that deteriorates, so the discussion here focusses on this category of replacement problems. For equipment that deteriorates, the problem is to decide when costs due to lost efficiency or high maintenance requirements on old equipment outweigh the costs of obtaining and installing new equipment (Churchman et al., 1957)8. In comparing alternative replacement policies the correct measure of efficiency is the discounted value of all future costs associated with each policy. In principle, all cash costs that depend on the choice or age of the equipment must be considered9. Normally, the total costs of operating, repairing, and maintaining equipment (plus possible opportunity costs from lost production) increase monotonically with age. Assuming that total costs do increase monotonically with age makes it possible to ignore secondorder conditions when determining optimal replacement policies. 8 The following three pages also draw heavily from Churchman et al. (1957). 9 Accrued costs are only considered when they affect cash flows, as in depreciation deductions on income taxes. 32 The derivation of the optimal rule for replacement with identical equipment, assuming an infinite planning horizon and discrete time, follows. According to Preinreich (1940), the optimal replacement rule in continuous time was first published by Harold Hotelling in 1925, and can be found in Preinreich (1940) or Perrin (1972) . However, tillage and planting machinery is generally used at discrete intervals, so the discrete time formulation is more useful here. Consider a series of annual costs C1( C2, C3, .... Assume that each cost is paid at the beginning of the year, that the initial cost of new equipment is A, and that the annual discount rate is r per period. The discounted value Kj, of all future costs associated with a policy of replacing equipment after each n periods is given by: Kj, = ( A + + + 1+r Ci (1+r)2 C2 ( A + + (l+r)n (l+r)n+1 + ... + (l+r)"'1 ) + Cn + ... + -------- ) (l+r)2n'x + ... (3) The right hand side of this equation may be written as a geometric series and expressed in the following form: A + E [C± / (l+r)1’1] i=l Kn - . (4) 1 - [1/(1+r)]n If Kn is less than Kn+1, it is preferable to replace the equipment every n years rather than every n+1 years. Furthermore, if the best policy is to replace equipment every n years, then the two inequalities: 33 Kn+1 - Kn > 0 must hold. and - K„ > 0 It is shown in Appendix A that Kn-i - K„ > 0 is equivalent to Cn -------------- < V i (5) 1 - [1/(1+r)] and that Kn+1 - K„ > 0 is equivalent to Crq-L > Kn. (6) 1 - [1/(1+r)] Writing f1/(1+r)] as W, inequality (5) implies that Cn < (l-W)]^-!- By substituting n-1 for n in equation (4) and substituting this into inequality (5), one obtains (A + Cx + C2W + ... + Cn-iW"'2) Cn < (1-W)-------------------------------- , 1 - W"'1 (7a) or (A + Cx) + C2W + ... + Cn-iW"'2 Cn < • (7b) 1 + W + W2 + ... + W"'2 The expression on the right hand side of inequality (7b) is the weighted average of all costs up to and including year n-1. The weights 1, W, W2, ..., W""2 are the discount factors applied to the costs in each period. Similarly, inequality (6) may be expressed as (A + C-l + C2W + ... + Cn-iW"'2) Cn+1 > (1-W)--------------------------------, 1 - W" (8a) (A + Ci) + C2W + ... + Cn-iW"'2 Cn+i > -------------------------------- . 1 + W + W2 + ... + W"’1 (8b) or 34 As a result of inequalities (7b) and (8b), the cost-minimizing replacement rules are: (1) Do not replace if the next period'scost weighted average of previous (2) Replace if the next period's weighted average of previous islessthan the costs. cost isgreater than the costs. Numerical examples are provided in Churchman et al. (1957, p. 488) and Perrin (1972, p. 66). Dynamic Programmins The replacement rule just derived works fine when costs in future periods can be predicted and replacement equipment is identical to the old equipment, but technology generally is not static and future costs are uncertain. For more complex and stochastic replacement problems it is advantageous to use the recursive method of dynamic programming to derive optimal replacement strategies. In fact, equipment replacement strategies were one of the first applications of dynamic programming10. Dynamic programming is a mathematical optimization technique that is particularly useful for sequences of interrelated decisions. The essential characteristics of a dynamic programming problem are (Hillier and Lieberman): (1) The problem can be divided into stages, with a policy decision required at each stage. 10 Churchman et al. (1957) cite a study by Richard Bellman in 1955 for the RAND Corporation, entitled "Notes in the Theory of Dynamic Programming--III: Equipment Replacement Policy". This was two years before Bellman published his "Dynamic Programming" (1957) textbook. 35 (2) Each stage has a number of states associated with it. The states are the various possible conditions that may be in effect at each stage. (3) The effect of the policy decision at each stage is to transform the current state into a state at the next stage. (4) Given the current state, an optimal policy for the remaining stages is independent of the policy adopted in previous stages. Knowlege of the current state conveys all the information that is necessary for determining the current optimal policy. This is called Bellman's principle of optimality. (5) There is a recursive relationship between the value of an objective function at stage n and the optimal value of that objective function at stage n+1 that allows the optimal value of the objective function for the entire problem to be obtained by working backward from the final stage and determining the optimal policy and associated value of the objective function at each stage. Since sequential stages can easily represent sequential time periods and investment or replacement decisions in one period do affect opportunities in subsequent periods, dynamic programming is an appropriate technique for finding optimal investment and replacement policies for production durables. The standard, intertemporal dynamic programming problem is formulated as follows11. Let xt be an (n x 1) vector of state 11 The notation follows Sargent (1987) . 36 variables at time t and let ut be a (k x 1) vector of control variables at time t. In each period (stage) one seeks to maximize (or minimize) a one-period return function, rt(xt,ut). At the end of the planning horizon, denoted by T, the value function for period T+l, W0(xI+1) is a function only of the state variable. "Transition equations" or "laws of motion", xt+1 = gt(xt,ut), govern the effect of current state and control variables on the state variables in the next period. The complete problem is then to maximize (minimize): r0(x0,u0) + rx(xx,ux) + ... + rT(xT,uT) + W0(xT+1) , subject to having either the vector of initial state variables, x0, or the vector of state variables at period T+l, xT+1, given and subject to the transition equations: xt+i = gt(Xt.ut), t = 0, ...,T. The first step in the solution is to find the vector of control variables at the end of the planning horizon, uT, that maximizes: Wx(xT) = max) rT(xT ,uT) + W0(xI+1)), subject to xT+1 = gT(xT,uT) with xT given. then used to find the u ^ The value function W 1(xT) is that maximizes: W2(xT_i) = max(rT_j(xT_2,u ^ ) + W1(xT)), subject to xT = gT-x(xT_x, with x ^ given, and this process is repeated until all of the ut have been found. The state and optimal control variables in each period constitute the optimal policies. The general functional equation: Wj+i(xT-j) = max{rT.j(xT-j,uT.j) + Wj(xT.j+1) }, subject to xT_j+1 = equation. ,uT.j) with xT.j given, is called a Bellman's 37 The dynamic programming problem above is usually simplified by assuming that the return functions and transition equations are time invariant: rt(xt,ut) = fi^Cxt.Ut), 0 < £ < 1 gt(xt .ut) = g(x t>u t) - where £ is the discount factor expressing time preferences. A current value function is then defined as v j + i < x T-j) = £j-TWj+1(xT_.i) , and Bellman's equation becomes: v j + i ( x T-j) = max{r(xT.j ,uT.j) + £vj (xT.j+1) ) , which often is more simply written (Myers, 1990) as vt(xt) = max(r (xt,ut) + £vfc+1(xt+1)} . The dynamic programming replacement problem is usually formulated as a cost minimization problem over a finite (and often short) planning horizon. The length of the planning horizon, the initial age of the machine, and a maximum useful life of the machine (all in years) must be set initially. current year. The state variable is the age of the machine in the It is usually assumed that replacement, if it occurs, occurs at the beginning of the year. x.t+i xt + 1, 1, Hence the transition equation is: if the machine is kept at time t if replacement occurs at time t Necessary data include: c(xt) = the annual cost of operating a machine which is of age xt at the start of year t, t(xt) = the trade-in value received when a machine which is of age xt is traded for a new machine, s(xT) = the salvage value received for a machine that has just turned age xT at the end of the planning horizon, T (s(xT) may equal t(xT)), and 38 the price of a new machine (of age 0). P The current value function, vt(xt) , is the minimum cost of owning and operating a machine from year t through year T, starting year t with a machine just turned age xt. It may be expressed as the Bellman's equation: vt(xt) mm Buy: p - t(xb) + c(0) + vt+1(1) Keep: c(xt) + vt+1(xt + 1) Example replacement problems solved with dynamic programming can be found in Bellman and Dreyfus (1962), Cooper and Cooper (1981), Dreyfus and Law (1977), Gillet (1976), and Winston (1987). The same texts also present formulations for extensions to the simple replacement problem that include the possibilities of overhauling a machine rather than replacing it, replacing a machine with a leased rather than purchased machine, technological change, and stochastic outcomes. Larson and Casti (1978) also present a formulation that includes the possibility of replacing with a used machine. These extensions are similar in structure to the simple replacement problem, but include more state variables, more control variables, and more comparisons of alternative policies in each period. Dynamic programming has one major deficiency as a numerical optimization procedure that becomes quite evident in machinery replacement problems. As the number of states and possible state values becomes even moderately large, the number of calculations and amount of computer memory required by dynamic programming problems increase geometrically and can be enormous. Richard Bellman referred to this difficulty as "the curse of dimensionality". Replacement problems for agricultural machinery are particularly troublesome, because the machinery often stays productive for 15 years or more. For example, a recent combine replacement study by Weersink and Stauber (1988) that allowed for 6 possible prices, 16 possible tax options, and 15 possible combine ages consisted of 1,440 (6 x 16 x 15) states. As a result, dynamic programming replacement models must be parsimonious in the number of state variables, control variables, and possible values for state and control variables. Chapter 3 THE ANALYTICAL MODEL State Variables and Control Variables The model used to analyze the conservation tillage adoption problem is an extension ot the dynamic programming replacement model discussed in Chapter 2. The standard replacement model determines the optimal period to trade in a used machine and purchase a new, but otherwise identical machine. The replacement model is first extended by considering the replacement of two machines, a tractor and a planter, and by considering their replacement with an alternative tractor and planter. A no-till planter is the key machinery component of a no-till system, so replacement of a conventional planter with a no-till planter represents adoption of no-till technology. Tractor replacement with two possible sizes is included because most budget analyses of conventional tillage and no-till systems assume a smaller and less costly tractor for the no-till system than for the conventional tillage system. A second extension of the replacement model is to consider the possibility of renting a planter. Third, costs for the no-till system are varied according to years of experience with that technology. are sufficient for the deterministic analysis. These extensions The additional extensions required for stochastic analysis are discussed in the last section of this Chapter. Since the dynamic programming model must be kept small enough that it can be solved, state variables and control variables are restricted to those that most affect the adoption decision. included in the deterministic model are: The state variables 41 1) an ownership variable indicating which machines are owned at the start of each crop season (5 possibilities are allowed); 2) age (in years) of the planter (17 years are allowed); 3) age (in 400 hour units) of the tractor (34 units are allowed); and 4) levels of experience with a no-till planter (4 levels are allowed). The ownership variable determines which control variables may be considered in each year, including the possible sale of machinery. The ages of the planter and tractor determine repair costs and salvage or trade-in value. The tractor's age is measured in 400 hour units, rather than years, because usage per year will vary according to whether a conventional tillage or no-till system is selected. Usage of the conventional tillage system for 600 acres of corn and soybeans is approximately 800 hours per year. Usage for the no-till system in the same situation is approximately 400 hours per year. Therefore, the tractor ages by two 400-hour units per year when conventional tillage is selected and by one 400-hour unit per year when the no-till system is selected. The combination of four state variables with the number of levels indicated for each state variable result in a total number of 14,450 states to be considered each year, with one policy determined for each state. The control variables included in the deterministic model are: 1) use of a conventional tillage or no-till planter; 2) rent, purchase, keeping, or replacement by purchase of the planter; 42 3) keeping or replacementby purchase of the tractor; and 4) choice between a large or small tractor. Selection of a conventional tillage planter implies that primary tillage operations with a moldboard plow and secondary tillage operations with a tandem disk are performed before planting and that row cultivation is performed after planting. The preplant plow and disk operations are needed to obtain an adequate crop stand with a conventional tillage planter. Row cultivation is a cost-effective means of controlling weeds, but is difficult to do with the relatively heavy crop residues found on the soil surface under a no-till system. Therefore, when the conventional planter is selected, the costs of the plow, disk, and row cultivator operations are included. Other cost adjustments for the alternative tillage systems are explained in Chapter 4. All of the control variables are binary. Hence, the alternative choices or policies are a combination of options to purchase, sell, rent, or keep machinery. When only the large tractor is owned there are 10 policy options (Table 3.1). When only the small tractor is owned there are 8 policy options (Table 3.2). When the large tractor and conventional planter are owned and renting options are limited to renting a planter for the entire 600 acres there are 14 policy options (Table 3.3). The addition of options to rent a no-till planter on 60, 120, or 240 acres while keeping the conventional planter add another 6 policy options (Table 3.4). When the large tractor and no-till planter are owned there are 13 policy options (Table 3.5). Finally, when the small tractor and no-till planter are owned there are 11 policy options (Table 3.6). This means that a total of 18 policy options are 43 Table 3.1 Control Options When a Large Tractor but No Planter is Owned 1. Buy and use the conventional planter. 2. Buy and use the no-till planter. 3. Replace the large tractor, then buy anduse the conventional planter. 4. Replace the large tractor, then buy and use the no-till planter. 5. Replace the large tractor with the small tractor, then buy and use the no-till planter. 6. Rent and use the conventional planter. 7. Rent and use the no-till planter. 8. Replace the large tractor, then rent and usethe conventional planter. 9. Replace the large tractor, then rent and usethe no-till planter. 10. Replace the large tractor with the small tractor, then use the no-till planter. rent and 44 Table 3.2 Control Options When a Small Tractor but No Planter is Owned 1. Buy and use the no-till planter. 2. Replace the small tractor, then buy anduse theno-till planter. 3. Replace the small tractor with the large tractor, then buy and use the conventional planter. 4. Replace the small tractor with the large tractor, then buy and use the no-till planter. 5. Rent and use the no-till planter. 6. Replace the small tractor, then rent anduse the planter. 7. Replace the small tractor with the large tractor, then rent and use the conventional planter. 8. Replace the small tractor with the large tractor, then rent and use the no-till planter. no-till 45 Table 3.3 Control Options when a Large Tractor and Conventional Planter are Owned and Renting Options are Limited 1. Replace and use the conventional planter. 2 Replace the conventional planter with the no-till planter and use the no-till planter. . 3. Replace the large tractor and use the conventional planter. 4. Replace and use the large tractor and the conventional planter. 5. Replace the large tractor, replace the conventional planter with a no-till planter, then use the no-till planter. 6. Replace the large tractor with the small tractor and the conventional planter with the no-till planter, then use the no-till planter. 7. Sell the conventional planter, then rent and use a conventional planter. 8. Sell the conventional planter, then rent and use a no-till planter. 9. Replace the large tractor, sell the conventional planter, then rent and use a conventional planter. 10. Replace the large tractor, sell the conventional planter, then rent and use a no-till planter. 11. Replace the large tractor with the small tractor, sell the conventional planter, then rent and use a no-till planter. 12. Keep the conventional planter, but rent and use the no-till planter. 13. Replace the large tractor, keep the conventional planter, then rent and use the no-till planter. 14. Keep and use the large tractor and conventional planter. 46 Table 3.4 Additional Renting Options when a Large Tractor and Conventional Planter are Owned 1. Keep the large tractor and conventional planter, but rent the no-till planter on 60 acres (of both corn and soybeans). 2. Keep the large tractor and conventional planter, but rent the no-till planter on 120 acres. 3. Keep the large tractor and conventional planter, but rent the no-till planter on 240 acres. 4. Replace the large tractor, keep the conventional planter, and rent the no-till planter on 60 acres. 5. Replace the large tractor, keep the conventional planter, and rent the no-till planter on 120 acres. 6. Replace the large tractor, keep the conventional planter, and rent the no-till planter on 240 acres. 47 Table 3.5 Control Options when a Large Tractor and No-till Planter are Owned 1. Replace the no-till planter with the conventional planter, then use the conventional planter. 2. Replace and use the no-till planter. 3. Replace 4. Replace the large no-till planter. 5. the large tractor and use the no-till planter. tractor with the small tractor, then use the Replace the large tractor, replace the no-till planter with the conventional planter, then use the conventional planter. 6. Replace and use the large tractor and no-till planter. 7. Replace the large tractor with the small tractor, replacethe no-till planter, then use the no-till planter. 8. Sell the no-till planter, then rent and use a conventional planter. 9. Sell the no-till planter, then rent and use a no-till planter. 10. Replace the large tractor, sell the no-till planter, then rent and use a conventional planter. 11. Replace the large tractor, sell the no-till planter, then rent and use a no-till planter. 12. Replace the large tractor with a small tractor, sell the no­ till planter, then rent and use a no-till planter. 13. Keep and use the large tractor and no-till planter. 48 Table 3.6 Control Options when a Small Tractor and No-till Planter are Owned 1. Replace and use the no-till planter. 2 . Replace the small tractor with a large tractor, then use the no-till planter. 3. Replace the small tractor, then use the no-till planter. 4. Replace the small tractor with a large tractor and the no-till planter with a conventional planter, then use the conventional planter. 5. Replace the small tractor with a large tractor, replace the no­ till planter, and use the no-till planter. 6. Replace and use the small tractor and no-till planter. 7. Sell the no-till planter, then rent and use a no-till planter. 8. Replace the small tractor with a large tractor, sell the no­ till planter, then rent and use a conventional planter. 9. Replace the small tractor with a large tractor, sell the no­ till planter, then rent and use a no-till planter. 10 . Replace the small tractor, sell the no-till planter, then rent and use a no-till planter. 11. Keep and use the small tractor and no-till planter. 49 considered for each of 136 combinations of tractor age and years of experience when only a tractor is owned. A total of 38 or 44 policy options are considered for each of 2,312 combinations of planter age, tractor age, and years of experience when both a tractor and a planter are owned. Other potential state and control variables are ignored. In particular, state variables describing soil qualities are not included, in contrast to Smith (1986) in which depth of soil layers is included as a state variable in order to consider soil erosion effects on crop yields and revenues. This model ignores soil erosion effects on crop yields because their magnitude is estimated to be negligible for 100 years on the soils assumed for this analysis (see Chapter 5) and the discounted value of any effects more than 100 years into the future is small. Second, it is assumed that all purchases are made with equity capital, rather than financed with borrowed capital. Allowing purchases with borrowed capital would increase the number of total permutations of state variables by at least 4 times. One state variable with 2 levels would be needed to indicate whether loan repayments have to be made that year for the planter1. Another state variable with at least 2 levels would be needed to indicate whether loan repayments have to be made that year for the planter2. Tax considerations are ignored because another 1 This assumes either that all payments are equal or only a new planter is purchased. If payments are not equal, but a new planter is purchased, the age of the planter can be used to determine the year within the payment schedule. If neither of these conditions are met, another level would be needed for each year in the payment schedule. 2 This assumes that all payments are equal. Otherwise, another level must be added for each year in the repayment schedule. 50 state variable would be required to keep track of tractor depreciation, and yet another state variable would be required if Section 179 expensing deductions were considered. Finally, long-term leasing of equipment is ignored because the economic differences between purchasing and long-term leasing depend on individual tax and financial constraint considerations that are ignored in this analysis3. Although it has often been argued that tax effects should be considered in machinery replacement analyses (Chisolm, 1974; Kay and Rister, 1976; Reid and Bradford, 1983; Weersink and Stauber, 1988), most economic analyses have indicated that the optimal replacement decision is not very sensitive to tax depreciation rules. The studies by Chisolm (1974), Kay and Rister (1976) and Reid and Bradford (1983) all indicated that only investment tax credits (discontinued in 1987) have a large effect on the optimal timing of replacement. An exception is the study of combine replacement by Weersink and Stauber (1988) which found that lengthening the depreciation period beyond 5 years greatly affected the optimal year of replacement. However, Kay and Rister (1976), Reid and Bradford (1983) and Perry and Nixon (1991) all argue that changes in repair costs and remaining values are much more important than changes in tax depreciation schedules in determining optimal replacement policies. Therefore, it is reasonable to assume that the effect of tax deductions on expenses is approximately equal for all types of expenses 3 Consideration of financial constraints would either require entirely arbitrary constraints or expanding the dynamic programming model to include the whole-farm. A whole-farm model would limit or prevent the consideration of other adoption issues due to the limited computer capacity to handle additional dimensions in a dynamic programming problem. 51 and that any possible bias in the optimal adoption strategies caused by ignoring taxes is probably small. Some important simplifying assumptions must be made to leave out other control variables. 200 acres of soybeans. Acreage is held fixed at 400 acres of corn and This corresponds to a corn-corn-soybeans rotation, which is common in southern Michigan. Quantities of seed, fertilizer, and pesticide inputs are fixed at levels recommended by the Michigan State Cooperative Extension Service for each tillage system. Static economic analyses typically allow one or more of these inputs and/or the crop mix to vary. However, acreage for each crop often is constrained by ASCS guidelines for participation in commodity price support programs, competition for fixed resources (e.g. labor) by other farm enterprises, or feed requirements for farm livestock enterprises. Pesticide quantities are legally constrained by label directions4, and seed and fertilizer quantities are usually set according to standard agronomic recommendations. Another reason for fixing quantities of seed, fertilizer, and pesticides is that few agronomic studies in Michigan have varied tillage practice and these quantities in multifactorial experiments, so there is little scientific basis for estimating responses to changes in input quantities. Several features in the model reflect agricultural and engineering constraints. The model includes a choice between a moderately large tractor of 140 PTO horsepower and a relatively small tractor of 85 PTO 4 Criminal penalties for not following pesticide labels for corn and soybeans are not yet common, but civil suits are increasing in frequency. Also the manufacturer makes no promise that non-labelled doses are effective or safe to other crops, which often is an effective deterrent. 52 horsepower. The large tractor is initially owned because it is assumed that conventional tillage and planting have been practiced before the planning horizon starts and the power of the small tractor is inadequate to pull a moldboard plow large enough to complete plowing in a timely manner5. Whenever the large tractor is owned, using either the conventional or no-till planters is considered. However, when the small tractor is owned, only the no-till planter is considered, because the conventional planter does not work effectively unless the soil has been plowed and the small tractor cannot pull the plow. The model assumes that all machinery decisions are made before the crop season begins. For corn and soybeans in Michigan, this means that all machinery decisions are made before May 1, when it usually is desirable to plant (Neild and Newman, 1986). Actual planting dates depend on soil moisture, soil temperature, and the scheduling of preplant tillage operations. Three different scenarios for the proportion of acreage that is moldboard plowed in the fall are considered: 45%, 70%, and 100%6. Inability to complete plowing in the fall tends to retard planting in the spring, and thereby reduce crop yields. Farmers who are generally able to complete less of their plowing in the fall than their neighbors, due to less harvesting capacity or available time 5 Hunt (1983) and Bowers (1987) provide good explanations of power requirements for field operations, and appropriate sizing of tillage and planting equipment. Chapter 5 also provides more explanation. 6 The 45% and 70% proportions are based on crop progress reports for NE Indiana by the Indiana Crop and Livestock Reporting Service. Reported proportions for 1978-90 were sorted according to magnitude. The average of the lowest 7 reports is 45% and the average of the highest 6 reports is 70%. The overall average proportion is 58% for 1978-1990. 53 during the fall, will therefore be more inclined to adopt the no-till technology. Modeling of Learning Curve Effects The model assumes that production costs for the no-till technology are higher than their long-term average in the first year of adoption and fall with cumulative experience with that technology. This is consistent with the empirical evidence for learning curves in manufacturing processes (Mahd and Pindyck, 1989). The representative farmers are assumed to be fully experienced in using conventional tillage, so production costs for conventional tillage do not change with experience. It is assumed that costs for herbicide, fuel and oil, and labor are sensitive to years of experience with no-till technology. Repair costs for the planter and tractor also are assumed to be sensitive to years of experience with no-till. Herbicide costs are expected to be initially higher for no-till because herbicide effectiveness varies with the timing of applications and other variables. Until no-till adopters have learned how to maximize the effectiveness of their herbicide applications, it is expected that they will have to repeat some applications in order to obtain acceptable weed control. Fuel, oil, tractor repairs, and labor costs increase if field operations have to be repeated or when field efficiency is reduced. No-till planter repair costs also increase if any replanting is needed, or if inexperienced farmers use them in ways for which they were not designed. 54 Three different learning curves are considered in the analyses of optimal adoption strategies. The 20% learning curve raises these costs by 20% in the first year of adoption, 14% in the second year of adoption, and 7% in the third year of adoption. The 10% learning curve reduces each of these cost factors by one-half. A zero learning curve, for which all production costs are insensitive to years of experience also is considered. Based on the estimate by Lichtenberg (1988) that average internal adjustment costs for replacement investment are 21% of the investment amount, the 20% learning curve is assumed for most of the analyses of optimal adoption strategies. This very simple model of learning curve effects is used because there is a lack of empirical cost data regarding learning curves in US agriculture and because dimensionality constraints limit learning curve effects to only four levels. According to Jerry Grigar, SCS state agronomist and no-till farmer (personal communication, 1991), no-till farmers probably experience learning curve problems over at least five years. Also, the learning curve effect on costs for no-till technology probably does not decline linearly, because each year presents a different set of problems. A more likely functional form would be a reverse sigmoid curve, falling slowly at first, then falling quickly, and falling slowly again after several years of experience. However, the four levels of experience included in the dynamic programming model cannot represent a sigmoid curve very well, so a simple, nearly linear relationship is used. This at least provides a preliminary indication of learning curve effects on the optimal timing of adoption decisions. 55 Length of the Planning Horizon Numeric dynamic programming optimizes an objective function over a finite time horizon. Solutions to dynamic programming replacement models therefore differ from solutions of methods that optimize over an infinite time horizon, but approach the same solutions as the time horizon approaches infinity. Modigliani (1952, p. 482) proposed an appropriate criterion for determining the best length of the planning horizon. He suggested that, "The problem of choosing the plan that will maximize the outcome of the firm's activity can be reduced logically to the problem of solving a system of simultaneous equations involving all future parameters and moves. This system, however, needs to be 'solved' only with respect to the first move." Therefore the appropriate length of the planning horizon is the time for which plans must be made in order to arrive at the correct decision for the first period. According to Boussard (1971), such a planning horizon may not exist for objective functions that maximize the discounted value of consumption over time. Boussard also claims that for problems which include long-lived durables with small salvage values (e.g. a machinery replacement problem), any planning horizon that satisfies Modigliani's criterion will tend to be lengthy. Boussard shows that a planning horizon exists that will satisfy Modigliani's criterion when the objective function is the maximization of terminal period wealth, and argues that this planning horizon will be shorter than that for an objective function with discounting. However, in order to maximize 56 terminal period wealth in a dynamic programming problem, wealth would have to be included as another state variable, and many discrete levels of wealth would have to be included to minimize errors due to approximating a continuous function with discrete values. Therefore, an objective function that discounts future values is preferred to one that maximizes terminal period wealth for the machinery replacement problem. Boussard (1971) also suggests searching for the planning horizon that satisfies Modigliani's criterion by comparing first period outcomes as the length of the planning horizon is increased and stopping when first-period results become insensitive to further increases in the length of the planning horizon. Kwack (1991) applied this criterion to a dynamic programming machinery replacement problem and found significant differences between the results for planning horizons of 15, 20, and 25 years. However, Kwack chose a 20-year planning horizon due to computer memory constraints. Boussard's rule is used to set the length of the planning horizon for this analysis. The length of planning horizon that satisfied this rule was found to vary according to the choice of discount rate. With a 37= discount rate, the dynamic programming results sometimes changed as planning horizons were varied up to 60 years, so an 80-year planning horizon was finally used. With a 6% discount rate, a 60-year planning horizon was found to be adequate. Finally, with a 9% discount rate, a 50-year planning horizon was found to be sufficient. The length of these planning horizons also ensured consistency in the optimal policies for years 2-16. 57 Formulation of the Deterministic Model The problem is to minimize: V(Qt,KTit,KPjt,Xt) = 2 fit-HPTitCQt) + PPjt(Qt) - STitCQ^KT^) - t=i SPjt(Qt,KPjt) + [CTidt(Qt,KTlt + CPjt(Qt,KPJt)]*CX(Xt) - Rdt(Qt)}, subject to the following laws of motion: STijt+1(KTiit+1) ~ 8ii*Li*[Hi(l)]A8i2 if STit(KTit) > 0 if STit(KTit) = 0 i-1,2, SP if SPjt(KPjt) > 0 (KP, t+i) “ 8ji*Lj*[Hj(KPjt)+Hj(l)]A«j2 if SPjt(KPjt) - 0 j-1,2, CTiJft+1(KTi>t+1)- ei^Li^tHiCl) ]Aei2 if STit(KTifc) > 0 eil*Li*[Hi(KTit)+Hi(l)]Aei2 if STit(KTit) = 0 i=l,2, j=li2, CPjit+1(KPd>t+1) - ®j1*Lj*[Hd(l)]AeJ2 if SPjt (KPjt) > 0 ej1*Lj*[Hj(KPjt)+Hj(l) ]Aej2 if SPjt(KPjt) = 0 j-1,2, KTi>t+1 1 if STit(KTit) > 0 KTit + 1 if STit(KTit) - 0 i-1,2, KP j,t+l 1 if SPjt(KPjt) > 0 KPjt+ 1 if SPjt(KPjt) j-1,2, X.t+i Xt Xt + if R2t = 0 1 if Rzt > 0 = 0 58 subject to initial levels for KTi, KP^, and , and subject to the terminal condition: VI+i(0T+i,KTiiT+llKPjiT+lfXT+1) = -STiT+1(KTiT+1) SPj,T+l(K]?j,T+l) , i=l,2, j=1,2, where: Qt = the ownership state in year t; KTit = the age of tractor i in year t, i=l,2; KPjt = the age of planter j in year t, j=1,2; Xt = years of experience with planter 2 before year t; £ = a discount factor, 0<£<1; PTit = the price paid for tractor i if purchased in year t,i=l,2; PPjt = t^rie ptice paid for planter j if purchased in yeart or the rental cost of planter j if rented in year t, i=l,2; STit = the salvage or trade-in value of tractor i when it is KTifc years old if it is sold in year t, i=l,2; SPjt = the salvage or trade-in value of planter j when it is KPjt years old if it is sold in year t, j=1,2; CTiJt = repair costs for tractor i when it is KTit years old in year t if it is used in year t with planter j and associated implements, CPjt = i=l,2, j=l,2; repair costs for planter j when it is KPjt years old in year t if it is used in year t, plus variable input costs associated with use of planter j that are affected by CXt (herbicide, fuel, labor), j=l,2; 59 CXt = a cost factor that depends on years of experience before year t with planter 2; Rjt = gross revenues for 400 acres of corn and 200 acres of soybeans if planted with planter j in year t, minus variable costs that are not affected by CXt, and minus constant fixed costs, j=l,2; 6ii, 6i2 = repair cost parameters for tractor i, i=l,2; ^ = the list price of tractor i, i=l,2; Hi = cumulative hours of use of tractor i after KTit years (divided by 1000), i=l,2; ®jii ®j2 = repair cost parameters for planter j, j=l,2; Lj = the list price of planter j, j=l,2; and Hj = cumulative hours of use of planter j after KPjt years (divided by 1000), j=l,2. The control variables, which depend on the ownership state in year t, are the selection of planter and tractor in year t and the choices between buying, renting, selling, and keeping planters and tractors in year t (listed in Tables 3.1 through 3.6). Formulation of the Stochastic Model The stochastic model is similar to the deterministic model, except that crop yields and crop prices become stochastic variables and the objective function is changed to the maximization of an expected utility function. Since corn and soybean prices exhibit high variation but strong serial correlation from one year to the next, they are included as a stochastic state variable and a separate optimal policy is 60 determined for each price state outcome. Thirty-three crop yield outcomes for corn and soybeans grown with both conventional tillage and no-till are included in the model. However, the crop yield outcomes are assumed to be independent from one year to the next and only become known after machinery decisions are made, so an optimal policy choice is made for the entire set of crop yields, not for each crop yield. Other possible sources of variation in net returns from corn and soybean production had to be ignored due to computer capacity and expense constraints. It would be desirable to include the proportion of fall plowing that is completed in the fall as an additional stochastic state variable because it affects both the mean and variance of crop yields and is known early enough that farmers can respond by changing machinery before planting. However, this was not feasible due to the limited computer memory addressing capacity of Microsoft FORTRAN 5.1, and the extreme expense of obtaining solutions for the stochastic model on the mainframe computer at Michigan State University. Michigan corn and soybean prices exhibit such a high degree of serial correlation that they needed to be considered as a stochastic state variable for which probabilities of price states in the current period are determined by price state outcomes in the previous period. When the Michigan annual average corn prices for the 1956-1990 marketing years (Appendix B) were regressed on the previous years' corn prices, the resulting t-statistic for the lagged corn price was 7.33. When the Michigan annual average soybean prices for the 1956-1990 marketing years were regressed on the previous years' soybean prices, the resulting 61 t-statistic for the lagged soybean price was 6.107 Therefore, a Markovian probability matrix was estimated, based on the 1955-1990 price data (Appendix B ) . Levels of the price state variable were limited to combinations of three levels of corn prices and three levels of soybean prices due to computer capacity constraints. The combination of 3 price levels for corn and 3 price levels in soybeans results in a joint distribution of 9 levels, but combinations of high corn and low soybean prices and vice versa are not observed in the 1956-1990 Michigan data. This is to be expected, since Michigan corn and soybean prices are highly correlated. A regression of Michigan corn prices on soybean prices for 1955-1990 results in a t-statistic of 7.78 for the soybean price8. Therefore, the 9 price levels for the joint distribution were pared to 7 levels. Transition probabilities for the Markovian probability matrix (Table 3.7) also were determined directly from the 1956-1990 Michigan price data. Some adjustments were made to the empirical transition probabilities (Appendix B), since a sample of 36 observations can only provide a crude indication of movements between 7 price states. Crop price distributions were assumed to be independent of the crop yield distributions. Michigan soybean price data do exhibit a statistically significant negative relationship with Michigan average soybean yields. Michigan corn price data also exhibit a negative relationship with Michigan average corn yields, but the effect is not 7 These regressions were performed using ordinary least squares estimation with the SHAZAM econometrics program, Ver. 6.2 (White, 1990). 8 Ibid. 62 statistically significant at a 5% level of error. However, the magnitude of even the soybean yield effect on soybean price is small in comparison with the differences between the three soybean price levels. Furthermore, below-average Michigan corn and soybean yields during the period 1956-1990 are associated with declines in their price levels about as often as they are associated with increases in their price levels, and similarly for above-average Michigan corn and soybean yields. Therefore, probabilities for the 7 joint price levels were assumed to be independent of crop yields. Table 3.7 If Previous Price was: 1 2 3 4 5 6 7 Markovian Matrix of Price State Probabilities. Corresponding to the Historical Mean Prices. Probability of Each Current Price State Is: 1 0.,70 0. 10 0.,22 0.,08 0..18 0.,15 0.,0 2 0.,10 0.,23 0,,18 0.,20 0.,10 0,.0 0,.0 3 0,,08 0,.22 0 .40 0,,10 0,.0 0 .15 0,.0 4 0..12 0..15 0,.20 0,.40 0,.15 0 .15 0,.05 5 0..0 0..15 0 .0 0,.07 0,.20 0 .15 0,.05 6 0.,0 0..0 0..0 0,.07 0.,20 0..15 0..20 7 0.,0 0.,15 0.,0 0.,08 0.,17 0..25 0..70 Crop yields do not exhibit significant serial correlation once technological trends are removed (see Chapters 4 and 5) since weather during the crop season is essentially independent from one year to the 63 next9. Therefore it is assumed that the crop yield variable is independent from one year to the next. Each of the 33 crop yield outcomes is given an equal probability of 3.03% because each is determined from a different year of climatic data (see Chapter 4). The stochastic problem is to maximize: T V(Qt,KTit,KPjt,Xt,*,at) = E{ 2 S ^ 1 U[-PTit(flt) - PPjt(Qt) t-1 + STit(Qt,KTit) + SPjt(Qt»KPjt) - [CTijt(Qt,KTit)+CPjt(Qt,KPjt)] * CX(Xt) + RJt(Qt,1r,«t)]} , subject to the same laws of motion and terminal condition as in the deterministic model, but also subject to: “t+i = g(«t); where, in addition to the previous definitions: U[-] - 33 7 £ j=l £ k=l Pj*Pkt*( [• ](1~r))/(l-r); r = a relative risk aversion coefficient; i|i = the j=33 possible outcomes for crop yield; Pj = the at = the stochastic outcome for prices in year t from a probability distribution of k=7 possible outcomes. pkt probability of each crop yield outcome; = the probability of each crop price state in year t, given the price state outcome in period t-1. The form of the utility function U reflects constant partial relative risk aversion (CPRRA). This functional form implies that risk 9 An exception might be trends caused by global warming. However, the inability of scientists to agree that global warming trends even exist shows that weather trends across years are difficult to detect. 64 aversion declines as annual net income rises (Chavas and Holt, 1990). It is a variation of constant relative risk aversion (CRRA) for which risk aversion falls as accumulated wealth rises. The CPRRA form is used despite empirical evidence by Pope and Just (1991) that rejects the CPRRA and constant absolute risk aversion (CARA) forms in favor of the CRRA form of risk aversion because of dimensionality constraints in the stochastic dynamic programming model. Using the CRRA form of risk aversion would require an additional state variable for levels of wealth that would have to cover a wide range of possible values. Since empirical data to support particular expected utility forms and risk aversion parameters are scarce and inconsistent, and because strong theoretical arguments have been made by Jones and Ostroy (1984) and Baldwin and Meyer (1979) that risk aversion is much less important for irreversible investments than the flexibility to respond to new information, more is gained by being precise about costs, prices, and yields in the model than by using the CRRA expected utility form. Furthermore, analysis using the CPRRA form of expected utility will produce results that approximate those that would be obtained using the CRRA form. One limitation of the CPRRA and CRRA forms of expected utility is that the income or wealth outcomes all must be positive. Otherwise, the utility function is not defined over the usual range of relative risk aversion coefficients (0 o < 150- Q. _CO Q> sz 100 CO Z3 CO 500 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year 70% Fall Plow H | No-Till 112 Figure 5.4 Estimated Soybean Yields, MB Plow and No-Till, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 70602 o < 50- 0 40-] Q. cn cd ■C cn CQ 3020- 10 - 0- 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year 70% Fall Plow No-Till 113 (Figure 5.5) and soybean yields (Figure 5.6) between the two tillage systems. In 10 out of 33 years (30%) there is at least a 5 bushel per acre difference in corn yields and in 12 out of 33 years (36%) there is at least a 2 bushel per acre difference in soybean yields. The average corn and soybean yield estimates vary very little between the three levels of fall plowing completion under conventional tillage. The average corn yield in bushels per acre is 110.1 for 100% fall plowing, 109.7 for 70% fall plowing, and 109.3 for 45% fall plowing (Table 5.4). The average soybean yield actually increases slightly as spring operations are delayed due to the need to complete plowing in the spring. The average soybean yield in bushels per acre increases from 34.1 for 100% fall plowing to 34.3 for 70% fall plowing, to 34.7 for 45% fall plowing (Table 5.4). Mean estimated corn yields for 100% fall plowing and 45% fall plowing are not statistically different from mean estimated corn and yields for the no-till system. A difference of 1.4 bushels per acre would be required to say that the mean corn yields for 100% fall plowing and no-till are significantly different (a=20%), compared to the estimated difference of 0.2 bushels5. A difference of 2.6 bushels per acre would be required to say that mean corn yields for 45% fall plowing and no-till are significantly different (a=20%), compared to the estimated difference of 1.0 bushel6. 5 The Chi-square statistic for the hypothesis of a normal distribution equals 6.4. 6 However, the Chi-square statistic for the distribution of differences between the mean yields for 45% fall plowing and no-till equals 11.2, which leads to rejecting the hypothesis of a normal distribution (a=.05). 114 Figure 5.5 Estimated Corn Yields, No-Till minus MB Plow, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 15 10 SI2 a> sz 0 I! 1 fl izr trrr TJ C/3 m -5 Hi. -10 -15 I I I I 1 1 I I 1 I I I I i 1 I 1 I 1 I I I 1— I I— | 1 1 1 1 1 [ 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year Figure 5.6 Estimated Soybean Yields, No-Till minus MB Plow, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 116 Table 5.4 Average Corn and Soybean Yields CBU/A') for 100%. 70 % _ and 45% comnletion of Dlowing in the fall. 70% Fall Plowing Soybean Corn 45% Fall Plowing Corn Soybean Year 100% Fall Plowing Corn Soybean 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 112.81 69.03 103.82 117.84 142.07 154.23 134.43 100.37 101.49 62.26 128.13 103.33 47.98 84.69 48.79 138.13 164.06 162.90 76. 31 97.08 55.84 54.16 106.87 62.86 139.64 82.51 70.01 174.96 213.96 102.68 77.61 161.96 178.79 27.63 17.33 33.55 48.00 29.70 43.45 57.38 36.75 47.90 21.28 42.25 28.95 21.38 20.95 19.70 30.00 38.10 41.13 17.43 39.03 17.03 21.58 35.08 15.98 40. 70 20.43 28.30 42.55 58.95 47.95 50. 83 45.50 39. 50 112.81 63.33 103.82 117.84 142.07 154.23 134.43 99. 81 101.49 62.26 128.13 103.33 49.48 84.69 48.82 138.13 162.91 165.41 76.29 97.10 55.84 55.26 106.63 62.86 139.64 82.59 69.86 174.96 213.96 102.68 77.61 161.96 178.46 27.63 16.58 33.55 48.00 29.70 43.45 57.38 36.43 47.90 21.28 42.25 28.95 23.13 20. 95 19.78 30.00 32.70 38.85 17.43 39.03 17.03 25.45 38.08 15. 98 40.70 25.90 28.73 42.55 58. 95 47. 95 50.83 45.73 41.45 112.81 60.90 103.76 109.27 142.07 154.23 134.30 81.45 101.49 62.26 128.13 103.33 43.69 84.70 49.24 138.13 161.95 173.88 76.29 98.18 55.84 57.90 106.87 62.86 139.74 84.95 74.74 174.96 213.96 102.68 77.50 159.09 174.21 27.60 16.20 33.43 48.33 25.08 43.45 59.53 24.98 47.90 21.28 42.25 28.95 29.95 20.95 20.60 30.00 27.65 37.18 17.43 43.83 17.03 27.58 45.08 15. 98 39.78 29.28 27.60 42.55 58.95 47.95 52.10 45.73 47.78 Mean C.V. 110.05 38.8% 34.13 35.9% 109.96 39.1% 34.37 34.9% 109.25 39.7% 34.66 36.1% 117 Mean estimated soybean yields for 100% fall plowing are significantly different than the mean estimated soybean yields for no­ till (a=l%)7. However, the mean estimated soybean yields for 45% fall plowing are not significantly different from the estimated no-till yields. A difference of 1.9 bushels per acre would be required to say that mean soybean yields for 45% fall plowing and no-till are significantly different (a=20%), but the difference in the estimated means is only 1.4 bushels.8. The level of estimated crop yield variation is not unusual for a sandy soil. Furthermore, all of the unusually high and low crop yields can be readily explained. The July and August precipitation amounts (Table 5.3) explain much of the variation in crop yields. July is when both corn and soybean plants usually start their reproductive development and are most sensitive to moisture stress. Corn and soybean plants usually are filling their grain or seed with biomass during August, so moisture stress in August directly reduces corn grain and soybean seed yield. The modified CERES-MAIZE and SOYGRO models provide additional information concerning the magnitude of stresses and the timing of those stresses with respect to phenological stage. 7 The t-statistic for the paired differences equals 7.3 and the Chi-square statistic for testing whether the distribution of differences is normal equals 3.3 in this case. 8 The Chi-square statistic for the distribution of differences between mean yields for 45% fall plowing and no-till equals 18.6, which leads to rejecting the hypothesis of a normal distribution (a=.05). However, the observed differences mostly depart from a normal distribution by having an extremely high density in the interval between zero and 0.5 standard deviations above the mean. 118 The average corn yield exceeded 150 bushels per acre in 7 of the 33 years, with the average corn yields exceeding 200 bushels per acre in 1986. In 1986, 17.5 inches of rainfall in May-September were so well distributed that the CERES-MAIZE model reported zero moisture stress in every phenological stage for both conventional tillage and no-till. Five of the 7 years with corn yields in excess of 150 bushels per acre had July rainfall in excess of 4.5 inches. The other two years with corn yields in excess of 150 bushels per acre (1989 and 1990) had May and June rainfall in excess of 4 inches and rapid phenological development, so corn plants were able to complete the silking stage before moisture became limiting. The average corn yield was less than 80 bushels per acre in 9 of the 33 years. In 5 of these 9 years the July or August rainfall was less than 1.5 inches, and in 8 of these 9 years either the July or August rainfall was less than 2.1 inches. The other year with average corn yield less than 80 bushels per acre was 1988, in which only 2.6 inches of rain fell from May 1 to July 15. In both of the years with the average corn yield less than 50 bushels per acre, the July rainfall was less than 1.5 inches. In each of the two years with corn yield less than 50 bushels per acre, corn plants also matured early due to low September temperatures. In 7 of the 9 years with corn yields less than 80 bushels per acre, the average soybean yields were less than 25 bushels per acre. Again, low rainfall in July or August was largely responsible for the low soybean yields. The one year in which soybean yielded around 50 bushels per acre, but corn yielded less than 80 bushels per acre, was 119 1988, in which soybeans were little affected by the drought in May through mid-July and benefitted greatly from the abundant rainfall after mid-July. In the three years with soybean yields greater than 50 bushels per acre (1959, 1986, and 1988), July and August rainfall were at least 4 inches. For 1986, the SOYGRO model reported only one growth stage with drought stress above 0.1 on a 0-1 scale. For 1959 and 1988, the maximum drought stress levels were similar to those of other years, but occurred at a much earlier growth stage (first pod) than in most other years. Comparative Budget Results After multiplying average estimated yields by historical median prices and subtracting variable costs9 for each tillage system, the most striking result is the near equality of revenues net of variable costs for the alternative tillage systems and levels of fall plowing completion. The highest revenues net of variable costs, $84,241, are obtained for the no-till system (Table 5.5). However, the revenues net of variable costs for the conventional tillage system with 70% of plowing completed in the fall are only $416 less, a difference of only 0.5%, and the revenues net of variable costs for the other two levels of fall plowing completion are within $783 of those for the no-till system, a difference of only 0.9%. Gross revenues are slightly higher for the no-till system than for conventional tillage under any level of fall 9 The variable costs considered here exclude repair costs for the tractor and planter because these repair costs varied with accumulated usage. 120 plowing completion, but variable costs also are slightly higher for the no-till system (Table 4.10), resulting in little or no net advantage. Under the current prices of $2.30 per bushel of corn and $5.45 per bushel of soybeans, the no-till system provides revenues net of variable costs that are only $88 (0.15%) more than those for 70% fall plowing. Table 5.5 Revenues Net of Variable Costs*. MB Plow and No-Till Tillage system and percent fall plowing completion Corn Net Revenue ($/acre) Soybean Net Revenue ($/acre) 600 Acre Net Revenue ($) Average Net Revenue, C-C-S Rotation ($/acre) With $2.66/bu. corn and $6. 65/bu. soybeans 100% Fall Plow 136.54 144.89 83,593 139.32 70% Fall Plow 136.31 146.50 83,825 139.71 45% Fall Plow 134.42 148.45 83,459 139.10 No-Till System 133.63 153.95 84,241 140.40 With $2.30/bu. corn and $5. 45/bu. soybeans 100% Fall Plow 96.92 103.93 59,555 99.26 70% Fall Plow 96.73 105.26 59,742 99.57 45% Fall Plow 95.09 106.85 59,407 99.01 No-Till System 93.94 111.28 59,830 99.72 Based on mean yields estimated for 33 years on an Oshtemo soil, as presented in Tables 5.3 and 5.4. Variable costs are presented in Table 4.10, and exclude tractor and planter repair costs. Since the no-till system provides slightly higher yields than conventional tillage but has higher variable costs, any reduction in crop prices hurts the relative profitability of the no-till system. * 121 Furthermore, since the no-till system provides a greater yield advantage over conventional tillage for soybeans than for corn, the low ratio between current soybean and corn prices of 2.37 also hurts the relative profitability of the no-till system. If the tillage implements not used under the no-till system were sold, the reduction in fixed costs for shelter, insurance, and taxes according to Hunt (1983)10 would be $733. Hence, even ignoring depreciation which is by far the largest component of fixed costs11, the relative profitability of the no-till system increases greatly when possible reductions of fixed costs are considered. Revenues net of variable costs also would be significantly higher for the no-till system than for the conventional tillage system under any level of fall plowing completion if average repair costs for the planter and tractor are considered and the 85 HP tractor is used for the no-till system. Almost all previous analyses of the relative profitability of no-till systems (e.g. Smith and Hallam, Klemme, Williams) have made both of these assumptions and concluded that the no-till system is more profitable than conventional tillage in the long run. 10 Hunt (1983) states that costs for shelter, insurance, and taxes are very nearly fixed, and can be estimated as 2.5% of the purchase price. If the purchase price is assumed to be 85% of the list price, 2.5% of the purchase price for the moldboard plow, tandem disc, field cultivator, and row cultivator is $733. 11 Under any depreciation method, the annual depreciation cost will be at least 8% of list price according to estimates by Bowers (1987). This assumes that tillage equipment is kept 10 years and sold after 10 years for 20% of its list price. Use of any declining-balance method of depreciation and any positive discount rate will increase the annual depreciation cost above 8%. 122 Variation in Net Revenue and Stochastic Dominance Results Although there are only small differences in mean net revenues between the alternative tillage systems, there often are very sizeable differences in the annual results for revenue net of variable costs (Figures 5.7-5.9). Comparing revenues net of variable costs for no-till and 100% fall plowing, there are 2 years in which the no-till system provides at least $10,000 more, but 3 years in which the no-till system provides at least $10,000 less than 100% fall plowing (Figure 5.7). The number of years in which the difference in revenues net of variable costs for no-till and 70% fall plowing exceeds plus and minus $10,000 is the same (Figure 5.8). What is more interesting about the comparison of revenues net of variable costs for no-till and 70% fall plowing is the result that no-till provides at least $5,000 more in 9 years but at least $5,000 less than 70% fall plowing in five years. The variability of relative revenues net of variable costs is still greater when comparing the no-till system with 45% fall plowing (Figure 5.9). In 8 of 33 years no-till provides revenues net of variable costs that are at least $10,000 more or $10,000 less than 45% fall plowing. In 20 of 33 years, no-till provides revenues net of variable costs that are at least $5,000 more or $5,000 less than 45% fall plowing. Revenues net of variable costs clearly do not exhibit first-degree stochastic dominance (FSD) for the no-till system over conventional tillage with any of the three levels of fall plowing completion because the cumulative distribution functions (CDF's) cross (Figures 5.10-5.12). 123 Figure 5.7 Revenue Net of Variable Costs, No-Till minus 100% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 10 - CO •+•-1 C/2 O O .Q *i_ _ CO > o 5C/2 •a c rd C/2 o o % -5- CD o c CD > CD cc - 10 -15 - 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year 124 Figure 5.8 Revenue Net of Variable Costs, No-Till minus 70% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 10 •c +-o» - CO o O _0 X! co .55 ■0 c rt > o CD 0 0 0 o JZ H 2 0 0 C 0 -5- > 0 oc - 10 -15 - 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year 125 Figure 5.9 Revenue Net of Variable Costs, No-Till minus 45% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 40 35 30- cn •4— 1 25- C/3 O o 20 _CD - X3 .05 *k_ 05 > O CD t- 2: CD 3 C CD > CD CL - 10 - -15-20 53 55 57 59 61 63 65 67 69 71 73 75 77 84 86 88 90 54 56 58 60 62 64 66 68 70 72 74 76 78 85 87 89 Year 126 Figure 5.10 Net Revenue CDF’s, No-Till and 100% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. c CD O t— CD CL Jp 5 OJ O CD > ■D E o iii -20 fiii 0 rrn n 20 n i t "1 n r- 1 i n n rn n — i i— i— r~i— rn— m — rn— n— n - !— m— n— rY 40 60 80 100 120 140 160 180 200 220 240 Revenue minus Variable Costs ($1,000) 100% Fall Plow No-Till 127 Figure 5.11 Net Revenue CDF’s, No-Till and 70% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 100 c 0 O k_ O Q. 9080- £ 70- & 60- -Q ro 50 _Q oi— Q. 0 > 03 4030- "5 E 20- o 1°- Revenue minus Variable Costs ($1,000) 70% Fall P lo w No-Till 128 Figure 5.12 Net Revenue CDF’s, No-Till and 45% Fall Plowed, on an Oshtemo Sandy Loam in Michigan, 1953-78, 1984-90. 100 90CD 80- Q. £ 70~ & 6050- Q_ 0 > 403020 - 10 - R evenue m inus Variable C osts ($1,000) 45% Fall Plow ------ No-Till 129 Using long-term median corn and soybean prices, revenues net of variable costs12 for the no-till system almost but do not quite exhibit seconddegree stochastic dominance (SSD) over those for the conventional tillage system with the various levels of fall plowing. The no-till system would exhibit second-degree stochastic dominance over the conventional tillage system if the integral of the difference between the cumulative distribution function (CDF) for the conventional tillage system and the CDF for the no-till system is always non-negative. The graph of the CDF's of revenues net of variable costs for no-till and conventional tillage with 100% fall plowing (Figure 5.10) is not detailed enough to show that the lowest observation for no-till is about $198 less than the lowest observation for 100% fall plowing, but this violates SSD. The graphs of the CDF's of revenues net of variable costs for no-till and conventional tillage with 70% fall plowing (Figure 5.11) and 45% fall plowing (Figure 5.12) clearly show a range of net revenue values in the left tail of the CDF's for which this difference is negative, which violates SSD. However, if all tillage implements not used under the no-till system were sold, a conservative estimate of annual fixed-cost savings of $3,07813 would clearly make revenues net of both variable and fixed costs exhibit SSD for the no-till system over the conventional tillage 12 Again, repair costs for the planter and tractor are not included in these variable cost estimates because they change with accumulated usage. 13 This includes annual fixed costs for shelter, insurance, taxes, and depreciation. Annual fixed costs for shelter, insurance, and taxes are estimated as 2.5% of purchase price (85% of list price), following Hunt (1983). Annual fixed costs for depreciation are estimated as 8% of list price, which is an extremely conservative estimate. 130 system. Second-degree stochastic dominance implies that all risk-averse individuals would prefer the choice that exhibits SSD (see Chapter 2). Consideration of fixed-cost savings would not make the no-till system exhibit first-degree stochastic dominance over conventional tillage, because their respective CDF's would still cross at around $100,000 net revenue and again at around $215,000 net revenue. First-degree stochastic dominance would imply that all individuals who prefer more net revenue to less would prefer the choice that exhibits FSD, regardless of their risk preferences. Summary of Crop Yield and Static Economic Results The no-till and moldboard plow tillage systems exhibit large variation in crop yields and net revenues, but the mean crop yields and mean revenues net of variable costs are very nearly equal. Mean revenues net of variable costs are slightly higher for the no-till system than for the moldboard plow system with any level of fall plowing completion. Variation in the proportion of plowing completed in the fall did not alter the essential equality in mean crop yields and mean revenues net of variable costs between the no-till and moldboard plow tillage systems. Indeed,, net revenue results for 100% fall plowing, 70% fall plowing, and 45% fall plowing are so similar, that only the 70% fall plowing scenario which provided the highest net revenue results is evaluated in the dynamic programming analysis. Consideration of possible reductions in annual fixed costs greatly increases the difference in net profits between the no-till system and the moldboard plow tillage system. 131 There also is no clear difference in the riskiness of the no-till and moldboard plow systems, as measured by second-degree stochastic dominance, unless possible reductions in annual fixed costs are considered. When conservative estimates of reductions in annual fixed costs are considered, net revenues do exhibit second-degree stochastic dominance for the no-till system over the moldboard plow system. These results are very consistent with previous studies by Klemme (1985) and Williams (1988). The near -equality of crop yields for the no-till and moldboard plow tillage system also is consistent with studies in Michigan by Bronson (1989) and Hesterman et al. (1988) which found no significant tillage effect on crop yields. The small effect of soybean planting date on the estimated mean soybean yields for different levels of fall plowing completion is somewhat surprising. Rotz et al. (1983) claim that soybean yields decline by 1% per day as planting is delayed after May 20. However, Rotz et al. (1983) only cite unpublished data to support this claim, and Johnson (1987) claims that there is little effect of planting date on soybean yield through the first week in July. The SOYGRO model, which was developed in Florida, appears to exhibit much less sensitivity to near-freezing temperatures in September than the CERES-MAIZE model. This may be a deficiency in the SOYGRO model that partly causes the lack of response in estimated soybean yields to late planting dates. However, modeling soybean yield response to low September temperatures was beyond the scope of this analysis. Chapter 6 OPTIMAL ADOPTION STRATEGY RESULTS In general, the results of the dynamic programming analyses tell a much more interesting story about no-till adoption than the static economic analyses presented in the previous chapter. The results of the dynamic analyses confirm that adoption of the no-till system is the optimal choice in the long run for the profit-maximizing farmer. The results of the dynamic analyses also confirm that adoption of the no­ till system usually is the optimal choice in the long run for the riskaverse, expected utility-maximizing farmer, particularly when possible savings in machinery fixed costs are considered. But the dynamic programming results also show that machinery replacement issues, learning curves, and renting options all may play a role in determining the optimal timing of adoption and how machinery is acquired. The dynamic programming results also indicate that the optimal adoption strategies for the profit-maximizing farmer and the risk-averse, expected utility-maximizing farmer can be quite different. This chapter presents the optimal adoption strategies for both the profit-maximizing and the risk-averse, expected utility-maximizing farmer. Optimal adoption strategies for the profit-maximizing farmer are solutions to the deterministic dynamic programming model, and are presented first. Optimal adoption strategies for the expected-utility maximizing farmer are solutions to the stochastic dynamic programming model, and are presented last. Because results for the stochastic dynamic programming model are conditional on the value of the stochastic 133 price variable in each period, only the optimal policies for the first year are presented for this model. Results are presented for different price, learning curve, discount rate, and crop yield assumptions. Optimal adoption strategies for the profit-maximizing farmer are presented both for historical median corn and soybean prices and for current (1991-92) prices. Optimal adoption strategies for the risk-averse, expected utilitymaximizing farmer are presented for seven different current price states. The price states are based on the previous year's corn and soybean prices and determine probabilities for a range of possible prices in the current year1. The three learning curve assumptions are: (1) the 20% learning curve, in which herbicide, fuel and oil, labor, tractor repair, and planter repair costs are raised by 20% in the first year, 14% in the second year, and 7% in the third year of using the no­ till system; (2) the 10% learning curve, in which each of these cost- inflation factors is reduced by one-half; and (3) no learning curve. Optimal adoption strategies are determined for both a 3% and a 6% discount rate. strategies based A few sensitivity analyses for optimal adoption on a 9% discount rate are also presented. The two crop yield assumptions are: (1) the yields estimated with CERES-MAIZE and SOYGRO for conventional tillage with 70% fall plowing and no-till; and (2) crop yields for both tillage systems set equal to those estimated for conventional tillage with 70% fall plowing. 1 Price states and their probabilities are explained in Chapters 3 and 4 and in Appendix B . 134 For both the deterministic and stochastic models, results are presented first for the case in which rental options are limited to renting a planter for the entire acreage of corn and soybeans at a price of $10 per acre plus a $320 delivery-retrieval fee. Presentation of the results is then repeated for the case in which farmers have the option to rent a no-till planter on 60 acres, 120 acres, or 180 acres for $10 per acre plus the delivery-retrieval fee of $320. Results for the Deterministic Model Limited Rental Options and Estimated Yields The profit-maximizing farmer always adopts the no-till system in the first year if a 3% or 6% discount rate is used. The optimal adoption strategy is identical for the 20% learning curve, 10% learning curve, and no learning curve. The optimal adoption strategy also is identical for the historical mean prices of $2.80 per bushel of corn and $7.46 per bushel of soybeans, historical median prices of $2.66 for corn and $6.65 for soybeans, and the current prices of $2.30 for corn and $5.45 for soybeans. Provided that the 140 HP tractor has accumulated at least 1,600 hours of use, the optimal adoption strategy for a 6% discount rate is to immediately sell the conventional planter, purchase a no-till planter, sell the 140 HP tractor, and purchase the 85 HP tractor (Table 6.1). If the 140 HP tractor has not accumulated 1,600 hours of use, then only the planter is changed in the first year and the tractor is replaced when its accumulated use reaches 1,600 hours. The optimal adoption strategy is the same for a 3% discount rate except that 135 Table 6.1 Optimal Adoption Strategies based on Estimated Yields, Limited Renting Options, and a 6% Discount Rate. Initial Ages1* Planter Tractor (years) (hours) Adoption Year Purchases at Adoption** Ages at Adoption Planter Tractor (years) (hours) 1 1 1 1 1 800 1600 2400 320 0 4000 1 1 1 1 1 PL PL PL PL PL 2 2 & TR 2 2 & TR 2 2 & TR 2 2 & TR 2 1 1 1 1 1 800 1600 2400 3200 4000 2 2 2 2 2 800 1600 240 0 320 0 4000 1 1 1 1 1 PL PL PL PL PL 2 2 & TR 2 2 & TR 2 2 & TR 2 2 & TR 2 2 2 2 2 2 800 1600 2400 3200 4000 4 4 4 4 4 800 160 0 2400 32 0 0 4000 1 1 1 1 1 PL PL PL PL PL 2 2 & TR 2 2 & TR 2 2 & TR 2 2 & TR 2 4 4 4 4 4 800 1600 2400 3200 4000 6 6 6 6 6 800 160 0 2400 3200 4000 1 1 1 1 1 PL PL PL PL PL 2 2 6c T R 2 2 6c T R 2 2 6c T R 2 2 6c T R 2 6 6 6 6 6 800 1600 2400 3200 4000 8 8 8 8 8 8 00 1 60 0 2400 3200 4000 1 1 1 1 1 PL PL PL PL PL 2 2 6c T R 2 6c T R 2 6c T R 2 6c T R 2 2 2 2 8 8 8 8 8 800 1600 2400 3200 4000 10 10 10 10 10 800 160 0 2400 320 0 4000 1 1 1 1 1 PL PL PL PL PL 2 2 6c T R 2 2 6c T R 2 2 6c T R 2 2 6c T R 2 10 10 10 10 10 800 1600 2400 3200 4000 Optimal strategies for older planters and tractors are identical to those for the oldest planter and tractor shown, except that the machinery ages at adoption are higher. PL 2 is the no-till planter and TR 2 is the 85 HP tractor. 136 the 140 HP tractor is kept until it has accumulated at least 2,400 hours of use. The profit-maximizing farmer occasionally waits one year before adopting the no-till system if a 9% discount rate is used and a 20% learning curve is expected. If historical median prices are expected, the initial planter age is at least 4 years, and the initial tractor age is less than 1,200 hours, the optimal strategy is to wait until the tractor has accumulated 1,200 hours, and then replace both the planter and the tractor (Table 6.2). If the current prices are expected to continue, the optimal adoption strategy is generally to wait until the tractor has accumulated 1,600 hours before replacing both the planter and the tractor. However, with a 10% learning curve and a 9% discount rate, the profit-maximizing farmer only delays adoption if current prices are expected, the tractor has accumulated 800 hours or less, and the planter is between 5 and 9 years old. If the historical median prices are expected or if no learning curve is expected, the profitmaximizing farmer with a 9% discount rate adopts the no-till system In the first year. Limited Rental Options and Equal Yields If equal crop yields for conventional tillage and no-till and a 20% learning curve are expected, the profit-maximizing farmer usually waits to adopt the no-till system until the tractor has accumulated at least 3,600 hours of use or the planter is more than 15 years old. Although there are a few exceptions (shown in Figure 6.1), these usually are the conditions for adoption with a 3% discount rate. If the planter 137 Table 6.2 Optimal Adoption Strategies for Current Prices, Limited Renting Options, a 207= Learning Curve, and a 97= Discount Rate. Planter (years) Tractor (hours) Adoption Year Purchases at Adoption** Planter (years) Tractor (hours) 1 1 1 800 1600 2400 1 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 1 1 1 800 1600 2400 2 2 2 800 1600 2400 1 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 2 2 2 800 1600 2400 4 4 4 800 1600 2400 2 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 5 4 4 1600 1600 2400 6 6 6 800 1600 2400 2 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 7 6 6 1600 1600 2400 8 8 8 800 1600 2400 2 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 9 8 8 1600 1600 2400 10 10 10 800 1600 2400 2 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 11 10 10 1600 1600 2400 12 12 12 800 1600 2400 1 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 12 12 12 800 1600 2400 14 14 14 800 1600 2400 1 1 1 PL 2 & TR 2 PL 2 & TR 2 PL 2 & TR 2 14 14 14 800 1600 2400 Optimal strategies for older planters and tractors are identical to those for the oldest planter and tractor shown, except that the machinery ages at adoption are higher. PL 2 is the no-till planter and TR 2 is the 85 HP tractor. 138 Figure 6.1 Profit-Maximizing Policies for Equal Yields, a 3% Discount Rate, a 20% Learning Curve, and Various Machinery Ages. 1817-] 1615cn 14« 132 12 - c 11- < 8 7- •■=> 100 O) 9H 0 c _ro CL - 6H 5432 - 1 0- T T f T V - - - 1- - - T- - - V- - - - - - 1- - - - - T- - - - 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) | Adopt No-Till Keep M achinery 139 reaches 16 years of age before the tractor accumulates 2,800 hours, the optimal strategy is to only replace the conventional planter with the no-till planter. Otherwise, the optimal strategy is to replace both the conventional planter with the no-till planter and 140 HP tractor with the 85 HP tractor. With a 6% discount rate, the profit-maximizing farmer usually waits until either the tractor has accumulated at least 4,000 hours or the planter is more than 16 years old before adopting the no-till system (Figure 6.2). The profit-maximizing farmer with a 6% discount rate will replace both the tractor and planter at the same time if the tractor has accumulated at least 1,600 hours. These optimal adoption strategies are identical for the expectation of historical median prices or current prices for corn and soybeans. If a 10% or zero learning curve are expected, the profitmaximizing farmer often will adopt the no-till system one or two years earlier than if the 20% learning curve is expected. With a 10% learning curve and 3% discount rate, the profit-maximizing farmer will adopt the no-till system if the tractor has accumulated 3,200 hours of use and the planter is more than 9 years old, or for any planter age if the tractor has accumulated 3,600 hours of use. With a zero learning curve and 3% discount rate, the minimum planter age for no-till adoption by the profit-maximizing farmer is reduced, and drops to one year if the tractor has accumulated 3,200 hours (Figure 6.3). With a 6% discount rate, the profit-maximizing farmer will always adopt the no-till system if the tractor has accumulated 3,600 hours and a 10% learning curve is expected or if the tractor has accumulated 3,200 hours and no learning 140 Figure 6.2 Profit-Maximizing Policies for Equal Yields, a 6% Discount Rate, a 20% Learning Curve, and Various Machinery Ages. 181716- m |!§ '" % *<* It 15-1 (/> *_ 1413- CD 12 11H 10 Cu > C - - - © 03 < © C J2 -t—> CL 9- 8H 76 - - - 432 - - 1 0- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 141 Figure 6.3 Profit-Maximizing Policies for Equal Yields, a 3% Discount Rate, No Learning Curve, and Various Machinery Ages. 1817161514'cn' k_ a? 13a 12c 1110a> O) < _ 1 UJ c CC CL Q8i 7654-| 3210- if t r 7 r r— r— t— — — t— — t— r— r 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 142 curve is expected. These results also are not affected by whether the historical median or current corn and soybean prices are expected. Multiple Renting Options and Estimated Cron Yields When the farmer is allowed to rent the no-till planter on 60, 120, or 240 acres and a 20% learning curve is expected, the profit-maximizing farmer usually rents the no-till planter to plant 60 acres for one or two years before purchasing the no-till planter (Tables 6.3, 6.4, and 6.5). This corresponds to the frequently recommended practice of trying a new technology out on a limited acreage, both for evaluation and for learning how to make it work more effectively before full-scale adoption. However, if the 10% learning curve or no learning curve is expected, the optimal adoption strategy usually is to ignore rental possibilities and follow the optimal strategy determined above for limited renting options2. Also, after the tractor has accumulated more than 3,200 hours, the optimal adoption strategy is to immediately replace the 140 HP tractor with the 85 HP tractor and purchase the no­ till planter. This implies that once repair costs for the 140 HP tractor have risen to moderately high levels, the benefit of limiting the costs of learning the no-till technology to a small acreage is outweighed by the benefit of reducing repair costs by switching to a new 85 HP tractor. There are a very few cases when current prices and a 10% learning curve are expected for which the profit-maximizing farmer will rent the no-till planter for one year before adopting no-till. For example, with a 6% discount rate the optimal policy is to rent the no­ till planter on 60 acres if the tractor age is 800 hours and the planter age is 6-10 years. 143 Table 6.3 Optimal Adoption Strategies for Median Prices, Multiple Renting Options, a 20% Learning Curve, and a 3% Discount Rate. Initial Ages* Planter Tractor (hours) (years) Adoption Year Purchases at Adoption** Ages at Adoption Planter Tractor (hours) (years) 2 2 2 2 2 800 1600 2400 3200 4000 2 2 2 1 1 PL 2 PL 2 PL 2 & TR PL 2 & TR PL 2 & TR 4 4 4 4 4 800 1600 2400 32 0 0 4000 2 2 2 2 1 PL 2 PL 2 PL 2 & TR 2 6 6 6 6 6 800 1600 2400 3200 4000 2 2 2 2 1 8 8 8 8 8 800 1600 2400 3200 4000 2 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 6c 6c 6c 6c 6c TR TR TR TR TR 10 10 10 10 10 800 1600 2400 3200 4000 2 2 2 1 1 PL PL PL PL PL 2 2 2 2 2 6c 6c 6c 6c 6c TR TR TR TR TR Years Rented 3 3 3 2 2 1600 240 0 3200 320 0 4000 1 1 1 0 0 5 5 5 5 4 160 0 2400 320 0 4000 4000 1 1 1 1 0 7 7 7 7 6 24 0 0 2400 320 0 4000 4000 1 1 1 1 0 2 2 2 2 2 9 9 9 9 8 1600 240 0 3 20 0 4000 4000 1 1 1 1 0 2 2 2 2 2 11 11 11 10 10 1600 240 0 3200 320 0 4000 1 1 1 0 0 2 2 2 P L 2 6c T R 2 P L 2 6c T R 2 P L 2 6c T R 2 PL 2 6c TR 2 P L 2 6c T R 2 P L 2 6c T R 2 P L 2 6c T R 2 Optimal strategies for older planters (up to 16 years) and tractors (up to 9600 hours) are identical to those for the oldest planter and tractor shown, except that the planter and tractor ages at adoption are higher. PL 2 is the no-till planter and TR 2 is the 85 HP tractor. 144 Table 6.4 Optimal Adoption Strategies for Median Prices, Multiple Renting Options, a 20 % Learning Curve, and a 6% Discount Rate. Initial Ages’* Planter Tractor (hours) (years) Adoption Year Purchases at Adoption** Ages at Adoption Planter Tractor (years) (hours) Years Rented 2 2 2 2 800 1600 2400 3200 3 2 2 1 PL PL PL PL 2 2 2 2 & & & & TR TR TR TR 2 2 2 2 4 3 2 2 2400 2400 3200 3200 2 1 1 0 4 4 4 4 800 1600 2400 3200 3 2 2 1 PL PL PL PL 2 2 2 2 & & & & TR TR TR TR 2 2 2 2 6 5 5 4 2400 2400 3200 3200 2 1 1 0 6 6 6 6 800 1600 2400 3200 3 2 2 1 PL PL PL PL 2 2 2 2 & & & & TR TR TR TR 2 2 2 2 8 7 7 6 2400 2400 3200 3200 2 1 1 0 8 8 8 8 800 1600 2400 3200 3 2 2 1 PL PL PL PL 2 2 2 2 & & & & TR TR TR TR 2 2 2 2 10 9 9 8 2400 2400 3200 3200 2 1 1 0 10 10 10 10 800 1600 2400 3200 3 2 2 1 PL PL PL PL 2 2 2 2 & & & & TR TR TR TR 2 2 2 2 12 11 11 10 2400 2400 3200 3200 2 1 1 0 Optimal strategies for older planters (up to 16 years) and tractors (up to 9600 hours) are identical to those for the oldest planter and tractor shown, except that the planter and tractor ages at adoption are higher. PL 2 is the no-till planter and TR 2 is the 85 HP tractor. 145 Table 6.5 Optimal Adoption Strategies for Current Prices, Multiple Renting Options, a 20% Learning Curve, and a 6% Discount Rate. Initial Ages* Planter Tractor (years) (hours) Adoption Year Purchases at Adoption** Ages at Adoption Planter Tractor (hours) (years) Years Rented 2 2 2 2 2 800 1600 2400 3200 4000 3 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 & & & & & TR TR TR TR TR 2 2 2 2 2 4 3 3 3 2 2400 2400 3200 4000 4000 2 1 1 1 0 4 4 4 4 4 800 1600 2400 3200 4000 3 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 & & & & & TR TR TR TR TR 2 2 2 2 2 6 5 5 5 4 2400 2400 3200 3200 4000 2 1 1 1 0 6 6 6 6 6 800 1600 2400 3200 4000 3 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 & & & & & TR TR TR TR TR 2 2 2 2 2 8 7 7 7 6 2400 2400 3200 4000 4000 2 1 1 1 0 8 8 8 8 8 800 1600 2400 3200 4000 3 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 & & & & & TR TR TR TR TR 2 2 2 2 2 10 9 9 9 8 2400 2400 3200 4000 4000 2 1 1 1 0 10 10 10 10 10 800 1600 2400 3200 4000 3 2 2 2 1 PL PL PL PL PL 2 2 2 2 2 & & & & & TR TR TR TR TR 2 2 2 2 2 12 11 11 11 10 2400 2400 3200 4000 4000 2 1 1 1 0 Optimal strategies for older planters and tractors are identical to those for the oldest planter and tractor shown, except that the machinery ages at adoption are higher. PL 2 is the no-till planter and TR 2 is the 85 HP tractor. 146 Optimal adoption strategies when multiple renting options are available vary slightly for different discount rates and crop prices. When the discount rate is increased from 3% (Table 6.3) to 6% (Table 6.4) and historical median prices are expected, the profit-maximizing farmer usually rents the no-till planter one additional year if the initial tractor age is 800 hours or 3200 hours. The profit-maximizing farmer also rents the no-till planter one additional year if the tractor age is 3200 hours and the current corn and soybean prices are expected (Table 6.5) rather than the historical median prices (Table 6.4). Multiple Renting Options and Equal Crop Yields If a 20% learning curve and equal crop yields for the two tillage systems are expected, the profit-maximizing farmer often rents the no­ till planter to plant 60 acres for one or two years before buying the no-till planter (Table 6.6). The profit-maximizing farmer rents the no­ till planter for a wider range of planter and tractor ages when equal yields for the two tillage systems are expected than when the estimated crop yields are expected (compare Table 6.6 to Table 6.3). Under the optimal adoption strategy, the 140 HP tractor is replaced with the 85 HP tractor at the same time as the conventional planter is replaced with the no-till planter. However, with a 10% learning curve and 6% discount rate, the profit-maximizing farmer only rents the no-till planter if the tractor age is less than 1,600 hours and planter age is less than 16 years (regardless of price expectations). With a 10% learning curve and 6% discount rate, the profit-maximizing farmer also occasionally rents the 147 Table 6.6 Optimal Adoption Strategies for Equal Yields, Median Prices Multiple Renting Options, a 20% Learning Curve, and a 6% Discount Rate. Initial Ages* Planter Tractor Adoption (years) (hours) Year Purchases at Adoption** Ages at Adoption Planter Tractor (years) (hours) Years Rented 2 2 2 2 2 2 2 800 1600 2400 3200 4000 4800 5200 4 3 3 2 2 2 1 PL PL PL PL PL PL PL 2 2 2 2 2 2 2 & & & & & & & TR TR TR TR TR TR TR 2 2 2 2 2 2 2 5 4 4 3 3 3 2 3200 3200 4000 4000 4800 5200 5200 2 2 2 1 1 1 0 4 4 4 4 4 4 4 800 1600 2400 3200 4000 4800 5200 4 3 3 2 2 2 1 PL PL PL PL PL PL PL 2 2 2 2 2 2 2 & & & & & & & TR TR TR TR TR TR TR 2 2 2 2 2 2 2 7 6 6 5 5 4 4 3200 3200 4000 4000 4800 5200 5200 2 2 2 1 1 1 0 8 8 8 8 8 8 8 800 1600 2400 3200 4000 4800 5200 4 3 3 2 2 2 1 PL PL PL PL PL PL PL 2 2 2 2 2 2 2 & & & & & & & TR TR TR TR TR TR TR 2 2 2 2 2 2 2 11 10 10 9 9 9 8 3200 3200 4000 4000 4800 5200 5200 2 2 2 1 1 1 0 12 12 12 12 12 12 12 800 1600 2400 3200 4000 4800 5200 3 3 3 2 2 2 1 PL PL PL PL PL PL PL 2 2 2 2 2 2 2 & & & & & & & TR TR TR TR TR TR TR 2 2 2 2 2 2 2 14 14 14 13 13 13 12 2400 3200 4000 4000 4800 5200 5200 2 2 2 1 1 1 0 This is limited initial PL 2 is a representative sample ofinitial ages. Renting is to initial tractor ages less than 3200 hours if the planter age is 16 years. the no-till planter and TR2 is the 85 HP tractor. 148 no-till planter when the tractor age is 2,000 hours. With no learning curve, the profit-maximizing farmer never rents the no-till planter. An interesting result is that if the initial tractor and planter ages are no more than 800 hours and 10 years, respectively, the optimal adoption strategy is to keep the initial machinery in the third year without renting (Table 6.6). The 20% learning curve raises herbicide, fuel, labor, tractor repair, and planter repair cost by only 3.5% after 2 years of experience. This implies that the rental fee of $10 per acre plus a $320 delivery-retrieval fee outweighs the benefit of incurring the remaining learning costs for the no-till system on only 60 acres versus 600 acres. If a 20% learning curve is expected, the opportunity to rent the no-till planter on a small proportion of the corn and soybean acres slightly accelerates adoption if the initial tractor age is less than 3600 hours. However, this opportunity delays full adoption by the profit-maximizing farmer if the initial tractor age is 4400-4800 hours and has no effect if the initial tractor age is more than 4800 hours. This result suggests that it may not be an optimal strategy for machinery dealers to attempt to increase sales of no-till equipment by making it more convenient and less expensive to rent no-till planters. However, this result depends on the not very realistic assumption that the farmer is certain that he or she knows what the expected crop yield will be on his or her farm. In practice, the farmer probably experiments with a new technology just as much to discover what the expected results would be as to learn how to reduce costs (or equivalently, increase crop yields) for that technology. 149 Results for the Stochastic Model Limited Renting Options and Estimated Crop Yields The optimal adoption strategies for the risk-averse, expected utility-maximizing farmer clearly indicate that risk aversion may greatly delay the adoption of the no-till technology. Using probability expectations for crop prices that correspond to the historical mean prices of $2.80 for corn and $7.46 for soybeans, there are many combinations of initial planter age, tractor age, and price state for which the expected utility-maximizing farmer will keep the conventional planter and 140 HP tractor. Most of these cases include the first price state of low corn and low soybean prices in the previous year. Since the probability of continued low prices for the current price state of low corn and low soybean prices is very high2, the optimal risk-averse strategy is to postpone machinery investments when crop prices are low. With a 6% discount rate and moderate risk aversion, the expected utility-maximizing farmer usually keeps the initial machinery in price state 1 unless the planter is more than 15 years old or the tractor has accumulated more than 8,000 hours of use (Figure 6.4). Under price state 3, the expected utility-maximizing farmer usually will change to the no-till planter if the tractor has accumulated less than 3,600 hours or more than 6,400 hours (Figure 6.5). Otherwise, the expected utility- maximizing farmer usually keeps the conventional planter until it is about 15 years old or until the tractor accumulates more than 6,400 hours. Also, in price state 2, if the tractor has accumulated exactly 2 For example, the probability that price state 1 will be followed by price state 1 is set at 70% (see Chapter 4). 150 Figure 6.4 Optimal Policies for Moderate Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 1. 'TT CD >. r. CD O) < i_ G ■(— ' CO Q. 181716151413121110Q876543210- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 151 Figure 6.5 Optimal Policies for Moderate Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 3. 18 t 17- 16 - 15- "c/T 14- c5 13- 12c ~ 11- 10 98 76 5432 - Q) D) < i O — -t- 1 c CL s - - - 1 0- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) | Adopt No-Till a Keep Machinery 152 3,200 hours and the planter is 7-11 years old, the optimal policy is to keep the initial machinery. Similarly, in price state 4, if the tractor has accumulated exactly 3,200 hours and the planter is 8-11 years old, the optimal policy is to keep the initial machinery. Otherwise and in the other price states, the optimal policy for a 6% discount rate and moderate risk aversion is to immediately adopt the no-till system. In contrast to the optimal adoption strategies for the profitmaximizing farmer, the risk-averse, expected utility-maximizing farmer rarely purchases the no-till planter and 85 HP tractor in the same year. Furthermore, the expected utility-maximizing farmer often chooses to rent the no-till planter on all 600 acres of corn and soybeans rather than purchase the no-till planter. This is especially true in the price states with relatively high corn and soybean prices, price states 5-7, and when the tractor has accumulated more than 6,000 hours. However, the difference in expected utility between renting the no-till tractor and purchasing the no-till tractor usually is small when renting is selected. The optimal adoption strategy for the expected utility-maximizing farmer is sensitive to the degree of risk aversion. A reduction in the relative risk aversion coefficient from 1.0 to 0.5 increases the number of cases for which the optimal strategy is to sell the conventional planter and either purchase or rent the the no-till planter (compare Figures 6.6 and 6.7 to Figures 6.4 and 6.5). When the risk aversion coefficient is set at zero (risk neutrality), the optimal strategy is to adopt no-till for every combination of planter age, tractor age, and price state, just as in the results for the deterministic model. 153 Figure 6.6 Optimal Policies for Slight Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 1. 18 ,, r’ " l""r - 17-1 16- 15-1 14w w~ CO 13CD >. 12H c. 11 10-1 CD CD 9- CD C 7 6 5 < CL 8H - 432 - 1- 0- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 154 Figure 6.7 Optimal Policies for Slight Risk Aversion, a 6% Discount Rate, Estimated Yields, and Price State 3. 1817- 16H 15c_n 14i re 130 >. 1 2 - 0 11 10 - cn 9- k_ 7- < 0 ' c J2 CL 8-j 6H 543H 2 - 1 0- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till |-(4 i| Keep Machinery 155 The optimal adoption strategy for the risk-averse, expected utility-maximizing farmer also is sensitive to the discount rate. Reducing the discount rate from 6% to 3% increases the number of cases for which the optimal policy for risk-averse farmers is to adopt the notill system in the first year (compare Figures 6.8-6.11 to Figures 6.4-6.7). However, the results of the stochastic dynamic programming model for a 3% discount rate should be viewed with some caution because of the 30-year planning horizon used in the stochastic analyses. Any loss in value caused by having to sell equipment at the end of 30 years is much more heavily weighted with a 3% discount rate than with a 6% discount rate. The number of cases for which the expected utility-maximizing farmer adopts the no-till system also increases slightly when using price state probabilities that roughly correspond to the historical median corn and soybean prices4 (Compare Figures 6.12-6.15 to Figures 6.4-6.7). Thus, reducing crop prices for the risk-averse, expected utility-maximizing farmer has the opposite effect to reducing crop prices for the profit-maximizing farmer. However, prices were reduced for the expected utility-maximizing farmer by reducing the probabilities of the highest crop prices, which has the effect of reducing price variance. It therefore appears that stabilizing crop prices, even at slightly lower levels, may encourage risk-averse farmers to adopt the no-till technology. 4 Probability weights were adjusted such that 50,000 random draws using 20 different random number seeds resulted in an average corn price of $2.63 and average soybean price of $6.70 (see Chapter 4 and Appendix B). These average prices are very close to the historical median prices of $2.66 for corn and $6.65 for soybeans. 156 Figure 6.8 Optimal Policies for Moderate Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 1. 181716- 15-| 'co' 14- t5 13- 5 12 c 11 ~ 10H . 12r 11100 Q05 8< 70* •f— 6c CO 5CL 4321O-i i T T T T r T T T T r— 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 158 Figure 6.10 Optimal Policies for Slight Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 1. 18171615In' 14cd 13o 12■>, r 11100) QO) 8< 70> 6c 03 5CL 43210J L_ 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 159 Figure 6.11 Optimal Policies for Slight Risk Aversion, a 3% Discount Rate, Estimated Yields, and Price State 3. 18- 171615- 'w 14 - c5 13a> >. 1 2 - c - 0 D3 < _ I 0 C Q. 11 10 - 98 - 7-j 6 5432 - - 1H o- 1 f Y Y- - - Y- - - Y- - - - - - Y- - - - - - 7- - - - - T~ 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 160 Figure 6.12 Optimal Policies for Moderate Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 1. 18171615ci_ n 1403 13CD 12■>, 11r 10CD (3) < u. CD C 03 CL wS>; .^>w:< q- 876543210J i t t r i -- 1------ r. . . . 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 161 Figure 6.13 Optimal Policies for Moderate Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 3. 1817H 1615CO L_ CO 1413- cd >> 1 2 _c 1 1 10- - CD O) < k_ -*CD —> 98 7-j - C 6 a 5- Q_ 4H - 32 - 1 0- 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 162 Figure 6.14 Optimal Policies for Slight Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 1. Planter Age (in years) 18- 17-1 16151413-| 12 11 10 - 976 543H 2 - - H o- “I I T J T T T T T t X T- - X 1- - - 1 X- - - X 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 163 Figure 6.15 Optimal Policies for Slight Risk Aversion, Median Prices, a 6% Discount Rate, Estimated Yields, and Price State 3. 1817- 16- Planter Age (in years) 15- 141312H 11 10-j 98 7H 6 5432 1 0- - - - 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 Tractor Age x 1000 (hours) Adopt No-Till Keep Machinery 164 Two contrasts between the deterministic results and the riskaverse, stochastic results are remarkable. First, the profit-maximizing farmer always adopts the no-till technology in the first year under historical median or mean prices with limited renting options. The risk-averse, expected utility-maximizing farmer often waits until the initial machinery is worn out before adopting the no-till technology, although results vary according to the current price state. Secondly, the cases in which the profit-maximizing farmer keeps the current machinery all include relatively low tractor ages. Indeed, the tractor age appears to be far more important than the planter age in determining the optimal time of adoption for the profit-maximizing farmer. However, for the risk-averse, expected utility-maximizing farmer, the current planter and tractor are more often kept when they are middle-aged than when very new, and the planter age is very important. The reason for this difference appears to be that the risk- averse farmer is much more influenced by declining trade-in values than is the profit-maximizing farmer. Although it is not a very realistic assumption, in this model the trade-in value is certain, as well as being very substantial. Therefore, the risk-averse, expected utility- maximizing farmer is anxious to capture as much of this large, certain value as possible, rather than use new equipment to produce highly uncertain net revenue from crop production. Another simplistic assumption that contributes to the preference by risk-averse, expected utility-maximizing farmers to keep aging equipment is that machinery reliability is ignored in the model. If the model assumed more variable crop yields or crop production costs for 165 aging equipment than for new equipment, risk-averse, expected utilitymaximizing farmers would have less tendency to keep aging equipment. Limited Renting Options and Equal Crop Yields The effect of risk-aversion on optimal adoption strategies for the expected utility-maximizing farmer is even more severe when the long-run average yields for conventional tillage and no-till are expected to be equal'*. If a 20% learning curve is expected, no-till adoption does not occur in any case. If a 10% learning curve is expected, no-till adoption usually occurs when the tractor age reaches 8,800 hours for price state 1, 7,600 hours for price state 3, 6,000 hours for price states 2 and 4, about 5,200 hours for price states 5 and 6, and 3,600 hours for price state 7 (Table 6.7). When no learning curve is expected, no-till adoption by the expected utility-maximizing farmer begins to occur when the tractor has accumulated about 1600 to 2800 less hours than for the 10% learning curve, or earlier if the planter is either very new or very old (Table 6.7). Multiple Renting Options When either the estimated crop yields or equal crop yields and a 20% learning curve are expected, the risk-averse, expected-utility maximizing farmer prefers to rent a no-till planter on 60 acres, 4 The long-run average yields were set equal to each other by multiplying all crop yields for the conventional tillage system by the ratio of the no-till mean yield divided by the moldboard plow mean yield. Table 6.7 Conditions for which the Optimal Risk-Averse Policy* is to Adopt No-Till, Assuming Equal Yields and Limited Renting Options. No Learning Curve** 10% Learning Curve** Initial Price State*** Initial.Ages Tractor Planter (years) (hours) 17 16-17 1-17 1-17 17 13-17 1-17 1-17 1-17 1-17 1-17 2000-3600 6800-8400 8800-max. 6000-max. 1600-2400 7200 7600-max. 6000-max. 5600-max. 5200-max. 3600-max. 1 1 1 2 3 3 3 4 5 6 7 No Learning Curve** Initial Ages Tractor Planter (years) (hours) 16-17 17 16-17 1-17 16-17 17 Initial Price State*** 400-4400 4800-5600 6000-8000 8400-max. 400 800 1 1 1 1 2 2 Initial Ages Tractor Planter (hours) (years) 16-17 15-17 14-17 13-17 1-17 16-17 17 16-17 14-17 1-17 16-17 17 16-17 15-17 14-17 12-17 1-17 14-17 13-17 1-2,9-17 1-17 13-17 11-17 1-17 1-17 2000-2400 2800 3200 3600 4000-max. 400-3200 3600-4000 4400-6400 6800 7200-max. 400-800 1200 2000-2800 3200 3600 4000 4400-max. 2000 2400 2800 3200-max. 2000 2400 2800-max. 1200-max. Initial Price State*** 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 6 6 6 7 * Low risk aversion, defined as having a CPRRA coefficient equal to 0. 5, is assumed (CPRRA is explained in Chapter 3). * The 10% learning curve raises herbicide, fuel and oil, and labor costs for the no-till system by 10% in the first year, 7% in the second year, and 3.5% in the third year of using no-till. For no learning curve, these costs are not affected by experience. *** Price Price Price Price Price Price Price State1: State2: State3: State4: State5: State6: State7: $2.18 Corn $2.18 Corn $2.62 Corn $2.62 Corn $2.62 Corn $3.59 Corn $3.59 Corn and $5.63 Soybeans in previous year. and $6.65 Soybeans in previous year. and $5.63 Soybeans in previous year. and $6.65 Soybeans in previous year. and $10.08 Soybeans in previous year. and $6.65 Soybeans in previous year. and $10.08 Soybeans in previous year. 167 regardless of price state or age of machinery unless the conventional planter is at least 16 years old. If the conventional planter must be replaced, the optimal strategy depends on the tractor age, price state, and crop yield expectations. Considering the reluctance of the risk- averse, expected utility-maximizing farmer to adopt no-till when a 20% learning curve is expected, the opportunity to rent a no-till planter on a limited acreage and reduce learning costs may greatly accelerate adoption. Indeed, if equal mean yields for no-till and conventional tillage are expected, a comparison of the expected utility-maximizing farmer's optimal strategies for different learning curves indicates that this farmer will not adopt no-till at all unless a planter can be rented for a limited acreage or learning costs are small. Differences between Optimal and Second-Best Policies The profit-maximizing farmer and the expected utility-maximizing farmer often choose to keep existing machinery rather than purchase a no-till planter. However, when this occurs, the difference between the value functions for these two alternatives is usually small. For example, when the age of the tractor is 1,600 hours, the age of the conventional planter is less than 16 years, equal yields are expected for the the alternative tillage systems, and a 20% learning curve is expected, the profit-maximizing farmer chooses to keep these machines. However, the discounted net revenues for buying a no-till planter and 85 HP tractor are only $1,000 to $2,500 less than those for keeping the current machinery (Figure 6.16). When the moderately risk-averse farmer chooses to keep a 1,600 hour tractor and conventional planter 168 rather than purchase a no-till planter (under price state 1 with a 6% discount rate), the difference in expected utility for these two choices exhibits a similar curve for different planter ages (Figure 6.17). One distinction between Figures 6.16 and 6.17 is that the risk-averse farmer is more inclined than the profit-maximizing farmer to purchase the no­ till planter when the conventional planter is less than 8 years old. Another distinction is that there appears to be no meaningful way to measure the differences for the 30-year discounted sum of a CPRRA expected utility function in monetary terms. Review of the Research Hypotheses Five research hypotheses were proposed in Chapter 1. Although no formal criteria for acceptance or rejection of the hypotheses were proposed, the results of this chapter mostly support those hypotheses. The first hypothesis was that the profit-maximizing farmer and expected utility-maximizing farmer would adopt the no-till system, but the timing of this adoption would depend on the age of the currentlyowned machinery, the magnitude of learning curves, and whether opportunities to rent the no-till planter on a limited acreage exist. The profit-maximizing farmer always does adopt the no-till system within the range of parameters tested. Based on the estimated yields for corn and soybeans under the alternative tillage systems, the timing of adoption by the profit-maximizing farmer is not sensitive to age of the currently-owned machinery or the magnitude of learning curves. However, based on equal yields for the alternative tillage systems, the timing of adoption is sensitive to both of these variables. Small-scale renting 169 Figure 6.16 c o Q. Penalty for Adoption with Various Planter Ages, a 1600 Hr. Tractor, and Profit-Maximization. 3000 n 2500- ~o < (f) D 2000- C E _c o co Q. C D CC -500 (D 2 -1000- 6 8 10 Planter Age (Years) Figure 6.17 c o Q _ Penalty for Adoption with Various Planter Ages, a 1600 Hr. Tractor, and Exp. Utility Maximization. 0.004 0.002 O "O < 0 and - K„ > 0 must hold, where K„ and Kn+1 are the discounted values of all future costs associated with a policy of replacing equipment every n and n+1 years, respectively. It is shown here that Kr,-! - K„ > 0 is equivalent to: Cn < K^-l , which is inequality (5) in Chapter 2, 1 - [1/(1+r)] and that Kj,+1 - > 0 is equivalent to: Cn^ > Kj,, which is inequality (6) in Chapter 2. 1 - [1/(1+r)] Writing [l/(l+r)] as W, equation (4) in Chapter 2 becomes: A + 2 C^W1' 1 i=l Kh _ ------------------- 1 - W" Substituting n+1 for n: 197 n A + Kn +1 » 2 C ^ W 1'1 i=l --------------------- 1 - W"+1 n+1 2 C ^ W 1"1 + C n+ ^W 1 i=l A + 1 - W"+1 (1 - W")Kn + Cn+1*W" 1 - W"+1 1 - Cn+1*^ W" + 1 - W"+1 1 - W"+1 Hence: 1 - W" Kn+1 - Kn - ------ (----------- Cn+^W" - 1 ) + ----------- 1 - W"+1 1 - wn+1 Kn (W"+1 - W") + Cn+1*W" ------------------------- • 1 - W"+1 Since W < 1, which implies that (1 - Wn+1) > 0; if - Kp >0, then: [Kn (W"+1 - W") + C n + ^ W 11] > 0. Dividing this inequality through by W”: K„ (W - 1) + Cn+1 > 0. Hence: Cn+1 > (1 - W) Kn, (Al) 198 ^n+l or: > 1^. 1 - W Cn+1 Equivalently: > Kn, which is inequality (5) in Chapter 2. 1 - 1/(1+r) Multiplying equation (Al) by -1, one obtains: ]<„ (VP - VP+1) - Cn+1*W" K n +1 - Kn = ------------------------------ 1 - VP+1 Replacing n by n+1: Kn-: Kn_i - Kn = (VP'1 - VP) - C n* V P _1 -------------------------------1 - VP +1 Then if Kn-i - K„ > 0, Kn-X (VP'1 - VP - Cn^VP'1 > 0. Dividing this inequality through by VP: (1 - W) Hence: V i - C„ > 0. < Kn-i1 - W Equivalently: < Kn-i, which is inequality (6) in Chapter 2 1 - 1/(1+r) Appendix B DETERMINATION OF DISCOUNT RATE AND CROP PRICES This appendix provides further explanation of how the discount rates and crop price parameters in the deterministic and stochastic dynamic programming models were determined. Chapter 3 states that optimal adoption strategies are determined for discount rates of 3%, 6%, and 9%. However, Chapter 3 did not explain why these discount rates were chosen, so an explanation is provided here. Chapter 4 provides a partial explanation of how historical crop prices were adjusted for inflation and technological improvement. Results for the estimation of the technology trend are presented here. Explanation also is provided for how the Markovian price state probabilities were determined for the stochastic model. The choice of discount rate is important in the determination of the optimal time to replace and possibly change machinery. The optimal time to replace with a new but otherwise identical machine depends on the comparison between a large current expense and many future years of reduced repair costs. The optimal time to replace with alternative machinery also depends on the comparison between possible short-term adjustment costs and increased future net revenues. A relatively high discount rate reduces the value of future net revenues and therefore delays the optimal replacement time until repair costs for the current machinery have increased enough to offset this loss of future value. The appropriate discount rate for this analysis is a real before­ tax cost of capital. The rate must be adjusted for inflation because the future prices and costs used in the dynamic programming model are 200 current values that reflect zero price inflation. In order for the discount, rate to be consistent with prices and costs, it also must reflect zero price inflation. The cost of capital is adjusted for inflation by the Consumer Price Index for all items minus shelter (CPI-S) since this index was used to adjust crop prices for inflation. A before-tax cost of capital is appropriate because tax deductions are excluded from this analysis. Use of a before-tax cost of capital therefore provides consistency with before-tax cash flows. A wide range of values for the appropriate cost of capital can be supported. There are three reasons why such a wide range exists. First, an appropriate discount rate is a weighted average of returns to equity capital and interest rates on borrowed capital (Aplin et al., 1977), and the relative weights vary for different farmers. Second, there are a variety of alternative investments that offer different rates of return to equity capital, largely depending on the risk associated with each investment. Third, average rates of return on equity capital and interest rates on borrowed capital have been higher in some periods than in others, so any average cost of capital depends on the historical period selected. Data for the period 1950-1991 are evaluated here, following Barry's (1980) argument that previous data may be biased by major wars and economic depression. Barry (1980) shows for the period 1950-1977 that the return to investments in farmland is similar to the returns on stocks and bonds. For that period, the total rate of return (value return plus production return in nominal values) averaged 10.8% per year for farmland, 11.6% for stocks (the Standard and Poors 500 index), 8.5% for a portfolio of 201 stocks and bonds, and 8.9% for a portfolio of stocks, bonds, and farmland. The average annual rate of inflation, as measured by the CPI- S, was 3.3% and the average rate of return on a risk-free asset (3-month Treasury Bills) was 3.9% during this period. For 1950-1991, the total real rate of return for all farm production assets (Federal Reserve Bank, 1985; NAS, various years), including farmland, averaged 3.45% per year. For 1950-1991, the average interest rate, adjusted for inflation by the CPI-S, was 1.28% for Treasury Bills, 2.93% for Moody's Aaa bonds, and 3.85% for Moody's Baa bonds. The average total return to stocks, adjusted for inflation by the CPI-S was 8.56% from 1950 to 1991. From these data, it appears that the average annual rates of return on most diversified investment portfolios range from about 3% to 6%, depending on risk aversion and the proportion of equity capital invested in agriculture. Interest rates for non-real estate agricultural loans by commercial banks have averaged 1.51% above Aaa bond rates and 0.27% above Baa bond rates for the period 1969-1991 (Federal Reserve Bank, 1986; ERS, various years). The average annual rate for 1977-19911, adjusted for inflation by the CPI-S, is 6.63%. However, the 6.63% average real interest rate is heavily influenced by high real interest rates during the 1980's. The average annual rate for 1969-1991, adjusted for inflation by the CPI-S is 5.06%. Yet, either of these average real interest rates on borrowed capital impliy that farmers with a relatively high debt/asset ratio will have a weighted average cost of 1 This average reflects all Federal Reserve Districts, whereas the 1969-1976 data are for the Minneapolis Federal Reserve District alone. 202 capital in the upper end of the 3-6% range of rates of return for equity capital investments. The replacement analysis is therefore conducted using both a 3% and a 6% discount rate. Additional sensitivity analysis is conducted using a 9% discount rate to reflect the situations of: (1) a risk-taking farmer for which returns to stock market investments are the most appropriate standard for a discount rate; (2) a farmer who borrowed a lot of money in the 1980's when real interest rates ranged from 7-10%; or (3) a highly leveraged farmer who needs high current net revenues to avoid foreclosure. This range of interest rates provides reasonable upper and lower bounds for the effect of the chosen discount rate on the optimal replacement results. Using these three discount rates also facilitates comparison with previous studies, since Smith (1986) used a 6% discount rate and Weersink and Tauber used 3%, 6%, and 9% discount rates for their analyses of optimal machinery selection and replacement. Adjustment of Crop Prices for Technology Improvement The 1955-1990 annual average prices for corn and soybeans exhibit a strong negative time trend that is strongly correlated with a positive time trend for average corn and soybean crop yields in Michigan. The functions for the estimation of the crop yield time trend are presented in Chapter 4. The ordinary least squares estimates presented in Table B.l indicate that the positive time trend for corn and soybean yields is very strong. 203 Table B.l Regression Results for Technology Trend in Crop Yields* Dependent Variable Constant Year R2 ln(Corn Yield) -36.53 (-10.29) 0.0207 (11.50) .796 -24.72 (-6.93) 0.0142 (7.84) .644 ln(Soybean Yield) ____________________________________________________________________ j * T-statistics are in parentheses. | The corn and soybean yield trends presented in Table B.2 were calculated by exponentiating the results of Table B.l and fitting them into the equations: YIELDC = exp{a+b*YEAR}, and YIELDS = exp(c+d*YEAR}. Then the technology adjustment constants (the third and fourth columns of Table B.2) were calculated by dividing the estimated corn and soybean yields for each year by the estimated 1990 corn and soybean yields. Determination of Price State Probabilities Price state probabilities also are based on the historical price data. However, 36 years is a very small data set for determining the probability that one price state will follow another, especially since 2 of the 7 price states occur only twice and 2 other price states occur only 4 times in the 36 years (Table B.3). If the observed Markovian price state probabilities (Table B.4) were used directly, some very likely price transitions would not be considered. For example, the 204 Table B.2 Crop Yield Technology Trends Year Corn Yield 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 52.15 53.24 54.35 55.49 56.65 57.84 59.05 60.28 61.54 62.83 64.15 65.49 66.86 68.26 69.69 71.15 72.63 74.15 75.71 77.29 78.91 80.56 82.24 83.97 85.72 87.52 89.35 91.22 93.13 95.07 97.06 99.09 101.17 103.28 105.45 107.65 Soybean Yield Corn Adj . 20.05 20.33 20.62 20. 92 21.22 21.52 21.83 22.14 22.45 22.78 23.10 23.43 23.76 24.10 24.45 24.80 25.15 25.51 25.87 26.24 26.62 27.00 27.38 27. 77 28.17 28.57 28.98 29.40 29.81 30.24 30.67 31.11 31.55 32.00 32.46 32.93 0.4844 0.4946 0.5049 0.5155 0.5262 0.5373 0.5485 0.5600 0.5717 0.5837 0.5959 0.6083 0.6211 0.6341 0.6473 0.6609 0.6747 0.6888 0.7032 0.7180 0.7330 0.7483 0.7640 0.7800 0.7963 0.8129 0.8300 0.8473 0.8651 0.8832 0.9016 0.9205 0.9398 0.9594 0.9795 1.0000 Soybean Adj . 0.6089 0.6176 0.6264 0.6353 0.6444 0.6536 0.6629 0.6724 0.6820 0.6917 0.7016 0.7116 0.7218 0.7321 0.7425 0.7531 0.7639 0.7748 0.7858 0.7971 0.8084 0.8200 0.8317 0.8436 0.8556 0.8678 0.8802 0.8928 0.9055 0.9185 0.9316 0.9449 0.9584 0.9720 0.9859 1.0000 205 Table B 3 Price State Price State Definitions and Freauencie s Corn Mean Corn Range Soybean Mean 2.18 2.18 2.62 2.62 2.62 3.59 3.59 1.56-2.35 1.56-2.35 2.36-2.78 2.36-2.78 2.36-2.78 2.79-5.21 2.79-5.21 5.63 6.65 5.63 6.65 10.08 6.65 10.08 1 2 3 4 5 6 7 Table B.4 Ob ser vations 5.16-6.05 6.11-7.23 5.16-6.05 6.11-7.23 7.49-12.80 6.11-7.23 7.49-12.80 8 4 4 6 . 2 2 10 Fre­ quency 22.2% 11.1% 11.1% 16.7% 5.6% 5.6% 27 .8% Observed Markovian Price State Probabilities If Previous Price State was: 1 2 3 4 5 6 7 Table B.5 If Previous Price was: 1 2 3 4 5 6 7 Soybean Range Probability of Each Current Price State Is 1 2 3 4 5 6 7 0.75 0.0 0.25 0.0 0.50 0.50 0.0 0.13 0.25 0.0 0.33 0.0 0.0 0.0 0.0 0.25 0.50 0.0 0.0 0.0 0.0 0.13 0.0 0.25 0.67 0.0 0.0 0.0 0.0 0.25 0.0 0.0 0.0 0.0 0.10 0.0 0.0 0.0 0.0 0.50 0.0 0.10 0.0 0.0 0.0 0.0 0.0 0.50 0.80 Assumed Markovian Price State Probabilities. Corresponding to the Historical Mean Prices. Probability of Each Current Price State Is: 1 0.,70 0.,10 0.,22 0.,08 0.,18 0.,15 0.,0 2 3 0.,10 0.,23 0.,18 0.,20 0.,10 0. 0 0,,0 0.,08 0,.22 0,,40 0.,10 0..0 0.,15 0..0 4 0,,12 0,.15 0,.20 0.,40 0,.15 0.,0 0..05 5 6 7 0..0 0,.15 0,.0 0..07 0,.20 0,.15 0,.05 0.,0 0..0 0..0 0..07 0..20 0..15 0..20 0..0 0..15 0..0 0,.08 0..17 0.,25 0..70 206 Table B.6 Assumed Markovian Price State Probabilities. Corresponding to the Historical Median Prices. If Previous Price was: i JL 2 3 4 5 6 7 Probability of Each Current Price State Is: 1 2 3 0.70 0.10 0.20 0.08 0.18 0.15 0.0 0.10 0.25 0.20 0.15 0.10 0.0 0.0 0.10 0.20 0.30 0.15 0.0 0.15 0.0 4 0.10 0.25 0.20 0.35 0.22 0.25 0. 30 5 6 7 0.0 0.10 0.0 0.07 0.10 0.0 0.10 0.0 0.0 0.10 0.10 0. 20 0. 30 0.20 0.0 0.10 0.0 0.10 0.20 0.15 0.40 observed probability of medium corn and medium soybean prices (price state 4) following medium corn and high soybean prices (price state 5) or following high corn and medium soybean prices (price state 6) is zero. Therefore, adjustments were made to the observed probabilities in order to allow for these possibilities. The adjusted probabilities are shown in Tables B.5 and B.6. The adjusted probabilities were tested for consistency with the historical data using Monte-Carlo simulation. The Monte-Carlo simulation made repeated random draws2 from a uniform distribution, determined which price state occurred for each draw using the Markovian price state probability matrices (Tables B.5 and B.6), and finally calculated the frequency that each price state occurred. These frequencies were then compared to the historical frequency of each price state (Table B.3). 2 Five thousand random draws were made with ten different seeds for the random number generator, for a total of 50,000 random draws. 207 Two sets of price state probabilities are used in the stochastic dynamic programming analyses. Most of the stochastic dynamic programming analyses are based on the price probabilites that replicate the historical frequency that each price state occurs (the probabilities in Table B.5 replicate the frequencies presented in Table B.3) in repeated Monte-Carlo simulations. When these frequencies are divided by the number of total observations and multiplied by the mean corn and soybean prices for each price state, the resulting weighted average prices approximately equal the historical mean prices of $2.80 for corn and $7.46 for soybeans. The other set of price state probabilities (Table B.6) reflect an expectation that the combination of high corn and high soybean prices (price state 7) will not occur as frequently in the future as it did in the period 1955-1990. Eight out of the ten historical observations of prices corresponding to price state 7 occurred during the 1970's, a period of dramatic structural change in the world grain markets. In order to evaluate optimal adoption strategies for farmers that do not expect crop prices to frequently return to the levels of the 1970's, the probabilities for price state 7 were greatly reduced in the second set of price state probabilities. The second set of price state probabilities also were adjusted to approximately replicate the historical median prices when weighted average corn and soybean prices were calculated from the price state frequencies of repeated Monte-Carlo simulations. Appendix C MODIFICATIONS OF THE CERES-MAIZE AND SOYGRO MODELS The current versions of the CERES-MAIZE and SOYGRO crop growth simulation models distributed by the IBSNAT project1 do not include any mechanism for showing the effects of surface residues. This Appendix describes modifications made to CERES-MAIZE version 2.IS and SOYGRO version 5.42 in order to include surface residue effects on corn and soybean growth. The source code modifications are listed in Appendix H. Many of the modifications to CERES-MAIZE were developed by Frederic Dadoun of the Dept, of Crop and Soils Science at Michigan State University. Dadoun's modifications, which are acknowleged below, were extended and refined for this analysis. Similar modifications were then made to the SOYGRO model so that it would show the same kinds of surface mulch effects as the modified CERES-MAIZE model. The modifications to the CERES-MAIZE and SOYGRO models start with the addition of a subroutine developed by Dadoun to estimate daily amounts of surface residues and the proportion of soil surface covered with residues. Surface residues decompose throughout the crop season, and provide additional nitrogen to corn after decomposed residues are washed into the soil by rainfall and mineralized. The modifications to the CERES-MAIZE and SOYGRO models also account for the effects of surface mulch on soil evaporation and soil temperature. Surface mulch reduces soil evaporation by insulating the soil surface from solar radiation and reducing air flow over the soil surface. Surface mulch 1 International Benchmark Sites Network for Agrotechnology Transfer, funded by the US Agency for International Development, and implemented by the University of Hawaii and other collaborators. 209 also reduces soil temperature (see the references in Chapter 4) by reflecting more solar radiation than the soil surface and by insulating the soil surface (Van Doren and Allmaras, 1978). Both the CERES-MAIZE and SOYGRO models emphasize water balance dynamics and the effects of soil moisture stresses on plant growth. Both models estimate daily soil moisture contents in each soil layer, daily water uptake by the growing plant, and daily moisture stress factors. Since soil evaporation is one of the principal ways that the soil loses moisture, reduced soil evaporation reduces plant moisture stresses and contributes to increased crop yields in both models. Soil temperature is completely ignored by the SOYGRO model and is considered by the CERES-MAIZE model only for the purpose of regulating soil nitrogen dynamics (Jones and Kiniry, 1986; Godwin and Jones, 1991). Yet the CERES-MAIZE model does estimate daily temperatures in each soil layer, so the soil temperature effects on corn growth described in Chapter 4 were considered simply by adding other mechanisms for soil temperature effects to the model. For the SOYGRO model, both a subroutine for calculating daily soil temperature and mechanisms for soil temperature effects on soybean growth had to be added. Three important mechanisms for soil temperature effects on corn and soybean growth were added to the CERES-MAIZE and SOYGRO models. First, the rate of phenological development before emergence and during juvenile, or vegetative growth stages was changed from being a function of air temperature to being a function of both air and soil temperature. Second, photosynthate production during the same growth stages was made a function of soil temperature. In CERES-MAIZE, this is accomplished by 210 making the rate of leaf appearance be a function of soil temperature, and each leaf adds to the amount of intercepted solar radiation and photosynthate production. In SOYGRO, a temperature stress factor that reduces the rate of photosynthesis is changed from being a function of air temperature to being a function of soil temperature during these early growth stages. Third, a soil temperature stress factor was added to root growth in both models, following the root growth model of Jones et al. (1991). Effects of no-till systems on soil physical characteristics, such as increased soil bulk density, increased soil acidity, and changes in the distribution of organic matter (Blevins et al., 1983; Blevins et al., 1985) were not incorporated in the CERES-MAIZE and SOYGRO models. Such effects have been documented in the agronomy literature, but they often require several years to be detectable and have not been as consistent as soil temperature and soil evaporation effects. Also, the effects of these changes in soil physical characteristics on plant growth generally have not been separated from soil temperature effects on plant growth. Since suitable data were not available to calibrate the effects of soil physical characteristics on corn and soybean growth in no-till production, any change in soil parameters for the no-till system would have been very arbitrary. Therefore, possible changes in soil bulk density, soil acidity, and the distribution of soil organic matter associated with no-till systems were ignored. 211 Specific Modifications to CERES-MAIZE Basic Structure of CERES-MAIZE version 2.IS The FORTRAN code for CERES-MAIZE 2.IS consists of a main program, "MAIN.FOR", and 68 subroutines. Although the number of subroutines is large, they fall into 7 functional groups. These groups and specific subroutines that were modified, are listed in Table C.l Table C.l Subroutine Groups in CERES-MAIZE Subroutine Group Modified Subroutines Within each Group 1. Initialization IPNIT (initializes nitrogen parameters) 2. Water Balance POTEV (estimates potential evaporation) 3. Nitrogen Balance NTRANS (tracks soil nitrogen dynamics) SOLT (estimates soil temperatures) 4. Phenology PHENOL (determines growth stages) 5. Growth GROSUB (estimates photosynthate production and leaf emergence) ROOTGR (estimates root growth in mass and distribution in the soil) 6. Output 7. Utilities The initialization subroutines read input files and set initial parameters. The water balance subroutines estimate soil moisture dynamics. The nitrogen balance subroutines estimate soil nitrogen dynamics. The phenology subroutines determine when the plant progresses from one growth stage to the next and reset parameters for different growth stages as needed. The growth subroutines determine the amount of 212 photosynthate (biomass) produced, its partitioning among leaves, stem, roots, and reproductive organs, and the growth in size, mass, and number of those plant parts. Output and utility subroutines write output files and perform various repetitive tasks. Dadoun's Modifications The subroutine IPNIT reads an input file containing levels and depths of incorporation of crop residue, which the nitrogen balance subroutines use to estimate the contribution of crop residues to the soil nitrogen pool through mineralization (Godwin and Jones, 1991). This input file is read as "FILE4" by CERES-MAIZE, and must have the filename extension, ".MZ4". Dadoun made IPNIT partition these crop residues between surface residues and incorporated residues depending on the depth of incorporation (variable SDEP). He assumed that if the depth of incorporation is no greater than 1 cm., all crop residues should be treated as surface mulch. is used. This implies that a no-till system An incorporation depth of 1-10 cm. would leave 70% of crop residues on the surface and an incorporation depth of 10-20 cm. would leave 30% of crop residues on the surface. An incorporation depth of 20 cm. or more corresponds to moldboard plowing in which all crop residues are assumed to be incorporated. Dadoun then added a subroutine, MULCHE, to calculate decomposition of surface mulch over time and its contribution of organic matter for nitrogen mineralization. He assumed that surface mulch decomposes by exp(-.0075) per day, subject to the influence of air temperature and soil moisture. A few lines added to the NTRANS subroutine (lines 176- 213 182) cause water infiltration to bring this organic matter from the surface into the soil. Dadoun also added mulch effects to reduce soil evaporation and increase albedo (reflectance of solar radiation) in subroutine POTEV. He also added a mulch cover effect to the calculation of soil temperature in subroutine SOLT. Finally, Dadoun had the PHENOL subroutine use soil thermal time in place of the daily thermal time based on air temperature (DTT) to calculate plant development until the appearance of the 9th leaf in the third growth stage. Soil thermal time was defined as the accumulation of temperature in the top soil layer minus the same base temperature as CERES-MAIZE uses for the DTT based on air temperature. A common block, "RESI", was added to pass values of mulch variables between these subroutines. Additional Major Changes Made to CERES-MAIZE Three substantial changes and additions were made to Dadoun's modifications of CERES-MAIZE for surface mulch effects. First, the accumulation of thermal time to regulate phenological stages was made a weighted average of soil and air temperature, rather than soil temperature alone, and the period of soil temperature influence was restricted to growth stages 9, 1, and 2 that end with tassel initiation. This weighted average of soil and air temperature also was used to regulate the rate of leaf appearance during growth stage 2. Second, portions of surface mulch were incorporated in the soil during planting and anhydrous ammonia application. factor was added to the Third, a soil temperature stress estimation of root density in each soil layer (by changing the calculation of variable RLDF in subroutine ROOTGR). 214 A weighted average of soil and air temperature was used to calculate thermal time because it was observed that basing thermal time on soil temperature alone greatly altered phenological development for corn grown with conventional tillage. Since phenological development in CERES-MAIZE has passed many validation tests based on empirical data (Kiniry, 1991), phenological development for the standard and modified models must be consistent for conventional tillage. Weighted averages of soil and air temperature kept errors between estimated growth stage dates and observed growth stage dates at nearly the same level as exhibited by CERES-MAIZE 2.IS. During growth stage 9 (germination to seedling emergence), soil temperature in the top layer is given a 50% weight and air temperature is given a 50% weight. During growth stages 1 and 2, the respective weights are 30% and 70%, respectively. The partial incorporation of surface mulch into the soil during planting and anhydrous ammonia application is well documented in the agronomy literature (Griffith et al., 1986). Approximately 10% of surface residue is incorporated during planting (Dickey et al., undated). It was assumed that the same amount would be incorporated when anhydrous ammonia is knifed into a no-till field because a similar coulter would be used. Incorporating these portions of the surface residue also provided much closer agreement between the values reported for mulch cover at planting time (Griffith et al., 1986) and later in the season (Parker, 1962) and the values estimated by the modified CERES-MAIZE model. The soil temperature stress factor, RTLTF, was added to the estimation of corn root growth because effects of soil temperature on 215 root growth are well documented (see Chapter 4) and because a formula to calculate this effect had already been proposed by Jones et al. (1991). The formula proposed by Jones et al. (1991) is: RTLTF = sin [1.57 where ST(L) is the soil * (ST(L) - TBASE) / (TOP -TBASE)], temperature in a specified layer, lowest temperature at which growth occurs, and TOP temperature for growth. is the This formula also is used in the TBASE isthe optimal EPIC model (Williams, Jones, and Dyke, 1990, p. 57). Parameter Changes Made in CERES-MAIZE Additional changes were made to parameters in Dadoun's version of CERES-MAIZE in order to get results from the model to closely approximate results reported in the agronomic literature. These changes were in the calculation of surface mulch (variable MULCH, measured in tons per ha.) in Dadoun's subroutine, MULCHE, the calculation of mulch cover (variable MULCHCOV, measured in percent) in subroutine SOLT, and the calculation of the current day's input into a 5-day moving average temperature in the top soil layer (variable TMA(l)) in subroutine SOLT. One additional change was made to the radiation use efficiency coefficient in CERES-MAIZE 2.IS, based on results reported by Kiniry et al. (1989). This coefficient, used in the calculation of the variable PCARB in subroutine GROSUB, was changed from 5.0 to 3.9. The change in the radiation use efficiency coefficient has the effect of reducing estimated corn yields for ideal growing conditions to realistic levels. Dadoun calculated the daily value of the variable, MULCH, as: MULCH=MULCH*exp(-.0075*aminl(TEDECF,WADECF). 216 The MULCH value on the right-hand side of the equation is the previous day's MULCH value. Based on results reported by Parker (1962), this calculation was changed to: MULCH=MULCH*exp(-.009*aminl(TEDECF,WADECF). Based on research by Gregory, (1982) Dadoun calculated the daily value of the variable, MULCHCOV, as: MULCHC0V=1.0- exp(-.4*MULCH/1000). However, in order to get better agreement with CERES-MAIZE mulch cover estimates and estimates reported by Griffith et al. (1986) and Sloneker and Moldenhauer (1977), this calculation was changed2 to: MULCHCOV=1.0-exp(-.35*MULCH/1000). Finally, CERES-MAIZE uses a 5-day moving average soil surface temperature, variable TMA(l), in its calculation of temperatures for each soil layer. Dadoun calculated the current day's input into this 5- day moving average as: TMA(1) = (1.0-ALBEDO-0.2 27*MULCHC0V)*(TEMPM+(TEMPMX-TEMPM)* SQRT(SOLRAD*0.005)) + (ALBEDO+O.227+MULCHCOV)*TMA(1). Again, the value of TMA(l) on the right-hand side of the equation is the previous day's value. Based on the soil temperature results reported by Bronson (1989), this calculation was changed to: TMA(1)=(1.0-ALBEDO-0.42*MULCHC0V)*(TEMPM+(TEMPMX-TEMPM)* SQRT(SOLRAD*0.02)) + (ALBEDO+O.38*MULCHC0V)*TMA(1). 2 Dadoun's model used a slightly different formula in the subroutine P0TEV, which was not found in time to be corrected. In subroutine POTEV, the coefficient for the negative exponential function is 0.32 rather than 0.35. This error results in a slightly lower value of surface mulch cover being used for the calculation of soil evaporation than for the calculation of soil temperature. However, Gregory's (1982) results ranged from a coefficient of 0.32 to 0.40, so any of these estimates can be defended. 217 Model Validation Suitable data for the validation of the model for both tillage systems have not yet been found, so the modified CERES-MAIZE model must be viewed as preliminary. However, the modified CERES-MAIZE model produced results that very closely agreed with results for an irrigated trial using conventional tillage near Mendon, in St. Joseph County, Michigan (Table C.2). Table C.2 Validation Results for 1988 at Mendon. Michigan SILKING DATE GRAIN YIELD (KG/HA) KERNEL WEIGHT (G) GRAINS PER SQ METRE GRAINS PER EAR MAX. LAI BIOMASS (KG/HA) STRAW (KG/HA) GRAIN N% TOT N UPTAKE (KG N/HA) STRAW N UPTAKE GRAIN N UPTAKE PREDICTED 200.0 10428.0 0.30 2919.0 430.6 4.2 18524.0 9712.0 1.6 183.5 46.4 137.0 OBSERVED 200.0 10848.0 0.29 3279.0 484.0 5.1 18762,0 9370.0 1.4 208.7 78.2 130.5 Results at the Cupp-Farm, Mendon Michigan on an Oshtemo sandy loam soil. Hybrid Pioneer 3475 was planted on May 5 with 10 kg N/ha as diammonium phosphate, after 200 kg N/ha was applied as anhydrous ammonia on April 20. The field received a total of 347 mm. of irrigation and 155 mm. of rainfall from March 15 until September 15. 218 Specific Modifications to SOYGRO Basic Structure of SOYGRO version 5.42 The FORTRAN code for SOYGRO 5.42 consists of a main program, "GRO.FOR", and 35 subroutines. The SOYGRO subroutines can be divided into 6 functional groups. These groups and specific subroutines that were modified, are listed in Table C.3 Table C.3 Subroutine Groups in SOYGRO Subroutine Group Modified Subroutines Within each Group 1. Initialization IPCROP (reads a crop parameters file) IPSOIL (initializes soil parameters) 2. Water Balance WATBAL (calculates daily water balance) 3. Phenology GPHEN (determines growth stages) 4. Growth CROP (calls growth subroutines) PHOTO (estimates photosynthate production) VEGGR (partitions photosynthate among plant organs) 5. Output 6. Utilities Modifications Made to SOYGRO Source Code SOYGRO was modified to exhibit similar surface mulch effects on plant growth as the modified version of CERES-MAIZE. As much as possible, the same source code was used in both models. However, SOYGRO was developed independently of CERES-MAIZE and emphasizes different aspects of plant growth (Wilkerson, 1983; Jones et al., 1991). Therefore, different mechanisms sometimes had to be used for surface 219 mulch effects in SOYGRO than were used for CERES-MAIZE. Modifications to the SOYGRO source code included introducing soil temperature calculations, adding a mulch subroutine (MULCHS), introducing surface mulch effects on soil evaporation and soil temperature, making early phenological development and photosynthesis rates partly dependent on soil temperature, and adding a soil temperature stress factor to the estimation of root growth. Additions to three subroutines were made in order to introduce soil temperature estimates. Source code for soil temperature initialization was taken from the CERES-MAIZE subroutine, SOILNI, and divided between SOYGRO subroutines, IPSOIL and CROP. The daily soil temperature calculations from the CERES-MAIZE subroutine, SOLT, were placed in the new SOYGRO subroutine, MULCHS. Subroutine MULCHS was called within SOYGRO subroutine WATBAL. In addition, to calculating daily temperatures for each soil layer, subroutine MULCHS estimated daily surface residue decomposition and percent coverage of the soil surface with crop residue (variable MULCHCOV). These estimates were made with the same formulas and parameters used in the CERES-MAIZE subroutine, MULCHE. Initial surface residue weights were added to SOYGRO's input file of crop parameters, "CROPPARM.SBO", which is read by subroutine IPCROP. As in CERES-MAIZE, a common block of variables named "RESI.BLK" was defined in order to pass crop residue variables between subroutines. Additions were made to the WATBAL subroutine, so that after it calls subroutine MULCHS, it uses the mulch cover estimates to adjust soil evaporation. This adjustment was made using the same formulas and 220 parameters used in the CERES-MAIZE subroutine, POTEV. Since the WATBAL subroutine also calculates a root length density factor (RLDF) when estimating root mass and distribution, the same soil temperature stress factor used in the calculation of RLDF in CERES-MAIZE was introduced to the calculation of RLDF in SOYGRO's WATBAL subroutine. The VEGGR subroutine in SOYGRO that partitions photosynthate (biomass) among various plant parts according to the current growth stage also calculates a root length density factor (RLDF). Therefore, the soil temperature stress calculation was also added to the VEGGR subroutine. A soil temperature effect was added to soybean phenological development during growth stages VO and VI (variables NVEGO and NVEG1 in SOYGRO). As with CERES-MAIZE, it was observed that phenological development under conventional tilage was distorted when based entirely on soil temperature during these stages, so a weighted average of soil and air temperatures was used. For both of these stages, the accumulation of thermal time was based 30% on the temperature of the top soil layer and 70% on air temperature. These weights were chosen because they caused minimal distortion of phenological development under conventional tillage, while still allowing for a soil temperature effect under no-till. The change in the calculation of thermal time accumulation for growth stages VO and VI was made in SOYGRO subroutine, GPHEN. The SOYGRO subroutine, PHOTO, regulates photosynthesis rates with both a moisture stress factor and a temperature stress factor. The temperature stress factor (variable TPHFAC) for growth stages VO and VI 221 was calculated using a weighted average of the temperature in the top soil layer (30%) and air temperature (70%). Calculation of TPHFAC was also changed from a very crude interpolation procedure using the TABEX subroutine to direct estimation using a cubic function. Parameters for the cubic function are based on data presented by Hofstra and Hesketh (1975). Wilkerson et al. (1983) chose a logistic function to represent the Hofstra and Hesketh (1975) results in SOYGRO, but a cubic function provides a much better fit. Parameters for the cubic function were added to the "CROPPARM.SBO" file and read by subroutine IPCROP. The formula used to calculate TPHFAC is: TPHFAC = (0.54*TDAY + 0.66*TDAY2 - 0.123*TDAY3) / 160, where TDAY is a daily thermal time increment analogous to a growing degree day. During growth stages VO and VI, TDAY is calculated as the weighted average of temperature in the top soil layer and air temperature. One additional parameter change was made to the estimation of photosynthesis rates in order to raise the highest estimates of soybean yields to levels observed in Michigan soybean variety trials (Vitosh et al. 1991). SOYGRO was calibrated in Florida, where soybean varieties are adapted to abundant solar radiation. The functional relationship between photosynthesis rates and solar radiation levels not only varies greatly within species, but also is quadratic rather than linear in form, with a much higher response at low solar radiation levels than at high levels (Zelitch, 1971). SOYGRO includes a parameter (PHAC3) in the soil data file input file (read as FILE2) for making a linear adjustment to the response of photosynthesis to solar radiation levels for a particular location. Due to its greater latitude, Michigan receives much less solar radiation than Florida. Therefore, the PHFAC parameter was set at 1.10 for this analysis, which had the effect of increasing photosynthesis rates by 10% when not constrained by moisture or temperature stresses. Appendix D TRACTOR REMAINING VALUE CALCULATIONS Remaining values, also called salvage or trade-in values, of farm machinery are critical parameters in an optimal replacement analysis, but they are difficult to estimate. Remaining values have been shown to be affected by age, usage, condition, size, and manufacturer (Perry et al., 1990). Even after all of these factors have been considered, remaining values are still highly variable, due to such factors as location and asymmetric information between the buyer and seller regarding the true condition of the machinery (Akerloff, 1970). Remaining values also are sensitive to macroeconomic variables such as interest rates and aggregate farm income (Perry et al., 1990). Perry et al. (1990) performed a great service by analyzing a large data set of auction prices for tractors and quantifying the effects of most of these variables on tractor remaining values. By using the Box- Cox flexible functional form for their estimation, Perry et al. also did not impose a functional form on the depreciation patterns for tractors. However, the Perry et al. estimates for tractor remaining values sometimes are not suitable for farm-level analyses. Although Perry et al. were able to detect separate, statistically significant effects for age and usage per year in a heterogeneous sample, accumulated usage is the dominant concern for an individual farmer. Very little in a tractor physically deteriorates with time if the tractor is not used. After accumulated usage is considered, any separate effect of age on remaining value usually reflects a belief that the newer tractor is technologically superior. Indeed, Perry et al. 224 (1990) admit in a footnote that their age variable captures some of the effect of usage on remaining values. Thus, their estimate of the effect of usage on remaining value is biased if age is not varied. This bias becomes important when the choice of tillage technology implies two different levels of tractor usage per year. A second difficulty in applying Perry et al.'s estimates to a farm-level replacement problem is that the Box-Cox estimates are for nonlinear transformations of the original variables. A little can produce a dollar estimate of remaining value for specified each variable, but a computer is needed to do it quickly. An exponential function algebra levelsof of accumulated usage and the square of accumulated usage was found which closely approximates Perry et al.'s results for tractor remaining values and avoids the two problems discussed above. First, Perry et al.'s estimates for remaining value were calculated for the cases of a 140 HP tractor used 800 hours per year, a 140 HP tractor used 400 hours per year, and an 80 HP tractor used 400 hours per year. assumed. Also, a 4% after-tax real interest rate was Parameters for manufacturer, real net farm income, location, and auction type were kept the same as in Perry et al.'s examples (see Perry et al's footnote 10). The remaining value estimates were extended for 30 years at these rates of annual usage, and transformed to dollar values. Third, the natural logarithms of these estimates were regressed on the natural logarithms of the usage variables. The usage variables 225 are accumulated hours of use, divided by 10003 (AHRS), and the same measure squared (AHRS2). The equation estimated for each case was: In RV = In S0 + AHRS * In + AHRS2 * In fi2 + e . Results for these estimates are shown in Table D.l. Table D.l Results for the RV Regression on Total Usaee Variables Case So Si obs S2 R2 140 HP tractor, 800 hrs/yr . -.5573 -.0751 - .0036 20 .9997 140 HP tractor, 400 hrs/yr . -.4519 -.1484 -.0126 20 .9998 80 HP tractor, 400 hrs/yr. -.4849 -.1194 -.0080 25 .9998 After exponentiating, the equations for estimating RV as a function of accumulated usage are: Case Estimating Equation 140 HP tractor, 800 hrs/yr . RV = .5727 * 140 HP tractor, 400 hrs/yr . RV = .6364 80 HP tractor, 400 hrs/yr. 9277AH R S * _9954AH R S2 * 8621ahrs * .9874AHRS2 RV = .6158 * 8875AH R S * 992] _ahrs2 Analysis of the residuals (Table D.2) indicated that these estimates are very close to Perry et al.'s estimates after the first year and continuing until after about 20 or 25 years. For very old tractors these estimates tend to be increasingly higher than Perry et al.'s estimates. Since tractors are rarely kept longer than 20 or 25 years at these rates of annual usage, the numbers of observations were imited to those indicated in order to get a closer approximation. 3 This measure is used by the American Society of Agricultural Engineers (1987) to estimate accumulated repair costs. 226 Table D.2 Residuals from the Approximation of RV Estimates based on Age and Hours per Year using a Function of Cumulative Hours*. 140 HP, John Deere tractor (800 HRS/YR) Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 •ft Estimate from age and hrs. 0.5482 0.5070 0.4681 0.4313 0.3964 0.3633 0.3321 0.3025 0.2747 0.2484 0.2238 0.2007 0.1791 0.1590 0.1403 0.1230 0.1070 0.0923 0.0790 0.0668 0.0558 0.0460 0.0373 0.0297 0.0230 0.0174 0.0126 0.0088 0.0057 0.0034 Estimate from only cum. hrs. 0.5381 0.5032 0.4685 0.4341 0.4004 0.3676 0.3360 0.3056 0.2767 0.2494 0.2238 0.1998 0.1776 0.1572 0.1384 0.1214 0.1059 0.0920 0.0796 0.0685 0.0587 0.0500 0.0425 0.0359 0.0302 0.0253 0.0210 0.0175 0.0144 0.0118 Residual 0.0101 0.0038 -0.0003 -0.0028 -0.0040 -0.0043 -0.0039 -0.0031 -0.0021 -0.0010 0.0000 0.0009 0.0015 0.0018 0.0018 0.0016 0.0011 0.0003 -0.0006 -0.0017 -0.0028 -0.0040 -0.0051 -0.0062 -0.0071 -0.0079 -0.0084 -0.0087 -0.0087 -0.0085 80 HP, John Deere tractor (400 HRS/YR) Estimate from age and hrs. 0.5960 0.5616 0.5288 0.4973 0.4671 0.4381 0.4103 0.3836 0.3581 0.3336 0.3102 0.2879 0.2665 0.2462 0.2268 0.2084 0.1909 0.1743 0.1587 0.1439 0.1299 0.1168 0.1046 0.0931 0.0824 0.0725 0.0633 0.0549 0.0472 0.0401 Estimate from only cum. hrs. 0.5863 0.5568 0.5275 0.4984 0.4698 0.4417 0.4141 0.3874 0.3614 0.3363 0.3121 0.2890 0.2669 0.2458 0.2259 0.2070 0.1892 0.1725 0.1569 0.1423 0.1288 0.1162 0.1046 0.0940 0.0842 0.0752 0.0670 0.0596 0.0528 0.0467 Residual 0.0097 0.0048 0.0013 -0.0012 -0.0027 -0.0036 -0.0038 -0.0037 -0.0033 -0.0026 -0.0019 -0.0011 -0.0003 0.0004 0.0009 0.0014 0.0017 0.0018 0.0017 0.0015 0.0011 0.0006 -0.0001 -0.0009 -0.0017 -0.0027 -0.0037 -0.0047 -0.0056 -0.0066 The remaining value (RV) estimates based on age and hours are based on Perry et al. (1990). The RV estimates based on cumulative hours alone are based on the results of Table D.l. Appendix E MACHINERY COST ESTIMATES This appendix explains how machinery cost parameters were determined. Machinery prices, fuel consumption, repair costs, and operating rates, all vary considerably, so a range of values is plausible for each variable. Therefore, it is important to identify the source of each machinery value used in the analysis. All repair cost estimates are based on machinery list prices (Table E.l). Prices for the 140 HP tractor and 85 HP tractor were taken from suggested retail prices listed for John Deere 4455 and 2955 tractors (NAEDA, 1992). Prices for these specific models were chosen because they are comparably equipped with a cab and air conditioning. Many machinery price guides, such as Snyder (1991) and Fuller et al. (1992) quote prices for tractors with less than 100 HP that are not equipped with cabs. However, a comparison of similarly equipped tractors is needed to avoid biasing the analysis of adoption strategies. Average 1991 list prices for the moldboard plow, disc harrow, row cultivator and sprayer were taken from Snyder (1991). Price estimates for the planters, field cultivator, stalk shredder and NH3 applicator in were taken from Fuller et al. (1992). Fuller et al. reported purchase prices, so these were divided by 0.9 to estimate list prices. The price of the NH3 applicator also was multiplied by 0.8 because the only price listed by Fuller et al. was for a size that appears to be 25% larger than the size assumed for this analysis'*. ** Fuller and McGuire do not report a size for their anhydrous ammonia applicator. However, the operating rate of 12.73 acres per hour that they report corresponds to approximately 25 feet of width with standard assumptions used for speed and field efficiency. Fuller and 228 Machinery sizes and operating speeds were checked for compatibility with 140 HP and 85 HP tractors using draft power estimates by White (1977), Hunt (1983), and Bowers (1987). Power requirements are limiting or nearly limiting for the moldboard plow, disc harrow, and NH3 applicator. Table E.l Machinery List Prices Machinery Item 140 HP tractor 85 HP tractor Moldboard Plow Disc Harrow Field Cultivator Conv. Planter No-till Planter Row Cultivator NH3 Applicator Stalk Shredder Sprayer size 5 18-inch bottoms 20 feet 20 feet 8 30-inch rows 8 30-inch rows 8 30-inch rows 20 feet, 8 knives 12 feet 30 feet List Price $60,875 $41,513 $10,064 $12,968 $6,412 $17,753 $21,365 $5,040 $13,401 $7,599 $3,917 Calculation of per acre cost estimates for machinery repairs and labor requires that machinery operating rates in acres per hour be determined. The operating rates reported in Table 4.7 are determined by multiplying the machinery width (in feet) by the operating speed (in mph) and field efficiency, then dividing by the constant, 8.25 (Bowers, 1987). The operating speeds are based on Hunt (1983), ASAE Standards McGuire also report that their anhydrous ammonia applicator requires a tractor of 160 HP, 20 more HP than is assumed to be available in this analysis. 229 (1987), and Richey (1982)5. Some operating speeds were lowered slightly from values suggested by these references in order to keep the draft requirements within the range that a 140 HP tractor can handle. Field efficiencies are based on Bowers (1987), ASAE Standards (ASAE, 1987) , and Richey (1982). Average machinery repair costs per acre (Tables E.2 and E.3)) for all machinery except the tractors and planters were calculated from list prices, repair cost factors proposed by Rotz and Bowers (1991), and the operating rates reported in Table 4.7. These estimates are based on average repairs over the entire working life of the machinery, as also defined by Rotz and Bowers (1991) . Annual repair costs for tractors and planters (Tables 4.8 and 4.9) are based directly on the formulas proposed by Rotz and Bowers (1991) and the annual usage of each machine. The annual usage for the conventional planter is 80 hours and the annual usage for the no-till planter is 82 hours. The annual usage for the 140 HP tractor is 693 hours if the conventional tillage system is used and only the direct fieldwork listed in Table A43.2 is considered. The annual usage for either the 140 HP tractor or the 85 HP tractor is 336 hours if the no­ till system is used and only the direct fieldwork listed in Table A43.3 is considered. However, it is customary to add roughly another 10% for trips between the farmstead and the fields. Also, tractors are normally used during harvest operations to haul grain wagons. When the direct 5 Clarence B. Richey reviewed and adjusted machinery cost coefficients for an M.S. thesis by Krause (1983) in October 1982. Richey, formerly in the Dept, of Agricultural Engineering at Purdue University, is one of the most respected authorities on questions concerning machinery costs. 230 tractor usage for each of the alternative tillage systems was multiplied by 1.18, the resulting usage was approximately 800 hours for the conventional tillage system and 400 hours for the no-till system. Therefore, the values of 800 hours and 400 hours were used to calculate annual tractor repair costs and trade-in values. Fuel requirements are based on estimates for a moderate soil draft rating by Siemens et al. (1985). Diesel fuel requirements, in gallons per acre are multiplied by $0.84 per gallon, the average price reported for the North Central region in April 1990 (Agricultural Statistics Board, 1991). Fuel and oil costs then are calculated by multiplying fuel cost per acre by 1.15 (Bowers, 1987). Because harvest operations play no role in this analysis, harvesting costs were not estimated, but simply taken from enterprise budgets prepared by Snyder (1990). Equal harvesting costs are assumed for the alternative tillage systems. Since corn drying costs do vary with grain yields, drying costs were estimated by multiplying per acre corn yields by $0.17 per bushel. This value was (1992), an extension associate at Michigan State suggested by Ed Martin University, for the preparation of budgets for irrigation investments. 231 Table E.2 Machinery Operations Performed. Conventional Tillage Fuel&Oil $/acre Repairs $/acre Labor hrs. per acre Corn Chop stalks (after corn) Moldboard plow Disc Spray herbicide Field cultivate Plant Apply NH3 Row cultivate 0.72/2 1.79 0.63 0.19 0.58 0.53 0.68 0.48 0.81/2 1.36 0.43 0.13 0.21 var. 0.69 0.26 0.150/2 0.276 0.113 0.088 0.092 0.154 0.139 0.134 All operations 5.24 3.91 1.071 Soybeans Chop stalks Moldboard plow Disc Spray herbicide Field cultivate Plant Row cultivate Row cultivate 0.72 1.79 0.63 0.19 0.58 0.53 0.48 0.48 0.81 1.36 0.43 0.13 0.21 var. 0.26 0.26 0.150 0.276 0.113 0.088 0.092 0.154 0.134 0.134 All operations 5.41 3.89 1.141 Crop and Operation 232 Table E.3 Machinery Operations Performed. No-Till Technology Crop and Operation Fuel&Oil $/acre Repairs $/acre Labor hrs. per acre Corn Spray herbicide Chop stalks (after corn) Plant Spray herbicide Apply NH3 0.19 0.72/2 0.48 0.19 0.68 0.13 0.81/2 var. 0.13 0.69 0.088 0.150/2 0.159 0.088 0.139 All operations 1.91 1.35 0.569 Soybeans Spray herbicide Chop stalks Plant Spray herbicide 0.19 0.72 0.48 0.19 All operations 1.59 0.13 0.81 var. 0.13 1.07 0.088 0.150 0.159 0.088 0.505 Appendix F DETAILED OPERATION DATE AND CROP YIELD RESULTS This Appendix presents more detailed results than are presented in Chapter 5 for operation dates and crop yields. The purpose is to provide a complete picture of the variation in these results to those who want to see more than a summary. The operation dates also are provided in order that anyone wishing to duplicate the average yield results can do so. Operation Dates Operation dates are presented as Julian dates for corn planting, soybean planting, and NH3 application in Tables F.1-F.12. The relative dates for corn planting and NH3 application correspond to each other, so the first NH3 application date was for corn planted on the first planting date. In Tables F.l, F.4, and F.5 the first 3 corn planting dates are for corn following soybeans, the last three planting dates are for corn following corn, and the middle planting date is split equally between the two corn sequences. For the no-till system, corn planting dates were allocated between corn following corn and corn following soybeans according to soil temperature and moisture conditions. For the first two planting dates, if the temperature in the first soil layer was less than 14° C., corn after soybeans was planted. Soybean residue covered the soil much less than corn residue, so this practice allows the soil to warm up more quickly after planting and speed emergence. Other corn planting days were allocated to corn after soybeans (up to 3.5 days 234 total) if the soil under soybean residue was warm enough and dry enough for planting but the soil under corn residue did not satisfy these criteria. Any remaining corn after soybean acreage was planted after the planting of corn after corn was complete. In Table 5.10, dates of planting corn after soybeans are underlined and the corn planting date split between the two corn sequences is indicated by bold print. Crop Yields Corn yields by corn sequence for various planting dates are presented in Tables F.13, F.15, F.17, and F.19. Soybean yields by planting date are presented in Tables F.14, F.16, F.18, and F.20. presented for eight planting dates. Corn yields are The average of the two yields marked "SPLIT" was included with corn yields for the other six dates to calculate annual corn yield means. The variation in yields by planting date is particularly noticeable for corn and is a powerful demonstration of the benefits obtained from comparing alternative technologies using multiple planting dates rather than only one planting date. 235 Table F.l Corn Planting Dates. MB Plow. 100% Fall Plowed Year C/S* C/S C/S SPLIT* C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 125 118 118 121 119 121 121 118 121 115 118 115 120 115 120 116 116 115 115 119 115 115 120 122 120 118 121 115 117 115 120 116 115 126 119 119 134 120 122 122 119 124 116 121 116 121 116 121 121 117 116 124 122 116 116 122 124 121 119 122 116 119 116 121 117 116 129 120 120 138 121 123 123 123 125 117 122 122 122 122 123 122 120 117 125 123 117 117 123 125 122 120 123 117 121 117 122 118 117 130 121 121 139 122 124 124 124 127 118 123 123 123 123 125 123 121 118 127 124 118 118 125 129 123 121 124 118 122 118 123 119 118 131 123 123 140 123 125 125 125 128 120 124 124 124 124 126 125 122 119 128 125 123 120 126 130 126 122 126 119 123 119 124 120 119 Mean Std. dev. C/C 134 124 124 141 124 126 126 134 130 125 126 125 126 125 130 126 123 121 129 129 125 121 127 132 127 123 127 120 124 120 125 121 120 C/C Mean 135 125 125 143 125 127 127 135 131 127 127 126 127 126 132 127 124 122 130 130 126 122 128 133 128 124 128 121 125 121 126 123 121 130.0 121.4 121.4 136.6 122.0 124.0 124.0 125.4 126.6 119.7 123.0 121.6 123.3 121.6 125.3 122.9 120.4 118.3 125.4 124.6 120.0 118.4 124.4 127.9 123.9 121.0 124.4 118.0 121.6 118.0 123.0 119.1 118.0 122.88 5.03 C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 236 Table F.2 Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 Soybean PlantinE Dates. MB Plow. 100% Fall Plowed PI* 138 134 127 147 127 129 129 154 133 129 132 130 129 140 135 131 126 124 133 132 131 124 133 135 130 131 130 123 127 124 128 125 123 Mean Std. dev. P2 P3 P4 139 135 128 148 128 130 130 155 134 130 133 131 130 141 136 132 132 125 134 133 132 134 134 139 131 137 136 124 128 125 129 131 126 140 136 132 149 136 131 132 157 135 131 134 138 131 142 137 133 135 126 135 136 133 145 135 140 132 139 137 127 129 126 132 136 127 143 137 133 150 137 132 133 158 136 133 135 140 132 143 138 135 148 127 136 137 134 146 136 141 133 140 138 128 130 127 134 137 128 Mean 140.0 135.5 130.0 148.5 132.0 130.5 131.0 156.0 134. 5 130.8 133.5 134.8 130.5 141.5 136.5 132.8 135.3 125.5 134.5 134.5 132.5 137.3 134.5 138.8 131.5 136.8 135.3 125.5 128.5 125.5 130.8 132.3 126.0 134.03 6.81 PI through P4 are the first through fourth days of soybean planting. 237 Table F.3 NH3 Application Dates. MB Plow. 100% Fall Plowed Year C/S* C/S C/S SPLIT* C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 144 142 134 145 142 139 135 144 139 134 136 135 134 145 147 137 136 128 138 138 135 130 137 142 136 142 142 130 131 134 135 142 131 145 143 135 151 144 140 136 145 140 135 139 137 137 146 148 138 140 129 140 139 136 139 138 143 137 143 152 131 134 135 136 143 141 147 144 136 152 146 141 137 146 141 136 140 141 138 147 149 140 141 130 141 140 137 140 139 144 139 144 153 132 142 136 138 144 142 148 145 137 153 147 143 138 147 142 137 141 142 140 148 150 141 143 131 142 141 138 141 140 145 140 145 154 133 143 137 139 146 143 149 146 138 155 148 144 140 149 143 138 142 143 141 149 151 142 144 137 143 142 139 142 143 146 141 146 155 134 144 140 140 147 146 Mean Std. dev. C/C 151 148 140 156 149 145 142 151 144 139 143 144 142 150 152 143 146 138 147 143 140 143 144 147 142 147 156 136 145 141 141 148 147 C/C 152 150 141 157 150 146 144 152 145 140 144 145 143 151 153 144 147 139 148 144 141 144 145 148 143 148 157 137 146 142 142 149 148 Mean 148.0 145.4 137.3 152.7 146.6 142.6 138.9 147.7 142.0 137.0 140.7 141.0 139.3 148.0 150.0 140.7 142.4 133.1 142.7 141.0 138.0 139.9 140.9 145.0 139.7 145.0 152.7 133.3 140.7 137.9 138.7 145.6 142 .6 142.33 5.63 NH3 applied to corn after soybeans on C/S dates. NH3 applied to corn after corn on C/C dates. NH3 applied to both corn after soybeans and corn after corn on SPLIT dates. 238 Table F.4 Corn Planting Dates. MB Plow. 70% Fall Plowed Year C/S* C/S C/S SPLIT* C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 125 123 118 121 119 121 121 119 121 115 118 115 121 115 120 116 120 117 124 119 115 115 126 122 120 118 121 115 117 115 120 116 115 126 124 119 134 120 122 122 123 124 116 121 116 122 116 121 121 121 118 125 122 116 116 127 124 121 119 122 116 119 116 121 117 116 129 125 120 138 121 123 123 124 125 117 122 122 123 122 123 122 122 119 127 123 117 117 128 125 122 120 123 117 121 117 122 118 117 130 133 121 139 122 124 124 125 127 118 123 123 124 123 125 123 123 121 128 124 118 118 129 129 123 121 124 118 122 118 123 119 118 131 134 123 140 123 125 125 134 128 120 124 124 126 124 126 125 124 122 129 125 123 120 130 130 126 122 126 119 123 119 124 120 119 Mean Std. dev. C/C 134 135 124 141 124 126 126 135 130 125 126 125 127 125 130 126 125 123 130 129 125 121 131 132 127 123 127 120 124 120 125 121 120 C/C Mean 135 136 125 143 125 127 127 136 131 127 127 126 128 126 132 127 126 124 131 130 126 122 133 133 128 124 128 121 125 121 126 123 121 130.0 130.0 121.4 136.6 122.0 124.0 124.0 128.0 126.6 119.7 123.0 121.6 124.4 121.6 125.3 122.9 123.0 120.6 127.7 124.6 120.0 118.4 129.1 127.9 123.9 121.0 124.4 118.0 121.6 118.0 123.0 119.1 118.0 123.61 5.29 C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 239 Table F.5 Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 Soybean Planting Dates. MB Plow. 70% Fall Plowed PI* 138 138 127 147 127 129 129 159 133 129 132 130 133 140 136 131 136 130 133 132 131 146 138 135 130 137 136 123 127 124 128 131 127 Mean Std. dev. P2 P3 P4 139 139 128 148 128 130 130 160 134 130 133 131 134 141 137 132 150 131 134 133 132 147 139 139 131 147 137 124 128 125 129 136 128 140 140 132 149 136 131 132 161 135 131 134 138 137 142 138 133 151 140 135 136 133 150 140 140 132 148 138 127 129 126 132 137 131 143 141 133 150 137 132 133 162 136 133 135 140 138 143 139 135 158 147 136 137 134 151 143 141 133 149 142 128 130 127 134 138 150 Mean 140.0 139.5 130.0 148.5 132.0 130.5 131.0 160.5 134.5 130.8 133.5 134.8 135.5 141.5 137.5 132.8 148.8 137.0 134.5 134.5 132.5 148.5 140.0 138.8 131.5 145.3 138.3 125.5 128.5 125.5 130.8 135.5 134.0 136.00 7.52 PI through P4 are the first through fourth days of soybean planting. 240 Table F.6 NH3 Application Dates. MB Plow. 70% Fall Plowed Year C/S* C/S C/S SPLIT* C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 144 143 134 145 142 139 135 144 139 134 136 135 141 145 147 137 141 137 138 138 135 139 144 142 136 142 152 130 131 134 135 142 141 145 144 135 151 144 140 136 145 140 135 139 137 142 146 148 138 143 138 140 139 136 140 145 143 137 143 153 131 134 135 136 143 142 147 145 136 152 146 141 137 146 141 136 140 141 147 147 149 140 144 139 141 140 137 141 147 144 139 144 154 132 142 136 138 144 143 148 150 137 153 147 143 138 147 142 137 141 142 148 148 150 141 146 141 142 141 138 142 148 145 140 145 155 133 143 137 139 146 146 149 156 138 155 148 144 140 155 143 138 142 143 149 149 151 142 147 142 143 142 139 143 149 146 141 146 156 134 144 140 140 147 147 Mean Std. dev. C/C 151 157 140 156 149 145 142 157 144 139 143 144 150 150 152 143 148 143 147 143 140 144 152 147 142 147 157 136 145 141 141 148 148 C/C 152 158 141 157 150 146 144 158 145 140 144 145 151 151 153 144 149 146 148 144 141 145 154 148 143 148 158 137 146 142 142 149 149 Mean 148.0 150.4 137.3 152.7 146.6 142.6 138.9 150.3 142.0 137.0 140.7 141.0 146.9 148.0 150.0 140.7 145.4 140.9 142.7 141.0 138.0 142.0 148.4 145.0 139.7 145.0 155.0 133.3 140.7 137.9 138.7 145.6 145.1 143.68 5.81 NH3 applied to corn after soybeans on C/S dates. NH3 applied to corn after corn on C/C dates. NH3 applied to both corn after soybeans and corn after corn on SPLIT dates. 241 Table F.7 Corn Planting Dates. MB Plow, 45% Fall Plowed Year C/S* C/S C/S SPLIT* C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 125 133 118 121 119 121 121 134 121 115 118 115 126 115 125 116 124 122 124 122 115 120 130 122 120 122 126 115 117 115 120 118 118 126 134 119 134 120 122 122 135 124 116 121 116 127 116 126 121 125 123 125 123 116 121 131 124 121 123 127 116 119 116 121 119 119 129 135 120 138 121 123 123 144 125 117 122 122 128 122 130 122 126 124 127 124 117 122 133 125 122 124 128 117 121 117 122 120 120 130 136 121 139 122 124 124 145 127 118 123 123 129 123 132 123 132 125 128 125 118 124 134 129 123 127 129 118 122 118 123 121 121 131 137 123 140 123 125 125 146 128 120 124 124 130 124 133 125 135 126 129 129 123 127 135 130 126 128 131 119 123 119 124 123 122 Mean Std. dev. C/C 134 138 124 141 124 126 126 147 130 125 126 125 131 125 134 126 136 127 130 130 125 130 136 132 127 130 133 120 124 120 125 124 123 C/C Mean 135 139 125 143 125 127 127 149 131 127 127 126 132 126 135 127 140 128 131 132 126 134 137 133 128 137 135 121 125 121 126 125 126 130.0 136.0 121.4 136.6 122.0 124.0 124.0 142.9 126.6 119.7 123.0 121.6 129.0 121.6 130.7 122.9 131.1 125.0 127.7 126.4 120.0 125.4 133.7 127.9 123.9 127.3 129.9 118.0 121.6 118.0 123.0 121.4 121.3 125.86 6.59 C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 242 Table F.8 Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 Soybean Planting Dates. MB Plow. 45% Fall Plowed PI" 139 141 132 149 136 129 134 160 133 129 132 130 141 140 140 131 161 139 133 140 131 153 145 135 133 150 162 123 127 124 129 131 152 Mean Std. dev. P2 P3 P4 Mean 140 142 133 150 137 130 135 161 134 130 133 131 142 141 141 132 162 140 134 141 132 154 147 139 134 151 163 124 128 125 132 136 153 143 143 134 151 151 131 136 162 135 131 134 138 156 142 143 133 163 141 135 142 133 155 148 140 135 152 164 127 129 126 134 137 154 144 144 135 152 153 132 137 170 136 133 135 140 157 143 145 135 165 142 136 143 134 156 149 141 136 153 166 128 130 127 135 138 155 141.5 142.5 133.5 150.5 144.3 130.5 135.5 163.3 134.5 130.8 133.5 134.8 149.0 141.5 142.3 132.8 162.8 140.5 134.5 141.5 132.5 154.5 147.3 138.8 134.5 151.5 163.8 125.5 128.5 125.5 132.5 135.5 153.5 140.71 10.68 PI through P4 are the first through fourth days of soybean planting. 243 Table F.9 NH3 Applic ation Dates. Plow. 45% Fall Plowed Year C/S* C/S C/S SPLIT' C/C* 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 145 148 137 144 142 139 140 158 139 134 136 135 147 135 146 137 148 143 138 144 135 144 152 142 140 144 153 130 131 134 138 142 143 147 150 138 153 144 140 142 159 140 135 139 137 148 139 147 138 149 146 140 145 136 145 154 143 141 145 154 131 134 135 139 143 146 148 156 140 155 146 141 144 171 141 136 140 141 149 145 148 140 150 147 141 146 137 146 157 144 142 146 155 132 142 136 140 144 147 149 157 141 156 147 143 145 172 142 137 141 142 150 146 149 141 151 148 142 147 138 147 158 145 143 147 156 133 143 137 141 146 148 151 158 143 157 148 144 147 174 143 138 142 143 151 147 150 142 158 149 143 148 139 150 159 146 145 148 157 134 144 140 142 147 149 Mean Std. dev. C/C 152 159 146 158 149 145 148 176 144 139 143 144 152 148 151 143 159 151 147 152 140 151 160 147 146 149 158 136 145 141 143 148 150 C/C 153 160 147 160 150 146 149 177 145 140 144 145 155 149 152 144 160 152 148 153 141 152 161 148 147 154 160 137 146 142 144 149 151 Mean 149.3 155.4 141.7 154.7 146.6 142.6 145.0 169.6 142.0 137.0 140.7 141.0 150. 3 144.1 149.0 140.7 153.6 148.0 142.7 147.9 138.0 147.9 157.3 145 .0 143.4 147.6 156.1 133.3 140.7 137.9 141.0 145.6 147.7 146.16 7.78 NH3 applied to corn after soybe on C/S dates. NH3 applied to corn after corn C/C dates, NH3 applied to both corn after oybeans and corn after corn on SPLIT dates. 244 Table F.10 Corn Planting Dates. No-Till System* Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 Mean 125 120 117 134 119 115 121 118 125 115 121 115 120 115 120 116 117 115 115 122 115 115 120 124 120 119 122 115 117 115 119 116 115 Mean Std. dev. * 126 121 118 138 120 122 122 119 127 116 122 116 121 116 121 121 120 116 124 123 116 116 122 130 121 120 123 116 119 116 120 117 116 129 123 119 139 121 123 123 123 128 117 123 122 122 125 123 122 121 117 125 124 117 117 123 132 122 121 124 117 121 117 121 118 117 130 124 120 140 122 124 124 124 130 118 124 123 123 126 125 123 122 118 127 125 118 118 125 133 123 122 126 118 122 118 122 119 118 131 125 121 141 123 125 125 125 131 120 126 124 124 127 126 125 123 119 128 129 123 120 126 134 126 123 127 119 123 119 123 120 119 135 126 123 143 124 126 126 135 132 125 127 125 126 128 133 126 124 121 129 130 125 121 127 135 127 124 128 120 124 120 124 121 120 138 134 124 144 125 127 127 136 133 129 128 126 127 129 134 127 125 122 130 131 126 122 128 139 128 131 129 121 125 121 125 1^3 121 130.6 124.7 120.3 139.9 122.0 123.1 124.0 125.7 129.4 120.0 124.4 121.6 123.3 123.7 126.0 122.9 121.7 118.3 125.4 126.3 120.0 118.4 124.4 132.4 123.9 122.9 125.6 118.0 121.6 118.0 122.0 119.1 118.0 123.55 5.67 Underlined dates are for corn after soybeans. Dates in bold print are split between corn after soybeans and corn after corn. Remaining dates are for corn after corn. 245 Table F.ll Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 PI* 140 136 126 147 127 130 129 151 135 131 132 131 129 139 137 129 131 124 133 133 131 124 130 141 130 137 137 123 127 124 127 125 123 Mean Std. dev. Soybean Planting Dates. No-Till System P2 P3 P4 143 137 127 148 128 131 130 152 136 133 134 143 130 140 138 130 132 125 134 137 132 140 131 142 131 139 138 124 128 125 128 136 127 144 138 128 149 136 132 132 157 137 134 135 144 131 141 139 131 135 126 135 138 133 141 135 143 132 140 157 127 129 126 129 137 128 154 139 131 150 137 133 133 158 139 135 136 145 132 142 140 132 136 127 136 139 134 142 136 145 133 144 158 128 130 127 132 138 150 Mean 145.3 137.5 128.0 148.5 132.0 131.5 131.0 154.5 136.8 133.3 134.3 140.8 130.5 140.5 138.5 130. 5 133.5 125.5 134.5 136.8 132.5 136.8 133.0 142.8 131.5 140.0 147.5 125.5 128.5 125.5 129.0 134.0 132.0 135.21 7.70 PI through P4 are the first through fourth days of soybean planting. 246 Table F. 12 NH3 Application Dates. No-Till Svstem Mean Year 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 145 145 132 151 142 139 135 144 140 136 139 130 133 146 145 137 133 128 137 140 135 130 137 144 137 142 145 129 131 133 134 141 142 Mean Std. dev. 147 146 133 152 144 140 136 145 141 137 140 135 134 147 146 138 134 129 138 141 136 134 138 146 139 143 148 130 132 134 135 142 143 148 148 134 153 146 141 137 146 142 138 141 137 137 148 147 140 140 130 140 142 137 139 139 147 140 145 152 131 133 135 136 143 147 149 150 135 155 147 143 138 147 143 139 142 138 138 149 148 141 141 131 141 143 138 143 140 148 141 146 153 132 134 136 139 144 148 151 156 136 156 148 144 140 149 144 141 143 140 140 150 149 142 143 137 142 144 139 144 143 153 142 147 154 133 143 137 140 147 141 152 157 137 157 149 145 142 154 145 142 144 141 141 151 150 143 144 138 143 145 140 145 144 154 143 148 155 134 144 140 141 148 146 153 158 138 158 150 146 144 155 147 143 145 142 142 152 151 144 146 139 147 146 141 146 145 155 145 149 156 136 145 141 142 149 149 149.3 151.4 135.0 154.6 146.6 142.6 138.9 148.6 143.1 139.4 142.0 137.6 137 .9 149.0 148 .0 140. 7 140.1 133.1 141.1 143.0 138.0 140.1 140. 9 149.6 141.0 145.7 151.9 132.1 137.4 136.6 138.1 144.9 145.1 142.52 6.38 247 Table F.13 Corn Yield Results (BU/A') . 100% Fall Plowed Year C/S C/S C/S SPLIT SPLIT C/C C/C C/C Mean 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 105.2 70.9 110.7 122.2 165.8 159.9 147.2 102.4 106. 3 74.1 129.3 104.6 50.3 82.0 48.1 138.4 168.0 161.8 75.5 94.3 55.0 46.7 109.6 59.5 128.4 78.8 74.8 177.0 218.3 117.8 64.8 165.4 173.7 103.6 79.3 115.6 116.8 150.1 159.6 141.8 103.5 101.2 72.6 126.4 98.5 52.7 82.0 49.1 141.2 166.8 162.4 75.7 95.8 53.9 53.8 109.6 68.0 130.9 82.1 59.1 177.2 215.5 102.9 68.4 163.0 180. 9 109.1 66.2 116.4 108.9 141.9 161.7 145.9 98.7 105.5 68.9 127.1 111.8 50.7 93.9 48.5 134.1 157.2 156.5 75.5 92.4 52.4 52.3 103.4 68.2 137.3 83.5 75.7 181.0 218.1 97.0 69.1 162.9 183.5 114.6 73.9 99. 2 108.9 140.0 156.1 134.4 98.5 100.8 64.2 128.9 108.8 47.9 93.9 48.4 139.7 161.8 152.5 77.8 96.5 52.4 53.0 105.8 66.3 140.4 83.8 75.8 175.7 214.0 97.5 72.6 163.0 179.1 114.7 73.3 97.9 108.5 139.4 154.1 134.4 97.9 100.9 63.5 125.7 109.2 48.2 94.3 48.4 139.7 162.0 152.7 77.5 96.2 52.3 53.3 105.6 66.6 141.0 83.6 75.3 175.7 210.4 97.4 72.4 162.3 178.7 116.4 64.3 83.4 104.8 139.4 148.1 128.9 104.5 101.0 51.9 123.9 100.9 48.4 80.3 48.4 139.3 163.9 150.4 76.5 99.0 54.9 59.1 110.2 65.3 150.0 81.6 81.2 174.8 213.4 99.2 93.3 162.8 178.6 120.3 64.2 99.6 133.7 139.1 147.6 126.0 97.7 98.4 51.3 129.1 104.5 41.6 80.2 49.5 139.5 162.7 173.5 75.2 98.8 64.2 58.0 100.2 63.9 138.1 84.0 61.8 168.5 213.3 102.2 78.2 162.8 178.9 120.4 64.7 102.5 129.8 118.5 147.6 116.8 97.6 97.2 53.2 133.8 94.0 44.1 80. 3 49.5 134.7 167.9 183.1 78.1 102.9 58.1 56.1 109.4 48.7 152.1 83.9 61.9 170.5 206.9 102.2 97.0 154.2 177.0 112.81 69.03 103.82 117.84 142.07 154.23 134.43 100.37 101.49 62.26 128.13 103.33 47.98 84.69 48.79 138.13 164.06 162.90 76.31 97.08 55.84 54.16 106.87 62.86 139.64 82.51 70.01 174.96 213.96 102.68 77.61 161.96 178.79 Mean Std. dev. C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 110.05 42.74 248 Table F.14 Soybean Yield Results (BU/A~) . 100% Fall Plowed Year PI P2 P3 P4 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 27.7 17 .4 33.5 47.9 32.0 43.7 56.5 39.7 47.6 20.4 42.1 28.8 21.8 20.6 19.8 29.6 39.5 41.5 17.3 36.2 17.6 18.7 34.9 15.4 40.9 18.0 27.5 41.9 59.5 47.2 49.1 45.5 39.5 27.7 17.4 33.5 47.9 31.6 43.6 56.5 40.7 47.6 21.2 42.2 28.9 21.8 20.7 19.7 29.6 38.5 41.4 17.3 37.8 16.8 19.5 34.8 15.5 40.8 20.0 28.5 42.0 59.0 47.3 49.2 45.5 39.4 27.5 17.5 33.6 48.0 27.6 43.5 58.3 33.7 47.9 21.9 42.4 27.9 22.3 21.2 19.6 29.9 38.3 40.8 17.5 40.3 16.8 23.9 34.7 15.5 40.7 21.8 28.5 43.1 59.0 47.8 52.5 45.1 39.4 27.6 17.0 33.6 48.2 27.6 43.0 58.2 32.9 48.5 22.0 42.3 30.2 22.5 21. 3 19.7 30.9 36.1 40.8 17.6 41.8 16.9 24.2 35. 9 17.5 40.4 21.9 28.7 43.2 58.3 49.5 52.5 45.9 39.7 Mean Std. dev. PI through P4 are the first through fourth days of soybean planting. Mean 27.63 17.33 33.55 48.00 29.70 43.45 57.38 36.75 47.90 21.28 42.25 28.95 21.38 20.95 19.70 30.00 38.10 41.13 17.43 39.03 17.03 21.58 35.08 15.98 40.70 20.43 28.30 42.55 58.95 47.95 50.83 45.50 39.50 34.13 12.25 249 Table F.15 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 Corn Yield Results (BU/A). 70% Fall Plowed C/S C/S C/S SPLIT SPLIT C/C C/C C/C Mean 105.2 64.1 110.7 122.2 165.8 159.9 147.2 103.5 106.3 74.1 129.3 104.6 52 .5 82 .0 48.2 138.4 157 .2 156.6 75.7 94.3 55.0 54.4 110.3 59.5 128.4 78.9 73.7 177.0 218.3 117.8 64. 8 165.4 171.4 103.6 64.1 115.6 116.8 150.1 159.6 141.8 98.7 101.2 72.6 126.4 98.5 50.1 82.0 49.1 141.2 161.8 152.4 75.4 95.8 53.9 53.8 100.4 68.0 130.9 82.5 59.1 177.2 215.5 102.9 68.4 163.0 180.9 109.1 64.1 116.4 108.9 141.9 161.7 145.9 98.5 105.5 68.9 127.1 111.8 47.8 93.9 48.6 134.1 163.8 150.1 77.6 92.4 52.4 52.3 110.6 68.2 137.3 83.6 75.8 181.0 218.1 97.0 69.1 162.9 183.5 114.6 65.3 99.2 108.9 140.0 156.1 134.4 104.8 100.8 64.2 128.9 108.8 48.6 93.9 48.4 139.7 162.9 173.1 75.6 96.5 52.4 53.0 110.8 66.3 140.4 83.8 75.8 175.7 214.0 97.5 72.6 163.0 179.2 114.7 65.7 97.9 108.5 139.4 154.1 134.4 104.5 100.9 63.5 125.7 109.2 48.3 94.3 48.3 139.7 162.7 173.5 75.8 96.3 52.3 53.3 110.0 66.6 141.0 83.6 75.4 175.7 210.4 97.4 72.4 162.3 178.7 116.4 62.3 83.4 104.8 139.4 148.1 128.9 97.8 101.0 51.9 123.9 100.9 48.4 80.3 48.4 139. 3 167.9 182.9 75.2 99.0 54.9 59.1 105.1 65.3 150.0 81.6 80.9 174.8 213.4 99.2 93.3 162.8 178.6 120.3 61.8 99.6 133.7 139.1 147.6 126.0 97.6 98.4 51.3 129.1 104.5 49.5 80.2 49.5 139.5 164.2 188.0 78.1 98.8 64.2 58.0 108.3 63.9 138.1 83.9 61.9 168.5 213.3 102.2 78.2 162.8 178.9 120.4 61.4 102.5 129.8 118.5 147.6 116.8 97.9 97.2 53.2 133.8 94.0 49.6 80. 3 49.6 134.7 162.7 154.6 76.3 103.0 58.1 56.1 101.3 48. 7 152.1 83.9 62.0 170.5 206.9 102.2 97.0 154.2 177.0 112.81 63.33 103.82 117.84 142.07 154.23 134.43 99.81 101.49 62.26 128.13 103.33 49.48 84.69 48. 82 138.13 162.91 165.41 76.29 97.10 55.84 55.26 106.63 62.86 139.64 82 .59 69.86 174.96 213.96 102.68 77.61 161.96 178.46 Mean Std. dev. C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 109.96 42.98 250 Table F. 16 Soybean Yield Results (BU/A), 70% Fall Year PI P2 P3 P4 Mean 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 27.7 17.0 33.5 47.9 32.0 43.7 56.5 32.8 47.6 20.4 42.1 28.8 22.1 20.6 19.7 29.6 38.3 41.1 17.3 36.2 17.6 24.2 36.5 15.4 40.9 20.0 28.5 41.9 59.5 47.2 49.1 45.5 39.4 27.7 16.6 33.5 47.9 31.6 43,6 56.5 36.7 47.6 21.2 42.2 28.9 23.1 20.7 19.6 29.6 31.8 41.1 17.3 37.8 16.8 24.7 37.6 15.5 40.8 27.3 28.5 42.0 59.0 47.3 49.2 45.1 39.7 27.5 16.6 33.6 48.0 27.6 43.5 58.3 36.8 47.9 21.9 42.4 27.9 23.7 21.2 19.7 29.9 31.3 37.6 17.5 40.3 16.8 26.2 37.5 15.5 40.7 28.2 28.7 43.1 59.0 47.8 52.5 45.9 40.0 27.6 16.1 33.6 48.2 27.6 43.0 58.2 39.4 48.5 22.0 42.3 30.2 23.6 21.3 20.1 30.9 29.4 35.6 17.6 41.8 16.9 26.7 40.7 17.5 40.4 28.1 29.2 43.2 58.3 49.5 52.5 46.4 46.7 27.63 16.58 33.55 48.00 29.70 43.45 57.38 36.43 47.90 21.28 42.25 28. 95 23.13 20.95 19.78 30.00 32.70 38.85 17.43 39.03 17.03 25.45 38.08 15.98 40. 70 25.90 28.73 42.55 58.95 47.95 50.83 45.73 41.45 Mean Std. dev PI through P4 are the first through fourth days of soybean planting. 34.37 12.22 251 Table F.17 Corn Yield Results (BU/A). 45% Fall Plowed Year C/S C/S C/S SPLIT SPLIT C/C C/C C/C Mean 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 105.2 65.3 110.7 122.2 165.8 159.9 147.2 98.0 106.3 74.1 129.3 104.6 41.3 82.0 48.4 138.4 167.4 182.4 75.7 95.9 55.0 59.8 108.9 59.5 128.5 81.1 81.4 177.0 218. 3 117.8 64.4 162.8 179.1 103.6 62.2 115.6 116.9 150.1 159.6 141.7 97.7 101.2 72.6 126.4 98.5 43.7 82.0 48.4 141.2 164.1 187.4 75.4 92.4 53.9 58.1 109.7 68.0 130.9 84.1 61.6 177.2 215.5 102.9 68.0 162.7 178.8 109.1 61.6 116.4 108.9 141.9 161.7 145.4 84.7 105.5 68.9 127.1 111. 8 45.6 93.9 49.5 134.1 160.8 153.9 77.6 96.2 52.4 56.2 103.4 68.2 137.3 84.1 61.6 181.0 218.1 97.0 69.1 162.7 179.0 114.6 61.5 99.1 108.9 140.0 156.1 134.1 78.6 100.8 64.2 128.9 108.8 39.0 93.9 49.5 139.7 163.5 154.1 75.6 99.2 52.4 55.5 106.4 66.3 140.5 84.9 68.6 175.7 214.0 97.5 72.6 162.9 177 .0 114.7 61.3 97.9 108.5 139.4 154.1 133.9 78.7 100.9 63.5 125.7 109.2 38.8 94.3 49 .6 139.7 164.0 154.2 75.8 99.1 52.3 55.9 105.8 66 .6 141.0 84.8 68.3 175.7 210.4 97.4 72.4 162.8 177.0 116.4 53.0 83.3 104.8 139.4 148.1 128.9 78.1 101.0 51.9 123.9 100.9 49.2 80.3 50.3 139.3 157.4 154.4 75.2 98.8 54.9 55.6 109.6 65.3 150.0 86.8 86.9 174.8 213.4 99.2 93.3 154.2 173.6 120.3 61.4 99.4 102.7 139.1 147.6 126.1 66. 9 98.4 51.3 129.1 104.5 52.2 80.2 49.2 139.5 164.7 195.0 78.1 103.0 64.2 60.4 100.8 63.9 138.6 89.3 69.3 168.5 213. 3 102.2 78.2 154.2 173.6 120.4 61.4 102.4 100.7 118.5 147 .6 116.8 66.1 97.2 53.2 133. 8 94.0 34.9 80.4 49.3 134.7 155.5 189.9 76.3 101.8 58.1 59.5 109.6 48.7 152.1 84.4 93.9 170.5 206. 9 102.2 97 .0 154.2 158.4 112.81 60.90 103.76 109.27 142.07 154.23 134.30 81.45 101.49 62.26 128.13 103.33 43.69 84.70 49.24 138.13 161.95 173.88 76.29 98.18 55.84 57.90 106.87 62 .86 139.74 84.95 74.74 174.96 213.96 102.68 77.50 159.09 174.21 Mean Std. dev. C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 109.25 43.35 252 Soybean Yield Results (BU/A). 45% Fall Plowed Table F.18 Year PI P2 P3 P4 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 27.7 16.1 33.6 48.0 27.6 43.7 59.6 24.2 47.6 20.4 42.1 28.8 25.0 20.6 20.2 29.6 28.4 38.0 17.3 42.0 17.6 26.8 44.3 15.4 40.4 28.3 27 .0 41.9 59.5 47.2 49.2 45.5 47.4 27,.5 16,.1 33 .6 48,.2 27 .6 43,.6 59,.6 25,.0 47,.6 21..2 42,.2 28,.9 26..4 20,.7 20,.6 29,.6 28,.1 37..6 17.,3 43..4 16. 8 27.,5 45. 0 15. 5 40. 2 29. 0 28..1 42. 0 59.,0 47. 3 52. 5 45.,1 47. 2 27 .6 16,.2 33 .4 48 .6 23 .0 43 .5 59 .6 25 .0 47 .9 21 .9 42 .4 27 .9 34 .2 21,.2 20 .7 29 .9 27 .9 36,.9 17..5 44,.4 16.,8 27,,5 45.,3 15..5 39..4 29.,7 27.,5 43.,1 59..0 47.,8 52.,5 45..9 48.,2 27..6 16..4 33 .1 48,.5 22 .1 43,.0 59 .3 25 .7 48,.5 22 .0 42,.3 30 .2 34,.6 21,.3 20,.9 30..9 26,.2 36,.2 17.,6 45.,5 16.,9 28.,5 45. 7 17.,5 39.,1 30. 1 27.,8 43. 2 58.,3 49..5 54. 2 46.,4 48. 3 Mean Std. dev. PI through P4 are the first through fourth days of soybean planting. Mean 27,.60 16,.20 33 .43 48,.33 25,.08 43,.45 59 .53 24,.98 47..90 21 .28 42,.25 28 .95 29,.95 20,.95 20 .60 30..00 27,.65 37.,18 17..43 43.,83 17. 03 27.,58 45. 08 15 . ,98 39.,78 29. 28 27..60 42. 55 58.,95 47..95 52. 10 45. 73 47. 78 34. 66 12. 50 253 Table F.19 Corn Yield Results CBU/A’ ). No-Till System Year C/S C/S C/S SPLIT SPLIT C/C C/C C/C Mean 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 104.5 75.6 108.9 115.2 148.4 170.0 140.7 103.1 106.7 74.1 130.0 109.4 60. 3 80. 7 54.1 134.1 163.0 160.8 76.3 103. 8 57.1 43.2 99.0 66. 9 137.4 84.1 86.4 165.2 204.5 103.8 69.5 155.6 184.3 102.0 65.6 110.7 106.9 131.7 162.3 143.9 106.3 101.1 51.7 129.9 112.8 55.6 80.8 49.4 127 .3 160.6 166 .9 75.0 100.3 58.6 47.7 109.8 64. 7 143.8 84.2 67.3 166.1 203.9 103.7 69.4 154.9 176.5 112.6 72.4 102.9 122.6 132.7 152.7 125.2 93.9 98.1 51.0 135.8 92.0 42.1 83.6 48.0 130.5 161.4 154.6 79.5 102.0 69.7 57.1 106.1 59.3 155.8 88.5 67.3 165.5 195.3 104.8 78.2 157.2 169.1 124.8 62.5 98.9 122.7 131.8 163.7 126.5 93.9 101.1 56.5 135.3 94.4 43.9 87.8 48.0 128.0 159.9 183.7 78.0 96.1 56.4 56.6 106.6 53.9 153.0 90.9 90.2 168.7 202.4 103.8 77.6 157.9 179.4 118.1 57 .7 106.2 107.7 126.4 177.9 125.5 93.6 107.2 53.6 141.7 100.6 46.9 85.1 49.1 126.6 166.3 154.8 85.8 103.4 54. 3 57.2 111.9 49.0 158.9 59.4 92.6 163.5 200.9 113.9 101.0 167.6 178.5 117.7 68.0 110.9 105.2 115.4 155.7 134.4 104.6 102.3 71.0 135.7 119.5 55.1 79.8 47.4 126.9 162.4 152.3 81.9 95.2 54.2 58.3 123.2 59.1 146.3 87.4 94.8 167.5 204.4 107.5 76.2 174.0 169.7 119.6 67.3 97.8 99.1 132.4 155.6 126.7 107.9 113.8 64.9 136.1 119.1 53.0 79.7 48.5 126.4 164.8 150. 3 81.5 95.2 54.6 58.4 114.6 53.9 151.9 95. 3 95. 9 170.2 201.0 107.3 77.2 165.4 183.0 122.8 67 .6 109.3 125.6 132.1 155.6 126.7 101.2 109.6 64. 5 136.3 101.7 46.7 78.0 48.5 127.5 164.7 161.4 83.3 99.2 54. 6 56.6 118.6 52.3 158.7 88.1 68.3 168.4 200.0 107.2 78.6 165.3 182.9 114.38 68.09 106.15 112.83 131.69 160.39 131.94 101.54 105.11 61.75 134.61 107.43 51.17 81.29 49.21 128.57 162.86 159.36 79.91 99.35 57.74 54.03 111.51 58.24 149.98 86.11 81.63 167.00 201.54 106.16 76.91 162.16 177.78 Mean Std. dev. C/S dates were planted to corn after soybeans. C/C dates were planted to corn after corn. SPLIT dates were split between corn after soybeans and corn after corn. 110.25 41.35 254 Table F.20 Soybean Yield Results (’BU/AI . No-Tlll System Year PI P2 P3 P4 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1984 1985 1986 1987 1988 1989 1990 29.4 19.4 35.7 49.7 32.2 44.1 58.6 37.7 49.3 24.5 43.4 29.8 20.4 22.0 20.3 29.9 38. 8 42.0 19.8 38.6 18.2 20.4 37.5 17.6 41.4 23.3 29.7 42.9 59.4 49.9 51.9 46.7 38.9 29,.1 19..2 35,,8 49,,6 31,,6 44,.0 60,.0 38,.8 49,.2 24 .4 43 .4 32,.2 21 .0 22 .1 20 .2 29 .9 38 .4 41 .9 19 .8 41 .4 18,.2 22,.0 38,.3 17,.4 41.,3 23,.7 29.,8 44. 4 59. 1 49. 9 52. 2 46. 8 39. 1 29,.0 18..8 36,.0 49,.7 28,.0 44..5 59 .7 34,.4 49,.8 25 .4 43 .6 33 .3 21 .5 22 .8 20 .2 30 .1 37 .5 42 .2 19 .8 41 .6 17,.5 22 .6 38..9 18,.5 41..3 23..9 29.,2 43.,9 58.,9 51. 2 52. 5 47. 0 39. 1 28,.0 18,.7 36..0 49,.6 27..7 44,.5 60,.7 34,.4 49,.3 25 ,4 43 .1 33 .0 21 .4 22 .8 20 .6 30 .0 37 .0 42 .2 19 .9 41 .5 17.,5 23 .0 38,,7 18..4 40..6 27,.2 28.,7 43..6 61. 4 51. 3 54. 3 46. 9 46. 7 Mean Std. dev. PI through P4 are the first through fourth days of soybean planting. Mean 28,.88 19..03 35..88 49,.65 29..88 44,.28 59,.75 36,.33 49,.40 24 .93 43 .38 32 .08 21 .08 22 .43 20 .33 29 .98 37 .93 42 .08 19 .83 40 .78 17,.85 22 .00 38,.35 17..98 41,.15 24,.53 29.,35 43.,70 59. 70 50. 58 52. 73 46. 85 40. 95 35. 56 12. 21 Appendix G FORTRAN CODE FOR THE DETERMINISTIC DYNAMIC PROGRAMMING MODEL This Appendix contains the FORTRAN code for the deterministic dynamic programming model that is used to determine optimal adoption strategies for the profit-maximizing farmer. the variable names also is provided. A list of explanations for Although the FORTRAN code was compiled and executed using Microsoft FORTRAN, Ver. 5.1, nearly all of the code follows the FORTRAN 77 standard. The only exceptions are a few statements regarding how variables are stored in computer memory. The statements or the parts of those statements that do not conform to the FORTRAN 77 standard are shown in bold print. The listed code is for the version of the model that includes options to rent the no-till planter on a limited acreage. The version that does not include these options is identical except that the additional rental rates are not read from the input file and value functions for the additional options are not calculated. Description of Variable Names (in order of appearance') TITLE N MP MT IAGE1 IAGE2 IAGE3 IAGE4 CX(i), i-1,4 DF KX PR1 RNT1 PR2 RNT2 Description of the run, printed on the output file. Number of years in the planning horizon. Maximum age that the planter can be used. Maximum age that the tractor can be used. Initial age of the conventional planter (may be 0). Initial age of the no-till planter (usually is 0). Initial age of the 140 HP tractor (may be 0). Initial age of the 85 HP tractor (usually is 0). Cost inflation factors for the learning curve effect. Discount rate. Years of no-till experience (1 implies no experience). Purchase price, conventional planter. Rental fee for the conventional planter on 600 acres. Purchase price, no-till planter. Rental fee for the no-till planter on 600 acres. 256 PR3 PR4 RK1 RK2 RK3 KPI KTI MPPl M.TP2 MPOL A OWN, OWNP, OWNT R1 R2 OB OT CN1 CN2 CN3 CN4 C1(K) C2(K) T1(K) T2(K) C3(K) C4(K) T3(K) T4(K) J KT KP II, IM1, JM1 IHI, JHI I PL3 VL3 PL4 VL4 PI P2 Purchase price, 140 HP tractor. Purchase price, 85 HP tractor. Rental fee for renting no-till planter on 60 acres. Rental fee for renting no-till planter on 120 acres. Rental fee for renting no-till planter on 240 acres. Initial age of whichever planter is owned. Initial age of whichever tractor is owned. Age at which planter must be replaced. Age at which tractor must be replaced. Last year that the policy variable is determined. l/(l+discount factor) Ownership state markers used to control printouts. Conventional tillage revenue on 600 acres minus Subtotal 1 variable costs (Table 4.10). Conventional tillage revenue on 600 acres minus Subtotal 1 variable costs (Table 4.10). Lower bound on years in detailed printouts. Upper bound on years in detailed printouts. Repair costs for a new conventional planter plus Subtotal 2 variable costs on 600 acres. Repair costs for a new no-till planter plus Subtotal 2 variable costs on 600 acres. Repair costs for a new 140 HP tractor. Repair Cost for a new 85 HP tractor. Repair costs for a conventional planter of age K. plus Subtotal 2 variable costs on 600 acres. Repair costs for a no-till planter of age K. plus Subtotal 2 variable costs on 600 acres. Trade-in value for a conventional planter of age K. Trade-in value for a no-till planter of age K. Repair costs for 400 hours use of a 140 HP tractor of age K. Repair costs for 400 hours use of an 85 HP tractor of age K. Trade-in value for a 140 HP tractor of age K. Trade-in value for an 85 HP tractor of age K. Counter variable for years of experience. Counter variable for tractor age (in 400 hour units) Counter variable for planter age (in years). Counters used to control the backwards recursion. Bounds used to control the backwards recursion. Year in the planning horizon. Optimal policy for owning the large tractor only. Current-period value function for owning the large tractor only. Optimal policy for owning the small tractor only. Current-period value function for owning the small tractor only. Optimal policy for owning the large tractor and conventional planter. Optimal policy for owning the large tractor and no-till planter. 257 Optimal policy for owning the small tractor and no-till planter. Next-period value function for owning the large tractor only. Next-period value function for owning the small tractor only. Next-period value function for owning the large tractor and conventional planter. Current-period value function for owning the large tractor and conventional planter. Next-period value function for owning the large tractor and no-till planter. Current-period value function for owning the large tractor and no-till planter. Next-period value function for owning the small tractor and no-till planter. Current-period value function for owning the small tractor and no-till planter. Next year's planter age (in years). Next year's tractor age (in years). Next year's experience level. Next year's ownership state. Desciption of the optimal policy in words. P4 VLN3 VLN4 VN1 VI VN2 V2 VN4 V4 NKP NKT NJ NOWN POLICY The remaining variables are control variables or printed results for control variables found in the subroutines. descriptions. See Tables 4.1-4.6 for The numbers assigned to the policy variables if each control variable is the optimal choice correspond to the numbers in Tables 4.1-4.6 that describe the control variables. The only exceptions are the rental options on limited acreage and the HOLD option in subroutine DEC01 when these additional rental options are considered. In this case the additional rental options correspond to policies 14-19 and the HOLD option corresponds to policy 20. 258 o n oo o The Program for the Deterministic Model DP Replacement With Leasing Problem, including 2 planters, 2 tractors, and experience with the 2nd planter. Includes the option of keeping planter 1 while renting planter 2. Subroutines include conditional print statements to limit output. $STORAGE:2 PROGRAM RPLS2XR CHARACTERS8 TITLE CHARACTERS2 POLICY INTEGERS. PI(20,36,5,36), P2(20,36,5,36) INTEGERS P4(20,36 ,5 ,36) INTEGERS PL3(36,5,36), PL4(36,5,36), OWN, OB, OT INTEGER*1 N, MP, MT, IAGE1, IAGE2, IAGE3, IAGE4, KX, OWNP, OWNT REAL PRl, PR2, PR3, PR4, RNT1, RNT2, CN1, CN2, CN3, CN4 REAL VL3(36,6), VL4(36,6) COMMON /VALS/ A, R 1 , R2, CNl, CN2, CN3, CN4, CX(5), OB, OT, MPOL COMMON /VALS/ PRl, PR2, PR3, PR4, RNT1, RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /0WN1/ Cl(20), Tl(20), Sl(20),Vl(20,36,6) COMMON /OWN2/ C2(20), T2(20), S2(20) COMMON /0WN3/ T3(40), S3(40), RK1, RK2, RK3 COMMON /OWN4/ C4(40), T4(40), S4(40) COMMON /OWN23/ V2(20,36,6) COMMON /OWN24/ V4(20,36,6) 20 22 25 30 32 35 OPEN (UNIT = 2, FILE = 'RPLS2XR.DAT') OPEN (UNIT = 4, FILE = 'D:\RPLS2X.OUT') READ(2,20) TITLE FORMAT(78A) WRITE(4,22) TITLE FORMAT(78A/) READ(2,25) N, MP, MT, IAGE1, IAGE2, IAGE3, IAGE4 WRITE(4,25) N, MP, MT, IAGE1, IAGE2, IAGE3, IAGE4 FORMAT(719) READ(2,30) CX(1), CX(2), CX(3), CX(4), DF, KX WRITE(4,30) CX(1), CX(2), CX(3), CX(4), DF, KX FORMAT(5F9.4,19) READ(2,32) PRl, RNT1, PR2, RNT2, PR3, PR4 WRITE(4,32) PRl, RNT1, PR2, RNT2, PR3, PR4 FORMAT(6F9.4) READ(2,35) RK1, RK2, RK3 WRITE(4,35) RK1, RK2, RK3 FORMAT(3F9.4) KPI = IAGE1 IF (IAGE2 .GT. IAGE1) KPI » IAGE2 KTI = IAGE3 IF (IAGE4 .GT. IAGE3) KTI = IAGE4 NP1 = N+l MPP1 = MP+1 MTP2 = MT+2 MPOL = 3 6 A = 1.0 / (1.0 + DF) OWNT = 0 IF (IAGE3 .GT. 0) THEN 259 OWNT - 1 IF (IAGE1 .GT. 0) THEN OWN « 13 ELSE IF (IAGE2 .GT. 0) THEN OWN = 23 ELSE OWN = 3 END IF ELSE IF (IAGE4 .GT. 0) THEN OWNT = 2 IF (IAGE2 .GT. 0) THEN OWN = 24 ELSE OWN = 4 END IF END IF OWNP = 0 IF (IAGE1 .GT. 0) THEN OWNP = 1 ELSE IF (IAGE2 .GT. 0) THEN OWNP = 2 END IF 40 45 50 60 65 15 o n 16 READ(2,40) Rl, R 2 , OB, OT WRITE(4,40) Rl, R 2 , OB, OT FORMAT(2F9.4,219) READ(2,50) CN1, CN2, CN3, CN4 WRITE(4,50) CN1, CN2, CN3, CN4 DO 45 K=l,19 READ(2,50) Cl(K), C2(K), Tl(K), T2(K) SI(K) = T1(K) S2(K) = T2(K) WRITE(4,50) C1(K), C2(K), T1(K), T2(K) FORMAT(4F9.4) DO 60 K=1,40 READ(2,65) C3(K), C4(K), T3(K), T4(K) S3(K) = T3(K) S4(K) = T4(K) WRITE(4,65) C3(K), C4(K), T3(K), T4(K) FORMAT(4F9.4) CLOSE (2) DO 15 K=MPP1,20 Cl(K) = 9999. C2(K) = 9999. SI(K) = 0. S2(K) = 0. T1(K) = 0. T2(K) = 0. DO 16 K-=MTP2 ,40 C3(K) = 9999. C4(K) - 9999. S3(K) = 0. S4(K) = 0. T3(K) - 0. T4(K) = 0. SET TERMINAL PERIOD VALUE FUNCTIONS 260 c * * rk* * * * 'k'sV * *■&* * * •&•&-jV•*■■jV •&'k■*'&■&■* # ,5V* 9c•&* ■&* ■&•A’■£■* -k•&•& * ‘k * -*■■&*k k k * *sVk •* ■*&■&k & * 2 3 C C C = -SI(KP) - -S2(KP) = -S2(KP) S3(KT ) -S4(KT) S3(KT) S3(KT) S4(KT) - kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk BACKWARDS RECURSIVE CALCULATION OF THE VALUE FUNCTION AND POLICIES kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk 80 6 C 38 39 36 8 C C C DO 3 J-1,5 DO 3 KT= =1,MTP2 DO 2 KP=1,MPP1 VN1(KP,K T ,J ) VN 2(K P ,K T ,J ) VN4(KP,K T ,J ) VLN3 (KT,J ) *= VLN4(KT,J ) CONTINUE DO 8 II = 1 ,N I = N - II + 1 IM1 = N - II JM1 = IM1 * 2 IF (IM1 .GT. MPP1) IM1 = MPP1 IF (JM1 .GT. MTP2) JM1 = MTP2 IHI = IM1 + KPI JHI = JM1 + KTI IF (IHI .GT. 20) IHI = 20 IF (JHI .GT. 36) JHI = 36 WRITE(4,80) I FORMAT('YEAR ',12) DO 6 J=l.,4 DO 6 KT=1,JHI CALL DECL3(KT, J , PL3, VL3) CALL DECL4(KT, J, PL4, VL4) DO 6 KP = 1,IHI CALL DECOl(KP KT, J, PI) CALL DEC02(KP, KT, J P2) CALL DEC04(KP, K T , J P4) CONTINUE RESET THE NEXT PERIOD VALUE FUNCTIONS DO 36 KT=1,JHI DO 38 J=l,4 VLN3(KT,J ) = VL3(KT,J ) VLN4(KT,J ) = VL4(K T ,J ) VLN3(KT,5) = VL3(KT,4) VLN4(KT,5) = VL4(KT,4) DO 36 KP=1,IHI DO 39 J=l,4 VN1(KP,K T ,J ) = VI(KP,K T ,J ) VN2(KP,K T ,J ) = V2(KP,KT,J) VN4(KP,K T ,J ) V4(KP,K T ,J ) VN1(KP,KT,5) VI(KP,K T ,4) VN2(KP,KT,5) V2(KP,KT,4) VN4(KP,K T ,5) V4(KP,K T ,4) CONTINUE CONTINUE RECONSTRUCT THE OPTIMAL POLICIES KP = KPI KT = KTI J = KX 261 NJ = KX IF (OWNT .EQ. 1) THEN WRITE(4,90) KP, OWNP ELSE IF (OWNT .EQ. 2) THEN WRITE(4,92) KP, OWNP END IF 90 FORMAT('OPT. POLICY STARTING WITH A ' ,12,' YR. OLD PLANTER OF TYPE' +,12,' AND LARGE TRACTOR IS:',/) 92 FORMAT('OPT. POLICY STARTING WITH A',12,' YR. OLD PLANTER OF TYPE' +,12,' AND SMALL TRACTOR IS:',/) DO 10 1=1,36 94 WRITE(4,94) I, KP, KT, J FORMAT(4X,'YEAR: ',12,' PLANTER AGE:’,I2,' +12,' J :',12) TRACTOR AGE:', IF (OWN .EQ. 13) THEN IF (PI(KP, KT, J, I) .EQ. 1) THEN POLICY = 'REPLACE PLANTER 1 ’ NKP = 1 NKT = KT + 2 NOWN = 1 3 ELSE IF (PI(KP, KT, J, I) .EQ. 2) THEN POLICY = 'REPLACE W/ PLANTER 2' NKP = 1 NKT = KT + 1 NJ = J + 1 NOWN = 23 ELSE IF (PI(KP, KT, J, I) .EQ. 3) THEN POLICY = 'REPLACE LARGE TRACTOR' NKP = KP + 1 NKT = 2 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 4) THEN POLICY = 'REPLACE BOTH MACHINES' NKP = 1 NKT = 2 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 5) THEN POLICY = 'REPLACE W/ LARGE TCTR, PLTR 2.' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 23 ELSE IF (PI(KP, KT, J, I) .EQ. 6) THEN POLICY = 'REPLACE W/ SMALL TCTR, PLTR 2.' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 24 ELSE IF (PI(KP, KT, J, I) .EQ. 7) THEN POLICY = 'RENT PLANTER 1' NKP = 0 NKT - KT + 2 NOWN = 3 262 ELSE IF (PI(KP, KT, J, I) .EQ. 8) THEN POLICY = 'RENT PLANTER 2' NKP = 0 NKT = KT + 1 NJ = J + 1 NOWN = 3 ELSE IF (PI(KP, KT, J, I) .EQ. 9) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 1' NKP = 0 NKT = 2 NOWN = 3 ELSE IF (PI(KP, KT, J, I) .EQ. 10) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN = 3 ELSE IF (PI(KP, KT, J, I) .EQ. 11) THEN POLICY = 'RPLCE W/SMALL TCTR. RENT PLTR 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN = 4 ELSE IF (PI(KP, KT, J, I) .EQ. 12) THEN POLICY = 'RENT PLANTER 2, KEEP PLANTER 1' NKP = KP + 1 NKT = KT + 2 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 13) THEN POLICY = 'RPLCE TCTR, RNT PLTR 2, KEEP 1' NKP = KP + 1 NKT = 1 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 14) THEN POLICY = 'RNT PL 2 ON 60 A, KEEP PI' NKP = KP + 1 NKT = KT + 2 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 15) THEN POLICY = 'RNT PL 2 ON 120 A, KEEP PI' NKP = KP + 1 NKT = KT + 2 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 16) THEN POLICY = 'RNT PL 2 ON 240 A, KEEP PI' NKP = KP + 1 NKT = KT + 2 NJ = J + 1 NOWN = 13 ELSE IF (P1(K P , KT, J, I) .EQ. 17) THEN POLICY = 'REPLACE T3, RENT PL 2 ON 60 A' NKP = KP + 1 NKT = 1 263 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 18) THEN POLICY - 'REPLACE T3, RENT PL 2 ON 120 A' NKP = KP + 1 NKT = 1 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 19) THEN POLICY = 'REPLACE T 3 , RENT PL 2 ON 240 A' NKP = KP + 1 NKT = 1 NJ = J + 1 NOWN = 13 ELSE IF (PI(KP, KT, J, I) .EQ. 20) THEN POLICY = 'KEEP BOTH MACHINES' NKP = KP + 1 NKT = KT + 2 NOWN = 13 END IF WRITE(4,95) I, OWN, P1(KP, KT, J, I), POLICY ELSE IF (OWN .EQ. 23)THEN IF (P2(KP, KT, J ,1) .EQ. 1) THEN POLICY = 'REPLACE W/ PLANTER 1' NKP = 1 NKT = KT + 2 NOWN = 13 ELSE IF (P2(KP, KT, J, I) .EQ. 2) THEN POLICY = 'REPLACE PLANTER 2' NKP = 1 NKT = KT + 1 NJ = J + 1 NOWN = 23 ELSE IF (P2(KP, KT, J, I) .EQ. 3) THEN POLICY = 'REPLACE LARGE TRACTOR.' NKP = KP + 1 NKT = 1 NJ = J + 1 NOWN = 23 ELSE IF (P2(KP, KT, J, I) .EQ. 4) THEN POLICY = 'REPLACE LRGE TCTR W/ SMALL TCTR' NKP = KP + 1 NKT = 1 NJ = J + 1 NOWN = 24 ELSE IF (P2(KP, KT, J, I) .E Q . 5) THEN POLICY = 'REPLACE W/ LARGE TCTR, PLTR. 1' NKP = 1 NKT = 2 NOWN = 13 ELSE IF (P2(KP, KT, J, I) .EQ. 6) THEN POLICY = 'REPLACE W/ LARGE TCTR, PLTR 2.' NKP « 1 NKT = 1 NJ = J + 1 264 NOWN - 23 ELSE IF (P2(KP, KT, J, I) .EQ. 7) THEN POLICY = 'REPLACE W/ SMALL TCTR, PLTR 2.' NKP = 1 NKT = 1 NJ - J + 1 NOWN = 24 ELSE IF (P2(KP, KT, J, I) .EQ. 8) THEN POLICY = 'RENT PLANTER 1' NKP = 0 NKT = KT + 2 NOWN = 3 ELSE IF (P2(KP, KT, J, I) .EQ. 9) THEN POLICY = 'RENT PLANTER 2' NKP = 0 NKT = KT + 1 NJ = J + 1 NOWN = 3 ELSE IF (P2(KP, KT, J, I) .EQ. 10) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 1' NKP = 0 NKT = 2 NOWN = 3 ELSE IF (P2(KP, KT, J, I) .EQ. 11) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN = 3 ELSE IF (P2(KP, KT, J, I) .EQ. 12) THEN POLICY = 'RPLCE W/SMALL TCTR. RENT PLTR 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN - 4 ELSE IF (P2(KP, KT, J, I) .EQ. 13) THEN POLICY -= 'KEEP BOTH MACHINES' NKP - KP + 1 NKT =■ KT + 1 NJ = J + 1 NOWN = 23 END IF WRITE(4,95) I, OWN, P2(KP, KT, J, I), POLICY ELSE IF (OWN .EQ. 24) THEN IF (P4(KP, KT, J, I) .EQ. POLICY = 'REPLACE NKP ■= 1 NKT = KT + 1 NJ -= J + 1 NOWN - 24 ELSE IF (P4(KP, KT, J, I) POLICY = 'REPLACE NKP ■= KP + 1 NKT - 1 NJ - J + 1 1) THEN PLANTER 2' .EQ. 2) THEN SMALL TCTR W/ LRGE TCTR' 265 NOWN = 23 ELSE IF (P4(KP, KT, J, I) .EQ. 3) THEN POLICY = 'REPLACE SMALL TRACTOR.' NKP = KP + 1 NKT = 1 NJ = J + I NOWN = 24 ELSE IF (P4(KP, KT, J, I) .EQ. 4) THEN POLICY = 'REPLACE W/ LARGE TCTR, PLTR. 1' NKP = 1 NKT = 2 NOWN = 13 ELSE IF (P4(KP, KT, J, I) .EQ. 5) THEN POLICY = 'REPLACE W/ LARGE TCTR, PLTR 2.' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 23 ELSE IF (P4(KP, KT, J, I) .EQ. 6) THEN POLICY = 'REPLACE W/ SMALL TCTR, PLTR 2.' NKP = 1 NKT - 1 NJ = J + 1 NOWN = 24 ELSE IF (P4(KP, KT, J, I) .EQ. 7) THEN POLICY = 'RENT PLANTER 2' NKP «= 0 NKT = KT + 1 NJ = J + 1 NOWN = 4 ELSE IF (P4(KP, KT, J, I) .EQ. 8) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 1' NKP ■= 0 NKT = 2 NOWN = 3 ELSE IF (P4(KP, KT, J, I) .EQ. 9) THEN POLICY = 'REPLACE L. TCTR., RENT PLTR. 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN = 3 ELSE IF (P4(KP, KT, J, I) .EQ. 10) THEN POLICY = 'RPLCE W/SMALL TCTR. RENT PLTR 2' NKP = 0 NKT = 1 NJ - J + 1 NOWN = 4 ELSE IF (P4(KP, KT, J, I) .EQ. 11) THEN POLICY = 'KEEP BOTH MACHINES' NKP = KP + 1 NKT ■= KT + 1 NJ = J + 1 NOWN = 24 END IF WRITE(4,95) I, OWN, P4(KP, KT, J, I), POLICY ELSE IF (OWN .EQ. 3) THEN 266 IF (PL3(KT, J, I) .EQ. 1) THEN POLICY = 'BUY PLANTER 1' NKP = 1 NKT = KT + 2 NOWN = 13 ELSE IF (PL3(KT, J, I) .EQ. 2) THEN POLICY = 'BUY PLANTER 2' NKP = 1 NKT = KT + 1 NJ = J + 1 NOWN = 23 ELSE IF (PL3(KT, J, I) .EQ. 3) THEN POLICY = 'KEEP RENTING PLANTER NKP = 0 NKT = KT + 2 NOWN = 3 ELSE IF (PL3(KT, J, I) .EQ. 4) THEN POLICY = 'RENT PLANTER 2' NKP = 0 NKT = KT + 1 NJ = J + 1 NOWN = 3 ELSE IF (PL3(KT, J, I) •EQ. 5) THEN POLICY = 'BUY PLNTR 1, REPLACE NKP = 1 NKT = 2 NOWN = 13 ELSE IF (PL3(KT,J, I) .EQ. 6) THEN POLICY = 'BUY PLNTR 2, REPLACE TRACTOR' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 23 ELSE IF (PL3(KT,J, I) .EQ. 7) THEN POLICY = 'BUY PLNTR2 & SMALLTRACTOR' NKP - 1 NKT = 1 NJ = J + 1 NOWN = 24 ELSE IF (PL3(KT, J, I) .EQ. 8) THEN POLICY = 'REPLACE TRACTOR, RENT PLANTER 1' NKP = 0 NKT = 2 NOWN = 3 ELSE IF (PL3(KT, J, I) .EQ. 9) THEN POLICY «= 'REPLACE TRACTOR, RENT PLANTER 2' NKP = 0 NKT - 1 NJ = J + 1 NOWN = 3 END IF WRITE(4,95) I, OWN, PL3(KT, J, I), POLICY ELSE IF (OWN .EQ. 4) THEN IF (PL4(KT, J, I) .EQ. 1) THEN POLICY = 'BUY PLANTER 2' 267 NKP = 1 NKT = KT + 1 NJ = J + 1 NOWN = 24 ELSE IF (PL4(KT, J, I) .EQ. 2) THEN POLICY = 'KEEP RENTING PLANTER 2' NKP = 0 NKT = KT + 1 NJ = J + 1 NOWN = 4 ELSE IF (PL4(KT, J, I) .EQ. 3) THEN POLICY = 'BUY LARGE TRACTOR & PLANTER 1* NKP = 1 NKT = 2 NOWN = 13 ELSE IF (PL4(KT, J, I) .EQ. 4) THEN POLICY = 'BUY LARGE TRACTOR & PLANTER 2' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 23 ELSE IF (PL4(KT, J, I) .EQ. 5) THEN POLICY = 'BUY SMALL TRACTOR & PLANTER 2' NKP = 1 NKT = 1 NJ = J + 1 NOWN = 24 ELSE IF (PL4(KT, J, I) .EQ. 6) THEN POLICY = 'RPLCE SMALL TCTR, RENT PLNTR 2' NKP = 0 NKT = 1 NJ = J + 1 NOWN = 4 END IF WRITE(4,95) I, OWN, PL4(KT, J, I), POLICY END IF IF (NJ .GT. J) J = NJ IF(J .GT. 4) J ■= 4 KP = NKP KT = NKT OWN = NOWN 95 FORMAT('IN YEAR ',12,' OWNING: ',12,' POLICY: ',I2,3X,A32) 10 CONTINUE 2000 CLOSE (4) END SUBROUTINE DECL3 (KT, J, I, PL3, VL3) INTEGER*1 PL3(36,5,36), OB, OT REAL VL3(36,6) COMMON /VALS/ A, R 1 , R 2 , CN1, CN2, CN3, CN4, CX(5), OB, OT, MPOL COMMON /VALS/ PR1, PR2, PR3, PR4, RNT1, RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) 268 COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /OWN3/ T3(40), S3(40), RK1, RK2, RK3 BUY1 = PR1 - R1 + CN1 + C3(KT)+C3(KT+1) + A*VN1(1,KT+2,J ) BUY 2 = PR2 - R2 + (CN2+C3(KT))*CX(J) + A*VN2(1,KT+1,J+l) CRNT1 == RNT1 - R1 + CN1 + C3(KT)+C3(KT+1) + A*VLN3(KT+2,J ) CRNT2 == RNT2 - R2 + (CN2+C3(KT))*CX(J) + A*VLN3(KT+1,J+l) - R1 + CN1+CN3+C3(1) + A*VN1(1,2,J) BUY13 == PRl + PR3 - T3(KT) - R2 + (CN2+CN3)*CX(J)+A*VN2(1,1,J+1) BUY23 ■= PR2 + PR3 - T3(KT) - R2 + (CN2+CN4)*CX(J)+A*VN4(1,1,J+1) BUY24 == PR2 + PR4 - T3(KT) - R1 + CN1+CN3+C3(1) + A*VLN3(2,J) CRNT31 = PR3-T3(KT) + RNT1 CRNT32 = PR3-T3(KT) + RNT2 - R2 + (CN2+CN3)*CX(J) + A*VLN3(1,J+l) CB = AMIN1(BUY1,BUY2,BUY13,BUY23,BUY24) CR = AMIN1(CRNT1,CRNT2,CRNT31,CRNT32) VL3(KT,J) = AMIN1(CB,CR) IF (I .LE. MPOL) THEN IF (VL3(KT,J) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J ) .EQ. IF (VL3(KT,J ) .EQ. END IF BUY1) PL3(KT,J,I) = 1 BUY2) PL3(KT,J,I) = 2 BUY13) PL3(KT,J,I) = 3 BUY23) PL3(KT,J,I) = 4 BUY24) PL3(KT,J,I) = 5 CRNT1) PL3(KT,J,I) = 6 CRNT2) PL3(KT,J,I) = 7 CRNT31) PL3(KT,J,I) = 8 CRNT32) PL3(KT,J,I) = 9 IF (I .GE. OB .AND. I .LE. OT .AND. J .EQ. 9) THEN WRITE(4,101) BUY1, BUY2, BUY13, BUY23, BUY24 101 FORMAT('RENTL:',5F9.1) WRITE(4,102) CRNT1, CRNT2, CRNT31, CRNT32, KT, J, I, PL3(KT,J,I) 102 FORMAT('RENTL:',4F9.1,12X, 'PL3(',12,',',11,',',12,') = ',12) END IF END SUBROUTINE DECL4 (KT, J, I, PL4, VL4) INTEGER*! PL4(36,5,36), OB, OT REAL VL4(36,6) COMMON /VALS/ A, R 1 , R 2 , CN1, CN2, CN3, CN4, CX(5), OB, O T , MPOL COMMON /VALS/ PRl, PR2, PR3, PR4, RNT1, RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /OWN4/ C4(40), T4(40), S4(40) BUY2 ~ PR2 - R2 + (CN2+C4(KT))*CX(J) + A*VN4(1,KT+1,J+l) CRNT2 «= RNT2 - R2 + (CN2+C4(KT))*CX(J) + A*VLN4(KT+1,J+l) BUY13 = PRl + PR3 -T4(KT) -R1 + CN1+CN3+C3(1) + A*VN1(1,2,J) BUY23 = PR2 + PR3 - T4(KT) -R2 + (CN2+CN3)*CX(J) +A*VN2(1,1,J+l) BUY24 = PR2 + PR4 -T4(KT) -R2 + (CN2+CN4)*CX(J) +A*VN4(1,1,J+l) CRNT42 ■= PR4-T4(KT) + RNT2 -R2 + (CN2+CN4)*CX(J) + A*VLN4(1,J+l) CB = AMIN1(BUY2,BUY13,BUY23,BUY24) CR = AMIN1(CRNT2,CRNT42) VL4(KT,J) = AMIN1(CB,CR) 269 IF (I .LE. MPOL) THEN IF (VIA(KT,J ) .EQ. BUY2) PL4(KT,J,I) = IF (VIA(KT,J ) .EQ. BUY13) PIA(KT,J,I) IF (VIA(KT,J ) .EQ. BUY23) PIA(KT,J,I) IF (VIA(KT,J ) .EQ. BUY24) PL4(KT,J,I) IF (VIA(KT.J) .EQ. CRNT2) PL4(KT,J,I) IF (VL4(KT,J ) .EQ. CRNT42) PL4(KT,J,I) END IF 1 -2 =3 =4 =5 = 6 IF (I .GE. OB .AND. I .LE. OT .AND. J .EQ. 9) THEN WRITE(4,201) BUY2, BUY13, BUY23, BUY24 201 FORMAT('RENTS,4F9.1) WRITE(4,202) CRNT2, CRNT42, K T , J, I, PL4(KT,J,I) 202 FORMAT('RENTS:',2F9.1,30X,'PL4(',12,',',11,',',12,') = ',12) END IF END SUBROUTINE DECOl (KP, KT, J, I, PI) INTEGER*1 PI(20,36,5,36), OB, OT COMMON /VALS/ A, R 1 , R 2 , CN1, CN2, CN3, CN4, CX(5), OB, O T , MPOL COMMON /VALS/ PRl, PR2, PR3, PR4, RNT1, RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /OWN1/ Cl(20), Tl(20), Sl(20), Vl(20,36,6) COMMON /OWN3/ T3(40), S3(40), RKl, RK2, RK3 REPL1 = PRl - Tl(KP) - R1 + CN1+C3(KT)+C3(KT+1) + A*VNl(1,KT+2,J ) REPL2 = PR2 - Tl(KP) - R2 + (CN2+C3(KT))*CX(J) +A*VN2(1,KT+1,J+l) REPL3 = PR3 - T3(KT) - R1 + C1(KP)+CN3+C3(1) + A*VN1(KP+1,2,J) REPL13 = PR1+PR3-T1(KP)-T3(KT) - R1 + CN1+CN3+C3(1) +A*VN1(1,2,J ) REPL23 = PR2+PR3-T1(KP)-T3(KT) - R2 + (CN2+CN3)*CX(J) + A*VN2(1,1, +J+1) REPL24 = PR2+PR4-T1(KP)-T3(KT) - R2 + (CN2+CN4)*CX(J) + A*VN4(1,1, +J+1) RENT1 = -SI(KP) + RNTl- R1 + CN1+C3(KT)+C3(KT+1) + A*VLN3(KT+2,J ) RENT2 = -SI(KP)+RNT2 - R2 + (CN2+C3(KT))*CX(J) + A*VLN3(KT+1,J+l) RNT13 = -Si(KP)+RNT1+PR3-T3(KT) - R1 + CN1+CN3+C3(1) + A*VLN3(2,J) RNT23 = -Si(KP)+RNT2+PR3-T3(KT) - R2 + (CN2+CN3)*CX(J) + A*VLN3(1, +J+1) RNT24 = -SI(KP)+RNT2+PR4-T3(KT) - R2 + (CN2+CN4)*CX(J) + A*VLN4(1, +J+1) RNT2K = RNT2 - R2 + (CN2+C3(KT))*CX(J) + A*VN1(KP,KT+1,J+l) RT23K = RNT2+PR3-T3(KT) - R2 + (CN2+CN3)*CX(J) + A*VN1(KP,1,J+l) RT2K2 = RKl-R1*0.9-R2*0.1+C1(KP)*0.9+C3(KT)+C3(KT+1)+CN2*CX(J)*0.1 + + (1+(CX(J)-1.0)*0.2)*C3(KT+1) + A*VN1(KP+1,KT+2,J+l) RT2K3 = RK2-R1*0.8-R2*0.2+Cl(KP)*0.8+C3(KT)+C3(KT+l)+CN2*CX(J)*0.2 + + (1+(CX(J)-1.0)*0.4)*C3(KT+1) + A*VN1(KP+1,KT+2,J+l) RT2K4 = RK3-R1*0.6 -R2*0.4+Cl(KP)*0.6+C3(KT)+C3(KT+1)+CN2*CX(J)*0.4 + + (1+(CX(J)-1.0)*0.8)*C3(KT+1) + A*VN1(KP+1,KT+2,J+l) R23K2 = PR3-T3(KT)+RK1-R1*0.9-R2*0.1+C1(KP)*0.9+C3(KT)+C3(KT+1)+ + CN2*CX(J)*0.1+(1+(CX(J)-1.0)*0.2)*C3(KT+1) + A*VN1(KP+1,2,J+l) R23K3 - PR3-T3(KT)+RK2-R1*0.8-R2*0.2+C1(KP)*0.8+C3(KT)+C3(KT+1)+ + CN2*CX(J)*0.2+(1+(CX(J)-1.0)*0.4)*C3(KT+1) + A*VN1(KP+1,2,J+l) R23K4 = PR3-T3(KT)+RK3-R1*0.6-R2*0.4+C1(KP)*0.6+C3(KT)+C3(KT+1)+ + CN2*CX(J)*0.4+(1+(CX(J)-1.0)*0.8)*C3(KT+1) + A*VN1(KP+1,2,J+l) HOLD - -R1 + Cl(KP) + C3(KT)+C3(KT+1) + A*VN1(KP+1,KT+2,J ) 270 CB = AMIN1(REPL1,REPL2,REPL3,REPL13,REPL23,REPL24,HOLD) CR - AMIN1(RENT1,RENT2,RNT13,RNT23,RNT24) CRK « AMINl(RNT2K,RT23K,RT2K2,RT2K3,RT2K4,R23K2,R23K3,R23K4) VI(KP,K T ,J ) = AMIN1(CB,CR,CRK) DRPLl = REPL1 - VI(KP,K T ,J ) DRPL2 = REPL2 - V1(KP,KT,J) DRPL3 = REPL3 - V1(KP,KT,J) DRPLl3 = REPL13 - V1(KP,KT,J) DRPL23 = REPL23 - V1(KP,KT,J) DRPL24 *= REPL24 - V1(KP,KT,J) DRNTl - RENT1 - V1(KP,KT,J) DRNT2 = RENT2 - V1(KP,KT,J) DRNT13 = RNT13 - V1(KP,KT,J) DRNT23 = RNT23 - V1(KP,KT,J) DRNT24 = RNT24 - V1(KP,KT,J) DRNT2K = RNT2K - V1(KP,KT,J) DRT23K = RT23K - V1(KP,KT,J) DRT2K2 = RT2K2 - V1(KP,KT,J) DRT2K3 = RT2K3 - V1(KP,KT,J) DRT2K4 = RT2K4 - V1(KP,KT,J) DR23K2 = R23K2 - V1(KP,KT,J) DR23K3 = R23K3 - V1(KP,KT,J) DR23K4 = R23K4 - V1(KP,KT,J) DHOLD = HOLD - V1(KP,KT,J) IF (I IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF IF END IF LE. MPOL) THEN (VI(KP,KT,J ) EQ. (V1(KP,KT,J) EQ. (VI(KP,K T ,J ) EQ. (V1(KP,KT,J) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,K T ,J ) .EQ. (VI(KP,KT,J ) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,KT,J) EQ. (V1(KP,KT,J) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,KT,J ) EQ. (VI(KP,K T ,J ) EQ. (VI(KP,K T ,J ) EQ. (V1(KP,KT,J) EQ. (VI(KP,K T ,J ) EQ. (V1(KP,KT,J) EQ. (V1(KP,KT,J) EQ. REPL1) REPL2) REPL3) REPL13) REPL23) REPL24) RENT1) RENT2) RNT13) RNT23) RNT24) RNT2K) RT23K) RT2K2) RT2K3) RT2K4) R23K2) R23K3) R23K4) HOLD) P1(KP,KT,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,KT,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,K T ,J PI(KP,KT,J PI(KP,KT,J PI(KP,KT,J PI(KP,K T ,J PI(KP,KT,J PI(KP,K T ,J P1(KP,KT,J PI(KP,KT,J PI(KP,KT,J I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) I) = = = = = = = = = = = = = = = - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 IF (I .GE. OB .AND. I .LE. OT .AND. J .LE. 3) THEN WRITE(4,301) DRPLl, DRPL2, DRPL3, DRPLl3, DRPL23, DRPL24, DRNT1, +DRNT2 WRITE(4,301) DRNT13,DRNT23,DRNT24,DRNT2K,DRT23K,DRT2K2,DRT2K3, +DRT2K4 301 FORMAT('OWN1L:',8F8.2) WRITE(4,302) DR23K2, DR23K3, DR23K4, DHOLD, KP, KT, J, I, +P1(KP, KT, J, I) 271 302 FORMAT('OWN1L:',4F8.2,3X,'Pi(',12,',',12,',',11,',',12,')— ',12) END IF END SUBROUTINE DEC02 (KP, KT, J, I, P2) INTEGER*1 P2(20,36,5,36), OB, OT COMMON /VALS/ A, R 1 , R 2 , CN1, CN2, CN3, CN4, CX(5), OB, OT, MPOL COMMON /VALS/ PRl, PR2, PR3, PR4, RNT1, RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /OWN2/ C2(20), T2(20), S2(20) COMMON /OWN3/ T3(40), S3(40), RKl, RK2, RK3 COMMON /OWN23/ V2(20,36,6) REPL1 =PRl - T2(KP) - R1 +CN1+C3(KT)+C3(KT+1) + A*VN1(1,KT+2,J) REPL2 =PR2 - T2(KP) - R2 + (CN2+C3(KT))*CX(J) +A*VN2(1,KT+1,J+l) REPL3 =PR3 - T3(KT) - R2 + (C2(KP)+CN3)*CX(J) +A*VN2(KP+1,1,J+l) REPL4 =PR4 - T3(KT) - R2 + (C2(KP)+CN4)*CX(J) + A*VN4(KP+1,1,J+l) REPL13 = PR1+PR3-T2(KP)-T3(KT) - R1 + CN1+CN3+C3(1)+ A*VN1(1,2,J) REPL23 = PR2+PR3-T2(KP)-T3(KT) - R2 + (CN2+CN3)*CX(J) +A*VN2(1,1, +J+1) REPL24 = PR2+PR4-T2(KP)-T3(KT) - R2 + (CN2+CN4)*CX(J) + A*VN4(1,1, +J+1) RENT1 = -S2(KP) + RNT1 - R1 + CN1+C3(KT)+C3(KT+1) + A*VLN3(KT+2,J ) RENT2 - -S2(KP)+RNT2 - R2 + (CN2+C3(KT))*CX(J) + A*VLN3(KT+1,J+l) RNT13 = -S2(KP)+RNT1+PR3-T3(KT) - R1 + CN1+CN3+C3(1) + A*VLN3(2,J) RNT23 = -S2(KP)+RNT2+PR3-T3(KT) - R2 + (CN2+CN3)*CX(J) + A*VLN3(1, +J+1) RNT24 = -S2(KP)+RNT2+PR4-T3(KT) - R2 + (CN2+CN4)*CX(J) + A*VLN4(1, +J+1) HOLD = -R2 + (C2(KP)+C3(KT))*CX(J) + A*VN2(KP+1,KT+1,J+l) CB = AMIN1(REPL1,REPL2,REPL3,REPL4,REPL13,REPL23,REPL24,HOLD) CR = AMIN1(RENT1,RENT2,RNT13,RNT23,RNT24) V2(KP,K T ,J ) = AM1N1(CB,CR) IF (I .LE. MPOL) THEN IF (V2(KP,K T ,J ) .EQ. IF (V2(KP,KT,J) .EQ. IF (V2(KP,KT,J) .EQ. IF (V2(KP,K T ,J ) .EQ. IF (V2(KP,K T ,J) .EQ. IF (V2(KP,K T ,J ) .EQ. IF (V2(KP,KT,J) .EQ. IF (V2(KP,K T ,J ) .EQ. IF (V2(KP,K T ,J) .EQ. IF (V2(KP,KT,J) .EQ. IF (V2(KP,K T ,J ) .EQ. IF (V2(KP,KT,J) .EQ. IF (V2(KP,KT,J) .EQ. END IF REPLl) REPL2) REPL3) REPL4) REPLl3) REPL23) REPL24) RENT1) RENT2) RNT13) RNT23) RNT24) HOLD) P2(KP,KT,J ,I) P2(KP,KT,J ,I) P2(KP,KT,J,I) P2(KP,K T ,J ,I) P2(KP,KT,J ,I) P2(KP,K T ,J ,I) P2(KP,KT,J,I) P2(KP,KT,J ,I) P2(KP,K T ,J ,I) P2(KP,KT,J,I) P2(KP,KT,J,I) P2(KP,K T ,J ,I) P2(KP,K T ,J ,I) = = = = = = = = = = = = 1 2 3 4 5 6 7 8 9 10 11 12 13 IF (I .GE. OB .AND. I .LE. OT .AND. J .EQ. 9) THEN WRITE(4,401) REPLl, REPL2, REPL3, REPL4, REPL13, REPL23, REPL24, +RENT1 401 FORMAT('OWN2L:',8F9.1) 272 WRITE(4,402) RENT2, RNT13, RNT23, RNT24, HOLD, KP, KT, J, I, P2(KP +,KT,J ,I) 402 FORMAT('OWN2L:',5F9.1,3X,'P2(',12,',',12,',',11,',',12,')=',12) END IF END SUBROUTINE DEC04 (KP, KT, J, I, P4) INTEGER*1 P4(20,36 ,5,36), OB, OT COMMON /VALS/ A, R 1 , R 2 , CN1, CN2, CN3,CN4,CX(5), OB, OT, MPOL COMMON /VALS/ PRl, PR2, PR3, PR4, RNT1,RNT2, C3(40) COMMON /VALS/ VN1(20,36,6), VN2(20,36,6) COMMON /VALS/ VN4(20,36,6), VLN3(36,6), VLN4(36,6) COMMON /OWN2/ C2(20), T2(20), S2(20) COMMON /OWN4/ C4(40), T4(40), S4(40) COMMON /OWN24/ V4(20,36,6) REPL2 = PR2-T2(KP) - R2 + (CN2+C4(KT))*CX(J) + A*VN4(1,KT+1,J+l) REPL3 = PR3-T4(KT) - R2 + (C2(KP) + CN3)*CX(J) + A*VN2(KP+1,1,J+l) REPL4 = PR4-T4(KT) - R2 + (C2(KP) + CN4)*CX(J) + A*VN4(KP+1,1,J+l) REPLl3 = PR1+PR3-T2(KP)-T4(KT) - R1 + CN1+CN3+C3(1) + A*VN1(1,2,J) REPL23 = PR2+PR3-T2(KP)-T4(KT) - R2 + (CN2+CN3)*CX(J) + A*VN2(1,1, +J+1) REPL24 = PR2+PR4-T2(KP)-T4(KT) - R2 + (CN2+CN4)*CX(J) + A*VN4(1,1, +J+1) RENT 2 -S2(KP)+RNT2 - R2 + (CN2+C4(KT))*CX(J) + A*VLN4(KT+1,J+l) RNT13 -S2(KP)+RNT1+PR3-T4(KT) - R1 + CN1+CN3+C3(1) + A*VLN3(2,J) RNT23 -S2(KP)+RNT2+PR3-T4(KT) - R2 + (CN2+CN3)*CX(J) + A*VLN3(1, +J+1) RNT24 -S2(KP)+RNT2+PR4-T4(KT) - R2 + (CN2+CN4)*CX(J) + A*VLN4(1, +J+1) HOLD = -R2 + (C2(KP) + C4(KT))*CX(J) + A*VN4(KP+1,KT+1,J+l) CB = AMIN1(REPL2,REPL3,REPL4,REPLl3,REPL23,REPL24,HOLD) CR = AMIN1(RENT2,RNT13,RNT23,RNT24) V4(KP,K T ,J ) = AMIN1(CB,CR) IF (I .LE. MPOL) THEN IF (V4(KP,K T ,J ) .EQ. REPL2) P4(KP,KT,J ,I) = 1 IF (V4(KP,KT,J ) .EQ. REPL3) P4(KP,K T ,J ,I) = 2 IF (V4(KP,K T ,J ) .EQ. REPL4) P4(KP,KT,J,I) = 3 IF (V4(KP,K T ,J ) .EQ. REPL13) P4(KP,K T ,J ,I) - 4 IF (V4(KP,K T ,J ) .EQ. REPL23) P4(KP,K T ,J ,I) - 5 IF (V4(KP,KT,J ) .EQ. REPL24) P4(KP,KT,J ,I) = 6 IF (V4(KP,K T ,J ) .EQ. RENT2) P4(KP,K T ,J ,I) = 7 IF (V4(KP,KT,J ) .EQ. RNT13) P4(KP,K T ,J ,I) « 8 IF (V4(KP,KT,J ) .EQ. RNT23) P4(KP,KT,J,I) - 9 IF (V4(KP,K T ,J) .EQ. RNT24) P4(KP,K T ,J ,I) = 10 IF (V4(KP,K T ,J ) .EQ. HOLD) P4(KP,KT,J ,I) - 11 END IF IF (I .GE. OB .AND. I .LE. OT .AND. J .EQ. 9) THEN WRITE(4,501) REPL2, REPL3, REPL4, REPL13, REPL23, REPL24, RENT2 501 FORMAT('OWN2S:',7F9.1) WRITE(4,502) RNT13, RNT23, RNT24, HOLD, KP,KT,J,I, P4(KP,K T ,J ,I) 502 FORMAT('OWN2S:',4F9.1,12X,'P4(',12,',',12,',' ,II,' ,',12,') = ’ 12) END IF END 273 Exerpts from the Output File Replacement with Renting Options 60 16 32 16 0 20 1.2000 1.1400 1.0700 1.0000 .0600 1 150.9000 63.2000 181.6000 63.2000 517.4400 352. 8600 9.2000 15.2000 27.2000 560.2671 595.8664 1 2 202.4880 234.1310 .6820 .4650 203.1760 235.0030 89.4750 107.6800 203.9190 235.9460 80.5280 96.9120 204.6940 236.9280 72.4750 87.2200 205.4920 237.9400 65.2270 78.4980 206.3080 238.9740 58.7050 70.6490 207.1400 240.0280 52.8340 63.5840 207.9840 241.0980 47.5510 57.2250 208.8400 242.1820 42.7960 51.5030 209.7050 243.2800 38.5160 46.3530 210.5800 244.3890 34.6640 41.7170 211.4640 245.5080 31.1980 37.5460 212.3550 246.6380 28.0780 33.7910 213.2530 247.7760 25.2700 30.4120 214.1580 248.9230 22.7430 27.3710 215.0690 250.0780 20.4690 24.6340 215.9860 251.2410 18.4220 22.1700 216.9090 252.4100 16.5800 19.9530 217.8370 253.5860 14.9220 17.9580 218.7700 254.7690 13.4300 16.1620 2.1790 1.4860 338.1260 243.3960 3.6320 2.4770 327.5590 231.1630 5.0840 3.4670 316.9570 218.9850 6.5370 4.4580 306.3430 206.9210 7.9900 5.4490 295.7440 195.0240 9.4420 6.4390 285.1820 183.3430 10.8950 7.4300 274.6800 171.9230 12.3480 8.4200 264.2600 160.8030 13.8010 9.4110 253.9420 150.0200 15.2530 10.4020 243.7450 139.6040 16.7060 11.3920 233.6880 129.5810 18.1590 12.3830 223.7870 119.9700 19.6110 13.3740 214.0590 110.7900 21.0640 14.3640 204.5170 102.0520 22.5170 15.3550 195.1760 93.7640 23.9690 16.3460 186.0460 85.9290 25.4220 17.3360 177.1380 78.5490 26.8750 18.3270 168.4630 71.6200 28.3270 19.3180 160.0280 65.1360 29.7800 20.3080 151.8390 59.0880 31.2330 21.2990 143.9040 53.4650 32.6850 22.2890 136.2260 48.2540 34.1380 23.2800 128.8090 43.4400 35.5910 24.2710 121.6550 39.0070 37.0440 25.2610 114.7660 34.9370 38.4960 26.2520 108.1420 31.2120 39.9490 27.2430 101.7830 27.8130 41.4020 28.2330 95.6880 24.7220 0 274 42.8540 44.3070 45.7600 47.2120 48.6650 50.1180 51.5700 53.0230 54.4760 55.9290 57.3810 58.8340 YEAR 60 YEAR 59 YEAR 58 YEAR 57 YEAR 56 YEAR 3 YEAR 2 OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: OWN1L:: 29.2240 30.2150 31.2050 32.1960 33.1870 34.1770 35.1680 36.1590 37.1490 38.1400 39.1300 40.1210 65.66 241.18 165.50 66.83 242.35 165.50 67.70 243.22 165.50 68.31 243.83 165.50 89.8540 84.2780 78.9570 73.8860 69.0620 64.4780 60.1290 56.0080 52.1100 48.4270 44.9530 41.6790 21.15 226.27 175.87 22.31 227.43 175.79 23.19 228.31 175. 23.80 228.92 175.64 21.9180 19.3820 17.0960 15.0420 13.2000 11.5550 10.0890 8.7860 7.6330 6.6130 5.7160 4.9270 174 .73 228,.13 185. 59 27. 83 76,.94 68 .50 63 .38 225. 91 00 10,.36 196 .59 12,.72 PK 1, l,l! 2) = 14 174 .47 229,.30 186. 76 78..11 29. 00 69 .67 63,.40 225. 93 00 10,.29 196 .37 12,.79 Pl< 2, l.li 2) = 14 174 .32 230 .17 187. 63 29 .87 78,.99 70 .55 63,.33 225. 86 00 10,.21 196. 14 12 .87 PI 3, '1,1, 2) ==14 174 .28 230 .78 188. 24 30. 48 79,.60 71 .16 63 .18 225. 71 00 10,.13 195 .90 12,.95 PK 4, 1,1, 2)=14 OPT. POLICY STARTING WITH A16 YR. OLD PLANTER OF TYPE 1 AND LARGE TRACTOR IS: YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR YEAR IN YEAR 1 PLANTER 1 OWNING: 13 2 PLANTER 2 OWNING: 24 3 PLANTER 3 OWNING: 24 4 PLANTER 4 OWNING: 24 5 PLANTER 5 OWNING: 24 6 PLANTER 6 OWNING: 24 7 PLANTER 7 OWNING: 24 8 PLANTER 8 OWNING: 24 AGE:16 POLICY AGE: 1 POLICY AGE: 2 POLICY AGE: 3 POLICY AGE: 4 POLICY AGE: 5 POLICY AGE: 6 POLICY AGE: 7 POLICY TRACTOR AGE:20 J: 1 6 REPLACE W/ SMALL TCTR, PLTR 2. TRACTOR AGE: 1 J: 2 11 KEEP BOTH MACHINES TRACTOR AGE: 2 J: 3 11 KEEP BOTH MACHINES TRACTOR AGE: 3 J: 4 11 KEEP BOTH MACHINES TRACTOR AGE: 4 J: 4 11 KEEP BOTH MACHINES TRACTOR AGE: 5 J: 4 11 KEEP BOTH MACHINES TRACTOR AGE: 6 J: 4 11 KEEP BOTH MACHINES TRACTOR AGE: 7 J: 4 11 KEEP BOTH MACHINES 61.,82 31,,09 62.,99 30.,87 63,,86 30,,63 64,.48 30,.40 Appendix H FORTRAN CODE FOR THE STOCHASTIC DYNAMIC PROGRAMMING MODEL This Appendix contains the FORTRAN code for the stochastic dynamic programming model that is used to determine optimal adoption strategies for the expected utility-maximizing farmer. Most of the variable names are the same as for the deterministic model, and are listed in Appendix G. Additional variable names are listed below. As in Appendix G, the statements or the parts of statements that do not conform to the FORTRAN 77 standard are shown in bold print. The listed code is for the version of the model that does not include options to rent the no-till planter on a limited acreage. The version that does include these options calculates their value functions in a manner that is similar to what is listed in Appendix G. The listed code also is for the version of the model that maximizes expected utility with the relative risk aversion coefficient equal to 1.0. The version of the model that is based on a relative risk aversion coefficient equal to 0.5 is identical, except that the "ALOG" function is replaced by "2.0*SQRT" in value function calculations. Description of Additional Variable Names (in order of appearance) AV RAV VC1 VC2 JL PP Risk aversion coefficient. This is no longer used. Log and square root functions are used instead of the CRRA utility function with exponent (1-AV). Equals (1-AV). No longer used for the reason above. Variable costs (Subtotal 1 in Table 4.10) on 600 acres for conventional tillage. Variable costs (Subtotal 1 in Table 4.10) on 600 acres for no-till. Counter variable used for price state (previous year). Markovian price probabilities for current year's price state, based on previous year's price state. 276 JP JC JW YC JA R IP1 WP JN Counter variable used for current year's price state. Counter variable for crop. Corn = 1, Soybeans = 2. Counter variable for weather (and its effect on yield). Yield for each weather, technology, and crop combination. Counter variable used for technology option. Conventional tillage = 1, No-till = 2. Gross revenue for each weather, technology, and crop price combination. Optimal policy in year 1 (replaces PI in determ, model). Probability weights for each combination of crop price and weather. Counter variable used for next year's price state. The Program for the Stochastic Model C C C C DP Stochastic Replacement Problem, including 2 planters, 2 tractors, renting, and experience with the 2nd planter. This problem maximizes a CPRRA utility function with risk aversion parameter equal to 1. c ' k ' k ' k ' k ‘k ‘k ' k ‘k ' k ' k ' k ' k ' k ' k ' k ' k ' k ' k ' k ‘k ‘k ‘k ‘k ’k ' k ' k ' k ' k ' k - k ‘k ' k ‘1 k & ' k ' k ‘k ' k ' k ' k ' k ‘k ' k ' k - k ‘k i k ' k ' k ‘k ' k ' k ‘k ' k ' k ' k ‘k ' k ' k ‘k - f r ' k ' k - & ' k ‘i $STORAGE:2 PROGRAM STORPLN CHARACTER*78 TITLE CHARACTERS2 POLICY INTEGERS N, M P , MT, IAGE1, IAGE2, IAGE3, IAGE4, KX REAL PRl, PR2, PR3, PR4, RNT1, RNT2, CN1, CN2, CN3, CN4 REAL VL3(34,5,7), VL4(34,5,7), PC(2,7), YC(33,2,2) COMMON /REV/ PRl, PR2, PR3, PR4, RNTl, RNT2, R(7,33,2) COMMON /REV/ CN1, CN2, CN3, CN4, CX(4), C3(40), VC1, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VN1(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18,34,5,7), VLN3(34,5,7), VLN4(34,5,7) COMMON /0WN1/ Cl(20), Tl(20), Sl(20), VI(18,34,5,7), IP1(7) COMMON /OWN2/ C2(2Q), T2(20), S2(20) COMMON /OWN3/ T3(40), S3(40) COMMON /0WN4/ C4(40), T4(40), S4(40) COMMON /OWN23/ V2(18,34,5,7) COMMON /0WN24/ V4(18,34,5,7) 20 22 25 30 OPEN (UNIT = 2, FILE = 'ST0RP2.DAT') OPEN (UNIT = 4, FILE = 'STORPLN.OUT') READ(2,20) TITLE FORMAT (78A) WRITE(4,22) TITLE FORMAT(78A/) READ(2,25) N, MP, MT, IAGE1, IAGE2, IAGE3, IAGE4 WRITE(4,25) N, MP, MT, IAGE1, IAGE2, IAGE3, IAGE4 FORMAT(719) READ(2,30) CX(1), CX(2), CX(3), CX(4), DF, AV, KX WRITE(4,30) CX(1), CX(2), CX(3), CX(4), DF, AV, KX FORMAT(6F9.4,19) Ill 35 READ(2,35) PRl, RNT1, PR2, RNT2, PR3, PR4 WRITE(4,35) PRl, RNT1, PR2, RNT2, PR3, PR4 FORMAT(6F9.2) KPI = IAGE1 IF (IAGE2 .GT. IAGEl) KPI = IAGE2 KTI = IAGE3 IF (IAGE4 .GT. IAGE3) KTI = IAGE4 NP1 = N+l MPP1 = MP+1 MTP2 = MT+2 A = 1 . 0 / (1.0+ DF) RAV = 1.0 - AV C *** READ VARIABLE COST BASE (VCi) FOR MB PLOW AND NO-TILL READ(2,40) VCI, VC2 WRITE(4,40) VCI, VC2 40 FORMAT(2F9.2) C *** READ COSTS AND TRADE-IN VALUES FOR PLANTERS AND TRACTORS READ(2,50) CN1, CN2, CN3, CN4 WRITE(4,50) CN1, CN2, CN3, CN4 DO 45 K=1,19 READ(2,50) Cl(K), C2(K), T1(K), T2(K) SI(K) = T1(K) S2(K) = T2(K) 45 WRITE(4,50) C1(K), C2(K), T1(K), T2(K) 50 FORMAT(4F9.1) DO 60 K=1,40 READ(2,65) C3(K), C4(K), T3(K), T4(K) S3(K) = T3(K) S4(K) = T4(K) 60 WRITE(4,65) C3(K), C4(K), T3(K), T4(K) 65 FORMAT(4F9.1) C *** READ PRICE STATE PROBABILITIES DO 67 JL=1,7 READ(2,75) (PP(JL,JP), JP=1,7) WRITE(4,75) (PP(JL,JP), JP=1,7) 67 CONTINUE C *** READ CORN AND SOYBEAN PRICES FOR EACH PRICE STATE DO 72 JC=1,2 READ(2,75) (PC(JC,JP), JP=1,7) WRITE(4,75) (PC(JC,JP), JP=1,7) 72 CONTINUE 75 FORMAT(7F9.2) C *** READ CROP YIELDS FOR FALL PLOWING AND NO-TILL C *** THE 33 OUTCOMES REPRESENT 1953-78, 1984-90. DO 77 JC=1,2 DO 77 JW=1,33 READ(2,79) (YC(JW,JA,JC), JA=1,2) WRITE(4,79) (YC(JW,JA,JC), JA=1,2) 77 CONTINUE 79 FORMAT(2F9.2) CLOSE (2) 278 CALL GETTIM (IHR.IMIN .ISEC .1100™) WRITE(4,'(3X, 12.2, 1H:, 12.2, 1H:, 12.2)') IHR, IMIN, ISEC C *** SET PENALTIES TO LIMIT AGES OF PLANTERS AND TRACTORS DO 15 K=MPP1,20 Cl(K) = 30000. C2(K) = 30000. SI(K) = 1. S2(K) = 1. T1(K) = 1. 15 T2(K) - 1. DO 16 K=MTP2,40 C3(K) = 30000. C4(K) = 30000. S3(K) = 1. S4(K) - 1. T3(K) = 1. 16 T4(K) = 1. o C *** SET REVENUES FOR PRICE, YIELD, AND TECH. COMBINATIONS DO 18 JP=1,7 DO 18 JW=1,33 DO 18 JA=1,2 R(JP,J W ,JA)=PC(1,JP)*YC(J W ,J A ,1)*400.0 + + PC(2,JP)*YC(JW,JA,2)*200.0 + 90000 18 CONTINUE n o SET TERMINAL PERIOD VALUE FUNCTIONS IF (KPI + MP .GT. 16) THEN MPPI = 16 ELSE MPPI = MPPI END IF IF (KTI + MT .GT. 32) THEN MTPI = 32 ELSE MTPI = MTP2 END IF 2 = ALOG(S1(KP)+S3(KT)) - ALOG(S2(KP)+S3(KT)) - ALOG(S2(KP)+S4(KT)) ALOG(S3(KT)) AL0G(S4(KT)) BACKWARDS RECURSIVE CALCULATION OF THE VALUE FUNCTION AND POLICIES o n o 3 DO 3 JP=1,7 DO 3 J=1,5 DO 3 KT=1,MTPI DO 2 KP=1,MPPI VN1(KP,KT,J ,JP) VN2(KP,K T ,J ,JP) VN4(K P ,K T ,J ,JP) VLN3(KT,J ,JP) = VLN4(KT,J,JP) = CONTINUE DO 8 II = 1,N 279 88 6 605 I = N - II + 1 IM1 - N - II JM1 - IM1 * 2 IF (IM1 .GT. MPPI) IM1 = MPPI IF (JM1 .GT. MTP2) JM1 = MTP2 IHI = IM1 + KPI JHI = JM1 + KTI IF (IHI .GT. MPPI) IHI = MPPI IF (JHI .GT. MTP2) JHI =■ MTP2 WRITE(*,88) I FORMAT(' YEAR ',12) DO 6 JL=1,7 DO 6 J=1,4 WRITE(*,605) JL, J DO 6 KT=1,JHI CALL DECL3(KT, J, JL, VL3) CALL DECL4(KT, J, JL, VL4) DO 6 KP = 1,IHI CALL DECOl(KP, KT, J, JL, I) CALL DEC02(KP, KT, J, JL) CALL DEC04(KP, KT, J, JL) CONTINUE FORMAT(4X, JL=',13,3X,'J=',13) C *** RESET THE NEXT PERIOD VALUE FUNCTIONS DO 36 JL=1,7 DO 36 KT=1,JHI DO 38 J=1,4 VLN3(KT,J ,JL) VL3(KT,J ,JL) 38 VLN4(KT,J ,JL) VL4(KT,J ,JL) VLN3(KT,5,JL) VL3(KT,4,JL) VLN4(KT,5,JL) VL4(KT,4,JL) DO 36 KP=1,IHI DO 39 J=1,4 VN1(KP,KT,J ,JL) V1(KP,KT,J,JL) VN2(KP,K T ,J ,JL) V2(KP,K T ,J ,JL) 39 VN4(KP,K T ,J ,JL) V4(KP,K T ,J ,JL) VNI(KP,K T ,5,JL) V1(KP,KT,4,JL) VN2(KP,KT,5,JL) V2(KP,K T ,4,JL) VN4(KP,KT,5,JL) V4(KP,K T ,4,JL) 36 CONTINUE o n o 8 CONTINUE ■ A ************* REPORT THE OPTIMAL POLICIES FOR EACH PRICE STATE IN YEAR 1 KP = KPI KT = KTI WRITE(4,90) KP, KT 90 FORMAT( ' OPT. POLICIES FOR A ',12,' YEAR OLD PLANTER AND A ',12, +' YEAR OLD TRACTOR ARE:',/) DO 10 JL=1,7 IF (IPl(JL) .EQ. 1) THEN 280 POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPI(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = ELSE IF (IPl(JL) POLICY = END IF WRITE(4,95) IPl(JL), POLICY FORMAT(' POLICY:— ',12,3X,A32) WRITE(4,98) V1(KP,KT,KX,JL) FORMAT(' EXPECTED UTILITY VALUE: '.E20.10) 95 98 10 'REPLACE PLANTER 1' .EQ. 2) THEN 'REPLACE W/ PLANTER 2' .EQ. 3) THEN 'REPLACE LARGE TRACTOR' .EQ. 4) THEN 'REPLACE BOTH MACHINES' .EQ. 5) THEN 'REPLACE W/ LARGE TCTR, PLTR 2.' .EQ. 6) THEN 'REPLACE W/ SMALL TCTR, PLTR 2.' .EQ. 7) THEN 'RENT PLANTER 1' .EQ. 8) THEN 'RENT PLANTER 2' .EQ. 9) THEN 'REPLACE L. TCTR., RENT PLTR. 1' .EQ. 10) THEN 'REPLACE L. TCTR., RENT PLTR. 2' .EQ. 11) THEN 'RPLCE W/SMALL TCTR. RENT PLTR 2 .EQ. 12) THEN 'RENT PLANTER 1, KEEP PLANTER 2' .EQ. 13) THEN 'RPLCE TCTR, RNT PLTR 2, KEEP 1' .EQ. 14) THEN 'KEEP BOTH MACHINES' CONTINUE CALL GETTIM(IHR,IMIN,ISEC,I100TH) WRITE(4,'(3X, 12.2, 1H:, 12.2, 1H:, 12.2)') IHR, IMIN, ISEC CLOSE (4) 2000 END SUBROUTINE DECL3 (KT, J, JL, VL3) REAL VL3(34,5,7), WP(7) COMMON /REV/ PRl, PR2, PR3, PR4, RNT1, RNT2, R(7,33,2) COMMON /REV/ CN1, CN2, CN3, CN4, CX(4), C3(40), VCI, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VN1(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18,34,5,7), VLN3(34,5,7), VLN4(34,5,7) COMMON /OWN3/ T3(40), S3(40) C *** CALCULATION OF CONSTANT VALUES FOR EACH ALTERNATIVE BY1B = PRl + CN1 + C3(KT) + C3(KT+1) + VCI 281 BY2B CRIB CR2B B13B B23B B24B C31B C32B = = = = = = = = PR2 + (CN2 + C3(KT))*CX(J) + VC2 RNT1 + CN1 + C3(KT) + C3(KT+1) + VCI RNT2 + (CN2 + C3(KT))*CX(J) + VC2 PRl + PR3 - T3(KT) + CN1 + CN3 + C3(l) + VCI PR2 + PR3 - T3(KT) + (CN2 + CN3)*CX(J) + VC2 PR2 + PR4 - T3(KT) + (CN2 + CN4)*CX(J) + VC2 PR3 - T3(KT) + RNT1 + CNl + CN3 + C3(l) + VCI PR3 - T3(KT) + RNT2 + (CN2 + CN3)*CX(J) + VC2 BY1 = 0 . 0 BY2 = 0.0 CR1 = 0.0 CR2 = 0.0 BY13 = 0 . 0 BY23 = 0 . 0 BY24 = 0 . 0 CR31 = 0 . 0 CR32 = 0 . 0 C *** DETERMINE PROBABILITY WEIGHTS DO 160 JP=1,7 WP(JP) = PP(JL,JP)/33.0 160 DO 130 JP=1,7 IF (WP(JP) .GT. 0.0) THEN DO 120 JW=1,33 BY1 = BY1+WP(JP)*AL0G(R(JP,JW,1)-BY1B) CRl = CR1+WP(JP)*AL0G(R(JP,JW,1)-CRIB) BY13 = BY13+WP(JP)*AL0G(R(JP,JW,1)-BY1B) CR31 = CR31+WP(JP)*ALOG(R(JP,JW,l)-C31B) BY2 = BY2+WP(JP)*ALOG(R(JP,JW,2)-BY2B) CR2 = CR2+WP(JP)*ALOG(R(JP,JW,2)-CR2B) BY23 = BY23+WP(JP)*ALOG(R(JP,JW,2)-B23B) BY24 = BY24+WP(JP)*ALOG(R(JP,JW,2)-B23B) CR32 = CR32+WP(JP)*ALOG(R(JP,JW,2)-C32B) 130 CONTINUE END IF CONTINUE 140 DO 140 JP-1,7 DO 140 JN = 1,7 BY1 = BY1 + CRl = CRl + BY1.3 - BY13 CR31 = CR31 BY2 = BY2 + CR2 = CR2 + BY23 = BY23 BY24 = BY24 CR32 = CR32 CONTINUE 120 A*VN1(1,KT+2,J,JP)*PP(JP,JN)*PP(JL,JP) A*VLN3(KT+2,J,JP)*PP(JP,JN)*PP(JL,JP) + A*VN1(1,2,J,JP)*PP(JP,JN)*PP(JL,JP) + A*VLN3(2,J,JP)*PP(JP,JN)*PP(JL,JP) A*VN2(1,KT+1,J+l,JP)*PP(JP,JN)*PP(JL,JP) A*VLN3(KT+1,J+1,JP)*PP(JP,JN)*PP(JL,JP) + A*VN2(1,1,J+l,JP)*PP(JP,JN)*PP(JL,JP) + A*VN4(1,1,J+l,JP)*PP(JP,JN)*PP(JL,JP) + A*VLN3(1,J+l,JP)*PP(JP,JN)*PP(JL,JP) 282 CB = AMAX1(BY1,BY2,BY13,BY23,BY24) CR = AMAX1(CRl,CR2,CR31,CR3 2) VL3(KT,J ,JL) = AMAX1(CB,CR) END SUBROUTINE DECL4 (KT, J, JL, VL4) REAL VL4(34,5,7), WP(7) COMMON /REV/ PRl, PR2, PR3, PR4, RNT1, RNT2, R(7,33,2) COMMON /REV/ CN1, CN2, CN3, CN4, CX(4), C3(40), VCI, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VN1(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18,34,5,7), VLN3(34,5,7), VLN4(34,5,7) COMMON /0WN4/ C4(40), T4(40), S4(40) C *** CALCULATION OF CONSTANT VALUES FOR EACH ALTERNATIVE BY2B CR2B B13B B23B B24B C42B = PR2 + (CN2 + C4(KT))*CX(J) + VC2 = RNT2 + (CN2 + C4(KT))*CX(J) + VC2 = PRl + PR3 - T4(KT) + CN1 + CN3 + C3(l) + VCI = PR2 + PR3 - T4(KT) + (CN2 + CN3)*CX(J) + VC2 = PR2 + PR4 - T4(KT) + (CN2 + CN4)*CX(J) + VC2 = PR3 -T4(KT) + RNT2+ (CN2 + CN4)*CX(J) + VC2 BY2 = 0.0 CR2 = 0.0 BY13 = 0 . 0 BY23 = 0 . 0 BY24 = 0 . 0 CR42 = 0 . 0 C *** DETERMINE PROBABILITY WEIGHTS DO 260 JP=1,7 260 WP(JP) = PP(JL,JP)/33.0 DO 230 JP=1,7 IF (WP(JP) .GT. 0.0) THEN DO 220 JW=1,33 BY13 = BY13+WP (JP)*AL0G(R(JP ,JW ,1)-B13B) BY2 = BY2+WP(JP)*ALOG(R(JP,J W ,2)-BY2B) CR2 = CR2+WP(JP)*ALOG(R(JP,JW,2)-CR2B) BY23 = BY23+WP(JP)*ALOG(R(JP,JW,2)-B23B) BY24 = BY24+WP(JP)*AL0G(R(JP,JW,2)-B24B) CR42 = CR42+WP(JP)*ALOG(R(JP,J W ,2)-C42B) 220 230 CONTINUE END IF CONTINUE DO 240 JP=1,7 DO 240 JN=1,7 BY13 = BY13 + A*VN1(1,2,J,JN)*PP(JP,JN)*PP(JL,JP) BY2 = BY2 + A*VN4(1,KT+1,J+l,JN)*PP(JP,JN)*PP(JL,JP) 283 240 CR2 = CR2 + BY23 = BY23 BY24 = BY24 CR42 = CR42 CONTINUE A*VLN4(KT+1,J+l,JN)*PP(JP,JN)*PP(JL,JP) + A*VN2(1,1,J+l,JN)*PP(JP,JN)*PP(JL,JP) + A*VN4(1,1,J+l,JN)*PP(JP,JN)*PP(JL,JP) + A*VLN4(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) VL4(KT,J,JL) = AMAX1(BY2,BY13,BY23,BY24,CR2,CR42) END SUBROUTINE DECOl (KP, K T , J, JL, I) REAL WP(7) COMMON /REV/ PRl, PR2, PR3, PR4, RNT1, RNT2, R(7,33,2) COMMON /REV/ CN1, CN2, CN3, CN4, CX(4), C3(40), VCI, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VN1(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18,34,5,7), VLN3(34,5,7), VLN4(34,5,7) COMMON /OWN1/ Cl(20), Tl(20), Sl(20), V I (18,34,5,7), IP1(7) COMMON /OWN3/ T3(40), S3(40) C *** CALCULATION OF CONSTANT VALUES FOR EACH ALTERNATIVE RP1B = PRl -Tl(KP) + CN1 + C3(KT) + C3(KT+1) + VCI RP2B = PR2 -Tl(KP) + (CN2 + C3(KT))*CX(J) + VC2 RP3B = PR3 - T3(KT) + Cl(KP) + CN3 + C3(l) + VCI RP13B = PRl + PR3 - Tl(KP) -T3(KT) + CN1 + CN3 + C3(l) + VCI RP23B = PR2 + PR3 -Tl(KP) -T3(KT) + (CN2 + CN3)*CX(J) + VC2 RP24B = PR2 + PR4 -Tl(KP) -T3(KT) + (CN2 + CN4)*CX(J) + VC2 RTlB = -Sl(KP) + RNT1 +CN1 + C3(KT) + C3(KT+1) + VCI RT2B = -SI(KP) + RNT2 + (CN2 + C3(KT))*CX(J) + VC2 R13B = -SI(KP) - T3(KT) + PR3 + RNT1 + CN1 + CN3 + C3(l) + VCI R23B = -SI(KP) - T3(KT) + PR3 + RNT2 + (CN2 + CN3)*CX(J) + VC2 R24B = -SI(KP) - T3(KT) + PR4 + RNT2 + (CN2 + CN4)*CX(J) + VC2 R2KB = RNT2 + (CN2 + C3(KT))*CX(J) + VC2 R23KB = RNT2 + PR3 - T3(KT) + (CN2 + CN3)*CX(J) + VC2 HOLDB = Cl(KP) + C3(KT) + C3(KT+1) + VCI RP1 = 0 . 0 RP2 = 0.0 RP3 = 0 . 0 RP13 = 0 . 0 RP23 = 0 . 0 RP24 = 0 . 0 RTl = 0 . 0 RT2 = 0 . 0 RTl3 = 0 . 0 RT23 = 0 . 0 RT24 = 0 . 0 RT2K = 0 . 0 RT23K = 0 . 0 HOLD = 0 . 0 C *** DETERMINE PROBABILITY WEIGHTS DO 360 JP=1,7 360 WP(JP) = PP(JL,JP)/33.0 284 DO 330 JP=1,7 IF (WP(JP) .GT. 0.0) THEN DO 320 JW=1,33 RP1 = RP1+WP(JP)*AL0G(R(JP,JW,1)-RP1B) RP3 = RP3+WP(JP)+ALOG(R(JP,J W ,1)-RP3B) RP13 = RP13+WP(JP)*ALOG(R(JP,JW,1)-RP13B) RTl = RT1+WP(JP)*AL0G(R(JP,JW,1)-RT1B) RT13 = RT13+WP(JP)*ALOG(R(JP,J W ,1)-R13B) HOLD = HOLD+WP(JP)*ALOG(R(JP,J W ,1)-HOLDB) RP2 = RP2+WP(JP)+ALOG(R(JP,J W ,2)-RP2B) RP23 = RP23+WP(JP)*ALOG(R(JP,JW,2)-RP23B) RP24 = RP24+WP(JP)*ALOG(R(JP,JW,2)-RP24B) RT2 = RT2+WP(JP)*ALOG(R(JP,JW,2)-RT2B) RT23 = RT23+WP(JP)*ALOG(R(JP,JW,2)-R23B) RT24 = RT24+WP(JP)*ALOG(R(JP,JW,2)-R24B) RT2K = RT2K+WP(JP)*ALOG(R(JP,J W ,2)-R2KB) RT23K = RT23K+WP(JP)+ALOG(R(JP,J W ,2)-R23KB) 320 330 CONTINUE END IF CONTINUE 340 DO 340 JP=1,7 DO 340 JN=1,7 RP1 = RP1 + A*VN1(1,KT+2,J,JN)*PP(JP,JN)*PP(JL,JP) RP3 = RP3 + A*VN1(KP+1,2,J,JN)*PP(JP,JN)*PP(JL,JP) RP13 = RP13 + A*VN1(1,2,J,JN)*PP(JP,JN)*PP(JL,JP) RTl = RTl + A*VLN3(KT+2,J,JN)*PP(JP,JN)*PP(JL,JP) RT13 = RTl3 + A*VLN3(2,J,JN)*PP(JP,JN)*PP(JL,JP) HOLD = HOLD + A*VN1(KP+1,KT+2,J,JN)*PP(JP,JN)*PP(JL, JP) RP2 = RP2 + A*VN2(1,KT+1,J+l,JN)*FP(JP,JN)*PP(JL,JP) RP23 = RP23 + A*VN2(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RP24 = RP24 + A*VN4(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RT2 = RT2 + A*VLN3(KT+1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RT23 = RT23 + A*VLN3(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) RT24 = RT24 + A*VLN4(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) RT2K = RT2K + A*VN1(KP,KT+1,J+l,JN)*PP(JP,JN)*PP(JL, JP) RT23K *= RT23K + A*VN1(KP,1,J+l,JN)*PP(JP,JN)*PP(JL,JP) CONTINUE CB ■= AMAX1(RP1,RP2,RP3,RP13,RP23,RP24,H0LD) CR = AMAX1(RTl,RT2,RT13,RT23,RT24,RT2K,RT23K) VI(KP,K T ,J ,JL) = AMAX1(CB,CR) 365 IF (KP .EQ. 1 .AND. KT .EQ. 2) THEN WRITE(*,365) RP2, RP24, RT2, HOLD END IF FORMAT(4(2X,E12.7)) IF (I .EQ. 1 .AND. J .EQ. 1) THEN IF (VI(KP,K T ,J ,JL) .EQ. RP1) IPl(JL) = 1 IF (VI(KP,K T ,J ,JL) .EQ. RP2) IPl(JL) = 2 285 IF IF IF IF IF IF IF IF IF IF IF IF (VI(KP,K T ,J ,JL) .EQ. RP3) IPl(JL) = 3 (V1(KP,KT,J,JL) .EQ. RP13) IPl(JL) = 4 (V1(KP,KT,J,JL) .EQ. RP23) IPl(JL) = 5 (VI(KP,K T ,J ,JL) .EQ. RP24) IPl(JL) = 6 (V1(KP,KT,J ,JL) .EQ. RTl) IPl(JL) = 7 (VI(KP,K T ,J ,JL) .EQ. RT2) IPl(JL) = 8 (V1(KP,KT,J,JL) .EQ. RT13) IPl(JL) - 9 (V1(KP,KT,J,JL) .EQ. RT23) IPl(JL) = 10 (V1(KP,KT,J,JL) .EQ. RT24) IPl(JL) = 11 (V1(KP,KT,J,JL) .EQ. RT2K) IPl(JL) = 12 (V1(KP,KT,J,JL) .EQ. RT23K) IPl(JL) = 13 (V1(KP,KT,J,JL) .EQ. HOLD) IPl(JL) = 14 DRPLl = VI(KP,K T ,J ,JL) - RP1 DRPL2 = VI(KP,K T ,J ,JL) - RP2 DRPL3 = V1(KP,KT,J,JL) - RP3 DRPL13 = V1(KP,KT,J,JL) - RP13 DRPL23 = V1(KP,KT,J,JL) - RP23 DRPL24 = V1(KP,KT,J,JL) - RP24 DRNT1 = VI(KP,K T ,J ,JL) - RTl DRNT2 = VI(KP,KT,J ,JL) - RT2 DRNT13 = VI(KP,K T ,J ,JL) - RTl3 DRNT23 = VI(KP,K T ,J ,JL) - RT23 DRNT24 = VI(KP,K T ,J ,JL) - RT24 DRNT2K = VI(KP,K T ,J ,JL) - RT2K DRT23K = VI(KP,KT,J ,JL) - RT23K DHOLD = VI(KP,K T ,J ,JL) - HOLD WRITE(4,301) DRPLl, DRPL2, DRPL3, DRPLl3, DRPL23, DRPL24 301 FORMAT(' ',6F11.5) WRITE(4,302) DRNT1, DRNT2, DRNT13, DRNT23, DRNT24 302 FORMAT(' ',5F11.5) WRITE(4,303) DRNT2K, DRT23K, DHOLD, VI(KP,K T ,J ,JL), K P , KT, + JL, IPl(JL) 303 FORMAT(' ',4F11.5,414) END IF END SUBROUTINE DEC02 (KP, KT, J, JL) REAL WP(7) COMMON /REV/ PRl, PR2, PR3, PR4, RNT1, RNT2,R(7,33,2) COMMON /REV/ CNl, CN2, CN3, CN4, CX(4), C3(40), VCI, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VN1(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18,34,5,7), VLN3(34,5,7), VLN4(34,5,7) COMMON /OWN2/ C2(20), T2(20), S2(20) COMMON /OWN3/ T3(40), S3(40) COMMON /OWN23/ V2(18,34,5,7) C *** CALCULATION OF CONSTANT VALUES FOR EACH ALTERNATIVE RP1B = RP2B RP3B = PRl - T2(KP) + CNl + C3(KT) + C3(KT+1) + VCI PR2 - T2(KP) + (CN2 + C3(KT))*CX(J) + VC2 PR3 - T3(KT) + (C2(KP) + CN3)*CX(J) + VC2 286 RP4B - PR3 - T3(KT) + (C2(KP) + CN4)*CX(J) + VC2 RP13B = PR1 + PR3 -T2(KP) - T3(KT) + CN1 + CN3 + C3(l) + VC1 RP23B = PR2 + PR3 -T2(KP) - T3(KT) + (CN2 + CN3)*CX(J) + VC2 RP24B = PR2 + PR4 -T2(KP) - T3(KT) + (CN2 + CN4)*CX(J) + VC2 RT1B = -S2(KP)+ RNT1 + CN1 +C3(KT)+C3(KT+1) + VC1 RT2B = -S2(KP)+ RNT2 + (CN2 + C3(KT))*CX(J) + VC2 R13B = -S2(KP) -T3(KT) + PR3 + RNT1 + CN1 + CN3 + C3(l) + VC1 R23B = -S2(KP) -T3(KT) + PR3 + RNT2 + (CN2 + CN3)*CX(J) + VC2 R24B = -S2(KP) -T3(KT) + PR4 + RNT2 + (CN2 + CN4)*CX(J) + VC2 HOLDB = (C2(KP) + C3(KT))*CX(J) + VC2 RP1 = 0.0 RP2 = 0.0 RP3 = 0.0 RP4 = 0.0 RP13 - 0. 0 RP23 = 0. 0 RP24 = 0. 0 RT1 = 0.0 RT2 - 0.0 RT13 = 0. 0 RT23 = 0. 0 RT24 = 0. 0 HOLD = 0. 0 C 460 DETERMINE PROBABILITY WEIGHTS DO 460 JP=1,7 WP(JP) = PP(JL,JP)/33.0 DO 430 JP=1,7 IF (WP(JP) .GT. 0.0) THEN DO 420 JW=1,33 RP1 = RP1+WP(JP)*AL0G(R(JP,JW,1)-RP1B) RP13 = RP13+WP(JP)*ALOG(R(JP,JW,l)-RP13B) RT1 = RT1+WP(JP)*AL0G(R(JP,JW,1)-RT1B) RT13 = RT13+WP(JP)*ALOG(R(JP,JW,1)-R13B) RP2 = RP2+WP(JP)*ALOG(R(JP,JW,2)-RP2B) RP3 = RP3+WP(JP)*AL0G(R(JP,JW,2)-RP3B) RP4 = RP4+WP(JP)*AL0G(R(JP,JW,2)-RP4B) RP23 = RP23+WP(JP)*ALOG(R(JP,JW,2)-RP23B) RP24 = RP24+WP(JP)*ALOG(R(JP,JW,2)-RP24B) RT2 = RT2+WP(JP)*ALOG(R(JP,JW,2)-RT2B) RT23 = RT23+WP(JP)*ALOG(R(JP,JW,2)-R23B) RT24 = RT24+WP(JP)*AL0G(R(JP,JW,2)-R24B) HOLD = HOLD+WP(JP)*ALOG(R(JP,JW,2)-HOLDB) 420 430 CONTINUE END IF CONTINUE DO 440 JP=1,7 DO 440 JN=1,7 287 440 RP1 = RP1 + A*VNl(l,KT+2,J,JN)*PP(JP,JN)*PP(JL,JP) RP13 = RP13 + A*VN1(1,2,J,JN)*PP(JP,JN)*PP(JL,JP) RT1 = RT1 + A*VLN3(KT+2,J ,JN)*PP(JP,JN)*FP(JL,JP) RT13 = RT13 + A*VLN3(2,J,JN)*PP(JP,JN)*PP(JL,JP) RP2 = RP2 + A*VN2(1,KT+1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RP3 = RP3 + A*VN2(KP+1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RP4 = RP4 + A*VN4(KP+1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RP23 = RP23 + A*VN2(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RP24 = RP24 + A*VN4(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RT2 = RT2 + A*VLN3(KT+1,J+1,JN)*PP(JP,JN)*PP(JL,JP) RT23 = RT23 + A*VLN3(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) RT24 = RT24 + A*VLN4(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) HOLD = HOLD + A*VN2(KP+1,KT+1,J+l,JN)*PP(JP,JN)*PP(JL,JP) CONTINUE CB = AMAX1(RP1,RP2,RP3,RP4,RP13,RP23,RP24,HOLD) CR = AMAX1(RT1,RT2,RT13,RT23,RT24) V2(KP,KT,J,JL) = AMAX1(CB,CR) END SUBROUTINE DEC04 (KP, KT, J, JL) REAL UP(7) COMMON /REV/ PR1, PR2, PR3, PR4, RNT1, RNT2, R(7,33,2) COMMON /REV/ CN1, CN2, CN3, CN4, CX(4), C3(40), VC1, VC2 COMMON /VALS/ A, PP(7,7) COMMON /VALS/ VNl(18,34,5,7), VN2(18,34,5,7) COMMON /VALS/ VN4(18 ,34,5,7), VLN3(34,3,7), VLN4(34,5,7) COMMON /OWN2/ C2(20), T2(20), S2(20) COMMON /0WN4/ C4(40), T4(40), S4(40) COMMON /OWN24/ V4(18,34,5,7) C *** CALCULATION OF CONSTANT VALUES FOR EACH ALTERNATIVE RP2B = PR2 - T2(KP) + (CN2 + C4(KT))*CX(J) + VC2 RP3B = PR3 - T4(KT) + (C2(KP) + CN3)*CX(J) + VC2 RP4B = PR3 - T4(KT) + (C2(KP) + CN4)*CX(J) + VC2 RP13B = PR1 + PR3 - T2(KP) - T4(KT) + CN1 + CN3 + C3(l) + RP23B = PR2 + PR3 - T2(KP) - T4(KT) + (CN2 + CN3)*CX(J) + RP24B = PR2 + PR4 - T2(KP) - T4(KT) + (CN2 + CN4)*CX(J) + RT2B = -S2(KP)+ RNT2 + (CN2+ C4(KT))*CX(J) + VC2 R13B = -S2(KP) -T4(KT) + PR3 + RNT1 + CN1 + CN3 + C3(l) R23B = -S2(KP) -T4(KT) + PR3 + RNT2 + (CN2 + CN3)*CX(J) R24B = -S2(KP) -T4(KT) + PR4 + RNT2 + (CN2 + CN4)*CX(J) HOLDB = (C2(KP) + C4(KT))*CX(J) + VC2 RP2 = 0.0 RP3 = 0.0 RP4 = 0 . 0 RP13 = 0 . 0 RP23 = 0 . 0 RP24 = 0 . 0 RT2 = 0.0 RT13 = 0 . 0 RT23 = 0 . 0 VC1 VC2 VC2 + VC1 + VC2 + VC2 288 RT24 = 0 . 0 HOLD = 0 . 0 C *** DETERMINE PROBABILITY WEIGHTS DO 560 JP=1,7 560 WP(JP) = PP(JL,JP)/33.0 DO 530 JP=1,7 IF (WP(JP) .GT. 0.0) THEN DO 520 JW=1,33 RP13 = RP13+WP(JP)*ALOG(R(JP,JW,l)-RP13B) RT13 = RT13+WP(JP)*ALOG(R(JP,JW,1)-R13B) RP2 = RP2+WP(JP)*ALOG(R(JP,JW,2)-RP2B) RP3 = RP3+WP(JP)*ALOG(R(JP,JW,2)-RP3B) RP4 = RP4+WP(JP)*ALOG(R(JP,JW,2)-RP4B) RP23 = RP23+WP(JP)+ALOG(R(JP,J W ,2)-RP23B) RP24 = RP24+WP(JP)*ALOG(R(JP,J W ,2)-RP24B) RT2 = RT2+WP(JP)*ALOG(R(JP,J W ,2)-RT2B) RT23 = RT23+WP(JP)*ALOG(R(JP,JW,2)-R23B) RT24 = RT24+WP(JP)*ALOG(R(JP,JW,2)-R24B) HOLD = HOLD+WP(JP)*ALOG(R(JP,JW,2)-HOLDB) 520 530 CONTINUE END IF CONTINUE 540 DO 540 JP=1,7 DO 540 JN=1,7 RP13 = RP13 RT13 = RT13 RP2 = RP2 + RP3 = RP3 + RP4 = RP4 + RP23 = RP23 RP24 = RP24 RT2 = RT2 + RT23 = RT23 RT24 = RT24 HOLD = HOLD CONTINUE + A*VN1(1,2,J,JN)*PP(JP,JN)*PP(JL,JP) + A*VLN3(2,J,JN)*PP(JP,JN)*PP(JL,JP) A*VN4(1,KT+1,J+l,JN)*PP(JP,JN)*PP(JL,JP) A*VN2(KP+1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) A*VN4(KP+1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) + A*VN2(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) + A*VN4(1,1,J+1,JN)*PP(JP,JN)*PP(JL,JP) A*VLN4(KT+1,J+1,JN)*PP(JP,JN)*PP(JL,JP) + A*VLN3(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) + A*VLN4(1,J+l,JN)*PP(JP,JN)*PP(JL,JP) + A*VN4(KP+1,KT+1,J+l,JN)*PP(JP,JN)*PP(JL,JP) CB = AMAX1(RP2,RP3,RP4,RP13,RP23,RP24,HOLD) CR = AMAX1(RT2,RT13,RT23,RT24) V4(KP,KT,J,JL) = AMAX1(CB,CR) END 289 Exerpts from the Output File Stochastic Replacement Analysis, RAV = 1.0 30 16 32 17 0 24 1.2000 1.1400 1.0700 1.0000 .0600 .5000 15090.00 6320.00 18160.00 6320.00 51744.00 35286.00 58682.82 57014.16 20248.8 23413.1 68.2 46.5 20317.6 23500.3 8947.5 10768.0 20391.9 23594.6 8052.8 9691.2 20469.4 23692.8 7247.5 8722.0 20549.2 23794.0 7849.8 6522.7 20630.8 23897.4 5870.5 7064.9 20714.0 24002.8 5283.4 6358.4 20798.4 24109.8 4755.1 5722.5 20884.0 24218.2 4279 .6 5150.3 20970.5 24328.0 3851.6 4635.3 21058.0 24438.9 3466.4 4171.7 4576.0 4721.2 4866.5 5011.8 5157.0 5302.3 5447.6 5592.9 5738.1 5883.4 .70 .10 .22 .08 .18 .15 .00 2.18 5.63 112.81 63.33 103.82 117.84 142.07 154.23 134.43 99.81 101.49 62.26 128.13 103.33 49.48 3120.5 3219.6 3318.7 3417.7 3516.8 3615.9 3714.9 3814.0 3913.0 4012.1 .10 .23 .18 .20 .10 .00 .00 2.18 6.65 114.38 68.09 106.15 112.83 131.69 160.39 131.94 101.54 105.11 61.75 134.61 107.43 51.17 7895.7 7388.6 6906.2 6447.8 S012.9 5600.8 5211.0 4842.7 4495.3 4167.9 .08 .22 .40 .10 .00 .15 .00 2.62 5.63 1709.6 1504.2 1320.0 1155.5 1008.9 878.6 763.3 661.3 571.6 492.7 .12 .15 .20 .40 .15 .15 .05 2.62 6.65 .00 .15 .00 .07 .20 .15 .05 2.62 10.08 .00 .00 .00 .07 .20 .15 .20 3.59 6.65 0 1 00 15 00 08 17 25 70 59 08 290 84 .69 48 .82 138 .13 162 .91 165 .41 76 .29 97 .10 55 .84 55 .26 106 .63 62 .86 139 .74 82 .59 69 .86 174 .96 213 .96 102 .68 77 .61 161 .96 178 .46 27 .63 16 .58 33 .55 48 .00 29 .70 43 .45 57 .38 36 .43 47 .90 21 .28 42 .25 28,.95 23,.13 20,.95 19..78 30..00 32..70 38. 85 17. 43 39. 03 17. 03 25. 45 38. 08 15. 98 40. 70 25. 90 28. 73 42. 55 58. 95 47. 95 50. 83 45. 73 41. 45 14:16:36 81 .29 49 .21 128 .57 162 .86 159 .36 79 .91 99 .35 57 .74 54 .03 111 .51 58 .24 149 .98 86 .11 81 .63 167 .00 201 .54 106 .16 76 .91 162 .16 177 .78 28 .88 19 .03 35 .88 49 .65 29 .88 44 .28 59 .75 36 .33 49..40 24 .93 43,.38 32..08 21..08 22.,43 20. 33 29. 98 37. 93 42. 08 19. 83 40. 78 17. 85 22. 00 38. 35 17. 98 41. 15 24. 53 29. 35 43. 70 59. 70 50. 58 52. 73 46. 85 40. 95 291 04005 07915 03424 04077 07935 03447 04155 07965 03479 04225 07993 03514 04266 07994 03519 04301 07993 .00055 .06804 .18510 .00177 .06847 .18530 .00301 .06897 .18568 .00412 .06944 .18588 .00490 .06963 .18573 .00562 .06978 .13387 .20961 .00000 .13373 .21095 .00000 .13370 .21230 .00000 .13385 .21353 .00000 .13391 .21442 .00000 .13408 .21523 .18292 .20485 176.73590 .18503 .20654 176.72950 .18709 .20821 176.72380 .18896 .20975 176.71870 .19044 .21089 176.71380 .19177 .21193 1 2 3 4 5 .15677 .10754 1 1 .15967 .10805 1 1 .16245 .10863 1 1 .16501 .10915 1 1 .16710 .10939 1 1 .16901 .10960 .07709 14 .07840 14 .07971 14 .08092 14 .08179 14 .08255 OPT. POLICIES FOR A 17 YEAR OLD PLANTER AND A 24 YEAR OLD TRACTOR ARE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: POLICY: 8 RENT PLANTER EXPECTED UTILITY VALUE: 07:22:11 2 .1764877000E+03 2 .1769176000E+03 2 .1766433000E+03 2 .1769064000E+03 2 .1770494000E+03 2 .1770789000E+03 2 .1775914000E+03 Appendix I MODIFICATIONS TO THE FORTRAN CODE FOR CERES-MAIZE This Appendix contains the modifications to the FORTRAN source code for CERES-MAIZE, Ver. 2.1s that account for the effects of surface crop residues on corn growth and yield. Chapter 4 and Appendix C explain why these changes were made. Appendix C also indicates which modifications were contributed by Frederic Dadoun1. Changes in the Main Program The only change made to the main program for CERES-MAIZE was to insert a call statement for the new MULCHE subroutine. This occurs directly after daily weather data are read and before subroutine SOLT is called to estimate soil temperatures. Also, the call statement for the SOLT subroutine is no longer conditional on whether the option to calculate nitrogen balances is selected. Hence the statement: IF (ISWNIT .NE. 0) CALL SOLT is replaced by: call mulche call solt Changes in Subroutine IPNIT After subroutine IPNIT reads crop residue data from input file, FILE4, the following code is added: c**** This portion allows you to partition the residues c If depth is 0-1 all residues are at the surface c If depth is greater than or equal to 20 (MB plow+secondary tillage) 1 Ph.D candidate, Crop and Soils Department, Michigan State University. 293 c c If c c If c all residues are incorporated depth is less than 20 (Chisel plow+secondary tillage) 30 % of residue cover = 7% of biomass stays at thesurface, depth is less than 10 (Disk plow) 70 % of residue cover = 33% of biomass stays at the surface. if (sdep .le. 1.) then imulch = straw straw = 0.0 elseif (sdep .le. 10) then imulch = 0 . 7 * straw straw = straw - imulch elseif (sdep .It. 20) then imulch = 0.3 * straw straw = straw - imulch else imulch = 0 . 0 endif Two small changes are made in the section that checks to see whether crop residue data are within the proper range. These are preceded by comment lines with a small "c". The statement "GOTO 350" terminates consideration of crop residues and moves to the section of the IPNIT subroutine that reads fertilizer application data. C *** 300 While any parameter has negative value do : ******** IF (STRAW .GT. 0. .AND. SDEP .GE. 0. .AND. & SCN .GT. 0. .AND. ROOT .GT. 0) GOTO 350 c ***One line is added to read data for mulch ********** if (straw ,eq. 0. .and. sdep .eq. 0.) goto 350 WRITE(*,1100) FILE4 READ (5,'(Al)') ANS IF (ANS .EQ. 'E' .OR. ANS .EQ. 'e') THEN CALL MENU4 ELSE IF (ANS .EQ. 'D' .OR. ANS .EQ. 'd') THEN IF (STRAW .LE. 0.) THEN STRAW = 800. ENDIF c *** The next statement is changed from .LE. to .Lt. IF (SDEP .Lt. 0.) THEN SDEP = 30. ENDIF 294 Changes to Subroutine POTEV The calculation of albedo and potential soil evaporation were changed in subroutine POTEV. Changes are printed in small letters. SUBROUTINE POTEV(EOS) Real*4 mulchalb,Ec,Em,mulchcov,cancov TD = 0.60*TEMPMX+0.40*TEMPMN c c c Coverage of the soil mulchcov=l-exp(-.32*mulch/1000) cancov=l-exp(-.75*lai) c c calculation of albedo c mulchalb = 0.3 IF (ISTAGE .LE. 6) THEN IF (ISTAGE .GE. 5) THEN ALBEDO=0.23+(LAI-4)**2/160 ELSE albedo=cancov*0.23+mulchcov*(l-cancov)*mulchalb+ & (l-mulchcov)*(l-cancov)*salb END IF ELSE albedo=(1-mulchcov)*salb+mulchcov*mulchalb END IF c c calculation of potential soil evaporation c EEQ = S0LRAD*(4.88E-3 - 4.37E-3*ALBEDO)*(TD+29.0) IF ((TEMPMX .GE. 5.0) .AND. (TEMPMX .LE. 35.0)) THEN EO = EEQ*1.1 ELSE IF (TEMPMX .GT. 35.0) THEN EO = EEQ*((TEMPMX-35.0)*0.05+1.1) ELSE EO = EEQ*0.01*EXP(0.18*(TEMPMX+20.0)) ENDIF c c Reducing factor due to canopy c IF (LAI .LE. 1.0) THEN Ec = (1.-0.43*LAI) ELSE Ec = EXP(-0.4*LAI)/l.1 ENDIF c c Reducing factor due to mulch c Em = exp(-0.22*mulch/1000) 295 c c c Real soil evaporation Eos = Ec*Em*Eo RETURN END Changes to Subroutine NTRANS After the NTRANS subroutine partitions fertilizer applications to various soil layers and calculates urea hydrolysis, the following code is added to bring in organic matter from decomposed crop residue: c **** fertilization due to mulch ************************************** c when water infiltrates, all the decomposed mulch goes in the first c pool of fresh organic matter in the first layer if (MFERTI .gt. 0.0) then fpool(l,l) = fpool(l.l) + mferti mferti = 0.0 endif Changes to Subroutine SOLT The calculation of the moving average temperature in the first (top) soil layer was changed and statements for writing soil temperature to an output file were added to subroutine SOLT. Changes are printed in small letters. SUBROUTINE SOLT real*4 mulchcov if (doy .eq. isim) then open (12,file='solt.out',status='unknown') SUMSTT = 0 write (12,120) 120 format (' DOY TEMPM TMA(l) STG ST(1) + SUMSTT MULCHCOV') endif XI = DOY ST(2) ST(3) 296 ALX = (XI - HDAY) * 0.0174 ATOT = ATOT - TMA(5) DO 100 K = 5,2, -1 TMA(K) = TMA(K-l) 100 CONTINUE mulchcov = 1 - exp(-3.5e-4*mulch) TMA(l) = (1.-ALBEDO-0.42*MULCHCOV) * (TEMPM + (TEMPMX-TEMPM) * & SQRT(SOLRAD * .02)) + (ALBEDO+O.38*MULCHCOV) * TMA(l) ATOT = ATOT + TMA(l) AW = PESW IF (AW .LE. 0.0) AW = 0.01 WC = AW / (WW * DEPMAX *10.) F = EXP(B * ((1. - WC) / (1. + WC)) ** 2) DD = F * DP TA =TAV + AMP * COS(ALX) / 2. DT = ATOT / 5. -TA DO 200 L = 1, NLAYR ZD = -Z(L) / DD ST(L) = TAV + (AMP/2. * COS(ALX-f-ZD) + DT) * EXP(ZD) 200 CONTINUE zdg = -2. / dd stg = tav +(amp/2. * cos(alx + zdg) + dt) * exp(zdg) stt = st(l) - 8 if (stt .le. 0.0) stt *=0.0 sumstt = sumstt + stt write (12,220) doy,tempm,tma(l),stg,st(1),st(2),st(3),sumstt, + mulchcov 220 format (2x,i3,6(2x,f6.2),2x,f8.2,2x,f6.2) RETURN END Changes to Subroutine PHENOL The following changes were made in the calculation of daily thermal time in subroutine PHENOL. c * * * Modifications for Surface Mulch Effects Start Here c STT = soil temperature degree days for early stages c DTT = value used to calculate phenological stages if (istage .le. 2 .or. istage .ge. 7) then STT = ST(1) - TBASE 297 endif if (stt. lt. 0.0) stt = 0.0 c *** Returning to original code c ***** More Changes for Surface Mulch Effects if (istage .gt. 7) dtt = 0.5*dtt + 0.5*stt if (istage .It. 3) dtt = 0.7*dtt + 0.3*stt c ***** End of Changes for Surface Mulch Effects Addition of Subroutine MULCHE Subroutine MULCHE was developed by Frederic Dadoun and added to CERES-MAIZE. This subroutine was modified to incorporate surface crop residues during crop operations. SUBROUTINE MULCHE C C C C C C ********** MULCH PARAMETERS ROUTINE ************************* Created by: F. Dadoun, Called by: MAIN April 1990 $Include:'maizl.blk' $Include:'maiz3.blk' $Include:'maiz4.blk' $Include:'resi.blk' $Include:'ntrcl.blk' REAL*4 td,tedecf,uppermo,lowermo,enterseptmo,wadecf,pmulch REAL*4 MDECOMP 5 C C C open (13,file='mulch.out',status='unknown') IF (DOY.EQ.ISIM) THEN write (13,5) format (' DOY TD RAIN MULCH MDECOMP MFERTI') MULCH = IMULCH ENDIF TEMPERATURE FACTOR FOR DECOMPOSITION TD = 0.60*TEMPMX + 0.40*TEMPMN IF ((TD .GE. 0.) .AND. (TD .LE. 60.)) THEN IF (TD .GT. 35.) TEDECF=2.4-.04*TD IF ((TD.GE.20.) .AND. (TD.LE.35.)) TEDECF=1.0 TEDECF=0.05*TD ELSE 298 o o o TEDECF=0.0 ENDIF MOISTURE FACTOR FOR DECOMPOSITION UPPERMO=LL(1)+0.3*(DUL(1)-LL(1)) LOWERMO=LL(1)/2.0 SLOPEMO=l.0/(UPPERMO-LOWERMO) ENTERSEPTMO=-SLOPEMO*LOWERMO IF ((SW(1).GE.LOWERMO) .AND. (SW(1).LT.UPPERMO)) THEN WADECF=SW(1)*SLOPEMO+ENTERSEPTMO ELSE IF (SW(1) .LT. LOWERMO) WADECF=0.0 IF (SW(1) .GT. UPPERMO) WADECF=1.0 ENDIF C C C MULCH DECOMPOSITION PMULCH=MULCH MULCH=MULCH*EXP(-.009*AMIN1(TEDECF,WADECF)) IF (MULCH.LT.1.) MULCH=0.0 C C C MULCH FERTILISATION IF (PRECIP .EQ. 0.0) THEN MDECOMP = MDECOMP + PMULCH - MULCH MFERTI = 0 . 0 ELSE C assume that rain is at the begining of the day MFERTI = MDECOMP MDECOMP = PMULCH - MULCH ENDIF C C INCORPORATE 10% OF SURFACE RESIDUES WHEN PLANTING if (doy .eq. isow) then mulch = mulch * 0.9 mferti = mferti + 0.1 * pmulch endif INCORPORATE 10% MORE SURFACE RESIDUES WITH NH3 SIDEDRESS APPLICATION do 125 j=l,nfert if (doy .eq. fday(j) .and. iftype(j) .eq. 4) then mulch = mulch * 0.9 mferti = mferti + 0.1 * pmulch endif 125 continue 130 WRITE(13,130) DOY,T D ,precip,MULCH,MDECOMP,mferti FORMAT(13,2x,f5.2,2x,f5.1,3(2x,f6 .1)) RETURN END 299 Changes to Subroutine GROSUB The GROSUB subroutine was only modified by changing the radiation use efficiency parameter from 5.0 to 3.9 in the calculation of the PCARB variable. The modified calculation is: PCARB = 3.9 * PAR / PLANTS * (1. - AMAX1(Y1,Y2)) Changes to Subroutine ROOTGR The calculation of a root length density factor was changed in the ROOTGR subroutine by adding a soil temperature factor and making it an argument of the AMIN1 function. c ****** Addition of Low Temperature Factor for Root Growth RTLTF = SIN(1.57 * (ST(L) - 8.) / (26. - 8.)) RLDF(L) = AMIN1(SWDF,RNFAC,RTLTF)*WR(L)*DLAYR(L) c ****** end of changes RESI.BLK for CERES-MAIZE The following block was included in the modified CERES-MAIZE subroutines to pass residue information between them. c ****** RESI.BLK used for CERES-MAIZE ****** c common block for the information about residues c real imulch,mferti,mulch common/resi/imulch,mferti,mulch,mulchcov Appendix J MODIFICATIONS TO THE FORTRAN CODE FOR SOYGRO This Appendix contains the modifications to the FORTRAN source code for SOYGRO, Ver. 5.42 that account for the effects of surface crop residues on soybean growth and yield. Chapter 4 and Appendix C explain why these changes were made. Changes in Subroutine IPCROP Subroutine IPCROP reads a long file of crop parameters, named CROPPARM.SBO. Surface residue weights were added at the end of the CROPPARM.SBO file and a statement was added to the end of subroutine IPCROP to read these data. The added statement is: READ (10,*) (RESIDU(II) ,II = 1,5). Changes in Subroutine IPSOIL Code from the CERES-MAIZE subroutine SOILNI which initializes soil temperature calculations was inserted in SOYGRO subroutine IPSOIL. The soil temperature initialization was inserted immediately following the calculation of runoff from precipitation. C C The inserted code follows: INITIALIZE SOIL TEMPERATURE INFORMATION ABD = TBD / (FLOAT(NLAYR)) FST = ABD / (ABD + 686. * EXP(- 5.63*ABD)) DP = 1000. + 2500. * FST WW = .356 - .144 * ABD B = ALOG(500. / DP) ALBEDO = SALB SUMSTT = 0 IF (TAV .LE. 0.) TAV = 20. IF (AMP .LE. 0.) AMP = 10. 301 Changes In Subroutine WATBAL Three major changes are made to subroutine WATBAL. First, a CALL statement to subroutine MULCHS is inserted between the calculation of soil water contents after drainage and the calculation of potential soil evaporation. Second, the calculation of potential soil evaporation was modified to account for the effect of surface residue. Finally, in the calculation of root length, a soil temperature factor was added to the calculation of the root length density factor, RLDF(L), for each soil layer, L. The CALL statement for subroutine MULCHS and the modified potential evaporation routine follow: C MAJOR CHANGES FOR TILLAGE SYSTEM EFFECTS START HERE C Subroutine MULCHS determines mulch decomposition, mulch C cover, and soil temperature. C..................... -............................................. CALL MULCHS ........ -....................................... C c c ********* POTENTIAL EVAPORATION ROUTINE *********** C C................................... -............................... TD = 0.60*TMAX+0.4Q*TMIN MULCHCOV = 1-EXP(-.32*RESDU/1000) CANCOV = 1-EXP(-.7 5*XHLAI) MULCHALB = 0 . 3 IF (XHLAI .LE. 0.0001) THEN ALBEDO = (1-MULCHCOV)*SALB + MULCHCOV*MULCHALB ELSE ALBEDO = CANCOV*0.23 + MULCHCOV*(1-CANCOV)*MULCHALB + + (1-MULCHCOV)*(1-CANCOV)*SALB END IF C Calculation of potential soil evaporation EEQ = SLANG*(2.04E-4-1.83E-4*ALBEDO)*(TD+29.) EO = EEQ*1.1 IF (TMAX .GT. 34.) EO = EEQ*((TMAX-34.)*0.05+1.1) IF (TMAX .LT. 5.0) EO = EEQ*0.01*EXP(0.18*(TMAX+20.)) C Reducing factor due to canopy IF (XHLAI .LE. 1.0) THEN 302 EC = (1.-0.43*XHLAI) ELSE EC = EXP(- 0.4*XHLAI)/l.1 END IF C Reducing factor due to mulch EM = EXP(-0.22*RESDU/1000) C Real soil evaporation EOS = EC * EM * EO C *** End of First Section of Changes for Surface Mulch Effects The changes to the root length density calculation are: c *** More Changes for Surface Mulch Effects * * * * * * * * * * * c old version RLDF(L) = SWDF*WR(L)*DLAYR(L) rltfac = sin(1.57 * (st(l) - tphmin) / (toptl - tphmin)) rldf(L) = aminl(swdf,rltfac)*wr(L)*dlayr(L) c **** End of Changes for Surface Mulch Effects * * * * * * * * Changes to Subroutine GPHEN The calculation of thermal time for the vegetative growth stages (less than or equal to NVEG1) was changed to a weighted average of thermal time based on air temperature and thermal time based on soil temperature. Variable DTT is thermal time based on air temperature, and already was calculated in Version 5.42. After DTT is calculated and before the cumulative sums of physiological days and photoperiod accumulator are calculated, the following code was inserted: c * * * * * changes to Introduce Soil Temperature Effects Start Here ***** if (n .le. nvegl) then stt = st(l) - tphmin dtt = 0.7*dtt + 0.3*stt dtx = dtt / (toptl-tphmin) endif c ****** Changes for Soil Temperature Effects End Here *************** 303 Changes to Subroutine CROP Additional code to initialize soil temperature was added to subroutine CROP after the initialization of variables for a new run and before the WATBAL subroutine is called. Also, the treatment dimension was removed from the RESIDU(NTRT) variable. The modified code follows: c *** Modifications for Surface Mulch Effects Start Here ***** C *** Determine Residue amount for the Treatment Selected **** resdu = residu(ntrt) C *** Initialize soil temperature routine from SOILNI in CERES-MAIZE IF (XLAT .LT. 0.) THEN HDAY = 20. ELSE HDAY =200. ENDIF 80 90 TEMPM = (TMAX + TMIN) / 2.0 DO 80 I = 1,5 TMA(I) = TEMPM CONTINUE DO 90 L = 1,15 ST(L) = TEMPM CONTINUE ATOT = TMA(l) * 5 *** End of Modifications for Surface Mulch Effects **** Changes to Subroutine PHOTO Two changes were made to subroutine PHOTO. First, the temperature factor used to calculate the effect of temperature on the photosynthesis rate was changed to a weighted average of air and soil temperature during vegetative growth stages. This variable is called TDAY. Second, the calculation of the temperature effect was given a cubic functional form, as is explained in Appendix C. The modified code follows: 304 c **** Change for soil temperature effect ***** if (n .le. nvegl) tday = 0.7*tday + 0.3*st(l) c ***** end of change for soil temperature effect ***** TDAYSQ = TDAYCU = TPHFAC = IF (TDAY TDAY*TDAY TDAYSQ*TDAY (XPHOT(1)*TDAY+XPHOT(2)*TDAYSQ+XPHOT(3)*TDAYCU)/YPHOTH .LE. 7.) TPHFAC = 0 . 0 c **** End of Changes to PHOTO **** Changes to Subroutine VEGGR Subroutine VEGGR also was modified to consider the effect of soil temperature on root growth. This modification occurs in the calculation of variable RFAC2. C ...................................................................... C CALCULATE ROOT DEPTH RATE OF INCREASE, CM/DEGREE DAY (RFAC2) C ...................... -..... RFAC2 = TABEX(YRTFAC,XRTFAC.VSTAGE,4) c ***** Modification for Soil Temperature Effect *************** rltfac = sin(l.57*(st(l)-tphmin)/(toptl-tphmin)) rfac2 = rfac2 * rltfac c ***** End of Soil Temperature Effect Changes ***************** Addition of Subroutine MULCHS The MULCHE subroutine used in CERES-MAIZE was modified for use in SOYGRO by adding soil temperature calculations and writing to a soil temperature output file. $STORAGE:2 SUBROUTINE MULCHS C C C ********** MULCH PARAMETERS ROUTINE ************************* 305 C Created by: F. Dadoun C April 1990 C C Called by: WATBAL C $Include: 'COMGRO.DAT' $Include: 'COMSOI.DAT' $Include: 'resi.blk' C Modified for SOYGRO by Mark Krause March 1992 REAL*4 td,tedecf,uppermo,lowermo,enterseptmo,wadecf,mulchcov TEMPERATURE FACTOR FOR DECOMPOSITION TD = 0.60*TMAX + 0.40*TMIN IF ((TD .GE. 0.) .AND. (TD .LE. 60.)) THEN IF (TD .GT. 35.) TEDECF=2.4-.04*TD IF ((TD.GE.20.) .AND. (TD.LE.35.)) TEDECF=1.0 TEDECF=0.05*TD ELSE TEDECF=0.0 ENDIF C C C MOISTURE FACTOR FOR DECOMPOSITION UPPERMO=LL(1)+0.3*(DUL(1)-LL(1)) LOWERMO=LL(1)/2.0 SLOPEMO=l.0/(UPPERMO-LOWERMO) ENTERSEPTMO=-SLOPEMO*LOWERMO IF ((SW(1).GE.LOWERMO) .AND. (SW(1).LT.UPPERMO)) THEN WADECF=SW(1)*SLOPEMO+ENTERSEPTMO ELSE IF (SW(1) .LT. LOWERMO) WADECF=0.0 IF (SW(1) .GT. UPPERMO) WADECF=1.0 ENDIF C C C MULCH DECOMPOSITION RESDU=RESDU*EXP(-,009*AMIN1(TEDECF,WADECF)) IF (RESDU.LT.l.) RESDU=0.0 IF (JUL .EQ. IPLT) RESDU = RESDU * 0.9 C PART OF SUBROUTINE SOLT IN CERES-MAIZE C AS MODIFIED BY DADOUN AND KRAUSE C C *** Subroutine to calculate daily average soil temperature at the C center of each soil layer. C C Changed 20 Aug 1990, F. Dadoun Modified March 1992, M. Krause C TEMPM = (TMAX + TMIN) / 2.0 XI = JUL ALX = (XI - HDAY) * 0.0174 ATOT = ATOT - TMA(5) 306 DO 300 K » 5,2,-1 TMA(K) = TMA(K-l) 300 CONTINUE mulchcov = 1 - exp(-3.5e-4*RESDU) TMA(l) = (1.-ALBEDO-0.42*MULCHCOV) * (TEMPM + (TMAX-TEMPM) * SQRT(SRAD * .02)) + (ALBEDO+O.38*MULCHCOV) * TMA(l) & ATOT = ATOT + TMA(l) AW = PESW IF (AW .LE. 0.0) AW = 0.01 WC = AW / (WW * DEPMAX * 10.) FST = EXP(B * ((1. - WC) / (1. + WC)) ** 2) DD = FST * DP TA = TAV + AMP * COS(ALX) / 2. 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