I‘v- ‘ It... N's/“f" Ti; "1' :9 t I I'. .' “5"!" LI II ’ g I ”I'm .flfim ’ 'AIIYF-I.‘ 3""..nv'v‘ru'1j‘wfl %; 1553‘ “5:? III.”- I,“ 'U' (I I V - . Lhr' ‘ Ir;1:}.‘f." ,I. ‘2'“? a - g. L " . ‘l , {LI I a" 'Zj-s} ‘L‘. \ I 3. "at .U . Hg: ‘;.’;‘:I 1Q." ‘13 \ {I}, .U 1-3 I rp-J- : . i9 ’ ‘4; III-II] '\ ’ iIIpI‘IQ“ N‘ .- "‘ . Lfiafl I ‘1 ‘ ‘— -.,_,‘I. II HI I‘D. «7-,; I“ , I; - I; * IIIIIII‘II .“ t, ‘3 u .295 .. l OI I v A . I It .'_’JI ,. .__‘l I i r L1,! "VIfiV \71‘4' {A}? a» :J'qu- .1?!“ :I 3:4" ‘ Inf; I : ,u. 'I m:- ‘T v-l ‘ .‘4 J ‘3’ : III a . .IUI:'1L‘1‘I Hahlutfiv "I' “9'5" ’:.I‘|"..'|N 1\ ll; ‘7' 'I _ '2'“. ‘ 5‘ _ t - 7‘ . V‘ ., ,- A A ‘ .' 'I V o . -‘ - ‘ ‘ ‘ . I O. ‘ " 5 - I ‘. I ‘ ‘ . ‘ ‘I ‘ I I . . 'I‘ "ILI I‘ {MN .I. NF. "' ‘l . . .‘ ‘ ' ‘ ‘, I‘ ' " I A“ "h‘ IH ' ' - ‘ - I ‘I " I “.I' I. .010. I " ”Y .‘.II'...'I ., ‘ - . I . , I ‘ H II II I - 0-» I. I I, 1 ‘ - I" ‘V , I I ‘ . I ' “fl" ‘ ‘ . V » . .l' 4 'I 1“. I J. ~ . I I . I I I I. II I I f I . I I . \ .II r? . I _, A .< ~ I I I I . .. ‘ . II I I .I .. I , , . I ' I I I I I I l I I ,III.,[| I II [I _ In I I. . ‘II II IIIgI‘ ‘ I.I‘I i .I‘v.'..;.' I w I ‘II I.) .'I ~, 'II " I ‘ .~ I I": I ‘,‘ I I‘ II'I MI -| “HIV U "I. '1 I . I I . I , II“. III . VI" “II a . ' " I I. . l I‘ I. ' " II I ‘ ‘ ‘ I 1“. | ‘ II |' I‘ II I I - III’I 'I III-‘FI‘I’ I ‘ 'I I” ‘ l| ' I ' I‘ I I I . . H '1 . I' ‘I. " 'II ‘I I"; MR“... II III. IIIIII' I I ‘ I ‘ V ‘ I I‘m" I 4 ."E‘.:I’&" I. II’hh "'h. Ij'inl‘ WWW! WWWWWWI 31300998 8787 _n. .-_._— I h LIBRA R Y ' Michigan Stats University 9,3 This is to certify that the thesis entitled AN ECONOMIC ANALYSIS OF ALTERNATIVE SAGINAN VALLEY CROP ROTATIONS--AN APPLICATION OF STOCHASTIC DOMINANCE THEORY presented by Roger L. Hoskin has been accepted towards fulfillment of the requirements for Ph.D. degree in Agricultural Economics : I zajor professor Date Feb. 25, 1981 0-7639 \ 915M FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: 3;“, Place in book return to remove «JV V a charge from circulation records l \\\ (I! .-\i\\‘ . 1"} U 0 W95 ' Jti‘ :3 4 aIK‘JV] AN ECONOMIC ANALYSIS OF ALTERNATIVE SAGINAW VALLEY CROP ROTATIONS--AN APPLICATION OF STOCHASTIC DOMINANCE THEORY By Roger L. Hoskin A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 198l ii (9 Copyright by ROGER L. HOSKIN 1981 AN ABSTRACT AN ECONOMIC ANALYSIS OF ALTERNATIVE SAGINAW VALLEY CROP ROTATIONS--AN APPLICATION OF STOCHASTIC DOMINANCE THEORY By Roger L. Hoskin Michigan's Saginaw Valley, with a fine textured lake plain soil, is one of the most productive agricultural areas in the United States. Over the past three decades there has been a shift from mixed livestock/ crop farming to intensive cash crop farming with emphasis on corn, Navy beans, soybeans, sugarbeets, and small grains. During this period, there has been a marked decline in average Navy bean yields. Agronomists contend that perhaps the single most important reason for declining Navy bean yields is deteriorating soil structure brought on by overproduction of cash crops, particularly Navy beans and sugarbeets. One proposed remedy for the problem is a return to the practice of including green manure crops, especially alfalfa, in cropping rotations. Agronomists have identified sixteen cropping rotations that are considered to be representative of those appropriate to Saginaw Valley. The objective of this study is the following: To rank these sixteen rotations in terms of their relative risks and returns to the farmer. The approach to a solution involves a comparative budget analysis witni simulation of the two main stochastic elements, crap yields and product prices. Roger L. Hoskin Gross income was simulated as a multivariate probability distribution in which the marginal distributions (prices and yields) were beta distributed. The beta distributions were defined in terms of the expected values, variances, upper bounds, and lower bounds. Betas were employed as the assumption of normality, particularly of yields, and not considered valid except as a special case. Gross income dis- tributions were developed for each of the sixteen rotations and one hundred "draws" were taken from each to represent one hundred possible "states of nature" of gross income. The resulting states of nature were th ranked from lowest to highest with the i state of nature representing th the i percentile of gross income. Cash costs were developed for each rotation. Fertilizer usage varies from rotation to rotation and reflects usage based on net removal, adjusted for losses. For example, the nitrogen required on corn after alfalfa is less than that required on corn after corn. Similarly, the impact of nutrients contained in the organic matter plowed down from crop residues was taken into account. The cost of operating capital was specifically included at this point. Unique machinery complements were developed for each cropping sequence using a simulation model developed in the Department of Agri- cultural Engineering. The model specifically accounts for timeliness of field operations for each crop in each rotation. Historical weather data for the region was used in calculating the odds of alternative good weather days suitable for field operations. The budgeting pro- cedure employed examines power requirements for each field operation, given the constraints outlined, then selects the tractor horsepower 4‘- Roger L. Hoskin and equipment size that will accomplish the most limiting of the field operations. Analysis was done for 400 and 600 acre farm configurations. The 400 acre farm configuration assumes one full-time family laborer. The 600 acre farm configuration assumes two full-time family laborers. A $l4,000 per year charge was made for family labor, this being approx- imately equal to the median Michigan family income, given appropriate adjustment for tax treatment of family farms. Hauling and drying costs were figured at custom rates. Results indicate that a corn-Navy bean-sugarbeet rotation offered the best prospects under prevailing relative prices. One rotation that included alfalfa and Navy beans showed evidence of being economically viable for some decision makers. Rotations with Navy beans out performed similar rotations with soybeans. Rotations with sugarbeets were more profitable than those without sugarbeets. Stochastic dominance theory offers a useful way to evaluate alternative risky prospects where decision makers' utility functions are unknown. Unfortunately, the resulting stochastic efficient set may include more than one alternative. Further work needs to be done to be able to further partition the set into efficient and inefficient alternatives. ohyfiu'fiuv'U-vv. ’-‘-l-- o‘— ACKNOWLEDGMENTS For their guidance and assistance, I wish to thank the members of my dissertation committee: Roy Black, Zane Helsel, Gerald Schwab, and Al Rotz. I also gratefully acknowledge the guidance provided by Larry Conner as chairman of my guidance committee. This project has benefited from helpful comments from fellow students; especailly, John Strauss, Ed Rister, Jerry Skees, Rob King, Fran Wolak, and Tom Christensen. I also give special thanks to members of the Agricultural Economics computer programming staff; particularly, Paul Nolberg, without whose assistance this dissertation would never have been completed; and Susan Chu whose last minute herotics with the plotter made possible the graphs in the Appendices. Funding for this study was provided by the Michigan Agricultural Experiment Station. I gratefully acknowledge their support. Finally, I thank my wife, Neesa, who shared all the good and bad days that come with an undertaking such as this. ***** --—~——~..—-....-_v.. v-‘_.a_...s- ,,’. .'._‘C 1-, ."h TABLE OF CONTENTS Page lJST OF TABLES .......................... vii lJST OF FIGURES ......................... IX Chapter I. INTRODUCTION ....................... I Background ...................... l Agronomics ...................... l Economics ...................... 3 Problem Statement .................. 4 Research Objectives ................. 4 Methodology ..................... 5 Construction of Enterprise Budgets .......... 6 Outline of Dissertation ............... 7 II. AGRONOMICS OF SAGINAW VALLEY CROPPING SYSTEMS ...... 9 Previous Research .................. ll Sixteen Saginaw Valley Cropping Systems ....... l5 III. RISK, UNCERTAINTY, AND DECISION MAKING .......... 20 Introduction ..................... 20 Previous Research in Agriculture ........... 26 The Assumption of Normality ............. 3O Stochastic Dominance as a Decision Criteria ..... 33 IV. INPUT/OUTPUT RELATIONSHIPS, EXPECTED PRICES, AND FIELD WORK TIME CONSTRAINTS .............. 44 Introduction and Chapter Objectives ......... 44 The Design Perspective ................ 44 The Enterprise Budgeting Approach .......... 45 Variable Cash Costs ................. 47 Machinery Costs ................... SO Hauling and Drying Costs ............... 56 Labor ........................ 56 Estimating Relative Prices .............. 58 iv “‘QA‘H b -4“ -— n— w 5"... q.. I vv..-r-Q._ ne.,_- '_- V.."“ r‘ M .-.». Chapter V. METHODOLOGY: SIMULATION OF CUMULATIVE DENSITY FUNCTIONS OF NET RETURN TO LAND ................. Introduction ..................... Methodological Approach ............... Random Variables--Prices and Yields ......... Measurement of Variability .............. Estimating Variability of Yields ........... Variability of Prices ................ Correlation Coefficients ............... Upper and Lower Bounds on Distributions ....... Simulation of Gross Income .............. Summary ....................... VI. RANKING OF SAGINAH VALLEY CROP ROTATIONS ......... VII. Appendix A. B. Introduction ..................... Comparison by Stochastic Dominance Rules ....... Results of Analysis on 400 Acres ........... Results of Analysis on 600 Acres ........... Sensitivity Analysis ................. Machinery Costs ................... Reliability Criteria ................. Summary ....................... SUMMARY AND CONCLUSIONS ................. Summary of Research Objectives ............ Theory ........................ Methodology ..................... Empirical Results .................. Conclusion ...................... Recommendations for Further Research ......... VARIABLE CASH COST BUDGETS ................ CONCEPTUAL BASIS FOR ESTIMATING EXPECTED RELATIVE PRICES ......................... RAN DATA USED TO ESTIMATE YIELD PROBABILITY - DENSITY FUNCTIONS ................... TEST FOR NORMALITY .................... POOLING TIME SERIES AND CROSS-SECTION DATA ........ Page 106 106 107 108 112 113 115 154 167 171 —-.._¢w..-... —A.J.<.‘H_ -~-._,~4. c... u ‘Lvouy‘. M .4 t‘ Page Appendix F. COMPUTATION OF CORRELATION COEFFICIENTS USING AGGREGATED VERSUS DISAGGREGATED DATA ......... 176 f G. STOCHASTIC ANALYSIS OF ENTERPRISE BUDGETS PROGRAM . . . 181 ‘ . i H. MULTIVARIATE PROCESS GENERATOR ............. 199 5 I. CUMULATIVE DENSITY FUNCTIONS .............. 203 o. PROBABILITY DENSITY FUNCTIONS ............. 220 BIBLIOGRAPHY .......................... 237 vi Tflfle 2.1 2.2 2.3 2.4 2.5 3.1 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.1 5.2 5.3 LIST OF TABLES Crop Grown in Previous Years to 1974 Navy Bean Crop . . . Five Year Average Navy Bean and Sugarbeet Yields as Affected by Three Systems of Cropping ......... Navy Bean Yields Versus Cropping System on Saginaw Bean and Beet Farm .................. Average Corn Yields for Alternative Rotations with 150 Pounds of Nitrogen Applied ............ Expected Yield Under Alternative Saginaw Valley Crop Rotations ....................... Simple Decision Problem ................ Fertilizer Application Rates ............. Herbicide and Pesticide Application Rates ....... Guidelines Used in Evaluating Nitrogen Contribution to Previous Crops to Subsequent Crops ......... Prices for Seed and Fertilizer ............ Prices of Herbicides and Pesticides .......... Timing of Field Operations .............. Machinery Cost and Fuel Consumption per Acre ..... Estimated Unit Hauling Costs for Each Crop ...... Expected Cash Prices ................. Estimates Of Yield Variation ............. Standard Deviation and Coefficient of Variation of Prices Received by Michigan Farmers ........ Correlation Coefficients for Yields .......... vii Page 10 12 13 14 17 22 48 49 50 51 51 53 57 58 63 73 75 77 “\4- s——-— du-.vln“.. Q‘Mofi: '1—QJQ' Lul- Table 5.4 5.5 6.1 6.2 6.3 6.4 6.5 6.6 6.7 E.1 E.2 E.3 Page Correlation Coefficients Estimated for Prices Received by Michigan Farmers ............. 77 Percentage Rates Used in Calculating Upper and Lower Bound Values .................. 79 Income-Expense Summary for 400 Acre Farm ....... 85 Income-Expense Summary for 600 Acre Farm ....... 86 Ranking Of Sixteen Cropping Systems on a 400 Acre Farm Using First and Second Degree Stochastic Dominance ....................... 93 Ranking Of Sixteen Cropping Systems on a 400 Acre Farm Using First, Second, and Third Degree Stochastic Dominance ................. 94 Ranking of Sixteen Cropping Systems on a 600 Acre Farm Using First and Second Degree Stochastic Dominance ....................... 96 Ranking of Sixteen Cropping Systems on a 600 Acre Farm Using First, Second, and Third Degree Stochastic Dominance ................. 97 Ranking Of Saginaw Valley Cropping Systems Without Sugarbeets Using First, Second, and Third Degree Stochastic Dominance ................. 99 "F" Ratios Testing Hypothesis l ............ T72 "F" Ratios Testing Hypothesis 2 ............ l73 "F" Ratios Testing Hypothesis 3 ............ l74 viii Figure 1.1 3.1 3.2 3.3 3.4 4.1 5.1 6.1 6.2 G.1 6.2 H.1 LIST OF FIGURES Michigan Dry Bean Yield per Acre ............. Comparison Of Non-Normal Density Function ........ First Degree Stochastic Dominance Illustrated ...... First Degree Stochastic Dominance Violated ........ Second Degree Stochastic Dominance Functions ....... Changes in Relative Prices, Illustrated ......... Block Representation Of Stochastic Generator to Simulate Net Returns to Land ............... Cumulative Density Function--6OO Acre Farm ........ Cumulative Density Function--6OO Acre Farm ........ Sample Input for Rotation #14 .............. Sample Output Generated for Rotation #14 ......... Illustration Of Inverse Transform Method ......... ix Page 31 35 37 37 61 82 9O 91 186 201 .\_5~ CHAPTER I INTRODUCTION Background Michigan's Saginaw Valley represents one of the most productive agricultural areas in the United States. Over time there has been a shift from mixed livestock/crop farming to intensive cash crop farming emphasizing corn, Navy beans, sugarbeets, and small grains. Increased acreage Of high value cash crops in a highly mechanized environment has become increasingly dominant. Navy beans represent a crop unique to the area and of supreme importance. Navy beans rank third behind corn and wheat as a source of income among Michigan's agricultural crops. Michigan and a concentrated anea of Ontario produce 95% of the world's Navy beans (Black and Love, 1978). In recent years, Navy bean yields have trended downward and appeared to plateau (Anderson et al. , 1975) (see Figure l.l). Agronomics Research conducted from 1940 to l970 at Michigan State Uni- versity's Ferden Farm (Robertson et al., 1976) included experiments on fErtilizer application methods and rates, crop rotations, row spacing, and use of supplemental nitrogen. (kmnparisons of alternative cropping systems indicated improved yields of corn, Navy beans, and sugarbeets when grown in rotations which included alfalfa and green manure crop. -ux—~_~.a- 4“..— .ITIIII... .... .. . ................... .u|1:,.,..n... ,'.v,.... .11141.44:]ll)‘l.1l.\-lIt-»n.l.~‘ullr|.r.,0o.e.nlel.1. «.wsemm mxowada «wownmwudum NogxuNxomsmv :dmwxomz “moexomy .mco< Lou upmw> comm ago cmmmsuwz _.P mczmwd owmp mnmp ONmF mom— comp mmap away (“‘4 4 q q - a a a 1 - d H 1 q - 1 u u q — u 1 7 . -(1 q i- d F ‘1.10‘§( 90 r aJDV/TMO — - ‘ --..P‘19_-§_m 3.»:- ‘1,, This was true even when nitrogen was not limiting. Inclusion of green manure crops and alfalfa was beneficial to soil structure and, in the case of Navy beans and sugarbeets, helped maintain soil organic matter levels. Use of alfalfa or green manure cover crops in rotation with other crops is not common on Saginaw Valley cash crop farms. Agrono- mists maintain inclusion Of alfalfa in crop rotations with Navy beans could reverse the Navy bean yield trend. -. ..__.._- fi/ZKZ:7 rs are made with the objective of It that a proposed problem/solution __ ‘_ it must also be economically ~3 i- “791 .1‘ I f farmers is influenced by cultural economic analysis must include net income cash crop rotations. in an environment of uncertain liain sources of variation. Farm K) J f e during the 19705 than during Efl/ ; ‘ " : Yde of the 1960s, yield variability g; uter than price variability, but g; ' as been greater than yield _ N . 1976). . ' K ' :, "I‘ "~' . . 3 ash crOp farmers face a business ' -- j .2’L/I _ . E cation of United States agriculture 9 ecline of the relative size of the s..- h ... .. .— .. up - r.-m‘ a“ h _ , ... This was true even when nitrogen was not limiting. Inclusion of green manure crops and alfalfa was beneficial to soil structure and, in the case of Navy beans and sugarbeets, helped maintain soil organic matter levels. Use of alfalfa or green manure cover crops in rotation with other crops is not common on Saginaw Valley cash crop farms. Agrono- mists maintain inclusion of alfalfa in crop rotations with Navy beans could reverse the Navy bean yield trend. Economics Production decisions by farmers are made with the objective of making a profit. It is not sufficient that a proposed problem/solution actually solve the agronomic problem; it must also be economically viable. The degree of risk faced by farmers is influenced by cultural practices and cropping system. Thus, economic analysis must include consideration of risk associated with net income cash crop rotations. Production decisions are made in an environment Of uncertain outcomes; yields and prices are the main sources of variation. Farm mfices were considerably more variable during the 19705 than during the 19505 and 19605. During the decade of the 19605, yield variability fbr all crops, except wheat, was greater than price variability, but during the 19705 price variability has been greater than yield variability for all crops (Knoblough, 1976). In summary, Saginaw Valley cash crOp farmers face a business environment in which increased integration of United States agriculture with international markets and the decline of the relative size Of the -.—_h_—‘—a—'-lw-lo-‘-‘v - mtg.‘ aw .— .o—."V--'-.ockv-._ N. .5- ..F..\ United States surpluses vis-a-vis world consumption, creates a potentially riskier environment; and there exists a trend toward stagnating if not declining per acre yields of navy beans, an important cash crop to the area. Problem Statement Ferden Farm research revealed higher yields and improved disease and pest control resulted from the inclusion of leguminous cover crops such as alfalfa in crop rotations. Research results also indicated the adverse impact on soil structure and soil organic matter level of continuous plantings of Navy bean and sugarbeet crops. Soil scientists suggest that intensive cash crop agriculture is a cause of the declining Navy bean yields. Given the problems associated with intensive cash cropping systems and the results Of agronomic research, the intent of this research to examine the economic viability Of alternative cropping systems, particularly those that included legumenous cover crops as part Of the rotation. Research Objectives The Objectives of this study are: 1. to describe the present economic environment in which Saginaw Valley cash crop farmers operate; 2. to identify crop rotations vvhich are agronomically feasible for the Saginaw Valley and illustrate a wide variety of agronomic practices; i.e., the range should be from intense cash crop rotations to agronomically desirable rotations " g. .a returning more organic matter and contributing to better soil structure; 3. to analyze, from a design perspective, the economic viability of selected crop rotation patterns from the farmers' viewpoint; and 4. to determine the sensitivity of the ranking of crop rotations to changes in prices and yields. Methodology There are numerous criteria by which cropping systems may be evaluated; the focus here is a risk-return perspective. The assumption is that farmers prefer more income to less and prefer less risk to more. Crop rotations are evaluated using a design perspective. Con- sequently, the investigation considers: (1) yield relationships; (2) seed, fertilizer, and chemical regemines; (3) labor and machinery requirements; and (4) input and crop prices. The measure of profitability used is returns to land; that is, gross revenue produced in a period less total in expenses incurred in the production period. From an accountant's perspective, it is assumed that all revenue produced is realized in the year in which associated costs are incurred. The analysis abstracts from storage, either of inputs or crops. When comparing systems, relative returns are more important than absolute returns. Absolute returns are critical in evaluating debt capacity; but in the present context, it is relative returns, hence relative yields, prices, and costs that are significant. This >.--l‘-.‘uu— _4_<- ... -... .4....... u o ._¢--_.a~.a study, while attempting to estimate absolute values as accurately as possible, focuses upon relative values. The major source of risk associated with alternative crop- ping patterns is variability of yields and variability of prices. Variability of prices will be estimated using a historical measure of variability and estimates from the MSU Agricultural Forecasting Model. Variability of yields will be estimated using historical records of yields On Saginaw Valley farms. Sixteen alternative cropping systems appropriate to the Saginaw Valley are identified and evaluated in terms of the net returns and the variability Of net return to land. Construction of Enterprise Budgets The approach adopted abstracts from the exigencies Of any particular farm and examines the economic performance of each cropping system under the operating constraints typical of the Saginaw Valley area. Each system is presumed to be produced on a 400 and 600 acre family operated cash crop farm. Machinery costs reflect employment of a machinery complement tailored to each cropping system, and accounting TOr the technical complementarities in terms of yields and inputs inherent in each system. Enterprise budgets are constructed for each of the cropping systems under consideration. The budget derived for each cropping system was unique; that is, the technical complementarities inherent in each system were accounted for economically. To illustrate: corn following alfalfa requires less fertilizer, a different herbicide O.'-J\~Q.-‘-O_ .5 V... .J _-.. ..w...u. v ‘ ..v-..‘ ..A- J" H, _. ..V.-. ..q_ .-- regime, and has a higher yield per acre than does the corn following corn. These kinds of differences were accounted for in each cropping system. The net return to land represents a measure of the residual remaining after cash costs, machinery costs, and living expenses have been deducted from gross income. There is no attempt to inpute wage rate for family labor or a return on land. Nor is there any attempt to estimate taxes or assume a particular financial structure for the farm. These characteristics are unique to each farm operation and desired rates Of return on invested capital are, to some degree, set by management. The impact of risk on production decisions will be evaluated using stochastic dominance criteria. To measure the production vari- ability Of crop enterprises, data on yields for individual farms over a number of years is needed. These data were obtained from a selection of Saginaw Valley farm records Obtained from the TELFARM Records Project at Michigan State University. Price variability is measured from the series of prices received by Michigan farmers published in Michigan Agricultural Statistics. Outline of Dissertation Chapter 11 contains a presentation Of the agronomic concepts necessary to develop the crOp rotations for study, expected yields, and fertilizer and pesticide reghnens. Chapter 111 contains a dis- cussion of the relevant theory regarding decision making under uncertainty. Chapter IV presents development of the methodology _-._._ ... ..‘s. —v. «-..-.... ‘H h employed in estimating commodity prices, input prices, price and yield variability, machinery and labor requirements. Chapter V describes the analytical model and the method of computing income variability. Chapter VI contains empirical findings and sensitivity analysis and implications. Chapter VII summarizes the study and includes suggestions for further research. v-‘L. .... ...» .-.-..-, n-» CHAPTER II AGRONOMICS OF SAGINAN VALLEY CROPPING SYSTEMS Two broad classifications of cropping systems are represented in the Saginaw Valley (Christensen, 1978). One is described as ”hap- hazard"; acreage allocation decisions are made one year at a time on the basis Of price expectations. This approach is a "problem creator." This is particularly true for Navy beans and sugarbeets since growing Navy beans and sugarbeets in successive years or in short rotations with other crops that return little organic matter to the soil has been shown to be associated with poor soil structure (Robertson et al., 1976), depletion of organic matter (Lucas and Vitosh, 1978), and disease and pest problems (Andersen et al., 1975). Furthermore, (early research on the Ferden Farm indicated a trend toward declining eaverage Navy bean yields when grown in systems where no effort was made 'to maintain soil structure and soil organic matter. The yield trend for Michigan Navy beans was upward to the "Md-sixties but recently has shown a declining trend (Andersen et al., 1975; Wright, 1978). In 1974, a 100 farm survey was conducted (Ander- sen, 1975) which indicated a trend among Michigan Navy bean producers to grow Navy beans on the same field in consecutive years and to exclude any soil building crops from their planting decisions. According to this survey, summarized in Table 2.1, almost one-fourth of the fields 10 Table 2.1 Crop Grown in Previous Years to 1974 Navy Bean Crop (Percent of Fields) Previous Crop 1972 1973 Alfalfa 2 2 Navy beans 37 3O Corn 12 23 Small grains 13 17 Soybeans l 3 Sugarbeets 21 15 Other 13 10 surveyed had been in beans the previous year and 37% had been in beans two years previously. Two-thirds of the fields surveyed exhibited poor soil structure. Twenty-four percent showed a high enough degree of Fusaruim root rot to substantially impair yields, and an additional 27 percent exhibited a moderate degree of root rot, but still enough to impair yields. Rota- tion practices are partially to blame for declining Navy bean yields. In contrast to the "haphazard" systems, some farmers plant acreage in a well defined rotation which changes little from year to year. The evidence indicates cropping rotations including crops which contriubute to good soil structure and high organic matter levels improve yields and reduce disease and pest problems. —‘.____ou..-..n .u’wrtag -.. _ ~ 11 Previous Research Early research supporting the agronomic advantages of clearly defined cropping rotations which benefit soil structure was conducted on the Ferden Farm near Chesaning, Michigan. These experiments were begun in 1926 and concluded in 1970 when this research was moved to Saginaw Valley Bean and Beet Research Farm near Saginaw, Michigan. In 1940, a series Of experiments at the Ferden Farm was initiated to investigate the effect Of different crop rotations on yield, soil structure, and disease incidence. The results of exper- iments conducted between 1940 and the mid-19505 indicated that the highest yields of Navy beans and sugarbeets were Obtained from "livestock" cropping systems, i.e., those that included two years of alfalfa-brome hay as a soil building crop. The lowest yields were Obtained in "cash" crop rotations where no effort was made to maintain soil structure (see Table 2.2). Rotation B-Ba-A-A-NB, a "livestock" rotation, includes two years Of alfalfa to maintain soil structure. Rotation w-C-C-Ba-NB, a "cash" crop rotation, includes fewer crops that contribute to soil organic matter and structure. RotatiOn #3 is identical to #2 except 'sweet clover was included as a companion crop with wheat and barley and left as a winter cover crop. The experiments included two levels of fertilizer. Plots receiving greater amounts of fertilizer had higher yields; the effects of fertilizer were similar in all three rotations. The average differences were equal to or less than 0.6 cwt. per acre of Navy beans. . \a ‘L‘ .. y- 11 Previous Research Early research supporting the agronomic advantages Of clearly defined cropping rotations which benefit soil structure was conducted on the Ferden Farm near Chesaning, Michigan. These experiments were begun in 1926 and concluded in 1970 when this research was moved to Saginaw Valley Bean and Beet Research Farm near Saginaw, Michigan. In 1940, a series of experiments at the Ferden Farm was initiated to investigate the effect of different crop rotations on yield, soil structure, and disease incidence. The results of exper- iments conducted between 1940 and the mid-19505 indicated that the highest yields of Navy beans and sugarbeets were Obtained from "livestock" cropping systems, i.e., those that included two years of alfalfa-brome hay as a soil building crop. The lowest yields were Obtained in "cash" crop rotations where no effort was made to maintain soil structure (see Table 2.2). Rotation B-Ba-A—A-NB, a "livestock" rotation, includes two years of alfalfa to maintain soil structure. Rotation W-C-C-Ba-NB, a "cash" crop rotation, includes fewer crops that contribute to soil organic matter and structure. RotatiOn #3 is identical to #2 except ‘sweet clover was included as a companion crop with wheat and barley and left as a winter cover crop. The experiments included two levels of fertilizer. Plots receiving greater amounts of fertilizer had higher yields; the effects Of fertilizer were similar in all three rotations. The average differences were equal to or less than . 0.6 cwt. per acre of Navy beans. -'—‘ L.“'-"I-§— - H“ ..A-» ..ru.._.. o-u .-.— —-, -V-,..~_.‘ 12 .aoco cm>ou cwwcwz Aew>opo mm cuamv mgscme comem u Em ”paws: u 2 Magoo u o mmcmmn a>mz u mz ”wepmefim u < mxmpemn N am ”muwmngmmzm u m m _.NF F.¢F N.P— m.mp o.m_ m.op com: .. N.w_ -- m.¢~ .. m.mp omm_-ommp o.m_ m.vp _.ep N.e_ m.o~ m.mp mmmpnpmmp F.~F ~.N_ w.m m.P_ o.mp m.¢~ ommpumvmp F.o_ ~.PF o.m o.o_ N.o_ _.mp mempupvmp <\co» <\.u30 <\cok <\.pzu <\coh <\.uzo memm> mumwocmmzm mcwmm x>mz mummacmmsm mcmwm z>mz muwmncmmzm mcmmm a>mz mz-A5mvmm-m-u-AEmvz mz-am-u-u-z mz-<-<-am-m cowumwom mmcwaaogu mo mepmxm amuse an umaommw< mm mupmw> ummnemmsm new :mmm z>mz mmmgm>< me> m>wm N.m mpnmp 12 .l- .aoeo gw>oo gauze: Acm>opu mm zuamv Deuces :mmcm n Em ”pawn: n 3 Magoo u u mmcmmn >>mz u m2 MmCFmepw n < mxmpgmn u mm “mummngmmzm n ma _.N_ F.ep N.__ m.- o.mp m.o_ cam: -1 N.mp -1 m.e_ 1- m.mP comp-mmmp o.mp m.e_ _.ep N.ep a.m~ w.mp mmmp1pmmp _.~. «.mp w.m m.PF o.NF m.e_ swap-memp _.o_ N._F o.m o.o_ N.o_ _.m— memF-Femp <\coe <\.p2u <\:o» <\.pzu <\coh <\.uzo memm> mommaemmam mcmmm x>mz mpmwngmmzm mcwmm >>mz mpwmncmmam mcmmm a>mz mz-A5mvam-m-u-A2mV3 mz-am-u-u-3 mz-<-<-am-m cowumpom mmcwaaogu we mempmzm omen» an cmuomew< mm mupmw> ummncmmam uzm :mmm x>mz mmmgm>< Lam» m>wu N.m wFamh ’A.' 13 Research at the Ferden Farm ended in 1970. However, crop rotation experiments have been continued at the Bean and Beet Farm in Saginaw County. The objectives of the cropping system portion of this research are: (l) to study the effect of length of rotation on yield and quality of navy beans and sugar beets, and (2) to evaluate the effect of the return of organic matter on yields and selected soil properties. Preliminary results indicate a significant affect of both rotation and length of rotation on Navy bean yields. The highest Navy bean yields were Obtained on a four year rotation which included alfalfa, O-A-NB-B (see Table 2.3). Navy bean yields were greater where corn (stalks returned) was included than where it was not. The lowest yields were obtained from a three year system (NB-NB-B) where beans were grown in successive years and little organic matter was returned to the soil. Table 2.3 Navy Bean Yields Versus CrOpping System on Saginaw Bean and Beet Farma Average Yield 1973-1976 Cropping Systemb th./A TwO Year Rotation: C-NB 17.7 B-NB 16.4 O-NB 17.0 Three Year Rotation: C-NB-B 17.1 NB-NB-B 16.2 O-NB-B 17.5 Four Year Rotation: C-C-NB-B 17.9 C-NB-NB-B 17.3 O-A-NB-B 19.3 aChairty Clay soil; Management Group lcc. bA= alfalfa, B = sugarbeets, NB = Navy beans, C = corn, and O = oats. II 14 There was no rotational length effect on sugarbeet yields. Corn yields were more sensitive to nitrogen application than to rotational length or cropping system. Corn grown in successive years tended to be susceptible to corn root worm so an insecticice regimen was necessary. An eight year rotation study was conducted in Wisconsin examining five year rotations including corn, soybean, oats, and alfalfa versus continuous corn (Higgs et al., 1974). Corn yields were significantly higher in rotation than for continuous corn. In rotations where corn followed alfalfa, yields were higher than for subsequent corn .yields in the same rotation; however, second and third years Of corn offered higher yields than did continuous corn (see Table 2.4). ‘Table 2.4 Average Corn Yields for Alternative Rotations with 150 Pounds of Nitrogen Applied H Appearance lst Year 2nd Year 3rd Year Rotation Bu./A Bu./A Bu./A Continuous Corn 125.1 C-S—C-O-A 133.6 133.6 C—C-C-O-A 130.5 124.7 125.9 C-C-O-A-A 138.1 127 . 5 ' C-O-A-A-A 137 . 6 b aAverage yields for 1967-1974 on Rozetta Silt Loam soils, lJniversity of Wisconsin Experiment Station, Lancaster. One hundred- “fifty pounds of nitrogen were applied per acre. b5 = soybeans, and O = oats. 15 These experiments were repeated at three different nitrogen application rates. Corn yields were sensitive to application of nitrogen, and there was a statistically significant interaction between nitrogen application rate and rotation. The average yield of 125.1 bushels per acre for continuous corn was 5 to 13 bushels per acre less than first year corn in rotation even when nitrogen was not limiting; 150 pounds of nitrogen per acre was applied to corn in all rotations. Historically, specific crop rotations have been recommended to: (1) improve soil tilth and structure; (2) provide nitrogen to following crops; (3) improve infiltration Of ground water and reduce erosion; and (4) improve disease, weed, and insect control (Higgs et al., 1974). With the advent of relatively inexpensive nitrogen fertilizers and chemical herbicides and pesticides, the importance of crop rotation as a standard cultural practice has declined. Widespread production ()f Navy beans and sugarbeets, two crops that provide little organic ‘residue to the soil, make rotation practices more important in the Saginaw Valley than for the corn belt. Rotation practices will taecome of even greater value with rising real prices of fossil fuel laased fertilizers and chemicals. _§jxteen Saginaw Valley Cropping Systems Research documented above strongly suggests advantages to SYStematic crop rotation to include crops that contribute to soil structure and soil organic matter. Increased yields, reduced use Of fertilizer, improved control Of disease and pests, and reduced -‘hh-._..r_a._.-v -m-c.-.4- “'4'... ~‘Qr. y~._‘.l.._-_q ,‘__.- 9.. --,-.-v ,4 16 tillage are the potential advantages accruing to appropriate crop rotation. The issue is whether these advantages are substantial enough to warrant a change from current production practice. This issue is of particular significance since alfalfa, a major soil building crop, is not a high value cash crop. The major focus of this research is to evaluate the benefits of crop rotation from a perspective of economic viability. Agronomists, Drs. Don R. Christensen, Zane Helsel, and Vernon Meints, from Michigan State University, have drawn up sixteen cropping sequences which include alfalfa and six other commonly produced cash crops appropriate to conditions in the Saginaw Valley. The six cash crops included are: corn, Navy beans, soybeans, sugarbeets, oats, and wheat. In the context Of this research, alfalfa will be considered as a cash crop. The sixteen rotations and their expected (in a probabi- listic sense) yields are presented in Table 2.5. The yield relation- ships presented represent those obtainable to the top two-thirds to three-fourths of all operators. These rotations are assumed to be Produced as typical Saginaw Valley lake plane soils with slope less than 3%. Tile and surface drainage are assumed functional and ade- quate and irrigation is not considered. The yields obtained reflect timely field operations and machinery systems designed to insure near Optimum yields (see Table 2.5). There is an 8 bushel per acre differential in corn yields among Clr‘Oilping systems depending on where corn appears in the rotation. The highest yields are expected in sequences 9, 10, and 16 where corn fol- lows alfalfa. Field experiments at Michigan State University as well hwy—..-“- av”... -u — _ 17 7 ' Ill-5.1T: II‘01001.54 L17l11-pn'lei 9‘.- .1hv-.r.l 1!. u. 1. .mcwmn x>mz Lo mccmnxom oc_:o__oe :Louo .mw—mwpm ;u_3 umummm mono u <\o ucm ”me_me_m u < Amoco u o “Hams; u 3 ”mumongmosm u m umcm6o>0m H mm ”memos >>mz 1 m2 "ceou u on .mou_uoaea pmczu_:u umucmEEoomL use moecwcco mumecam ecu m__u mumzcwum .m__om spa—a mxmg vocauxmu mc_e mosamw A<\Av A<\=nv A<\=nv new on. A<\=;V nan new um. swastu uauauom .oz m:_umom mummaeomam mumo “can: -1111111111 mcmmn>om -11 :omumuom 2:33 3:2: A<\Pv mcmmn >>mz ccou mocwacom me_mw_< Ill-II III I- I' mm:o_umaoz coco xmp—m> 3mc_mmm m>_umccmu_< Love: u_o_> umuumaxm m.~ m—nmh 1‘- 18 as other studies in the mid-west, e.g., Higgs et a1. (1974) suggest that corn following alfalfa yields about 7% higher than continuous corn. Yields Of corn after sugarbeets are less than expected after other crops due to moisture depletion of beets and soil compaction in harvesting Operations. Yields in successive years, even after alfalfa, decline; this is attributed to increased disease problems associated with continuous corn. A five hundredweight per acre differential is estimated for Navy beans. This estimate reflects Observations on Saginaw Bean and Beet Farm and the Ferden Farm which indicate that longer intervals between successive bean crops and inclusion Of crops that contribute to the soil and structure promote better yields. Sequence number 8 (C-NB-BN-B) which is similar to much Of the actual practice in the Saginaw Valley represents the effect Observed at the Ferden Farm—- that successive crops of Navy beans will decline in yield. Finally, research results at the Bean and Beet Farm suggest that yield of Navy beans in longer rotations perform better then yields in shorter rota- tion. Thus, Navy bean yields in rotation 6, 11, and 13 outperform .Yields in rotations l and 15. The benefit that alfalfa provides to Soil structure and consequently Navy bean yields is illustrated by rotation 14. Yields of sugarbeets were assumed lower after wheat, due to the tendency of a straw mat forming under the plow layer. Work at the Ferden Farm suggests the inadvisability Of planting sugarbeets after alfalfa as experiment plots showed some tendency toward black 19 root in wet soils. However, the presence of alfalfa in the rotation was shown to be of benefit to sugarbeet yields. Wheat following soy- beans are estimated to be depressed five bushels per acre due to the difficulty in getting wheat planted. The expected yield Of oats in the Saginaw Valley is 100 bushels per acre. In rotations 9, 10, and 14, the yield is reduced to 80 bushels per acre to reflect companion seeding with alfalfa. It is assumed that one ton per acre of alfalfa could be harvested after oats in the seeding year. Alfalfa yields decline as stands become Older; this is reflected in the yield figures for subsequent years of alfalfa in rotations 9, 10, and 14. Two tons of oat straw is harvested and sold as a cash crop in those rotations where oats are companion seeded with alfalfa. In rotation 15 the oat straw is plowed down. .1....-...— v‘. v.71vav— *0..- n‘l" CHAPTER III RISK, UNCERTAINTY, AND DECISION MAKING Introduction The impact of planning decisions on the variability of net farm incomes has been a management problem and has been the focus Of much agricultural economics research for a number Of years. "Risk" and “uncertainty“ are terms associated with income variability and have been given specific technical meaning (Knight, 1921). The producer, under Knight's polar case taxonomy, faces two types Of eventualities. Under risk, the probability of alternative outcomes can be measured. Risk can be described using the calculus of probability: Alternative outcomes (states of nature) have a frequency of occurrence in a large number of trials. Probability distributions can be established for situations involving risks. Variation in crop yields can be considered as risks where fluctuations in weather repeat frequently enough that farmers can establish a mean outcome and the range of possible outcomes. The second type of eventuality decision makers face is desig- nated as uncertainty and represents occurrences whose probability cannot be established in an empirical way. Uncertainty has been categorized as being subjective in nature (Heady, 1952). A decision maker is TEQUired to formulate some "image Of the future“ but there is no quantitative manner in which these hypotheses can be verified. 20 -t»u..-U(a2). 2. The utility of a risky prospect is its expected utility value. In the case of discrete probabilities: U(a ) = Z. U(ajlsi) P(S.) 1 where S1 is a state of nature with probability of occurrence P(Si). 3. The scale on which utility is defined is arbitrary; there is no unique scale of utility and interpersonal comparisons of utility are analytically meaningless. Also, cardinal measures of utility are not defined, e.g., it makes no sense to speak of one prospect as having twice as much utility as another for a decision maker. Utility permits only an ordinal ranking of prospects not a scaling of their relative values. For research purposes it is Often desirable to be able to exPress utility functions in algebraic form. A common and popular way to dO this is to represent the utility function as a polynomial. This can be justified on the basis that a polynomial is a Taylor series approximation to an unknown utility function over some small range of s-. _ ..- .. b _, . 5 . . v 1- ‘1»--.A -..4 _ - ”H. an 25 values. Thus a utility function of any form may be approximated for any point U(x) in a neighborhood of U(x*) as: -1 . U(x) = u5 A :: IE 3 8 I O. I B I X Risky Prospect Figure 3.1 Comparison of Non-Normal Density Function. prospects. This is so because moments higher than the second are not considered in the analysis. This is acceptable if the prospects are normally distributed, since all higher order moments Of a Gaussian distribution are zero. In the example, differences between A and B are evident and the higher moments are not zero. In previous studies, the normality assumption was made as a matter of consequence and because evidence to the contrary was not strong. Perhaps one Of the reasons for this was that the yield data employed to estimate yield variability was always in aggregated form. That is, most time series used were county or township data. All authors recognized that the variances estimated from such a series would underestimate yield variability at the farm level; but the unavailability of field or experimental data necessitated reliance on the aggregated series. Such an aggregated series is most often some form of weighted average Of data from individual farm yields which may be described as random variables. By appeal to the central limit theorem (Kreyszig, 1970), it is easy to see that the mean yield 32 of a series of estimated yields would tend to be normally distributed regardless Of the underlying distribution Of the farm level yields. Day (1965) examined the assumption of normality of the distribution of yield data from field experiments conducted by the Mississippi State Experiment Station. A time series of 36 years was Obtained for cotton and corn yields at seven levels of nitrogen appli- cation. Twenty-one years Of data were obtained for oats. Pearson's test for skewness and the Geary's test for kurtosis were employed. There was overwhelming evidence of positive skewness for cotton. The evidence was not as clear for corn and oats, yet positive (although statistically not significant) skewness was evident for the seven sample series of corn. Negative skewness, significant in only two of the seven series was evident for oats. The conclusion is that some evidence exists for skewness Of corn and oat yield distributions although not to the degree evidenced by cotton. Geary's test of kurtosis offered strong evidence of kurtosis of cotton yields. The evidence of kurtosis in corn and oat yields although present was not as conclusive. The same procedure was repeated for the crop yields transformed to logarithms. The author concludes that the log normal transformation has no general validity as a theoretical density function for field crop yields. In light of the previous discussion concerning risk, its measurement and importance in farm planning, the evidence provided by Day suggests that at the farm level, planning decisions based only on expected yields and variances are not adequate. Tests conducted on 33 the field data Obtained for this study exhibit strong evidence of non-normality of Navy bean and sugarbeet yields. The evidence is less conclusive for the remaining crops. The normality assumption is even less tenable in terms of prices. Corn, wheat, oats, and sugarbeets have government maintained price support programs. The program's effect is to truncate the lower tail of the distribution of prices while the upper bound is unconstrained. The constituents of gross income, yield and price, cannot be assumed to be normally distributed. Furthermore, a quadratic utility function as is often assumed in mean-variance studies of risk has the theoretically undesirable property of exhibiting an increasing marginal utility of money. In light of these facts, employing a utility function or a risk efficient production set based only on the first two moments of the distribution is inadequate. Stochastic Dominance as a Decision Criteria Since this study is being conducted from a design perspective, i.e., a comparison Of the relative merits of alternatives, the notion of specifying a unique algebraic form for a decision maker's utility function is unrealistic. Perhaps a better approach is to identify classes Of decision makers based on behavioral assumptions about preferences in a decision making situation. An alternative approach to ranking rotations from an economic perspective, when decision makers' preferences are unknown, is to use the concept Of stochastic dominance. When individual decision makers' —""h-_.._,_o .mlcmu—aA -.I_ 34 preferences are unknown, it is not possible to generate an optimum decision. However, it is possible to develop an efficient set of decisions in the sense that an identified class of decision makers behaving in accordance with the presumed assumption will not select or prefer an alternative that is not part Of the efficient set. The concept Of stochastic efficiency further partitions the set of alter- natives into efficient and inefficient as additional assumptions about decision maker preferences are introduced. Quirk and Saposnik (1962) proved that given any two risky prospects P1 and P2, if P1 is stochastically larger than P2, then P1 will be preferred to P2 by all decision makers that prefer more to less, regardless of the specification of the utility function. Within the framework of the expected utility hypothesis this implies that the only restriction on the utility function for First Degree Stochastic Dominance, FSD, is that of a monotomically increasing utility function, i.e., U'(x)> 0. Consider the case of two continuous Cumulative Density Functions (see Figure 3.2) defined on the interval [ab] and associated with the possible outcomes of two alternative risky prospects, then F is said to dominate G in the sense Of first degree stochastic dominance if F(x)s;G(x) for all x in [ab] with at least one strong inequality holding, i.e., F(x)< O and U"(x) :0. To illustrate, return to the example of two alternative production plans presented above. If the distribution of outcomes are as represented in Figure 3.3 instead of Figure 3.2, it is no longer clear that F is the preferred Choice, since between points x and y, the distribution of F is to the right Of G. With the additional behavioral assumption that decision makers are risk averse, a clear ordering Of the alterantives F and G can be obtained, if it can be shown that F lies more to the right of G in terms of differences in the area between the two cumulative distribution functions. Referring to Figure 3.3, the area where F lies to the right Of G, which is A plus C, is greater than the area where G is to the right of F, area B. This relationship can be determined most clearly by defining a cumulative function that measures the area under a cumulative distribution over the range of the uncertain quantity. Such a relationship is illustrated in Figure 3.4. 37 Cumulative Probability Uncertain Quantity Figure 3.3 First Degree Stochastic Dominance Violated. SSD Cumulative Uncertainty Quantity Figure 3.4 Second Degree Stochastic Dominance Functions. 38 In terms of cumulative distribution functions, CDF's, the distribution F dominates G by second degree stochastic dominance if the total area under F is less than the total area under G. The $80- cumulative for F may be defined as, R F2(X) = f F(x)dx. a Then distribution F can be said to dominate G in the sense of $50 if F2(x)sG2(x) with at least one strong inequality holding.“ Analogous to FSD the property of transivity holds and similar theorems may be proven for discrete distributions. Dominated distributions in the sense of 550 are stochastically inefficient and would never be preferred by risk averse utility maxi- mizing decision makers. The undominated distributions constitute the second degree stochastic efficient set, SSE. Further identification of choice within this set would require more explicit knowledge about decision maker preferences than simple risk averse behavior. Whitmore (1970) introduced the concept of third degree stochas- tic dominance, TSD. This concept is based on the behavioral assumption that as people become wealthier they become decreasingly averse to risk. TSD implies a decision maker utility function where U"'(x) 1O. Analy- tically the T50 ordering rule follows from $50 rule. The third degree stochastic dominance function is defined as, R F3(x) = g F2(x)dx. 39 According to the theorem, F dominates G in the sense of TSD if F3(x):sG3(x) for all x with at least one strong inequality.3 As in the case Of $50, the T50 leaves a third degree efficient set which cannot be larger than the S80 set. The principle of transitivity can also be shown to apply to TSD as it does to $50 and F30. The approach to evaluation adopted here will be to employ stochastic dominance criteria to identify first, second, and third degree stochastic efficient sets. The advantages Of this approach over other methods are: (1) it is no longer necessary to make any prior assumptions as to the shape of the probability density functions describing yields, prices, or gross incomes. This is particularly important in light of evidence suggesting some degree of non-normality of some Of the stochastic terms in the model. (2) It is possible using stochastic dominance criteria to select an efficient set without prior knowledge of a particular decision maker's utility function. In other words, the second degree stochastic efficient set is efficient for all risk averse decision makers regardless of the shape Of or the algebraic expression Of their individual utility functions. The major drawback of this approach is that the risk efficient set selected under each of the dominance criteria may contain more than one possible alternative. In light Of research Objectives, this limi- tation may not be particularly burdensome since it is desired to select those cropping systems that are economically viable and examine their agronomic characteristics. 4O Footnotes--Chapter III 1Heady's approach has been standard practice in diversification studies. This may be illustrated by referring to a simple case Of two alternatives. When two enterprises, A and B, with income variances 0A2 and 032 are combined, the variance for the total Operation is: _ 2 2 OT GA + GB + ZPOAOB. If resources are constrained, say 500 acres is available and the decision is to determine the proportion Of acreage allocated to A and the proportion to B, the equation of total variance becomes: 0T2 = OZOA2+(1-q)2082+2p q(l-q)voB. Total variance is now a function of "q," the proportion of acreage allocated to enterprise A. Taking the derivative of the above expression results in: do 2 ——-—= 2- .. 2 .- dq 2qu 2(1 q)oB +2p(l 2Q)OAO'B. Setting the derivative to zero and solving for q, one can determine the variance minimizing proportions to allocate between two enterprises. The approach employed by Heady was to increment q from O to l and trace out the production possibility in EV space. 2The standard linear programming problem max S'x subject to TX 5 v and x12 0 where S is a column vector of net revenues of unit levels of production. X represents a vector of the number of units of S to be included in the Optimum set. T is a matrix of the coefficients of the amount of scarce resources necessary to produce one unit of X. V represents the limits of available scarce resources. The quadratic risk approach implies a change in the Objective function. Instead of maximizing profit, one maximizes profit subject to a level of variance. The utility function U(r), where r is the selected course of action, is assumed to be U(r) = l-e'ar; this function has U'(r)> O and U"(r)<:0. The Objective then becomes to maximize expected distributed random variable. E(u) = f (1_e-ar) e'(r'“)/202 dr. 41 Expected utility is maximized if the function E(u) = S'X-a/2 Xl (COV)X is maximized. The problem in a quadratic risk context becomes: max S'X-a/2 X'(COV)X subject to TX 5 V and X2 0. 3The proof of this proposition is presented by Hadar and Russell (1969) and Anderson (1974), It is required to prove if F(X)s G(X) or G(X)- F(X)2 0. Then Uf22Ug. Expected utility is defined as: Thus, - u = 1b U(X) f(X) dx - fb U(X) g(X) dx. a a The derivative of a cumulative density function is its probability density function. -U' = 1b U(X)[dF(X)] dx - [b U(X)[dG(X)] dx a a = 1b U(X)[dF(X)- dG(X)] dx. a Integrating by parts yields, Uf-U'+-[U(X) [F(X)- e1x>11b - Tb [F(X)-G(X)] u11x1 dx. 9 a a Since the CDf is defined on the range (0,1) a= O, b= l. 'The first term equals zero. 1 Cl 11 - Tb u' O or Uf>>U. A similar result has also been established for d15crete distr1butions. l'The proof for second degree stochastic dominance follows straightforwardly from the proof for first degree stochastic dominance. 1b u'(x) [G(X)- F(X)] dx. a The residual term from the integration in the first proof was declared to be non-negative as proof of FSD. Under second degree stochastic dominance, this assertion no longer holds. From the text F2(X) was defined as IR F(X) dx consequently d[F2(X)]/dx( = f(X), SO that 1" u'(x) [F(X) X)]dx =1 u 1:11:21»- G2(X))] dx. Again, integrating by parts u'(X) [5611-112611] - 1" [F21x1-G21x11u"(x1 dx. a This expanded expression can be substituted in the original expression in footnote 3. Uf-Ug = -[U (x) [F2(X)-G X)]] +abf U"( )[F2 (X) G2(x)] dsz. Since F2(a) = Gz(a) = O and F2(b) = G2(b) = 1, the first expression is zero. Since U" (X) < O by assumption and F2(X) - G2(X)s O by proposition Df-Dg 2 O. 5The proof for third degree stochastic dominance proceeds from as for second degree stochastic dominance. From the first term [-u'm IF, O by assumption and [F2(b)— G ) ]/d(X) = F2(X), then (b 2 expression is non-negative. Recalling d[F3(X) I" 11~1x1 [F2(X)- 112111)] dx a = T" U" (x) {d[F3(X)-G3(X)]/dX1 dx. a Integrating by parts I = [U"(X) [F3(X)- G3(X)ll: - lb U"'(X) [F3(X)-1G3(X)] dx. a Since U"(X) IO, [F3(b)- G (b)]s:0, U'“ (X)> O and [F3(X)- G3(X)]:;O 3 implies 01,- U9 2 O. CHAPTER IV INPUT/OUTPUT RELATIONSHIPS, EXPECTED PRICES, AND FIELD WORK TIME CONSTRAINTS Introduction and Chapter Objectives Budgets are developed for the sixteen crop rotations described in Chapter II and the rotations are ranked according to their net return to land. Comparisons are made first on the basis of expected values of prices and yields. Final comparisons are made according to the stochas- tic dominance criteria outlined in the previous chapter. The ranking criteria is: Gross Income - Costs = Return to Land. The objectives of this chapter are: 1. Define the concept of "return to land"; 2. Define the accounting procedures used to derive costs associated with each rotation; and 3. Describe the procedure employed to obtain estimates of expected commodity prices, input prices, machinery, labor, and fuel requirements. The Design Perspective Previously, it was stated that this analysis is conducted from the system "design" perspective. This method is often employed in developing economic models; that is, in order to understand the rela- tionship among the variables under study, it is necessary to make many 44 45 simplifying assumptions and consequently work with relatively simple models. Consequently, the approach used and the results Obtained, abstracted from a particular farm setting, may appear to ignore some important variables. The aim here is to construct an economic model whose purpose is an understanding, at a conceptual level, of the interaction Of a set of agronomic, physical, and economic variables. The product of this approach is an abstract model which provides a degree of understanding of real world behavior and the interdependence Of system structure, inputs, and performance. This is distinguished from the management or control function in which, given a model structure and a set Of desired system outputs, a set Of system inputs which achieve the desired Objective can be determined. The Enterprise Budgeting Approach Farm production economics studies are Often conducted using linear programming or a variant as a solution algorithm. However, there are several reasons why a mathematical programming approach is not appropriate for the problem at hand. There are sixteen cropping systems in which machinery complements, fertilizer, and chemical application rates are deterministic and unique, both to the particular cropping system and the assumed size of the farm; the additivity assump~ tion is not met. For example, the budget presented for rotation #8, C-NB-NB-B, on a 400 acre Operation is unique. A shift to less than 400 acres of this system modifies the aij in the activity matrix as the machinery complement would need to be re-specified. A further difficulty is encountered in specifying the objective function. In 46 previous studies, the Objective function was specified in terms of the unit contribution to income of a particular cropping enterprise such as corn or soybeans. As production Of one crop was increased, that Of the other must decrease. In the case under study, each of the systems represents a multi-crop farm plan where the complementar- ities of one crop to the output of another are expressly accounted for, e.g., the expected yield of corn following alfalfa is 118 bu./A whereas corn following Navy beans is 110 bu./A. The variable cost budgets, based on net nutrient removal are varied to expressly account for changes in expected yields and items such as nitrogen carryover from alfalfa to other crops. This implies that linear combinations Of cropping systems, i.e., an Optimal solution comprised of 0.8 C-NB and 0.2 C-SB-W-B would make no sense in a systems context; thus, an Optimal solution would have to be an integer solution. The approach of considering each of the seven individual crops as "activities" in a programming sense is impossible as the production coefficients (the aij in an LP sense) are not mutually exclusive and additive; only the rotations themselves are mutually exclusive. The problems encountered in a linear programming framework can be overcome by developing enterprise budgets for each of the sixteen crOp rotations. Rotations are ranked according to net returns to land which is defined as: Gross income less (1) cash costs which include seed, fertilizer, chemical costs, and interest on working capital; (2) machinery costs which include depreciation, maintenance, housing, fuel costs, and interest on investment; (3) handling and drying costs; and (4) family labor, then equals net return to land. 47 Net return to land represents the residual return not allocated to production period inputs necessary to produce period revenues. Income and property taxes are excluded since the primary focus is upon design, not system management and debt service capacity. The objective Of this accounting procedure is to match period revenues with period expenses in a flow sense and compare rotations on the basis of the size Of the residual. Variable Cash Costs Cash costs in the model include charges for seed, fertilizer, chemicals, and a finance charge on borrowed working capital. Fuel, while cash cost, is included in machinery costs. Cash costs were calculated for each crop in each rotation. Fertilizer application rates (Table 4.1) are based on the net removal Of soil nutrients by the crop; they represent the soil maintenance level recommendation. The fertilizer application rates assumed are presented in Table 4.1. Herbicides and pesticide use varies from farm to farm depending on the particular disease and pest problems encountered. The herbicide and pesticide programs here are representative of those commonly employed in the Saginaw Valley area when no unusual disease or pest problems are encountered. The herbicide and pesticide regimens are presented in Table 4.2, in pounds per acre of active ingredient. In an environment where strict rotational patterns are being adhered to, some crops can benefit from nutrients provided by previous crops in the rotation. These complementarities among crops are accounted for in the cash budgets and account for most of the variation 48 Table 4.1 Fertilizer Application Ratesa Crop Nitrogen (N) Phosphate (P205) Potassium (K20) Corn (grain) 1.13 lb/bu 0.35 lb/bu 0.27 lb/bu Navy beans 3.13 lb/cwt 0.83 lb/cwt 0.83 lb/cwt Soybeans 0 0.90 lb/bu 1.40 lb/bu Sugarbeets 5.0 lb/ton 1.30 lb/ton 3.30 lb/ton Oats 0.78 1b/bu 0.25 1b/bu 0.19 lb/bu Oats (straw removed) 1.09 lb/bu 0.44 1b/bu 1.19 lb/bu Alfalfa O 10.00 1b/t0n 45.00 1b/ton Wheat 1.30 lb/bu 0.62 1b/bu 0.38 1b/bu aAdapted from M. L. Vitosh and D. 0. Warnke (1979). Nitrogen fertilizer rates are increased 25% over recommendation to compensate for leaching. in recommended fertilizer application rates. The remainder of the variation is accounted for by variations in expected yields. Table 4.3 summarizes the guidelines used in evaluating the nitrogen contribution Of alfalfa and soybeans to subsequent crops. For example, if 115 bushel per acre corn follows soybeans, 130 pounds of nitrogen per acre is the recommended nitrogen application rate (1.13 pounds of nitrogen is required per bushel of corn). Soybeans contribute 30 pounds of nitrogen per acre; therefore, the application rate recommended for corn following soybeans is 100 pounds per acre. 49 Table 4.2 Herbicide and Pesticide Application Ratesa Application Rate Crop Chemical 1b/Aai Comments Corn Atrazine 0.50 Sutan 0.50 Lasso 2.00 Bladex 1.00 On corn preceding another crop Furadan 0.75 On corn following corn Soybeans Lasso 2.00 Lorox 0.75 Navy beans Eptam 2.25 Amiben 2.00 Treflan 0.50 Sugarbeets Pyramin 3.00 TCA 6.00 Oats MCPA 0.19 Companion seeded with alfalfa half cost allo- cated to seeded alfalfa Oats MCPA 0.38 NO companion seeding Alfalfa MCPA 0.19 Seeding year only, 8 cost allocated to oats companion crop Wheat 2-40 0.50 aThe chemical application rates and the weeds against which they are effective are from Schultz and Meggitt, 1978. 50 Table 4.3 Guidelines Used in Evaluating Nitrogen Contribution tO Previous Crops to Subsequent Cropsa Contribution Crop lb/A of N Soybeans .................. 30 Alfalfa .................. 70 aThe rates of nitrogen contribution are adapted from Warnke, Christensen and Lucas (1976). The values used were modified by Dr. Zane Helsel, Crops and Soils, Michigan State University. Prices for seed and fertilizer are presented in Table 4.4. Use Of herbicides and pesticides are given in pounds per acre Of active ingredient. Prices for chemicals are an average Of a sample Of retail prices Obtained by telephone survey of retail dealers in central Michigan. Prices were converted to values per pound Of active ingre- dient using the known concentration of active chemical in various commercial preparations. Prices of herbicides used in this study are presented in Table 4.5 Machinery Costs Per acre machinery charges and fuel consumption were derived for each rotation using a machinery simulation model developed in the Department of Agricultural Engineering (Wolak, 1980). The machinery complement selected for each of the sixteen cropping systems was unique. A "clean state" was assumed; that is, no current inventory of equipment was assumed to exist and the equipment complement was selected that 51 Table 4.4 Prices for Seed and Fertilizer Price Item per pound Seed: Corn .................. 1.00 Navy bean ................ 0.30 Soybeans ................. 0.28 Sugarbeets ................ 5.00 Oats ................... 0_]3 Alfalfa ................. 2.40 Wheat .................. 0.14 Fertilizer: Nitrogen (Urea) ------------- 0.24 Nitrogen (Anhydrous NH3) --------- 0.14 Phosphorous (P 05) ------------ 0.20 Potassium (K201 ------------- 0.11 Table 4.5 Prices of Herbicides and Pesticidesa Price Chemical per pound Atrazine .................. 2.27 Sutan ................... 2.27 Lasso ................... 3.85 Lorox ................... 3.34 Eptan ................... 2.67 Amiben ................... 6.02 Treflan .................. 7.01 MCPA .................... 0.68 2-40 .................... 2.44 Pyramin .................. 13.50 TCA .................... 1.45 Furadan .................. 7.48 Bladex ................... 3.34 aThe cash cost for each crop in each of the sixteen cropping systems is presented in Appendix B. These values were Obtained from a survey conducted by Dr. Gerald Schwab, Agricultural Economics, Michigan State University, in the spring of 1980. 52 would efficiently accomplish the field Operations for each rotation subject to the time and labor available. The yield estimates presented in Table 2.5 are based upon timely field operations. Starting and ending dates for various field operations are incorporated into the machinery model as constraints (Table 4.6). These dates were reviewed and revised by growers and extension agents and, as a result, represent a consensus of Opinion on the part of growers, extension agents, agronomists, and agricul- tural engineers as to appropriate timing Of field Operations in mid-Michigan. Weather variability, labor supply, and workday length also affect the availability Of time and required machinery productivity. An earlier edition of the machinery model assumed labor was readily available at a fixed wage rate. As a consequence, machinery comple- ments selected by the model tended to be smaller than those observed on Saginaw Valley cash crOp farms and hired labor input was substantial. This outcome was not in accordance with Observed practices in the area. Informed Opinion is that skilled farm labor is scarce, particularly at certain times of the year, e.g., at harvest. Farmers, therefore, tend to Opt for larger machinery complements and minimize hired labor input. This approach may not be the least expensive but it would reduce the uncertainty of field Operation scheduling. In lieu of a labor market "model," and in light of the evidence set forth above, the machinery model was constrained as to labor input to "family" labor. The maximum labor input available on a 400 acre 53 Agem Laaouoov see spew: .cpcoe gpcmp1-m_Fp\moo_ .nmxmwu mzmzpm m? sows: pews; com ugmoxm .cgoo mw mono mcwumumca a? xpco mcwxmwu Fpmu .Azpmp Lansa>ozv see ;S=888e_;p cocoa ep=a>apa as umzoppoe we use; on upaogm mowcpcm mmmcho a .Ammpmepm com Fpmv open umm>gmg m.aoeu mzow>mga umacm Awupau .- 1- -- wom\_om .- moo\mpm mpo\mpm mpm\eme smeam wom\o_e wom\o_e 11 opop\m~m mpm\o~e mom\mpm mpo\-m mpm\eme ucmpa mom\ope wom\ope 11 mpop\mmo mpm\ope moo\m_m m~o\mmm mpm\eme .ppzo vpmwu mpo\m~m mom\ope wmm\o_e -1 .- mpm\ope moo\o_e mpo\o_e .- xmwe mcweam “NFP\< NN—F\< oo 11 NNFP\< moo\< m_o\< mpm\< zap; mmp—\moo~ NNF_\moo_ 11 opo_\< Amp—\moop 5N_F\aoo_ NN_F\mooP ~NP~\mo~F nxmwc PFmd e~e\omm NNF_\< nmp_\< ~P©\Nmm o_o_\< ~N_P\< ace—Q\3 u:m_a\3 mNNFP\< LmNPPwucmd Npo\mmm eom\_mw e_m\emfi epw\emm em5\opm nom\mpn mFFP\mNo mmo_\mmm Nco_\mmw mFFp\moo_ pmm>gmz wepmw~< memo cm_me_< gems: mammnemmzm mammnxom mcmmm x>mz ccoo covpmemao \mpao aocu mcoeumeaao space to m=_swp o.a apaae 54 farm was one full time operator able to work up to 12 hours per day six days per week. Additional family labor is assumed to be available from a spouse or adolescent children during peak periods Of labor demand. On a 600 acre Operation, two full time labor Operators were assumed. The other major variable which affects field operations is weather availability. Weather variability is used to define sequences Of daily work/no work sequences for various field operations. Much of this work is based on a workday simulation developed by Tulu (1973). Inputs to this model includes five weather descriptions and two soil parameters. The weather data are: (1) maximum daily temperature; (2) minimum daily temperature; (3) daily precipitation; (4) daily open pan evaporation; and (5) a binary snow condition (snow/no snow). The soil parameters are water holding capacity and soil moisture level criteria. Tulu's model develops a soil moisture "budget" which accounts for the level of moisture in the soil. If on any day the moisture budget indicates a moisture level below a specified critical level, a workday has occurred. Spring planting is also constrained by a minimum soil temperature Of 50°F. Tulu's model continues to define work/no work days subject to the above criteria until the soil freezes in the fall. Tulu's workday simulator is employed to generate sets of work/no work day data for 28 years of Saginaw Valley weather data. The machinery model then develops a complement that accomplishes the designated field operations given the workday sets for each of the 55 28 years of available data. In years in which weather is more adverse, larger sets Of machinery are required than in those years of more favorable weather. The machinery sets are then ranked in descending order of cost. The 28 machinery sets are used to establish the per- centiles of the design criteria cumulative distribution function. For example, a machinery complement ranked 14th out of 28 in cost (the 50th percentile) would be able to accomplish the designated field operations required for a given cropping system on average, half the time. In this study, a design criteria of 80% was adopted. This means that the machinery complements selected for the enterprise budgets developed here would, given that historical weather data is an accurate predictor Of future weather patterns, accomplish the prescribed field operations within the established timeliness constraints in eight out of ten years. An average annual cost per acre is computed for each machinery set. Depreciation, interest, repairs, insurance, shelter, and fuel cost are considered. Machinery costs are based on 1979 dealer list prices. Machinery is assumed to have an eight year useful life with a salvage value of 10% Of original purchase price. Depreciation is calculated by the straight line method. Repairs are calculated on an annual use basis. Insurance and shelter costs are figured as a fixed percentage of original purchase price. Interest on the investment is computed at 13% on one-half the purchase price. Standard engineering calculations with respect to machinery size, load, and speed conditions were employed to calculate fuel consumption per acre for each rotation. 56 Diesel fuel is priced at $1.00 per gallon and presented separately in the budgets. The machinery costs, in dollars per acre, and fuel consumption figures in gallons of diesel per acre for each rotation for the 400 acre and 600 acre configurations are given in Table 4.7. The design criteria employed is 80% except where noted. Hauling and Drying Costs Since the machinery simulation model makes no computations for hauling and drying costs, these figures were derived on a less formal procedure based on standard enterprise budget costs. Corn was assumed to be harvested at 28% moisture and dried to 14% moisture for storage at a cost of $0.02 per point Of moisture per bushel. Table 4.8 depicts the unit costs for hauling for each crop. Law The budgets are constructed under the assumption that only family labor is employed. Family living expenses were estimated at about $14,000 per year which is approximately equivalent to median household income in Michigan once allowance is made for differences in income tax treatment of family farms. That results in $35.00 per acre and $23.33 per acre labor charges on 400 and 600 acre farms, respectively. The purpose here is to rank rotations within size configurations and no comparisons are made between the two size configurations. 57 Table 4.7 Machinery Cost and Fuel Consumption per Acrea 400 Acres 600 Acres Machinery Cost Fuel Machinery Cost Fuel Rotation ($) (gal) (gal) 1 C-NB 68.71 8.63 66.95 8.78 2 C-SB 74.57 7.94 75.12 8.07 3 C-C-SB 83.84 8.15 84.64a 8.26 4 C-NB-B 82.83 9.44 76.32 9.98 5 C-SB-B 99.15 9.44 97.62 9.71 6 C-NB-W—B 82.56 8.22 80.45 8.88 7 C-SB-W-B 132.62 8.03 99.84a 8.25 8 C-NB-NB-B 79.40 9.26 68.05 9.49 9 O/A-A-A-A- C-C-SB-C 91.68 8.29 81.87 8.47 10 O/A-A-A-A- A-C-C-C 97.50 8.62 102.00 7.24 11 C-C-NB-W 77.36 7.46 79.12 7.63 12 NB-C-SB 65.41 8.20 58.38 8.20 13 C-C-NB-B 100.08 9.37 96.09 9.59 14 O/A-A-NB-B 117.51 10.09 98.24 9.77 15 O-NB-B 122.91 10.09 105.14 9.38 16 O/A-A-A-A- C-C-NB-C 96.69 8.51 85.27 8.69 aFor rotations 10, 14, and 15, the fuel consumption per acre is higher on a 400 acre farm than on a 600 acre farm. This is due to the size of the machinery selected by the machinery model. Machinery size is selected with sufficient capacity to accomplish the most constraining field task. This implies that the machinery is relatively inefficiently used for other field Operations. Fuel efficiency varies by type of fuel and by percent load. 58 Table 4.8 Estimated Unit Hauling Costs for Each Crop Crop Unit Cost Navy beans ................ 0.12/cwt Sugarbeets . . . . . . . . . . . . . . . . 2.75/ton Alfalfa .............. . . . 4.50/t0n Small grains (corn, soybeans, wheat, and oats) ............. . . 0.07/bu Source: Nott et al., 1979. The philosophy of pricing family labor adopted is to treat it as a fixed cost rather than valuing it on an Opportunity cost basis. An advantage of this approach is that it is not necessary to estimate what is the actual Opportunity cost of labor. A major drawback is that a given rotation with a high net return to land, relative to another rotation, may require more hours Of labor than the less profitable rotation. The disutility of the additional work is not expressly accounted for. EstimatingiRelative Prices In modeling the prices received component, the purpose is distinctly different from that Of short range forecasting. The purpose in designing a design model is to determine long term price relationships in the market. 59 Neoclassical economic theory (Henderson and Quandt, 1971) describes the conditions for a long-run multi-market equilibrium in a perfectly competitive industry. A firm is considered to be Operating in a perfectly competitive environment if: 1. The price of each good is defined and is exogeneous to the firm and therefore independent of firm production decisions. 2. At the market price, a firm may acquire any quantity Of an input it requires or dispose of any quantity Of a good it has produced without impacting the market place. In a competitive environment, if general equilibrium exists, it is defined in terms of relative prices (see Appendix B). The issue then is whether the Neoclassical general equilibrium model approximates an adequate description of the economics of cash crop markets in the Saginaw Valley. The assumption that producers are generally price takers is probably satisfied in the context under study. However, this economic model also implicitly assumes the following. 1. Perfect knowledge Of prices and quantities, both present and future, on the part of all buyers and sellers. 2. The system is closed. The possibility Of introducing exogeneous demand on production from outside the system does not exist. 3. Production functions and utility functions are static over time. This implies static technology and constant consumer preferences. llll of the above assumptions must be relaxed to Obtain an adequate description of Saginaw Valley agriculture. 60 The production of agricultural commodities is the result of a biological process. Production of cash crOps requires that the decision as to the quantity to produce must be made at one point, and the harvest is completed at a later time. Producers make decisions as to what and how much to produce based on expectations about market conditions which may or may not be fulfilled. Knowledge about future quantities and prices is incomplete. With regard to the second assumption, there are many reasons that the "Saginaw Valley" cannot be regarded as a "closed system." First, the production process itself is subject to the vagarities of weather, disease, and pestilence. Also, there are numerous goods in the market place and inputs used in production that are assumed to be exogeneous simply to keep any resulting model of manageable size. The fundamental assumption made here is that although the above assumptions necessary for a purely deterministic general equilibrium model do not exist, there may be an underlying long-term equilibrium ratio Of relative prices. A great deal of the short-term variation in prices follows no distinct pattern and is thus transitory in nature. Such random variation is a source of price risk to farmers and may be described within the modeling context by an estimated value for variance Of a probability distribution. Some changes cannot be regarded as transitory from period to period. Development and adoption of new technology represents a change that is defined over time and once accomplished represents a permanent change. The non-transitory but gradual changes over time represent trend. 61 The implications Of trend may be illustrated as follows. In a two product, one input world, PPF1 represents the production possi- bility frontier. I1 represents consumers' indifference curve between the two goods. General equilibrium theory suggests that utility maxi- mizing consumers and profit maximizing producers Obtain a unique equilibrium in which the rate of exchange between goods determines relative prices. Technical change, which may alter not only the locus but the shape Of the production possibility frontier, will alter the relative price ratio at which goods exchange in the market. In Figure 4.1, this is illustrated by the shift from PPF1 to PPF2 and the corresponding change in the price line (and slope of the price line) from P1 to P2. A similar price occurs if changing consumer preference patterns alter the shape of consumer indifference curves, consequently altering the relative prices at which goods exchange. Figure 4.1 Changes in Relative Prices, Illustrated. 62 As stated at the outset, the purpose here is to identify the longer term trends in the relative price relationship while filtering out transient disequilibra. In order to derive relative price ratios, the price of one commodity must be selected as numeraire. The numeraire should have the following characteristics: the Saginaw Vally should comprise a small portion of overall market production. The "market price" should be based on a relatively large volume as distinguished from "thin" markets for specialty crops. The crop selected as numeraire is corn. Prices received by Michigan farmers were Obtained for the seven crops in the study for the years 1950 through 1978. Price ratios for the six crops relative to the price of corn were calculated for each of the 28 years of data, prices are from Michigan Agricultural Statis- tics, various years. The gradual, non-transitory change in relative prices such as represented by a change in the price line in Figure 4.1 is the basis of trend. This must be removed to obtain a more accurate estimate of the transitory change. To remove trend from the numbers, a least squares regression was estimated with time as the independent variable. The estimated equations are presented below: Navy bean price _ - 2 _ l. . — -2.64 + 0.146 t1me R — 0.46 Corn pr1ce (_].33) (4.74) Soybean price _ - 2 _ 2. . - -O.35 + 0.0395 t1me R - 0.62 Corn pr1ce (_0.9]) (6.53) Sugarbeet price _ - 2 _ 3. . — 1.99 + 0.129 t1me R - 0.26 C""" "T'"9 (0.726)(3.02) 63 4. Oat pr1ce . = 0.240 + 0.0053 time R = 0.32 Corn pr1ce (2.45) (3.48) *5. AlifilfaYBZLfe = 2.36 + 0.253 time R = 0.33 p = 0.390 p (0.277)(1.93) *6. Wheat price _ 0 57 p = 0 677 Corn price -(§‘;g) —‘O 030 U'IN v0 (9. u-l S (D 30 ll These equations preceded by an asterisk exhibited auto correlation and and were re-estimated using the Cochrane-Orcutt technique. Examination of the residuals Offers no evidence of a non-linear relationship to time. Forecasting with a simple linear regression equation can give spurious results particularly when forecasting substantially beyond the range of the original data set. This approach, despite its shortcomings, was employed here. The expected price employed in the analysis are presented in Table 4.9 Table 4.9 Expected Cash Prices Crop Price Corn .............. $ 2.50/bu Navy beans ........... 22.60/cwt Soybeans ............ 6.53/bu Sugarbeets ........... 30.94/t0n Oats .............. 1.44/bu Alfalfa ............. 60.73/ton Wheat .............. 3.30/bu 64 At this point all expected value elements of the model have been defined. It is now possible to rank the sixteen crOpping systems according to net returns to land, and such results are presented in Chapter VI. CHAPTER V METHODOLOGY: SIMULATION OF CUMULATIVE DENSITY FUNCTIONS OF NET RETURN TO LAND Introduction The data and methodology necessary to rank the cropping systems in an expected value sense were set forth in Chapter IV. One of the primary objectives of this research is to evaluate the economic per- formance of alternative crop rotations in a risky environment. The Objective of this chapter is to present the necessary methodology for evaluating the riskiness associated with each of the sixteen crop rotations. Included are: 1. modeling risk using stochastic dominance; 2. an explanation of the ”tools" used and the data required; and 3. the method used to obtain the data used in the model. Methodological Approach The basic form Of the model outline used was presented in the last chapter as follows: Gross Income - Costs = Return to Land. A net return to land is developed for each rotation, not for each crop, due to the "complementarities" among crops. This was illustrated in the last chapter with development of the budgets for each crop in each rotation and the machinery simulation model used to develop machinery costs for each crop rotation. Costs are not deterministic since prices 65 66 and application levels for inputs are not known with certainty before planting; but their variability is of a much lower order of magnitude than variability of gross income. In this analysis, costs are to be regarded as deterministic while gross income is a random variable. The approach adopted is to define the probability distributions of the components of gross income and then simulate 100 "draws" rep- resenting lOO alternative states of nature. Upon arranging the net th returns to land (NRTL) in ascending order of size, the i observation can be taken as a reasonable estimate of the ith/(100+l) fractile. This approximation works irrespective of the form of the underlying probability distribution (Anderson, 1974). Gross income is defined as: The yield of crop i per acre times the price of crop i per unit, times the number of acres planted to crop i. Acreage alloted to each crop in the rotation is equipro- portional. For example, on a 600 acre farm planted to a corn-Navy bean-Navy bean-sugarbeet rotation (C-NB-NB-B), there would be 150 acres in corn following sugarbeets, 150 acres in Navy beans following corn, 150 acres in Navy beans after Navy beans, and 150 acres of sugarbeets after Navy beans. Costs are presented on a per acre basis; gross income and net returns to land are on a per acre basis. Gross income is: (yield/acre), x (price/unit), i = 1 to N number of crops. 21 ll M2 1 l 67 The variability of yields and prices give gross income its stochastic nature. Therefore, for any rotation, the probability density function for gross income is determined by the probability density functions for price and yield. The determination of a distribution involving several random variables is considerably more difficult than assessment of a distribution of a single random variable. However, there is a plau- sible simplifying assumption that makes the simulation of the gross income distribution tractable. The assumption is made that each farm is a price taker; each operator may vary output as much as he wishes and have no impact on market price. This assumption assures the statistical independence Of the price and yield variables and insures that their relationship is multiplicative; there is then no need to attempt to define condi- th crop is E(P) x tional probabilities. Thus, gross revenue for the i E(Y), where E is the expectation operator. The relationship between income distributions for each crop within a rotation is additive. It can be shown that for X1 random variables that E(x +X +...+x1.) = E(X])+E(X2)+...+E(X.). l 2 1 For the present case, TIM: E (income for crop i) i= 1, ..., n crops 1 E (gross income) = .i in a rotation. 68 For cropping systems as they are defined for this study, E(gross income) =1fiE(P] x Y1) +1Nupz x Y2) + + f'q— E(Pn x Y") where N = the number of crops in the rotation; Pn = price of crop n; and Yn = yield of crop n. The next step is to determine the parameters of the probability density functions. Expected yields of each crop in each rotation were presented in Chapter II and procedures for determining expected prices were developed in Chapter IV. Random Variables--Prices and Yields Evidence suggests that yields are not normally distributed in many instances; Day (1965) found that yield distributions may be some- what negatively skewed. One hypothesis is that as management techniques improve, expected yields will approach the biological limit of the system; thus, the preponderance of yields Observed will be Closer to the upper bound of possible yields. However, in a year of adverse weather or unusual pest or disease problems, yields could be quite low despite best management practice. This suggests a long left tail for yield probability density functions. Also the effect of government price support mechanisms is to truncate the left tail of the price distribution while the upper bound is not Similarly limited (see Appendix I). This introduces skewness in the distribution of prices. 69 In light of these facts, probability density functions should be flexible enough to accommodate the possibility of normality as well as varying degrees of skewness and kurtosis in sample distributions. Beta distributions were considered to be an adequate approximation. The Beta distribution has the probability density function of the form: R-l S-l Y B(A—YS if OsYsl fB(Y) = ( 9 ) 0 elsewhere R and S are positive real numbers. B(R, S) is given by: : i2 where F (X) is (A-l)! MA B(R, S) = T ('8, I" The Beta distribution has the desirable property that the density function may adopt a wide variety of shapes, depending on the values of R and S (Derman et al., 1973). The Beta function has the less desirable property that it exists only on the closed interval [0, l] interval unlike the standard normal which is defined on the open interval - 0°, + co . Estimates Of the Beta parameters are derived from estimates of the mean and variance from the following formula (Derman et al., 1973): “ 1-" -1 §=Gy[5( HZ) ] (1) 6y (“H-“)4 ’s‘=(1-13)[“J(“L ] (2) .Y 82 70 Since the Beta distribution exists only on a [0, l] interval, it is necessary to transform estimates for the mean and variance to a O, 1 scale. This implies that upper and lower bounds must be defined for each distribution; then the random variable, in this case yield or price, can be transformed to a value on the proper interval scale. Measurement of Variability The total variation in prices and income can be partitioned into two parts, that which is systematic and reflects long run biolog- ical, technological, and economic trends and a second random portion which may be regarded as unpredictable. The assumption is that farmers do recognize long term trends in yields and relative prices and, therefore, view deviations from trend as a "random" element. There are several methods used to determine the current level of the time series. A simple approach is to assume that the current level is identical with the value for the previous year, hence the random element would be represented by first differences. Another approach is to employ some form of moving average as an estimate for the current value and then differences between observed values and estimated values represent the random elements. A third approach is to employ some general index to represent "real" values and deviations from the long run deflated series represents the random element. There are arguments for and against each alternative procedure. The approach adopted here assumes that the systematic component Of the time series can be approximated by a polynomial function. This assumption appears substantiated by the sample yield and price data. Once the systematic 71 component of total variability is estimated, it can be removed. The remainder represents an estimated random variability. Estimating Variability of Yields Yield probability density functions were estimated from a time series of yield Observations from a sample of six farms (see Appendix B for raw data). Each of the time series for each crop was detrended using linear regression of yield on time. As pointed out earlier, some of the yield probability density functions may be non-normal. The residuals of each regression were tested using the Wilks-Shapiro test (see Appendix D). Variance was estimated from the pooled regressions; the least- squares-with-dummy-variables (LSDV) method is a commonly used method of pooling time series with cross-section data (Madalla, 1977). The set of six detrending equations for sample yields are of the form: Yieldi = “i + 8i time where i= 1, ... , G sample time-series. In order to determine the desirability Of LSDV as a pooling technique, Madalla (1977) suggests testing a set of three hypotheses concerning equation parameters. 1. H0: 0] = 02 = ... = on; B1 = 82 = ... = B HA:01:02:...za;811822...28 1'1 1'1 Rejection of the null hypothesis implies that there are differences among the coefficients of the sample detrending equations and the 72 data should not be directly pooled. The null hypothesis was rejected in all cases using a 5% test. The second step tests the hypothesis that the Slope coefficients are equivalent; that is: The F ratio Obtained for each of the seven crops indicated that the null hypothesis could not be rejected at the 5% level. The third set of hypotheses represents a conditional test: 11 M m 3. H0: 0] = oz ... on given 81 = 82 z 02 ... x on given 81 = 82 = ... = B . The null hypothesis was rejected for all seven cases at the 5% level. The results of these tests indicate that a LSDV approach is appropriate for pooling the data. LSDV equations were estimated for each crop. The mean-squared error of the estimates represents an estimate of yield variation. The estimated standard error represents an estimate based on an expected value of the field sample yields. Since the expected value of yields employed in this model are obtained from a different source than the field data used in estimating variability, the coefficient of variation is employed to determine the variance of yields with different expected values than those of the same in the field sample. Furthermore, this approach provides differing values for estimated variance depending 73 on the expected yield of a crop in a specific rotation. For example, the coefficient of variability for corn is 24.9%; therefore, the standard deviation used for corn with 115 bushels per acre expected value is 28.6 bushels per acre, while the value used for 110 bushels corn is 27.4 bushels per acre. Presented in Table 5.1 is the estimate Of variance obtained for each crop and the coefficient of variation. Table 5.1 Estimates of Yield Variationa Coefficient of Variation Crop Unit Standard Deviation (%) Corn bu 20.0 24.9 Navy beans cwt 4.6 31.5 Soybeans bu 7.9 26.9 Sugarbeets ton 3.2 17.9 Oats bu 20.2 31.1 Alfalfa ton 0.9 25.5 Wheat bu 10.8 25.6 aSee Appendix E for a more detailed discussion of the procedure used and the parameter values obtained for the estimated equation. Variability of Prices The approach in this study for the estimation of price varia- bility is similar to that employed in estimating yield variabiltiy. A time series of prices received by Michigan farmers is detrended by regression and the mean square error is used as an estimate of price variance. The approach adopted is controversial when applied to prices. 74 The difficulty encountered by employing the simple detrending scheme used here is the assumption that estimates of price variability based on historical data are necessarily good predictors of future price variability. In the 19505 and 19605, grain surpluses coupled with government price support programs became minimized price varia- bility. In the 19705, U.S. grain markets became much more interde- pendent with the rest of the world and more volitile. These changes may have a differential impact on different crops. A case can be made for the alternative that the 19805 may see a return to more stable farm prices as price stability is a direct objective Of government policy. At any rate, the model is flexible enough to accommodate changes in price variability scenarios and the assumption is set forth here that historical price variability is a reasonably good predictor of future price variability. For all price series a quadratic function represented a superior fit to the data over a linear fit or a 3rd degree polynomial. This sug- gests falling nominal (and real) farm prices through the 19505 and 19605 and increasing nominal prices through the 19705. Farm prices (at least in Michigan) have not followed the trend suggested by indices, such as the C.P.I. The approach adopted for this analysis is to estimate price variability as the mean square error of a regression of prices received on time (see Appendix F. As suggested above, a quadratic equation was appropriate for all seven crops and the price variances estimated are presented in Table 5.2. 75 Table 5.2 Standard Deviation and Coefficient of Variation of Prices Received by Michigan Farmers Coefficient of Variation Crop Unit Standard Deviation (%) Corn . $/bu 0.45 18 Navy beans $/cwt 2.65 31 Soybeans $/bu 1.08 18 Sugarbeets $/ton 3.56 41 Oats $/bu 0.45 14 Alfalfa $/ton 2.34 9 Wheat $/bu 0.95 25 / The coefficient of variation is computed from mean square error and is used to compete a variance based on expected prices. For example, the coefficient of variation estimate of the price of corn is 18%. This translates to a variance of 0.20 based on a $2.50 expected corn price.1 Correlation Coefficients It can be shown that the variance of a linear combination of random variables is: 02(Y1'1'Y +...+Yn)=o; +02 +...+62 + z z o izj. 2 1 Y2 yn i=1 j=1 yiyj For the present case, 02 (gross income) = 02 (income cropl) + 02 (income cropz) + . n n + 02 (income crop") + Z Z cov (income crOpi, income cropj) i=1 j=1 iz,j. 76 In determining gross income variance, covariance between crops must be determined. It was previously assumed that covariance between yields and prices is zero. This is based on the assumption that individual farm units are perfect competitors and is appropriate only at the firm level. The covariance between crop incomes is due to covariance between prices and yields of different crops in a rotation. ’ Correlation coefficients were computed using the random disturbances of the least squares dummy variables (LSDV) pooled regression equations. Since all crops (except soybeans) were grown in close geographical proximity, weather stresses and soil types would be similar among all samples. It is realized that some inaccuracy may be introduced since management practices vary from sample to sample. The correlatiOn coefficient between soybeans and other crops is least accurate since the sample soybean yields were obtained from Monroe County farms which are about 60 miles south Of the Saginaw Valley region. 1 Correlations between prices were computed between the residuals 0f the price detrending equations. The coefficient estimates used in this study are presented in Tables 5.3 and 5.4. Appendix F presents a more detailed discussion of the method employed in estimating correlation coefficients. 77 Table 5.3 Correlation Coefficients for Yields Crop Corn Navy Beans Soybeans Sugarbeets Oats Alfalfa Corn 1.00 Navy beans 0.07 1.00 Soybeans 0.11 -0.03 1.00 Sugarbeets 0.05 -O.15 0.07 1.00 Oats 0.10 0.21 0.05 -0.15 1.00 Alfalfa 0.08 0.13 0.16 -0.13 0.00 1.00 Wheat -0.01 0.02 -0.05 -0.05 -0.14 -0.27 Table 5.4 Correlation Coefficients Estimated for Prices Received by Michigan Farmers Crop Corn Navy Beans Soybeans Sugarbeets Oats Alfalfa Corn 1.00 Navy beans -0.07 1.00 Soybeans 0.94 -0.08 1.00 Sugarbeets 0.81 0.18 0.75 1.00 Oats 0.97 -0.15 -O.l4 0.74 1.00 Alfalfa 0.95 -0.27 0.96 0.62 0.98 1.00 Wheat 0.25 0.51 0.13 0.61 0.13 -0.04 78 Upper and Lower Bounds on Distributions The Beta distribution is defined on the closed interval [0, 1]. It is, therefore, necessary to estimate an upper and lower bound for each yield and price distribution. All information regarding the effect of moments higher than the second is embodied in the values of the bounds of each distribution. The procedure used to estimate upper and lower bounds involved selecting the extreme observations from the detrending equations for yield and prices. The value of the extreme observation was computed as a percentage of the trend value at that point in time. The value that represented the‘greatest percentage increase over trend was selected as the upper bound of the distribution. Conversely, the value that fell below its respective trend values by the greatest percentage was selected as the lower bound of the distribution. The only exception to this procedure was that the lower bound of prices was set at the government support or loan rate for those crops where a support program exists. Presented in Table 5.5 are the percentages used in computing upper and lower bound values for the distributions. With information on expected values, variances, and bound values, it is possible to describe an univariate probability dis- tribution for the yield and price of each crop. These distributions become the "marginal" distributions of a multivariate gross income distribution. The remainder of this chapter will be devoted to a description of the program that simulates net returns to land. 79 Table 5.5 Percentage Rates Used in Calculating Upper and Lower Bound Values Crop Upper Bounda Lower Bound Prices: Corn 1.52 2.10b Navy beans 1.89 0.60 Soybeans 1.51 5.25C Sugarbeets 1.89 6.40 Oats 1.34 7.60 Alfalfa and oat straw 1.12 8.90 Wheat 1.76 2.35C Yield: Corn 1.56 0.37 Navy beans 2.05 0.32 Soybeans 1.56 0.37 Sugarbeets 1.46 0.53 Oats 1.66 0.13 Alfalfa and oat straw 1.70 0.30 Wheat 1.51 0.44 aExpected value times all upper bound and lower bound figures except those indicated by other footnotes. bLoan rate. CSupport price. 80 Simulation of Gross Income It is common in attempting to derive the behavior of probabilistic systems to turn to Monte Carlo solution procedures (e.g., Wagner, 1975). Exogeneous variables can be described as random variables and sample states of nature obtained. System output levels may then be derived for each state of nature. The initial step is to describe the exogeneous variables as probability density functions (PDF). Numerical procedures exist which enable PDF's to be simulated on a computer (Naylor et al., 1966). Such procedures have been devel- oped for a wide variety of probability distributions. Process gener- ators exist for many univariate distributions. These methods may be employed to simulate any number of stochastic variables in a system assuming all underlying processes are statistically independent. If this assumption is not satisfied, as is the case here, a multivariate generator is required. Multivariate process generators have been developed for some distributions, notably the multivariate normal and Wishart distributions (Naylor et al., 1966). A generalized, multivari- ate process generator has been developed to approximate the situation in which the marginal distributions are not normal (King, 1979) and is used here. Experience with the process generator in this study indicates an error of about 10% between the correlation coefficients among the generated sample vectors and the correlation values entered as data.1 1For a complete discussion of the theoretical justification of this approach and presentation of a Monte Carlo experiment with 1,000 draws to examine behavior of correlation, see Appendix A (King, 1979). 81 As used in the present situation, a vector of 100 "draws" is selected from a distribution describing yield and a distribution describing price for each crop in each rotation. The distribution of gross farm income is then defined as: Yieldij x Priceij)/M 1= 1, 2, ... , n draws "ME Gross Income. = ( 1 1 J .j= 1, 2, ... , M crops. The non-stochastic elements comrpising the costs associated with a particular rotation are then subtracted from each of the i gross income samples leaving "i" net returns to land. The 100 net return to land values are then rank ordered from lowest to highest. The ith return to land is then an estimate of the ith fractile of the cumulative probability distribution of returns to land. These discrete estimates of the cumulative probability distri- butions of net returns are employed to rank rotations according to the rules of first, second, and third degree stochastic dominance. Fig- ure 5.1 represents in block form the decision model as used in this analysis. Appendix G presents the FORTRAN code of the model along with sample output. Summary As stated in the research objectives, the goal is to rank six- ‘teen cropping systems as to desirability to the individual farm decision rnaker operating in an uncertain environment. This chapter described the process by which the probability distributions for crop- yield and Input: Mean, variance, upper bound, and lower —-—¢ Uniform to MY bound for each distribution simulated 82 Multivariate (MV) Standard Normal Generated l Transform: MV Standard Normal to MY Uniform on [0, 1] Interval Transform: MV Beta on [0, l] I Transform: Beta [0, l] to Appropriate Scale Interval Compute: Beta Parameters K1, K2 from " 2 X, ox. UBX, LBx Less: Generated Cash Costs 1 Sample Vectors for Price and Yield 1 Generate Gross I Income Values I Less: Machinery, Fuel Costs and Hired Labor Costs Less: Hauling, Drying Costs Less: iFamily Labor Re-order Values from Low to High DistribUtion of Net Returns to Land Input: 100 random numbers for each yield and price distribution gen- erated and correlation matrix. Uses inverse transform method to generate multivariate uniform distribution (see Appendix H). Uses inverse transform method. Sample vectors have covariance as specified by user. Use sample vectors to generate lOO gross income values. Generates cash costs for each rotation. Subtract from gross income. Inputs: Application or use rate of input and price of input. Input as data from machinery simulation model. A machinery cost per acre based on farm size (400 A; 600 A) and reliabil- ity critical (80%). Fuel use per acre. Input as data. Based on custom rates. A constant: $35.00/acre on 400 acre and $23.33 on 600 acre farms Reorder 100 values of net return to land from lowest to highest: ith va;ie repre- sents estimate of ith fractile such that P (net returns i). Prints 100 fractiles for net return to land for each rotation. Then apply stochastic dominance rules to evaluate. Figure 5-1 Block Representation of Stochastic Generator to Simulate Net Returns to Land. 83 crop price are obtained and assembled to estimate a distribution for gross farm income and ultimately an estimate for net returns to land. The next chapter will present the results of ranking sixteen cropping systems using both the deterministic model and a stochastic model for a 400 acre and a 600 acre owner/Operator cash crop farm. CHAPTER VI RANKING 0F SAGINAW VALLEY CROP ROTATIONS Introduction The sixteen rotations for 400 and 600 acre operations are ranked using alternative criteria; they are expected value and first, second, and third degree stochastic dominance. The input/output, yield, and price relationships used were presented in Chapter V. Tables 6.1 and 6.2 present the expected value rankings in order of their net return to land. The C-NB-B rotation has the highest net return to land for 400 and 600 acre configurations. In contrast, the C-C-SB and O/A-A-A-A-A-C-C-C rotations yield the poorest return on the 400 acre and 600 acre farms, respectively. Rotation #14, O/A-A-NB-B, ranked second for both sizes and is considered to be agronomically superior in terms of impact on soil structure and organic matter. Rotation #8, C-NB-NB-B, ranked third. If the agronomists estimates of relative yield differentials are correct, then comparing rotation #8, C-NB-NB-B, with #14, O/A-A-NB-B, O/A-A could be preferable to C-NB in the first two years. All rotations through the sixth place included sugarbeets; arni no rotation that included sugarbeets ranked lower than ninth. Tfue inclusion of successive years of Navy beans on the same field was C<>r15idered by agronomists to be an instrumental factor in the declining 84 85 mpnwmmoa we mmwcw>m umpsmwmz mgu .mw page ”mmcmm ovumwpwamaoca m cw com: me =umpomnxm= .mmeouuao a .pmmgz u 3 ”me_me—m u < ”mono u o “mummncmmam u m mmcmmnaom u m mmzmmn x>mz u mz accoo u on _N.mm oo.mm so.- m_.w ew.mm Pe.~m mm.mmm mm1U1u m oo.mm oo.mm an.mm No.w om.mm mo.mm Fm.eo~ u-o-u-<-<1<1<-<\o op mo.mm oo.mm mm.¢~ mo.w Nc.mmp mm.~m om.m~m m-21mm1u N Nc.mo oo.mm Fn.o~ we.“ om.- mm.om op.omm 31m21u-u PP o_.o~ oo.mm oo.mm mm.m wo.Pm mo.wm mn.mom u-mm-u-u-<1<-<\o m mm.mm oo.mm mm._m em.“ um.e~ mm.me mo.mmm mm-u N nm.m~ oo.mm mm.e~ Pm.w mo.mm No.0e N~.Pmm u-mz-u-u-<1<-<\o op mm.nm oo.mm op._~ mo.o~ _m.mmp o_.om mp.~mm m-mz-o mp mp.mm oo.mm o~.ep o~.m F¢.mo om.mv ~¢.No~ mm-U1mz N_ wm.mop oo.mm mm.o~ mc.m -.mo P~.Nm mo.om~ mz-u _ om.mm_ oo.mm o_.em mm.m wo.oo~ mo.~o eo.mnm m-mz-u-o m_ Fm.mmp oo.mm mm.em NN.m om.mw m~.mo mo.~mm m-3-mz-u o mm.wep oo.mm om.mm ee.m m~.mm mm.wm me.ewm m-mm-u m o~.mep oo.mm mo.e~ o~.m oe.am Po.Fo mo.mmm m-mz-mz-o m _m.omp oo.mm mm.mm mo.o_ _m.mpp mm.me mm.mwm . m-m21<1<\o «P op.mmp oo.mm mm.~m ee.m mw.~m m~.oo mo.wmm m1mz1u a use; op Loom; mcwxeo pmou mpmou mumou meoocH mumpmpom maceu .oz eczema >F_Emu mew—so: Foam xewcwsomz gmmu mmoew cowumpom n=umpomaxm= n:nmuumgxm= Amco<\mv seed mco< cov Low >L6553m omcoaxu1m5ouz~ ~.o m_ocp .mmeoouzo wpnwmmoa mo mmmem>m emanmwmz asp .mw was» ”mmcmm ovumwpmnmnoea m cw vow: mw =umaomaxm=n .pmmcz u z moerNFm n < ”mama u o ”mpwmncmmzm n m mmcmmnxom n m mmcmma a>mz n mz "ceoo u on 86 —N.Nm mm.MN e~.mN eN.N oo.No— om.mm FN.voN u-U1Q1<1<1<1<1<\o OP Nm.No mm.mN No.NN 0N.m eo.em F¢.Nm mo.moN mm-o-u m om.mN mm.mN FN.ON mm.N NF.mN mm.mm o_.ooN 21mz1U1u FF eN.om mm.mN mm._N No.w N_.mN Nm.me mo.mmN mm-o N oe.Pm mm.mN oo.mN Ne.m Nm.Fm mm.mm NN.moN u-mm1o1u1<1<1<\o m me.mm mm.m~ ww.eN mm.m NN.mw Nm.o¢ NN._NN u-mz-o-u-<-<-<\o o_ Pm.o_p mm.MN om.ep ON.N mm.wm oo.oe Ne.NmN mm-o1mz Np Pm.N—P mm.mN mm.eN mN.w ew.mm mN.Nm om.mNm m-3-mm-u N wo.m__ mm.MN o~.—N mm.m ¢P.mo~ o_.oo m_.Nmm m-mz-o mp mo.mpp mm.MN mm.ON mN.w mm.oo PN.Nm mm.omN mz-u p oo.me_ mm.mN o_.em mm.m mo.om mm.Nm eo.mnm m-mz-u-o mp mm.FmP mm.mN mm.eN mw.w me.ow mN.mm mo.Nmm m-31mz-u o Nm.FoP mm.mN oo.Nm FN.m No.Nm mm.mm m¢.¢mm m-mm-u m me.NN_ mm.MN wo.¢N ae.m mc.wm _o._o mo.mmm m1m21mz-u w NN.Nm_ mm.mN mm.mN NN.m eN.wm mm.o¢ mm.mwm m-mz-<1<\o ep eN.mm_ mm.mN mm.Nm mm.m Nm.mN mn.co mo.wmm m-mz-u e use; ow Loam; mcwxco memou mpmou momou weoocH m umpmuom mnoeu .oz cczpmm NFPEmd acmpsm: Foam Ngmcwzumz smog mmoew cowuouom :umuomaxm: n=owpumaxm= Aweu<\wv acme meo< com com Nemeszm mmcmaxN1mEoucH N.o mpnep 87 Navy bean yields experienced in the Saginaw Valley. Most cash crop farms in the Saginaw Valley grow corn, Navy beans, and sugarbeets in some configuration. Sugarbeets are grown under contract with processors; not all Saginaw Valley crop farmers have such contracts (or the necessary equipment to harvest sugarbeets). The best alternative for growers who do not have sugarbeets is a C-NB rotation. Several rotations are identical with the exception of the type of bean crop included, soybeans or Navy beans. The directly comparable pairs are: rotations l and 2; rotations 4 and 5; rotations 6 and 7; and rotations 9 and 16. In all cases, the rotations with Navy beans were economically superior to soybeans. The "breakeven" point on a 600 acre farm between Navy beans and soybeans varies with the rotation. In comparing rotations 1 and 2, expected soybean prices would have to increase from $6.53/bu. to $8.40/bu. Or, expected yields would have to be 45 bu./acre rather than 35 bu./acre. In comparing rotations 4 and 5, expected soybean prices would have to be $2.38/bu. higher or yields 12.76 bu./acre higher. For rotations 6 and 7, the breakeven increments are: $4.46/acre cw“ 23.9 bu./acre. For rotations 9 and 16 the values are $1.42/acre cw‘ 7.61 bu./acre. Comparing rotations 9, 10, and 16 with rotation 1, the "breakeven" alfalfa price increment is $14.32/ton for rotation 9, $20.40/ton for rotation 10, and $14.37/ton for rotation 16. 88 Comparison by Stochastic Dominance Rules The differing degrees of risks associated with each crop and rotation make comparison on the basis of expected net returns to land invalid for many producers; it is comparing unlike items. This emphasizes the importance of comparison where risk is expressly accounted for. In the previous chapter, a process was presented to “simulate" net returns to land when prices and yields are random variables. The result is a discrete cumulative distribution function where the ith th fractile of the distribution. element is an estimate of the i Sixteen alternative cropping systems are ranked according to the rules of stochastic dominance which were discussed in Chapter III. The rules are reproduced here for convenience. 1. First degree stochastic dominance. If rotation A is first degree stochastic efficient over rotation B, it implies that all decision makers who prefer more income to less will select rotation A. 2. Second degree stochastic dominance. If rotation A is second degree stochastic efficient over rotation B, it implies that all decision makers who prefer more income to less and are risk averse will choose rotation A over rotation B. 3. Third degree stochastic dominance. If rotation A is third degree stochastic efficient with respect to rotation B, this implies that all risk averse decision makers prefering more income to less but who are less risk averse as the absolute level of wealth increases will prefer rotation A to rotation B. b. of .' '11 l:', oe‘“! \ J." -. np-A. \-1 o.»- tn» 3... a»... CJ[_ :‘fr if" 89 Stochastic dominance rules stand in hierarchical relationship to one another with first degree dominance being the most comprehensive; i.e., if rotation A is first degree dominant over 8, then it is also second and third degree dominant over B. However, if it is known that A is third degree stochastic dominant over 8, A may not be first or second degree dominant over B. The rule of transitivity also applies but only up to the weakest rule in the relationship. For example, if A dominates B by first degree and B dominates C by second degree, then A dominates C but only by second degree. The first degree relationship between A and C is undefined without a direct comparison of the two. Results of Analysis on 400 Acres Using a stochastic dominance criteria, a comparison of all rotations was undertaken for both a 400 acre and 600 acre farm. First, comparison was made among all rotations employing the first degree stochastic dominance rule. Where this was not decisive, comparison was made using the second degree stochastic dominance rule and similarly, comparison by third degree was undertaken where the second degree rule did not give a clear result. Figure 6.1 presents the cumulative distribution functions of rotations 1 and 14 for illustration. This represents an example of first degree stochastic dominance of rotation 1 by rotation 14. Figure 6.2 presents a comparison of rotations 4 and 14. In this case, first degree stochastic dominance suggests no clear choice between the alternatives. Application of second or third degree dominance criteria may resolve the issue. 90 .eemd wco< ooo1-cowuuczd xpwmcoo m>wpm_=E=o P.o mezmmd Ameo<\mv name on ccspmm amz mNo coo mNm omv mum oom mNN omp mm o mm- 1.4%....dq..._.n_JA-..........uJ.n.-J.]fiq.. .i 0.0 op. ON. m-mz-u v cowumuom m om. I «J 93 F8382. < N m L m. ”S...” I M. H a ”8.“... 1 o q I. D. l Om .uom u” 1. «1+ --. A ”non. mom. ...-.8. u oo._ 91 ELmd meo< oom1-cowpuczd apwmcmo m>wumF353u N.m mesmwd Ameu<\mv use; op ccapmm amz or. om. mum coo mmm omv mum oom mNN omp mu o mm: 1...quJ.—..44qaqua-.d.i1...d-.3q-ddu..i”4.3d.88_1 m-mz-u v cowuwuom m m-mz-<1<\o vp cowpmuom < ll]Lllrllllal[I'LallIllljillllllLlL.lllallJll.lll Om. ow. om. om. ON. om. om. co.— 92 Table 6.3 presents the results of ranking for a 400 acre farm using the first and second degree rules. Table 6.4 presents the result of a 400 acre farm using all three stochastic dominance rules. Some rotations appear on more than one line, thus their ranking appears ambiguous. This should be interpreted as follows: where a rotation appears at more than one rank level implies that the highest stochastic dominance rule (lst, 2nd, or 3rd) was inadequate to determine a preference between that rotation and others at that level or rank. For example, at rank 3, second degree stochastic dominance rules indicate no preference among rotations 8, 6, and 12. At rank 4, the preference among 5, 6, and 12 is ambiguous; however, the preference between rotations 8 and 5 is clear with 8 being preferred to 5 by all risk averse, income preferring decision makers. In other words, 8 is preferred to 5, and 5 is preferred to 13, but the relationship between any of these three and 6 or 12 cannot be determined on the basis of second degree stochastic dominance. Table 6.4 presents a ranking which includes third degree stochastic dominance. The use of third degree stochastic dominance reduces some of the ambiguity in the rankings, bUt not all. Second degree stochastic dominance is presented separately, since the assumptions necessary for first and second degree stochastic dominance are more easily accepted with respect to most farm managers. Third degree dominance requires declining risk aversion as the absolute level of wealth increases. This assumption is more tenuous; it Table 6.3 Ranking of Sixteen Cropping Systems on a 400 Acre Farm Using 93 First and Second Degree Stochastic Dominance Rotation Expected Net a Rank No. Crops Rotated Return to Land 1 4 C-NB-B 112.10 2 l4 O/A-A-NB-B 156.51 3 8 C-NB-NB-B 149.70 6 C-NB-W-B 138.21 12 NB-C-SB 92.19 4 5 C-SB-B 148.99 6 C-NB-W-B 138.21 12 NB-C-SB 92.19 5 13 C-C-NB-B 132.56 6 C-NB-W—B 138.21 12 NB-C-SB 92.19 6 l C-NB 105.22 12 NB-C-SB 92.19 7 15 O-NB-B 69.02 9 O/A-A-A-C-C-SB-C 70.10 10 O/A-A-A-A-A-C-C-C 58.66 16 O/A-A-A-C-C-NB-C 75.57 8 15 O-NB-B 69.02 10 O/A-A-A-A-A-C-C-C 58.66 16 O/A-A-A-C-C-NB-C 75.57 11 C—C-NB-W 69.02 2 C-SB 75.25 9 3 C-C-SB 57.21 7 C-SB-W-B 68.08 aExpected net return to land figures are taken from Table 6.1. Table 6.4 Ranking of Sixteen Cropping Systems on a 400 Acre Farm Using 94 First, Second, and Third Degree Stochastic Dominance Rotation . Expected Net a Rank No. Crops Rotated Return to Land 1 4 C-NB-B 172.10 2 l4 O/A-A-NB-B 156.51 3 8 C-NB-NB-B 149.70 6 C-NB-W-B 138.21 4 5 C-SB-B 148.99 6 C-NB-W-B 138.21 5 5 C-SB-B 148.99 12 NB-C-SB 92.19 6 l3 C-C-NB-B 132.56 12 NB-C-SB 92.19 7 l C-NB 105.22 8 9 O/A-A-A-C-C-SB-C 70.10 9 ll C-C-NB-W 69.02 10 O/A-A-A-A-A-C—C-C 58.66 16 O/A-A-A-C-C-NB-C 75.57 1 10 2 C-SB 75.25 11 15 O-NB-B 69.02 12 3 C-C-SB 57.21 7 C-SB-W-B 68.08 aExpected net return to land figures are taken from Table 6.1. 95 implies older farmers with a higher equity interest are less risk averse than younger, more highly leveraged farmers. Extension work- shop experience in Michigan indicates, at least with respect to forward pricing behavior, that some older farmers are more risk averse than many younger farmers, despite their higher net worth.1 Results of Analysis on 600 Acres On a 600 acre farm moves, rotation 14 becomes competitive with rotation 4. This is true with or without the use of third degree stochastic dominance. Rotations 7 and 15 tend to benefit most in the larger configuration; moving from positions 11 and 12, respectively, on 400 acres to 6 and 7, respectively, on 600 acres. Rotation 8 although clearly inferior to rotations l4 and 4, represents a superior strategy to rotation 6 on 600 acres. Rotation 6 differs from 8 by the substitution of a wheat crop for the second year of Navy beans. Although agronomists caution against successive plantings of Navy beans and expe- rience on the Saginaw Valley Bean and Beat Research Farm indicate that longer periods between successive plantings of Navy beans is desirable, the evidence here suggests that the simple substitution of wheat for Navy beans is a marginally inferior strategy particularly on larger operations. The long rotations, rotations 9, 10, and 16, would not be the rotations of choice on either the 400 or 600 acre farms although they were superior to the standard "corn belt" rotations, C-SB and C-C-SB, which by all measures of this study are unsuitable for Saginaw Valley cash crop farming at prevailing prices and yields. 1Dr. John Ferris, personal communication. 96 Table 6.5 Ranking of Sixteen Cropping Systems on a 600 Acre Farm Using First and Second Degree Stochastic Dominance Rotation Expected Net a Rank No. Crops Rotated Return to Land 1 4 C-NB-B 189.74 14 O/A-A-NB-B 187.77 2 8 C-NB-NB-B 172.49 3 12 NB-C-SB 110.91 6 C-NB-W-B 151.33 5 C-SB-B 161.92 4 13 C-C-NB-B 148.00 6 C-NB-W—B 151.33 12 NB-C-SB 110.91 5 15 O-NB-B 118.08 12 NB-C-SB 110.91 1 C-NB 119.03 6 9 O/A-A-A-C-C-SB-C 91.40 16 O/A-A-A-C-C-NB-S 98.48 7 7 C-SB-W-B 112.31 15 O-NB-B 118.08 8 2 C-SB 86.24 15 O-NB-B 118.08 9 ll C-C-NB-W 78.76 15 O-NB-B 118.08 2 C-SB 86.24 10 O/A-A-A-A-A-C-C-C 67.21 10 3 C-C-SB 67.97 aExpected net return to land figures are taken from Table 6.1. 97 Table 6.6 Ranking of Sixteen Cropping Systems on a 600 Acre Farm Using First, Second, and Third Degree Stochastic Dominance Rotation Expected Net a Rank No. Crop Rotated Return to Land 1 4 C-NB-B 189.74 14 O/A-A-NB-B 187.77 2 8 C-NB-NB-B 172.49 3 6 C-NB-W—B 151.33 5 C-SB—B 161.92 12 NB-C-SB 110.91 4 13 C-C-NB-B 148.00 12 NB-C-SB 110.91 5 1 C-NB 119.03 9 O/A-A-A-C-C-SB-C 91.40 16 O/A-A-A-C-C-NB-C 98.48 6 15 O-NB-B 118.08 7 C-SB-W—B 112.31 7 11 C-C-NB-W 78.76 15 O-NB-B 118.08 8 10 O/A-A-A-A-A-C-C-C 67.21 15 O-NB-B 118.08 9 2 C-SB 86.24 15 O-NB-B 67.21 10 3 C-C-SB 67.97 aExpected net return to land figures are taken from Table 6.2. 98 Since sugarbeets are grown on contract with processors, not all cash crop farmers can produce sugarbeets. The rotations with sugarbeet components were more profitable but this alternative is not feasible for all producers; therefore, Table 6.7 presents a ranking of those rotations without sugarbeet components. Rotation 12 represents the best alternative for those producers who are not sugar- beet producers. NB-C-SB represents a slightly better choice than C-NB which is a common cropping pattern for those farmers not producing sugarbeets. A comparison can be made between Soybeans and Navy beans in different cropping systems. Rotation sets 1 and 2, 4 and 5, 6 and 7, and 9 and 16, are identical except 1, 4, 6, and 9 include Navy beans while 2, 5, 7, and 16 substitute soybeans. For both 400 and 600 acre farm configurations, the system with Navy beans dominated its analogous system with soybeans by first degree stochastic dominance. Only in the case of the long rotations, 9 and 16, was the choice unclear. No dominance was attained between 9 and 16 on a 400 acre farm and 16 dominated 9 by the weakest of the three stochastic dominance rules on a 600 acre farm. Under the circumstances of this study, it appears that Navy beans are the crop of choice as opposed to soybeans. Despite the greater risk inherent in the production of Navy beans (coefficients of variability of yields of soybeans versus Navy beans is 26.9%< 31%, and similarly, for prices l3%<:31%), the relative prices used in this study ($22.60/cwt for Navy beans as against $6.53/ bu. for soybeans) is sufficient compensation for the added risk. 99 Table 6.7 Ranking of Saginaw Valley CrOpping Systems Without Sugarbeets Using First, Second, and Third Degree Stochastic Dominance Rotation Expected Net Rank No. Crops Rotated Return to Land 400 Acres: 1 12 NB-C-SB 92.19 2 l C-NB 105.22 3 9 O/A—A-A-C-C-SB-C 70.10 4 11 C-C-NB-W 69.02 10 O/A-A-A-A-A-C-C-C 58.66 16 O/A-A-A-C-C-NB-C 75.57 5 2 C-SB 75.25 6 3 C-C-SB 57.21 600 Acres 1 12 NB-C-SB 110.91 2 1 C-NB 119.03 9 O/A-A-A-C-C-SB-C 16 O/A-A-A-C-C-NB-C 3 11 C—C-NB-W 78.76 4 10 O/A-A-A-A-A-C-C-C 67.21 5 2 C-SB 86.24 6 3 C-C-SB 67.97 100 Perhaps one reason for this is that the expected yield of soybeans used in this study is 35 bu./acre; this is less than the usual yield attainable in the "corn belt" and would consequently imply that Saginaw Valley farmers are at a comparative disadvantage growing soybeans vis— a-vis farmers in other parts of the mid-west. New varieties of soybeans that would make 40 plus bu./acre yields, the norm in the Saginaw Valley, would be necessary to make the crop competitive with Navy beans. Expected soybean prices in the $9 to $10 per bushel range relative to $22.60/cwt Navy beans could achieve a similar result. Sensitivity Analysis Rotations like 4, 8, and 12 are common in the Saginaw Valley; their relatively high ranking is no surprise. However, rotation 14 which includes alfalfa as a soil building legume as well as a cash crop is a high ranking, although not the leading candidate. Alfalfa is the main crop that is unique among the leading set of rotations (rotations 4, 14, 8, and 12). The estimates of yield and price of alfalfa would affect the ranking of this rotation with respect to the other leaders. Therefore, the ranking of rotation 14 with respect to 4, 8, and 12, was analyzed as changes were made in assumed alfalfa yield, price, and price variance. The following scenarios were tested: 1. Expected alfalfa yield raised 10%; Expected alfalfa yield lowered 10%; Expected alfalfa price raised 10% and 20%; #00“) Expected alfalfa price lowered 10% and 20%; and 5. Alfalfa price variance raised 50%. 101 The relative ranking of rotation 14 with respect to rotations 4, 8, and 12 was unchanged for all adjustments except the 20% decline in the expected alfalfa price. In that case, rotation 14 dropped out of a first place tie with rotation 4 and into a second place tie with rotation 8. A decline in the expected cash price of alfalfa from $60.73/t0n to $48.00/t0n reduces the attractiveness of the rotation considerably. Many sensitivity analysis comparisons are possible, examination of this set was undertaken because these 4 rotations had among the highest net returns to land; 14 is considered to be an agronomically "desirable" rotation and ranked well compared with the common systems employed in the Saginaw Valley, which are variants of rotations 4 and 8. Less is known about the cash market for alfalfa as it is very often a market among farmers, hence there is probably a greater chance of error in the alfalfa price data than the other data series. Machinery Costs Systems which are agronomically desirable have among the lowest cash costs of all sixteen rotations. In terms of cash costs, rotations 9, 10, 14, and 16 ranked 16th, 15th, 11th, and 14th, respectively. Unfortunately, reduced variable cash costs were offset by higher machinery costs. Rotations 9, 10, 14, and 16 rank 9th, 2nd, 7th, and 4th in per acre machinery costs. Rotations 4 and 8 have the 2nd and 4th highest cash cost vis-a- vis rotation 14, which ranks 11th. lhn:rotation l4 ranks 4th per acre machinery costs while 4 and 8 rank 12th and 14th, respectively. This 102 implies that rotation 14 has a higher proportion of fixed to variable costs as compared with its two main competitors, rotations 8 and 4. This represents a higher level of operating leverage and represents an inherently "riskier" farm plan than does rotation 4 and 8 regardless of the shape of the gross income distribution. This same observation holds with respect to rotations 9, 10, and 16 and their primary competitors which would be rotation 12 and 2. Reliability Criteria Another issue with regard to machinery costs is the impact of machinery cost versus reliability on rotational ranking. The point was made in Chapter IV that the design critique used in this study for developing machinery complements was 80%. This implied that such a machinery set would be able to complete designated field operations in eight out of ten years given historical weather patterns and the number of derived work/no work days. The selection of 80% was somewhat arbitrary, but was based on experience and rule of thumb estimates of losses from not being able to complete field operations within desig- nated time allowances and the cost of excess machinery capacity. Cost is an increasing function of machinery "reliability." The machinery cost reliability curves as generated by the machinery simula- tion model are plotted for rotations 4, 8, and 14 in Figure 6.3. The dotted hash-mark represents the 80% design criteria assumed for this study. What is apparent is that although cost is an increasing function of reliability, as expected,the different shapes of each curve imply a different machinery complement cost for each rotation depending on the 103 .ELmu meo< coo 1-mempmam mcwnaocu am_~m> zucwmmm mouse com mm>ezo Newpwamwpmm umou xgmcwgomz m.o mesmmd so___aaw~om 82265220 cmemoo New Noop . em“ New - mN NN 9N mN em mN NN FN ON a_ mp NP op mp «F mp NF FF op - .q a a1 d . u q- . -4. q . d1 a a . q 1H a on 1 cc om l V TI!» L L J u . . _ . - _ . _ om m-mz-mz-u m-mz-u . 1 cop m-mz-<1<\o 1 opp 1- ONF I; om. 0; oep easy/1503 104 design criteria selected. At 8 % the per acre machinery cost is $98.24 for rotation 14 and $76.32 for rotation 4, the difference being $21.92 per acre. At 82% design criteria, the per acre machinery cost is $82.76 for rotation 4 and $99.61/acre for rotation 14 with a difference Of $16.85 per acre. At a 75% design criteria, the costs are $88.31 for rotation 14 and $73.61 for rotation 4 with a difference of $14.70. In the ranking analysis, rotations 4 and 14 were deadlocked most of the time. The relative ranking appeared somewhat insensitive to variations in price and yield parameters, yet the machinery cost estimate varies by some $5.00 to $7.00 per acre with slight alternatives in the selected design criteria. It would appear that further study and some greater logical justification would be helpful in assessing cost of machinery which appear to be very important in the relative ranking process. Summary Sixteen Saginaw Valley cropping systems were ranked on the basis of net returns to land. The rules of stochastic dominance were employed as the decision criteria. The rotations were ranked for a synthetic 400 and 600 acre cash grain operation. A sensitivity analysis was performed on alfalfa yield, price, and variance parameters for rotation 14 (O/A-A-NB-B) as it appeared that this agronomically desirable rotation appeared competitive with rotation 4 (C-NB-B) which is representative of common cropping practice in the area. Results suggest a 20% drop in the price of alfalfa is sufficient to drop rotation 14 out of the efficient set, yet a 20% increase in the price is not sufficient to drop rotation 4 out of the efficient set. 105 It was observed that those rotations which are agronomically superior (rotation 9, 10, 14, and 16) entail a higher proportion of fixed to variable costs and consequently represent a higher level of operating leverage. A final observation suggests that the overall ranking of rotations may be sensitive to the design criteria selected for the machinery complement. This is due to the fact that the shape of cost reliability curves for machinery complements are not identical. CHAPTER VII SUMMARY AND CONCLUSIONS Summary of Research Objectives Increased cash crop farming at the expense of mixed cash crop/livestock farming in the Saginaw Valley has led to increased problems of soil compaction, low levels of soil organic matter, and diseases and pests. Agronomists believe, based upon extensive research, that these problems are responsible for reductions in Navy bean yields. Sixteen crop rotations were identified; they range from the intense cropping practices currently in use to those emphasizing legumenous crops. The objectives of this study are: l. to describe the economic environment in which Saginaw Valley cash crOp farmers operate; 2. to identify crop rotations which are technically feasible illustrating a wide variety of agronomic properties; and 3. to analyze the economic viability, including explicit considerations of risk, of each of the cropping systems from the farm decision maker's perspective. Theory The theoretical basis for choice framework is deduced from the utility theory of a decision maker facing a risky environment. The study was conducted from the micro level system design perspective as opposed to a system management or sector level analysis. 106 107 Methodology Enterprise budgets were developed for each of the sixteen alternative crop rotations; interactions among crops in terms of yield, and fertilizer and chemical requirements were accounted for. Machinery costs were estimated using a simulation model which generates a unique machinery complement for each rotation taking account of optimal field operation date constraints and a predetermined level of reliability to complete required field operations on time. Hauling and drying charges were priced at the custom rate. All labor was assumed to be family labor and renumeration based on family living expense. Gross income is expected yield times expected price, and rotations are ranked according to the size of the residual remaining after costs are subtracted; the residual is labled as net return to land. Rotations are ranked according to two general criteria: net return to land and stochastic efficiency. Risk is introduced by treating gross income as a random variable since it is the product of two random variables, yield and price. Variances and correlations among yields were derived from detrended farm data. Variances of and correlation among prices were derived from detrended average annual Michigan prices. Prices and yields were assumed distributed as multivariate beta random variables. A multivariate generator was used to generate 100 states of nature; the cumulative probability density functions for net farm income were made estimated by ranking the "states of nature" from th th lowest to highest and using the i values as an estimate of the i fractile of the gross income cumulative distribution function. The 108 sixteen alternative cropping systems were ranked applying the rules of first, second, and third degree stochastic dominance. Empirical Results Major findings. Ranking the sixteen crop rotations for 400 acre and 600 acre farms on the basis of expected net returns to land suggests: 1. 3. The C—NB-B system presented the highest returns to land. This corresponds to one of the commonly used rotations in the Saginaw Valley. An O/A-A-NB-B rotation finishes second with $15.49/acre less income. This is one of the systems considered to be agronom- ically more desirable, as the inclusion of alfalfa improves soil structure. A C-NB-NB-B rotation, probably the most common rotation in the early and mid-19705, ranked third, $17.25/acre less than C-NB—B on a 600 acre farm. This rotation illustrates the common, but undesirable practice, of successive Navy bean crops. If the relative yield relationship suggested by agronomists are accurate, continuous years of Navy beans in a rotation is economically undesirable. Cash, machinery, fuel, and hauling costs are higher with C-NB-B than with C-NB-NB-B; however, gross income for C-NB-B system is estimated to be almost $40.00 higher than for C-NB-NB-B. Rotations which inlude sugarbeets are typically more profitable than those that do not. Rankings 1 and 6 and 8 and 9 were 109 rotations with beets for the 400 acre farm; rankings 1 through 8 were beet rotations on the 600 acre farm. Rotations with Navy beans were economically superior to analogous rotations where soybeans were substituted for Navy beans. C-NB was the best rotation for the non-sugarbeet producer. The soil building rotations 9, 10, and 16, which included several years of alfalfa were not nearly as profitable. The fact that rotations containing sugarbeets and/or Navy beans are more profitable than systems without them is no surprise. Since these crops are “riskier" to produce. This was one of the prime motivations for ranking the systems in a manner where risk is adequately accounted for. Findings based on stochastic dominance included: 1. The C-NB—B, O/A-A-NB-B and C-NB-NB-B rotations were ranked one, two, and three under both expected value and stochastic dominance criteria on the 400 acre farm. Rotations with beets gradually ranked ahead of those without beets. For only one rotation, O-NB-B, three rotations without beets ranked ahead of a rotation with beets. In the deterministic model, the C-NB rotation was superior to NB-C-SB when expected value was the criteria; the ranking was reversed under stochastic dominance. There was no clear preference between C-NB-B and O/A-A-NB-B for the 600 acre farm. 110 5. The long rotations, O/A-A-A-C-C-NB-B, O/A-A—A-C-C-SB—C, and O/A-A-A-A-A-C-C-C, were not highly ranked. 6. Rotations with Navy beans were preferred to analogous rotations with soybeans. This suggests that, given prevailing relative prices, that the premium on Navy beans is more than adequate compensation for the increased risk involved. A sensitivity analysis was conducted on the alfalfa yield, price, and price variance parameters for O/A-A-NB-B rotation. Since this rotation was a relatively strong performer in all rankings, the sensitivity of this ranking to alfalfa yield and price parameters is deemed important; particularly in comparison with the rotation's primary competition: rotations 4, C-NB-B; 8, C-NB-NB-B; and 12, NB-C-SB. The alfalfa parameters only were tested as alfalfa was the major difference between rotation 14 and 4, 8, and 12. Results of the sensitivity analysis suggest the following: 1. Raising and lowering expected yield values by 10% had no effect on the relative ranking of rotation 14. 2. Raising and lowering expected price by 1 % had no effect on relative ranking. 3. Raising the expected alfalfa price by 20% had no affect on relative ranking. Lowering the expected price by 20% dropped rotation 14 out of first place with rotation 4 and into second place with rotation 8. 4. Increasing alfalfa price variance by 50% had no effect on relative ranking. 111 Scope of the study. If the results of this study are to be placed in their proper perspective, recognition of the scope of this study are necessary. 1. The use of a “design parameter" which abstracts from some problems in order to highlight underlying relative relation- ships makes direct application of the absolute values gener- ated to a particular farm unrealistic. Issues of taxes, debt equity structure of the farm were not addressed. The labor market assumptions employed in this study are probably unrealistic. The machinery complements were designed such that one full time Operator was available on the 400 acre operation and one full time family operator was available on the 600 acre configuration with additional help available from other family members; e.g., spouse or adolescent children at peak labor demand periods. This assumption was made in lieu of good knowledge of the operation of the hired labor market. These rankings are based on the assumption that each system is operating in "steady state." Thus, if a producer wished to change from a C-NB-B system to O/A-A-NB-B, no investigation was made of the time-path of expected yields differential Changes. In other words, in shifting from one rotation to another, how many years would it take before the yield benefits expected under the new rotation would accrue? This question was not addressed. 112 4. The expected alfalfa price is based on invesitgations of historical relative price relationships. If many farmers were to shift to growing alfalfa as a soil building cash crop, the assumption of price insensitivity to increased crop production by an individual producer is unwarranted at the aggregate level. This is particularly true of alfalfa. Since the crop is bulky, its market tends to be localized. 5. The estimates of price variance and yield variance are based on historical data. This presumes the future is adequately predicted by past behavior. This assumption is probably more realistic for yield data than for price data. The probability density functions graphed in Appendix J, are probably too exponential in appearance. This is true because the information used to generate them encompassed two eras of substantially dif- ferent agricultural commodity price behaviors. The 19505 and 19605 was a period of stable prices and large surpluses, whereas the 19705 was a period of great volatility. If it is believed that the future will be similar to the recent past, then the price PDF's should be estimated using only the more recent data. Conclusion Based on the economic analysis conducted, the introduction of alfalfa as a soil builder into cash crop farming is not immediately a likely proposition. However, the possibility of introducing alfalfa is not as hopeless as some critics would believe. The strong ranking of the O/A-A-NB-B indicates that the economic benefits of good soil 113 structure are real in terms of decreased variable costs and improved yields. Successive crops of Navy beans are to be avoided. This is established since C-NB-B dominated C-NB-NB-B by first degree stochastic dominance in all ranking tests. Another point is that farmers are not employing "intense" cropping systems in a cash crop environment out of tradition or habit. They do it because it is profitable, at least in the short run; and any effort to modify or change agricultural practice must be attuned to the profitability test of decision makers. In this study, the level and variability of net returns on land were used as the basis for decision making. It is realized that other factors such as labor availability and requirements, the present financial position of the operator; current farm organization, investment require- ment, and the age of the operator are all important in selection of a cropping system strategy. Recommendations for Further Research One of the objectives accomplished with this study is to establish a methodology for analysis of many alternative crop rota- tions, cultural practices, and tillage systems. Given the methodology presented, it would be possible to analyze alternatives in light of generalized decision maker preferences. Possibilities include: 1. Application of conservation and no-till tillage practice. 2. Return to the practice of green manure winter cover crops which would offer some of the soil building benefits of alfalfa without tying-up productive farm land in a relatively unprofit- able crop for an entire growing season. 114 Further research is needed in the development of machinery complements. Some incongruities appear with machinery costs. For example, on a 400 acre farm the machinery costs are $82.83 with a C-NB-B rotation and $117.51 with a O/A-A-NB-B rotation. This appears implausible since with O/A-A-NB-B, the farmer fall plows only 200 acres. But the model sizes machinery to meet peek conditions which with O/A-A-NB—B is in the spring cutting alfalfa and planting Navy beans. Considerable work needs to be done to permit scheduling work and making more economically sound decisions as to acquiring machinery capacity. Further research should be carried out in evaluating stochastic sets where no clear choice is apparent. For example, on a 600 acre farm, stochastic dominance criteria are inconclusive between rotations 6, C-NB-W-B; 5, C-SB-B; and 12, NB-C-SB with expected returns of $151.53, $161.92, and $110.91, respectively. The difference between the expected returns of rotations 6 and 12 is $41.24 per acre. Despite this dif- ference, stochastic dominance suggests that for some decision makers, rotation 12 would be preferred. The methodology of Meyer and King and Robison on estimation of rich aversion coefficients and their implantation in the determination of stochastically efficient sets should be implemented. APPENDIX A VARIABLE CASH COST BUDGETS APPENDIX A VARIABLE CASH COST BUDGETS Variable cash cost per acre of each crop in each of the sixteen crop rotations is presented in this appendix. The cash cost per acre of a particular rotation is obtained by summing cash costs over all crops in the rotation and dividing by the number of crops in the rotation. Rotation number 8 (C-CB-NB-B), for example, has variable costs per acre of: corn, $50.70; lst Navy beans $46.50, 2nd Navy beans, $44.63; and sugarbeets, $90.60. The average variable cost 05 this system is $58.11 per acre. This is obtained by summing $50.70, $46.50, $44.63, and $90.60 and dividing by four. An interest charge of 13 percent for six months on variable cost is included to cover financing of working capital in the economic analysis. The finance charge is omitted in the following tables. 115 116 anon. u¢u< cum hmou Hac¢~¢¢> HChOh ------ '-"-- --- «non «ooh hzu~0u¢¢z~ u>nh0( u¢u<\md one acauuxh 99.99 99.9 9299999929 999999 9999999 99.9 299999 99.9 99.9 9299999929 999999 9999\99 99.9 99999 999999999: 99.9 99. 9999\999 99.99 991919 999999 99.9 99. 99999999 99.99 919919 999999919 99.9 99. . 9999\999 99.9. 919199 29999992 9999999999 99.99 99. 99999999 9.99 9999 9999 99:: 999 99999 29999299999 9999 9999x999 99 .299..99 9.99 99999» 99999 99929999999 929999992 99999 _ 9219 929999999 99.99 9999 999 9999 99999999 99999 1111mmum1-11111 99.9 9299999929 99999. 9999999 99.9 999999 99.9 99.9 9299999929 999999 9999\99 99.9 99999 99.9 99.9 9299999929 999999 9999999 99. 92999999 999999999: 99.9 99. 99999999 99.99 991919 :99999 99.9 99. 99999999 99.9. 919919 999:99919 99.99 .9. 99999999 99.999 919199 29999992 9999999999 99.99 99.9 99999999 9.99 9999 9999 99:: 999 99999 29999299999 9999 9999x999 99 .299..99 9.999 99999» 99999 99929999999 2999 99999 9219 . o!°~b<~°¢ 99.99999 mun"9.9»mu9uaaafiwwmm9zm999:959 w “9.1 117 hogan ween apes anon on.» Quota hmou u¢u¢xhau mo macho .ZOhooau omen chub cued Noon 099$ eooon anon“ hmou men‘shau co ozo»9o:o oonn gonna «New anon «no on. an. h2UuOU¢¢2~ hzunouzuZH but: cum Hence unau~> «non naon hNoN «no ow. two good hwxuk uuuz¢¢ 4~huc UKU¢\DJ who u>~hu¢ U¢u<\ma coca u¢0¢\mn4 ooomo u¢u<\mmd omoun u¢u<\mma coon zo~>¢zcdnxu wz¢um>ow ”coco xcxcd ommca muo~u~m¢uz conclo xw Jake» u>~hu< u¢u¢\ma anon u>nhu¢ Uz01\m4 oeoN w>~h0¢ u¢u:u co cachooao coo—n conu— 99.9 9299999929 929999 9999999 99. 2999999 . 999999999929 99.9 9299999929 929999 9999999 99.9 999999 99.9 9299999929 999999 9999999 99.9 99999 99.9 9299999929 999999 9999999 99. 92999999 9999999992 99. 99999999 99.99 991919 299999 99. 99999999 99.99 919919 999299929 99. 99999999 99.999 919199 29999992 9999999999 99.9 99999999 9.99 9999 9929 999 99999 29999299999 2999 99999» 929999 99929999999 2999 99999 . 9919-9 9999 999 9999 99999999 99999 99.9 9299999929 999999 9999999 99.9 99999 99.9 9299999929 999999 9999999 99. 29999 99.9 9299999929 999999 9999999 99. 92999999 9999999992 99. 99999999 99.99 991919 299999 99. 99999999 99.99 919919 999299929 99. 99999999 99.999 919199 29999992 9999999999 99.9 99999999 9.99 9999 9929 999 99999 29999299999 2999 99999» 99999 99929999999 2999 99999 991919 99999929 muumm ”wu9uuaamnwmmm92W999999929 ux0¢ sun hwou uao¢~¢<> 41h0h utOubeoz «acuhchoc n uoOJAIH uzu< cum hmou want—cc: u¢FOh 9299999929 999999 9999999 99. 99999 9299999929 999999.9999999 99.9 99999 9999999992 99999999 99.99 991919 299999 99999999 99.99 919919 999299929 9999999999 99999999 9.99 9999 99999 29999299999 2999 99999 99929999999 92999999 ”9999 991919 92999 999999 929999 29 92999 999 99 9999999 9999999929 0 UGCQ 120 uncut uxu‘ cum hmou UJn~pu¢ ugu¢~o4 on. z¢auuzp .e.~— «e.a pzu_ou¢ozn u>~pu‘ u¢U¢xo4 oo.~ gum—x. do.» pu.~ pzuuougoz~ u>~pu¢ u¢u<\04 n~.~ :«pau muo~u~m¢uz an." «a.. u¢u¢\mm4 ao.e~ ooua.o :m.»ca oo.~ aN. u¢u¢xmo4 oo.o~ °-o.-o up¢xamoza «a.» cw. u¢u«\mm4 eo.pn auauo. zuoozhuz ¢u-dupzuu eo.~u on. uxu‘\m04 9.9. ouum hwcu buzz CUB U0n¢£ ZOHP(Z¢J1XU IMP" uzu.\»au «a .zo»..:o e.- “cauup pm¢_u "uuz¢¢¢uag. mz¢um»>.z ”noun _ o-oz-u ”zo~»¢»o¢ a».cn u¢u¢ cu; buou uao.~¢«> 4.»cp ----umumu---u-- en.» pzu_9u¢92~ u>_»u< u¢9¢xm4 on.“ xuo‘aa e~.~ no.n pzu~ou¢azn u>.pu. u¢u«\o4 oo.~ omm.4 ._.~ p~.~ pzu~ou¢uz~ u>~pu¢ u¢u¢\o4 an. uz_~¢¢»‘ mun—uumxu: -.n «a. ugu.xmoa op.»~ eu-o-a :m¢»oa up.» °~. uxu.\mma on.on =-o¢-a upgzumoza o..~u o“. u¢u«\wna an..- =-o-~o zuooxh~z ¢u-aupcuu. on.nu ea.— u¢u¢xmm4 n.n_ ouum pmou p.23 «u; uuuga zo~p¢z‘aaxu xu»~ u¢u<\»:u «a .zo»..=o e.e~— "adunp pug—u uuuz¢¢¢uag¢ zxou ”nozu a-oz-u ”zo~»..ox ou»o4azu mun"w.»wu4n»uamnwmmmozmm~zuxuhzu n “9.; 121 oc.~a u¢u¢ «um pmou ugo¢~¢¢> u«»o» ----mmumr------ a... hzuuou¢a2_ u>~pu¢ u¢u«\o4 oe.o «up on.a. on.nu pzu.ou¢¢z~ u>_»u« u¢u¢\o4 on.n z~z¢¢pa mucuuuozu: ~o.» «u. u¢u¢xmoa an.oo aoua-o :m‘»oa o..m cu. u¢u«\mo4 an.p~ o-oc-o up¢xumoxa o~.m~ .~. uzu.\wo4 oo.no~ 9-9-o. zuoogh~z ¢u~_4~»¢uu oo.n no.» uzu.\mm4 a." ouum hmou buzz a“; uuuxg zo~h u.»o» ---ummumrnnnuu- ac.” pzuuou¢¢z~ u>~pu¢ u¢u¢xoa o°.o «up an.o. on.n— pawnoucazn u>_»u¢ u¢u<\o4 co.» z~:«z»a ‘ muouuumzu: we.” u". uuu¢xmoa on.ow oono-o zm cnon noon hNoN an. aw. two on." p mxnu buzz can uu—xn uOJU~> ouroaatu m m h menu quz¢¢¢uau¢ uuuz¢¢¢uaa¢ hZUnouxoz~ pawnouccz~ hzu~0u¢u2n hzunouxmz~ hzwuou¢02~ “cud cum hmou wan¢~¢<> u¢bch u>~pu< u¢u«\oa mp. gaze; u>.»u¢ u¢u¢\m4 oo.~ cmm«4 nuanunmuu: u¢u¢xmo4 oo.oc oouauo :m¢»oa u¢u¢xmma on.~n ouecne up¢zumcza ¢u~_4~»¢uu ugu¢xmm4 o.nn ouum zo.»¢z¢4nxu sup“ mz«um»om ”moxu . m-mwuu man: can hmou uaa¢~¢<> anhch u>~hu< w¢u¢\ma coon xu01am u>~hu¢ u¢u<\ma ecoN omm<4 u>~hu¢ u¢u¢\ma an. uz-¢¢h¢ wuo~u~m¢ux u¢U¢\wmd chomw conclo xm¢bon cocci: uhdxnmozn olelwo zuuozhnz U¢u¢\wma onoan uxutxwmq onocwn zu-4~p¢um u¢u12¢aaxu turn zzou uuczu mammnu m 2m :0 muxaxuh2u 123 o~.no ago. «an page u4a¢~¢¢> aqpo» u---mmumruun--u .nc.~ pzu_ou¢cz~ u>~pu¢ ucu¢\94 oo.o nu» on.o. om.n~ hzu.ou¢cz_ manhu‘ uau‘\m4 oe.n z~:.¢»u . muo~u~c¢uz ~¢.~ an. U¢u¢xmo4 an.oo co-o-o zm«»oa mc.m ow. u¢u«\mma an.- cumone u»¢:amo:a ao.m~ cw. u¢u«\mm4 ca.m~ a-o-oc zuao¢p~z ¢u-aupcuu co.n eo.m uxu‘xmma a." ouum .mou pug: «u; uu~¢a zo~»«z.4axu sup" u¢u¢xpzu «o .zo»..=o o.- "adu_» pmznu “wuz‘¢«uaa¢ mpuuc¢¢uam “mean o-mm-u 33.3.; mum"”...”.wuauuuzmfiwmmozmfl5......sz ”zenhdhoz a uo¢a 124 «Ooh: um”: mun hmou UJD<~¢<> J¢h0h --r 1 I- nn.n ue.p pzu~ou¢uz~ u>~pu¢ u¢u¢\oa an. 2.4uucp co.~— «o.o pawnouxcz~ u>~»u« u¢u«\ma oo.~ gum—x. «a.o ~o.~ pzuuouzozn u>_»u< ucu‘soa n~.~ x‘puu muonunoxu: aw." «a. ugu¢xmc4 no.—u no-9-o 1m J‘po» ----um~m-nu---m on.n pzu~ou¢¢z~ u>.»u¢ uxu.\m4 ea.“ xuo‘am up.” mo.n pzu~auzaz~ u>_»u¢ u¢u«\m4 ac.~ omm~»u« uzugxma on. uz-¢¢». mucuunmzux -.n a“. u¢u¢xmm4 op.o~ oouo-o 2m¢poa o~.~ on. u¢u¢xmm4 am.on auopga up¢zamoza c..~— cu. uxu‘xmma on..- auo-~o zuaozpnz ¢u-aupaug om.n~ oo.~ uxu‘xmmd m.n~ cum» pmou baa: can uu~¢a zo.»¢z‘4nxu twpn u¢u¢xbau «o .zo»..:o 9.9"“ ”o4u~» pmxuu uuuz¢¢¢uag¢ zxou ”moan a-:-ozuu ”go—p.»o¢ 88:5 muux‘xfigfimnwwmwozmfl5.5:: 3 o (a 125 €0.90 anon noon haunt uuu2¢¢¢uau¢ onooc anon" on.» «no cuom an. coacw ow. ocon coon hmou h~z= mun woman u¢UC\h:u x0 .20h.o=m nocN unaunr hmcuk snow. NNou coon «new an. etch cw. coon“ on. ooowu on. meu buzz cum wouca u¢u wt¢¢u >u ourcaaxu mzo~h ho u¢u¢ mun hmcu u40¢u¢¢> J¢b0h hzuuoucoz~ u>~hu< U¢U¢\oa 9900 top hzuuou¢¢z~ u>~hu¢ u¢u<\oa coon u¢u a¢»0h hzu~ou¢¢z~ u>~hu< U¢u<\oa on. u¢u<\mmd amoNN umu¢z aczwu AghOh u>~hU< u¢u¢\nd who loco; manhu¢ uxutxcd coca Dmmdd ”unwoumxux u¢u<\moa no.0. eclblo zwdhon u¢u°w "noxu ouaimmlu uzuc can bmou uao<~¢¢> AthOh u>~hu< u¢unhu< uKU¢xoa ooow owm¢4 u>~hu¢ w¢0¢\na an. uz~N¢xht mun—oumzu: u¢u¢\m04 choow confine Iatpon olwclo uhtznmczu alalfla zmoozbuz u¢0¢\mm4 anonn U¢u~pu¢ u¢u¢xo4 oo.¢ no.9. an.n_ pawnouxaz~ u>~pu¢ u¢u¢xo4 aa.n ow.» «a. uzu¢xmc4 oo.¢u o~.n ow. u¢u_pu. u¢U¢xm4 on. on.~ «a. uxu.\mm4 oo.o~ ~o.o ow. uau‘xmmd an..n em.~H on. uau‘\maa om.~n om.ou o". u¢U¢xmm4 o.o~u pmau p~za zua uu~an zo~h¢z.aaxu u¢u«\pzu «o .zo»..=a o.nn "a4u_» hm¢_g uuuz.¢¢uaa. ~¢uza "noxu mxa¢u >u44¢, ‘2 o.m z ou»o4a:u mac—p pox can upwuoao muncuxuhzu uxu¢ awn hmou UJQ¢~¢<’ Aa manUnmxux colon: Inthon unwelo uh thOh a. N muo~unm¢uz ounoua :m‘»oa ouonua “p.2amoxa cuouoo zuuoap~z ¢u~_4.»¢uu ouum. cu». 0-2-omuu "zo~»¢»o¢ Nu uo~pu¢ u¢u¢xo4 on. z¢4uucp .e.~— ~o.¢ pzu~ou¢mz~ u>~pu¢ u¢u«\u4 ea.“ zun~:« «o.o ~m.~ pzuuouxezu u>~pu¢ u¢u¢xu4 n~.~ :«pau mun—unocux an." "a. u¢U¢xmm4 no.9" omuauo 1mgpoa o«.~ o~. u¢u¢xmm4 an.on eaoouo uh¢xamoza ao.o .N. mau‘xmmd co.o. aua-oo zuoo¢p~z xu-4~»¢uu oo.~n on. u¢u¢xm¢4 a.oc ouum hmou p.23 gun uu.¢a zonp¢z.4axu sup— u¢u«\»:u «o .zo»..=o a.n~ ”94“.» pug"; «uuz¢¢¢uaa. mz¢ump>¢z ”coco m-ozumzuu “zo~»¢»o¢ o~.en “cu. gun pmou u4o«~¢.> a.»o» s--aumumun-n-uu .m.» ham—ouzez— u>npu¢ u¢u~pu¢ u¢u¢\md oc.~ omm¢4 ca." >~.~ pzuuou¢¢z~ u>~hu« azu‘xoa on. uz_~¢¢»‘ muo~u~o¢uz -.n in. u¢u¢xmm4 ap.o~ eoueue :m«»oa o~.~ ow. uzu«\mo4 on.on o-mc-a up¢zamoza ao.p« on. u¢u¢xmc4 on..- o-o-~o zuoocpuz ¢u-anbguu on.n~ oe.~ u¢u¢xwm4 n.n~ ouum pmou pnza can unuxa zo~»«z<4axu amp" uxu¢xpau co .zo»..:n 9.9"“ ”cam—p pm¢~u uuu2.¢«u¢a. axon "noun muozuozuu “zo~»¢»o¢ ou»o4a:w mum“m¢»wu4u»uamawwmwozwmnxauupzu nu uo‘a 129 mecca choc anooo ouch ouch coocw coon hmou u¢0¢\hnu «o .20».o:o nwoct anon ooowu «coo coon Noou wwoo ooown hmou u¢u¢\h:u co .ZObooam ncou anon «no em. cw. coon baa: cut uu~¢a ham—u uuuz<¢(UAA( coca unaunr «ooh «cow boom an. an. cw. on. haz: cum con" unauur ou>oaaxu a woman ozouum want «us hmou wan~hu¢ U¢u~hu< u¢u¢\m4 econ z~t¢¢>u muo~u~o¢wx U¢u¢xmmd 99.60 awicnc zm A¢h0h pzu_ou¢oz. m>~hu¢ uzu‘xma on. z‘guuxp pzu_ou¢az. u>_»u« uzu¢\04 no.~ zunux‘ kzu~ou¢oz~ u>~»u« uzu‘xo4 m~.~ z>cz "nozu oIOZOQZIu “Aguamfiwmwnzwmztrs ”zo~huhu¢ u¢u<\o4 on. U¢u¢xmma coonc uxu¢xwm4 coon" u¢0(\mma gown zo~h J«hcp hzunouzwz~ u>~hu¢ U¢U(\m4 Duo wandxmma ecownu U¢u<\woa crane w¢u¢z :(znodm 2m mzonh or com mhuuoam muzazubzu (nu: muo~u~m¢ux amlolo zmchou ol0¢le UFCIamoza analwc zuuozhuz ¢u-4~h¢wu ouuw xwhu usamnuuuc<0¢c¢\o «20~h¢hcx nu mods 131 0009» II II opumm au.o hwou u¢u¢\h:u mo .ZOhoosm pagan hficww oNoa hmou u¢o<\hzu x0 .20».o:m want can hmou uaocuct: achOh «no U¢U(\moa ooooo— eouolo 1m<>on on. wentxmod oooco clfitlo uhcxnmozn «UNnduhmuu but: «Us woman zcnh¢2¢anxu turn to. "04u~> a¢~xh uuuzdxduant uoantu “moan mmuxaxuhzu an Hutu 132 hnohn anon onon as.» on." «to» 00.0 canon anon" hmcu u¢u¢xhau co .20».o:o Ouown on.» ouou ouou anon omoo econ amend pmou u¢u<\h:u co .ZOhooao coma“ ocean u¢u¢ cum hmou UJD<~¢¢> anhOh ocoh hzuuou¢¢2~ u>~hu< u¢u¢\04 who 2¢O¢¢au muo~u~huumz~ onon h2u~0u¢52~ u>—>u« u¢u<\m4 been xuocuo noon hzunou¢¢z~ u>~hu< U¢u~hu< w¢u<\oa on. quN(¢h< muo~u~w¢uz «a. u¢u¢\mma anonn owtole zm ozcuum "MUZ¢¢ a<>o~ ma.n pzu_ou¢ez~ u>~»u. u¢u¢\m4 oo.~ omm<4 s~.~ pzuuouzazu u>~pu< uzugxma on. z¢ham s~.~ bzu~ou¢az~ u>~hu¢ uxugxog on. uz-¢¢p¢ muouunmxu: a". u¢U¢xmm4 oo.~n eunpuo :m¢poa ow. u¢u¢xmm4 an.~c onucuo up¢xumoxa ... uzu¢xmoa an.no onoumn zumozp.z ¢u-4~pcuu ea." u¢u¢xm¢4 m.nn ouum p.22 gun uu~¢a zo.p¢z«aaxu sup" ”gamu» pug—u uuu2¢¢¢waa¢ zzou uuoxu uuomuuuuu¢-<-<\o ”acupqsou mxcgu >u44¢> a¢z_u¢m zo ou»oau:u m2o.» box «on mhuuoam um.¢u¢u»zu sq mega 1133 «o.~o “cu. cum pmou ugo.~¢¢> 4¢»o» -cm.n-:- - on.» hzu.9u¢oz_ u>upu< u¢u¢\n4 ea." xuo¢4o up.» no.n pzunouzwz. u>~pu. U¢U¢xm4 oe.~ omm.4 ca." -.~ pzunougaz_ u,~»u¢ u¢u¢xo4 on. uz-¢¢p¢ muo_u~m¢u: ~¢.n a". uxu‘\mm4 a«.«n ao-o-o 1m¢hoa mo.o ow. uxu.\mo4 on.a. o-¢.-o u»«zamoxa 99.." cu. uzu‘\mo4 9°.99H enouuo zuoo¢»_z ¢u-4_»¢uu on.nu ac." u¢u¢xmm4 n.nn ouum hmou ~_z= can uu.¢a zo_»‘z‘4axu :u»~ u¢u«\»au go .zo~..:o o.n~u “o4u_» og_:» u~92¢¢¢uag. zacu “nozu uuom-u-u-.-.-«\o ”zo_»«»o¢ no.nn ugu. cum hmou uae.~¢.’ a.»o» ----mmumm----u- .n.n pzunou¢¢z~ u>.»u. u¢u¢xm4 oc.o xuo¢4o o¢.n -.~ haunouzoz~ ua~pu¢ u¢u¢xo4 mp. xocoa o~.~ ma.» pzunouzuzu u>~pu< uuu.\e4 oo.~ omm.a nuanu~o¢uz on.m .n. u¢U¢xmoa 99.». oo-oue zm‘poa an.o °~. uzu‘xmma on.~n c-o.-o up‘zawoza ¢u-4~pguu ea..— om. u¢u¢xmo4 c.9n ouum. pmou »_z: «u; uuuca zo_».z.4axu :u»~ u¢u«\»:u co .zo»..:o a.mn “94“.» hag—u “muz¢¢¢uaa. mz.um»om "moau u-mm-u-u-¢-.-.\o "zo~»¢»ox 35:: mangmeuqmfiwmmozmm:23: 2 “a: 134 coonn -'-'-"-----'-J nu. mmoc acow OQoQN hwou wrotxhzu «O ozohooam onohn nu. «moon mn.o ow.h nose hmou u¢u¢\hau «o .ZOhooam on. «no on. o¢o~ but: «at uu~¢t hmcuu unau~> no. «no ON. cw. nu. buzz mun unaunb ou>04&:u uu—xn hzu~ou¢92u uuu2¢¢ J~hu< u¢u¢\oa an. u¢u<\mod cache u¢u¢\woa ocoou u¢u¢\mma cow" zo~h¢244axu (matudd “maze (nu: mucuuumzuz cwlala zmdroa oi¢¢lo uhtzamoza ¢u-4~hcum ouuw turn QIUIUI(I(I¢I Jdbo» u>nhu¢ u¢u «no on. but: cut unau~> ouroaatu cant» uu~¢a ozouum nuu2¢¢ 4°u U¢U<\moa coco. esoOIo uhtzumaza «UNnanbcuu zo~h¢z 4 thunk uuu2¢x J¢h0h U¢u¢\mmd ooouhu canola Inchon U¢u¢\mma oooon cluelo wh¢ramcxa cuunanbcum zo~h12(anxu tuba UIUI00¢I¢I(I¢0¢\O "zouhchox U¢u< cum hmcu uam¢~¢<> d u¢U¢\mmJ cocoa" cwlono xmchoa U¢01\mm4 ccooc onOIo whu¢4¢> a.z.u.m zo ou»o4a:u mzo.h.»o¢ «on ”buooao umugazu»zu . «w uoOJAIU mzo coon noon hNoN swan as. aw. cu. coed buzz cum apnea unau~> ozcuum noon FNoN swam an. an. on. coca buzz mun uu—xa u¢u<\hau co .ZOhooam coouu unau~> hzu—ouzuz— hzu~ouxuz~ bzuuouzoz~ hzu~ou¢uz~ nuuz<¢¢MAA¢ hzu~ou¢¢z~ hzu~ouxoz~ hzuuoucuz~ uncut uuuz¢¢¢uau¢ u¢u< mun hmou uaodnxtt J‘hOb U>~h0¢ uxu<\oa who xtoczau mucuunhuumZn u>~hu¢ u¢u<\md coca ommta u>~hu< u¢u<\oJ on. z¢ham u>~hu< u¢u<\04 on. uz-<¢>¢ mun—Unmuu: u¢u A<>Oh u>~hu¢ u¢u¢\oa ooow oww~bu< u¢u¢\m4 on. zchzm u>~h0¢ u¢u¢\ma on. uz-<¢>¢ muo~u~m¢uz w¢u<\moa crown omlalo 1wzu UIUIUI¢I¢ho¢ NN menu 138 nNoon anon cnon ohob on." hwon up.» ocohu anon" hmou u¢u<\b:u co alchooao cook cnon noon hm.“ «no cm. on. aeo— hnza cum uu~¢n coauu «cannr O¢~zh mt: ou>oantu mzo 1"}:1'...r".,‘l 1| 1.1.4! 1!, wxud can hmou Ugo¢~¢¢> athOh h2U~cu¢oz~ u>nhu< U¢U¢NQJ nho hzunoucoz~ w>~hu¢ U¢U(\04 coon hzunouxuzn u>~>u< u¢u<\ma oaow bzu~ou¢ez~ u>~bu¢ u¢u<\oa an. uxu 4‘50» anon aooh haunowuuz~ u>~hu< w¢u<\ma who 2¢o¢¢Du mwo~u~huumz~ onon onon bzuuDHKGZu u>~hu¢ u¢u¢\m4 coon xuo~hu< u¢u¢\ua no.“ omw<4 tn." huow hammouzoZH u>~hu< u¢u<\md on. uz-<¢h¢ mucuuumuux hwon «no uzu¢\mma choow count: 1m J~>u< u¢u~hu¢ u¢u<\m4 an. z~hu¢ U¢u<\ma on. uz~N<¢h¢ mwo~u~o¢uz hwon «no uzu¢xmm4 okoow canon: Im¢hon chop an. U¢u¢\mm4 anoon Olmglo uh¢zumoza ocohu on. w¢u¢z¢4axu turn u¢u¢\»:u co o2¢hooam coca" «cau~> bmznu uuu2¢¢«uan< zxou “coco :umzuuuu «zo~b1h9¢ ou>OJAIu mum~m<”wmamwuamuwwmmozmmnzucuhzu ow uuca 140 hnoac «New «mow etch cmouw canon bmou u¢u¢xhzu co .zo»..:n ooohc «non ecouu «coo on." «new unocu ooowu bwou U¢94\hau co o20b.o:o coon coca coca «no on. em. on. h—za cum woman «Dawn» bmxnu «ooh Nana peou «a. on. 0N. aro buzz cum MUuzn uOdU~> pun—L wt“ ou>OJAtu mzo hzu~ouxwz~ u>nhu¢ uuuz<¢ U¢p0b U¢U(\moa ccoNN u¢u¢\mm4 owohn u¢u<\mma cacao uxuc\mmd eoomu zo~b<2 a¢h0h hzu~ou¢92~ u>~>u< u¢u<\04 hzu~ou¢wz~ u>nbu< u¢u¢\oa bzuuouzwz~ u>~hu< u¢u¢\oa uuuz¢¢>¢z "noxu w~¢a¢u~zu zcauuzh zum~t¢ t ou>04ntu .1]! ...:IhllbluL-QO I 1... I901! CIR u:u¢ cum hmou uao<~¢¢> dqho» . h2U~OU¢¢2~ u>~bu< u¢u«\m4 hzu—ouxuz~ u>~hu< u¢u¢\oa hzu~ou¢¢2n u>~bu< u¢u<\md u¢u<\mm4 euonn u¢u¢xm04 onooc u¢u<\wm4 coconu u19¢\mma menu woman zo~h uuhu¢ uxu<\md hzunouxez~ w>~wu< u¢u<\ma hzu~ou¢oz~ u>~h0¢ u¢u<\m4 u¢u>¢z unczu mzctu >u44<> J¢z~e¢m 2m mzo~b¢ho¢ con mhuooao muzazupZu an. xtduuxh ocou zumutc nNoN tcbau muo~u~m¢uz owlclo Imchou aloclo uh¢znmoxa alouuc zuoocruz zu-4~w¢uu ouuw xuhu mmtuomz ”acuhdhoc cw uuca 142 neonn "'---"'-'-I—'- omou nNoN Ohoh noon @nom an. Once ON. cent" on. hwcu but: mun U¢u¢\bzu «a .ZOhooDm coon «04u~> ouroautu wu~¢a hwcuu u¢u< mun bmou u40 4nbu¢ u¢u<\oa mp. xocoa bzu~ou¢w2~ u>nhu< u¢u<\m4 ooow omw¢a muo~u~m¢uz uxu¢\mca ooooo confine 1m¢hon u¢u<\mma onoun clmolo uhdxamozu «UNuanbxuu haucmeJ 90cm ouwm zo~h<2¢aaxw inbu uuuz<¢1Uca¢ mzom ”noxu mmIUIoz 44¢) ozouum moon nu...“ know «no on. On. econ buzz can uu~¢n «cau~> hmcnu mt: ou>OJAIU mzo u¢u¢ cum hwou u4c¢nx¢’ J~pu¢ u¢u4\na a». z¢9¢¢=u muo_u.»uumz~ pzunouxoz. u>~hu¢ uzu.\m4 no." xuompu¢ uxu‘\m4:°o.~ omm¢4 pzunouxozn u>~pu< u¢0¢xo4 an. uz-.¢». mucuuumzu: uzu‘xmma op.o~ oo-o-a :m«~oa u¢u 4¢poh pzu~ou¢oz. u>~pu¢ u¢U¢xm4 oo.~ omm.a pzu~ou¢uz~ u>~pu‘ uzu‘xma an. z.»=m haunouzuz. u>.hu¢ u¢u¢\o4 an. uz_~‘¢»¢ muo~u~m¢uz u¢u«\mo4 ap.o~ coueua zm«hoa u¢u<\mo4 om.¢n 9-3:-9 u».:amo:u uxu.\mo4 an..- cue-«o zuuoap~z ¢u~.4~»¢uu u¢9¢xmca n.n~ ouum zc_»¢z«4axu gm»— uuuz¢¢.uau. zccu ”coup a-oz-u-u gamfiwmmozmazgi uzc~h Agra» .I-"---" --- I-‘ 95.6 moon hzu~cu¢oz~ u>~huc u¢u<\mJ coco (Uh onooc omen" hzunou¢¢2n u>~hu¢ uxu¢\oa coon znt¢¢>a muoHonxuz «was «no u¢u<\mm4 anoow oolclo Im 4«»o» ----mmnmtuuuu-- do.» paw—ouxmzn u>~hu¢ u¢u¢xm4 on. 2.4uuzp .°.~u No.¢ pzuuouxazu u>~pu¢ uxu.\m4 oo.~ zumaz. "o.o pu.~ hzu_ou¢oz~ u>~hu‘ u¢u.z "nozu m-oz-u-u “zo~»¢»o¢ ou»oaa:u mum~n.»wuaumuamuwwmwozwwncaxupzu ow ua¢a 1115 Ocean uzuc mun bmou UJD¢~¢¢> J hmzuu uuuz<¢¢uua¢ 4.»o» nu. . no. »zu~ow¢cz~ u>~»u« u¢u¢xc4 o". ‘au: muo.u.o¢ux ~n..~ «a. u¢9‘\mc4 =o.~nd coupue xm¢poa anon ow. wentxmma omen. clooua uhtzamozn ow.» ca. ugu¢xmm4 oc.on e-g-o. zuwocpnz ¢u-4~p¢uu oo.o nu. uauc\mm4 e.nm ouum. hmou p_z= gun “9.x; zogp‘z¢4axu :bpu ugu.~»=u ac .zc»..:o c.9o ”o4u_» pmcuu uuu2¢¢.uua. m».o "acxu o-oz-‘-¢\a ”zo~»-»o¢ m1¢u44c> 3¢z~o¢m zo . cu»OJnxu mzo~b¢pox zou mpuooac um.¢a¢u»zu on uo.a 146 ouch» «non mach ooowu «new «9.0 peow wcou «no wmom cm. ocean an. hmou buzz mun u¢u¢\h:u co .zo»..=m coma uOJUur phone shomw «no cwoo ow. coco“ ccow bwou buzz can u¢u<\hau co cachooam 0.. «Dawn» curedutu 1 1‘ u "l'x':1,!.5lb\,.1 'l'.',.l.r\u 1.‘§11I.Il..'1l If uzut cum hmou u40¢~xt> anhOh hzu—cucoz~ u>uhu¢ u¢u¢xma on. bzuuouzcz~ u>~hu< u¢u<\oa econ hzunou¢u2~ u>~hu¢ u¢u<\m4 nNoN Hanan hmcuu nuu2(¢¢unn¢ uu—xu Dzouuw uuu2¢¢¢ua1¢ mt¢¢u rm um mzo~h¢bo macaw (m 2O um w¢u>¢wu ouum turn mnmzncat\o w¢u< mun Pmou uam¢n¢<> Hake» w¢U(\mmJ ocohaw wxucxwma ooowc uzuaxmma ooNu zo-¢z 4.»o» ----mmum---n-u- ac.“ pzu~au¢oz~ u>.»u¢ uzu.\c4 9°.o ‘9» an.oc an.n~ pawnouzgzu u’.pu¢ u¢u«\o4 oo.n zuz‘zyn _ mucuuumxu: ao.s H.. u¢U¢xmc4 ao.~s oona-e zm‘pan -.m am. uau‘xmm. oo.m~ ouocua up«:amoza oc.o~ cu. U¢u¢xmm4 09.9"” ouo-¢o zuuoap_z ¢u~.4~»¢uu oo.m on.» ugu.~ma4 a." can» pwou p.22 «um uu~¢a zo~h¢z‘4axu zuhu u¢u¢xhau mo .zc»..=m °.- ”o4u~» pm¢.u uuu2¢¢¢uan¢ mhuum¢«e=m ”nozu m-mz-«u.\o uz°_»¢»o¢ ou»o4uzu mun“N¢»wu4u»uamuwwmwozmm~zucubzu «n uu¢a 148 no... «non caowu «9.0 cc.” ~m.~ mmoo oo.Nu hmou w¢u<\h:u ¢o .zch..:m Noo¢n ow. ro.~ ooom «boon mh.o hmou u¢u¢\hzu «o .ZOhooso no.5 No.0 ho.~ an. om. cm. on. buzz cut uoaw~> no. an. an. on. nu. hut: cut undunb ou>04a1u uu~ ,uu— KB hmzuu uuuzdctwaa¢ an wax—u ¢u >u ~h no u¢u¢ run bmou u4n¢~¢<> 4<>Oh hauuouzuz~ u>~h0¢ uzucxoa on. bzu~ou¢uz~ u>~>u< uxu¢\na coon hzunouxoZn u>~hu< u¢U¢\od mN.N u¢u>¢z "accu 2 thch hzu~0mccz~ u>~b0¢ u¢u<\oa on. u¢0¢\mmd oc.a~ u¢u¢xmma oo.m~ u¢u ¢z~o¢m 2m x «on ”humonm MnxamuFZu «nu: muo~u~m¢uz owlolo zmdhoa 9009-9 uhdxnmoxn claim. zuoocbnz cuNnaupzum ouum tupu ataxia «acuhChox nn wads 149 .l'l'i1l I§AL|1§L1‘OIJ-V|l Ifillk .11 0o.oo wzuc cum hmou uao Ache» ohoo noon haw—ouxoZu U>uhu¢ u¢u<\o4 oo.o do» on.o¢ on.nu hZUuou¢u2~ wonbu¢ umu<~oa ooon z~x<¢>a muo~u~o¢ux mm.» mm. uzotxmoa oo.oo omoolo :mchon owon oN. ucuoxmoa oo.o~ oloclo uh J¢h0h a.“ co. paw—ou¢.z_ u>upu¢ u¢u¢\n4 on. ..u: muo.u_m¢ux n... u“. uxu.~mo4 ac... ..-.-. :mqpoa ca.~ a“. uxu.\wo4 no... .-..-. u».xawoza cu~.4.»¢uu o...~ ...“ uzu.\mo4 ..«u ouum .mou buzz cu. uuug. acup.z.4axu twpu u¢9.\»:u co .zo»..=a e._ «o4u~» paguu uuuz.¢¢uan. .....4. "moan uuoz-u-u-.-.-.\o ”20...... on.»n . uxu. «u. pmou u.o.~¢.> 4..o» ----mmu.n----u- no. pzu~ou¢uz~ u>_»u. u¢u«\m4 an. ..uz muo~u_m¢uz «a... an. uzu.\moa oo.~n~ ..-.-. 2m.pa. on.» o~. u¢u¢\me4 ...". .-..-. u».:amoza o~.~ .w. u¢u<\mo4 a...» a..... zu.o¢»~z ¢u~_4~»¢uu a... nu. uau.\mo4 9..» any. .mou pug: cu. mung. zo_»¢z.aaxu 1m.” azu.\»au zo .zo»..=o a... “adu~> »«¢~u uuuz¢¢¢u... m».o ”nozu u-oz-u-u-.-.-.\o “zo~»¢pou ouroaatu muummcwwuaawuamnwmmmozmnncnzwbzu an Heda 151 on.on chouw oo.o hmou uxuo\hau co ozo»..:o ho.un shomu owoo pmou u¢u<\hau co .20h..30 coo o.¢ an. on. but: cum "cam—p an. om. puz: out uoauur ou>oamxu wouxa ox—xh woman ozo uum ”woldzdumao uuuz<¢CUAA¢ mono cum bmou uno<~¢<> AorOh acctxmoa oo.o¢~ ooloio :w¢»om u¢U¢xmma ooooo oloolo Uh 4<»Oh uxu¢\woa ooohoN ootolo :mcroa ucuoxwoa oo.oc ouoclo uptzamozu ¢u-4~h¢uk zo~b¢2¢4uxu tuba (L44u44 unozu UUQZIUIUI 4¢w0h ocoh rzu~0u¢02~ u>nhu< uxucsoa nh. acoozou muo~u~ruum2~ cnon hzu~ou¢oz~ manhuc u¢u¢\o4 oo.u xuo~h0¢ u¢u¢xo4 ooon omm~hu< u¢u<\oa on. uz-<¢~< muo~u~o¢uz «a. u¢9¢\mo4 ououn oolfloo zw J~hu< u¢u¢\oa oo.~ ommta hm.“ hammouzozn u>~hu< uxu¢\oa on. Z¢h=w h~.~ haunouzoz~ u>~>u¢ u¢u<\oa on. uz-<¢h¢ mucuunoxuz an. u¢u¢\moa ovoun oololo zm(hon ow. w¢u¢\moa on.~c oiwclo urczamozn Cu. mootxmoa on.no olocNo zuooxpnz ¢u-auh¢uu ooou uxuoxmod n.nn ouwu but: out wouxs zo~»¢2¢4uxu turn «Odwur haunt uUUZ¢¢zu kn moon '153 mm." «oown cnon ohoh cu.u N¢.n 0o.o oN.on on.nn hmoo u¢uu.4., 3.2.a J¢h°b u>~hu< uxu<\oa u>~h04 u¢u<\o4 u>~hu¢ uzu<\04 mootxmoa on.un mootxmoa on.oc w¢u¢\mo4 oo.onu u:u«xmm4 non— zo~h¢zou ol0¢lo u> u¢hOh u>nbu< u¢u<\oa u>~bu< umu~hu< mootsoa u¢u<\mod o0.uu umpixmoa o0.~n u¢9¢\moa oo.nc uzuoxwma o.oc zo-¢z>— _o— .9.- . .. ...-u -.v‘.‘ 165 Sample Data for Alfalfa Year Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1976 -- 5.7 5.0 4.5 3.0 1975 -- 4.3 5.0 5.1 3.5 1974 2.5 4.0 5.0 4.4 3.5 1973 -- 5.1 -- 4.7 4.0 1972 -- 3.3 -- 4.4 3.0 1971 -- 4.7 -- 3.8 3.5 1970 —— 5.6 -- 4.7 4.0 1969 2.6 5.3 -- 4.8 3.5 1968 -- 3.8 5.0 4.6 3.5 1967 2.0 5.0 5.3 5.5 4.0 1966 3.3 6.1 4.0 4.0 4.3 1965 3.0 6.8 2.9 4.0 3.5 1964 2.4 4.1 3.5 -- 2.9 1963 1.8 2.3 5.9 -- 3.8 1962 -- 1.5 3.0 -- 2.4 1961 -- 3.1 2.4 -— 2.0 1960 4.0 4.0 4.2 4.9 4.0 1959 4.0 4.1 5.2 3.8 4.6 1958 3.0 3.0 5.6 4.1 3.4 1957 3.0 -- 3.3 4.1 3.0 1956 3.0 3.0 4.3 3.9 2.0 1955 2.5 -- 3.0 3.0 1.8 1954 2.5 -- 2.5 3.0 2.6 1953 2.5 0.8 4.0 2.5 4.4 1952 -- 2.6 3.6 3.2 2.0 1951 1.9 2.2 4.5 3.5 1.0 1950 2.5 2.9 4.1 3.0 2.0 Farm 12 Farm 6 Farm 11 Farm 13 Farm 2 Sample 6 03 0‘1 NWNdwwNDWN-wawwmbm ammoom—aboocnuuoooowoww I o I o o o I 01 I \l O \l Farm 3 “1‘- HT—‘h‘fl “0.4.0.... ---—1......“ .. .'."- fl. .-f—"—f’.-AA“ ..._.__._._-.__ ._. 166 Sample Data for Wheat Year 1976 1975 1974 1973 1972 1971 1970 1969 1968 1967 1966 1965 1964 1963 1962 1961 1960 1959 1958 1957 1956 1955 1954 1953 1952 1951 1950 Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 50.0 50.0 59.0 58.0 76.0 51.0 45.1 54.5 40.0 60.0 66.0 81.0 50.0 60.0 40.0 75.0 60.0 57.5 40.0 39.0 40.0 28.0 43.0 -- 46.5 53.8 30.0 25.0 61.3 -- 60.0 30.0 35.0 42.8 49.6 -- 60.0 49.1 17.0 55.0 50.0 -- 55.6 46.4 40.0 48.3 56.7 -- 35.5 36.0 40.0 46.7 50.0 50.0 66.8 40.0 40.0 36.5 62.1 55.4 50.0 43.3 -- 53.7 40.0 66.3 20.4 20.0 -- 16.3 -- ~- 56.1 50.0 41.3 -- 50.0 61.4 45.0 -- 39.3 25.3 -- 62.4 26.0 -- 37.0 34.0 -- 38.0 26.0 -- 49.0 19.0 -- 61.0 30.0 48.0 -- 15.0 39.0 54.0 35.0 30.0 30.0 29.0 46.0 55.0 -- 50.0 49.0 35.0 70.0 65.0 15.0 32.0 -- 12.0 40.0 40.0 35.0 32.0 38.0 21.0 60.0 46.0 20.0 36.0 20.0 40.0 55.0 40.0 24.0 36.0 35.0 33.0 44.0 47.0 23.0 37.0 33.0 -- 43.0 25.0 27.3 26.0 35.0 -- 40.0 —- 30.0 11.0 33.9 -- 37.8 32.7 25.0 40.0 29.3 -- 30.0 45.0 Farm 5 Farm 12 Farm 1 'Farm 2 Farm 13 Farm 11 vn‘.-u_—u-”-1d-Cvan .. cg_“_‘.- _o... _.'-_q 9-4.“ --‘v-‘c — v“ 0 '. I: ...—~.....—__ APPENDIX D TEST FOR NORMALITY 0-‘\—B“—.——I_O-n.-- us—‘u.‘_¢-.I~r-"'—rfl—...‘VOAU—JO-C<-.g _ APPENDIX D TEST FOR NORMALITY The Nilks-Shapiro test is a test used to determine whether a sample of observations was drawn from a normal distribution. The Nilks test is origin and scale invariant and a composite test of normality against alternatives (Shapiro and Milk, 1965; Bikel and Doksum, 1977). The Wilks statistic may take on values from 0 to l and the distribution is a function of the sample size being tested. The authors present the percentage points on the w distribution to be used for hypothesis testing. Presented below are the Nilks statistics for each sample for each crop. In the second column is the critical value of a 5 percent test of: 1. H Underlying Distribution is Normal; NULL: H Underlying Distribution is Non-Normal. ALT: Conclusions from any test depend on the form of the statement of hypothesis. The formulation of hypotheses in "1" suggests that the expectation is that the tested distributions are normal. An alternative formulation of hypotheses is possible under the expectation that the distributions are not normal. Previous evidence (Day, 1965) suggests that this might be a reasonable expectation. The formulation of hypothesis under this expectation would be: 167 —.-‘-‘_~>_-h_¢uo... ."nW‘-Q—vo»‘.~v—dlu.-\_4 _ 3‘ “A . ~. u—g us— 0‘ ~_ 9..- 168 2. H Underlying Distribution is Non-Normal; NULL: H Underlying Distribution is Normal. ALT: The third column presents the critical value of a 5 percent test of formulation 2. The fourth column is the 50th percentile point on the H distribution for the appropriate sample size for reference. It is impossible to reject the null hypothesis at the 5 percent level, regardless of the specification of hypothesis for most of the samples. Those where rejection of the null hypothesis is possible are labeled with an "R." Navy beans has the highest number of rejec- tions where the null hypothesis of normality is rejected four out of six times, and five out of six samples are below the 50th percentile point on the distribution. The null hypothesis of non-normality (formulation 1) could not be rejected once for corn; using the reformulated set of hypotheses (formaltion 2) a null hypothesis of normality could be rejected in one of six samples. The Nilks' statistic for three of six samples is below the 50th percentile mark. Five of the six sugarbeet samples had Nilks statistics below the 50th percentile level. The null hypotheses of formulation 1 was rejected only once in six times, but using formulation 2, the null hypothesis could not be rejected in any of the six samples. The Nilks statistics for all three soybean samples was below the 50th percentile mark. The null hypothesis could not be rejected for any of the three samples, regardless of the set of hypotheses used. Adv-— - Crop Sample Farm Sample Nilks Number Size Statistic Corn 1 27 .9371 2 26 .9735 3 27 .9695 4 26 .9151 5 24 .9633 6 23 .9699 Navy beans 5 25 .8903 4 25 .8672 7 20 .9120 8 20 .9707 9 20 .8848 10 22 .8783 Soybeans 14 19 .9181 15 18 .9403 16 18 .9380 Sugarbeets 7 20 .9825 8 19 .9361 9 19 .9569 10 22 .9102 4 25 .9598 11 21 .9120 Oats 12 27 .9147 6 27 .9825 11 24 .9352 13 26 .9875 2 26 .9619 3 24 .9571 Alfalfa 12 17 .9130 6 24 .9721 11 22 .9696 13 23 .9591 2 27 .9759 3 23 .9519 Wheat 5 26 .9857 12 24 .9489 1 23 .9090 2 22 .9585 13 23 .9642 11 20 .9660 R indicates null hypothesis is rejected. 169 5 Percent Value (1) .9230 .9200 .9230 .9200 R .9160 .9140 .9180 R .9180 R .9050 .9050 .9050 R .9110 R .9010 .8970 .8970 .9050 .9010 .9010 .9110 R .9180 .9080 .9230 R .9230 .9160 .9200 .9200 .9160 .8920 .9160 .9110 .9140 .9230 .9140 .9200 .9160 .9140 R .9110 .9140 .9050 5 Percent Value (2) .9850 .9850 .9850 .9850 .9840 .9840 .9850 .9850 .9830 .9830 .9830 .9840 .9820 .9820 .9820 .9830 .9820 .9820 .9840 .9850 .9610 .9850 .9850 .9840 .9850 R .9850 .9840 .9810 .9840 .9840 .9840 .9850 .9840 .9850 R .9840 .9840 .9840 .9840 .9830 50 Percent Value .9660 .9650 .9660 .9650 .9640 .9630 .9650 .9650 .9600 .9600 .9600 .9620 .9590 .9570 .9570 .9600 .9590 .9590 .9620 .9650 .9830 .9660 .9660 .9640 .9650 .9650 .9640 .9560 .9640 .9620 .9630 .9660 .9630 .9650 .9640 .9630 .9620 .9630 .9600 v~fo.'."_.u.-..-- _ —*\_l#-._ '._-5~4._,U..‘._. . ‘3:—-_+.- o...~.-—..v--._ . 170 The Nilks statistics generated for oat and wheat samples had one sample each where null hypotheses were rejected using hypothesis 1 and one rejection using hypothesis 2. The six Nilks statistics generated for alfalfa samples showed no null hypotheses rejection regardless of hypotheses formulation. Three of the six samples had Nilks statistics below the 50th percentile point on the N distribution. The conclusion of this analysis is that although there is some evidence of non-normality in the samples (measured by the number of samples where the Nilks statistic is less than the 50 percent value). The evidence is not overwhelming. The evidence of non—normality is strongest for Navy beans, sugarbeets, corn, and soybeans. For oats, alfalfa, and wheat the issue is one of open conjecture. - -§—. «— ... ._ —‘. _r u a u----..u-A—--..-¢.—r.~—.q—CAUJ“--u .— APPENDIX E POOLING TIME SERIES AND CROSS-SECTION DATA -.‘W—oh'_"——lv..‘-nn .. :‘""'I.“——"‘—-‘A—Co~vm‘.-u b APPENDIX E POOLING TIME SERIES AND CROSS-SECTION DATA For each crop, six farm level time series of yields were obtained (three for soybeans). Each time series was detrended by a linear regression of yield per acre on time. Yield + oi + Bi Time + 8i where i = l, ... , 6 farms Pooling of sample time series across farms, if possible, was desired. Three hypotheses were tested to determine appropriate procedures for pooling. This appendix presents the results of those tests and the final 1east-squares-dummy-variables (LSDV) equations estimated.1 The first hypothesis tested was: 1. Hnu11 oi = a2 = ... = a1 81 = 82 = ... = Bn Halt. 0‘1 i 0‘2 ’ °°° ’ “a1 81 ‘ B2 ‘ °°' ‘ B This is accomplished by estimating a common equation for each crop across all samples. To test the hypothesis, an F test is employed where S1 is the unrestructured residual sum of squares. S1 = Z RSS1 i = 1, 6 samples; and Ti = Number of observations in Sample 1; df = (Z T.) - 2N N = Number of Samples. 1 1The approach used here is essentially one presented in Madalla, 1977. pp. 323-326. 171 ..-vw— M“—..‘— --H'-v'-nnvh_<-A-do‘>-u _ - —‘_r—_ ...»...r‘. ...r u. .o - 172 S2 is the restructured residual sum of squares: 52 RSS of the common regression dt (ZTi) - 2 The F ratio is: 2 S / Uflk-ZN) F= 1 Hypothesis 1 was tested for each of the seven crops using the above test. The results are presented below. Table E.1 "F" Ratios Testing Hypothesis 1 Crop F Ratio Critical F (.05) Corn 7.07 > 1.91 Navy beans 29.68 > 1.91 Soybeans 7.65 > 2.53 Sugarbeets 12.36 > 1.91 Oats 4.12 >l.83 Alfalfa 21.63 > 1.81 Nheat 15.81 >l.91 The null hypothesis was rejected for all seven crops. Therefore. direct pooling of the data would be inappropriate. Hypothesis 2 tests the assumption. 2. H": B] = 82 = ... = 8n HA: B1 182:... :8” _- "’,.'.." _-_—.‘--_:v-—'—w-c-.-—.-.a.vm....- ... h 4._ 4w<-._ ..r‘ .— 'ge'.’ ..r c .4 .. . 173 It is necessary to determine S3 a second restructed residual sum of squares with df = (Eli) - (N+-l) to test this hypothesis. The F test is then: (53-511/(N-1) F = S1/(ZTi-2N) This ratio was generated for the set of seven crops and the results are summarized below. Table E.2 “F” Ratios Testing Hypothesis 2 Crop F Ratio Critical F (.05) Corn 0.60 > 2.29 Navy beans 0.58 > 2.29 Soybeans 0.73 > 3.23 Sugarbeets 0.46 > 2.45 Oats 0.62 > 2.29 Alfalfa 0.00 > 2.29 Wheat 0.60 > 2.29 The third set of hypotheses tested is: 3. H : a] = o2 = ... = a g1ven B1 = 82 ... = B Azalzazx to: 81=82...=B For this test the unrestructed residual sum of squares is $3 with af = ziTi - (Ni-1). The restructed residual sum of squares S2 with df = ziT‘Ti"2' The F test is: F ‘ 5.3/(21,411+ 111 174 The results of this test on yield data are presented in Table E.3. Table E.3 "F“ Ratios Testing Hypothesis 3 Crop F-Ratio Critical F (.05) Corn 13.75 >2.21 Navy beans 16.70 > 2.29 Soybeans 13.84 >»3.l9 Sugarbeets 24.81 >12.29 Oats 7.71 > 2.21 Alfalfa 25.80 > 2.29 Wheat 31.02 > 2.29 The LSDV approach to pooling data is based on the assumption that the 81's for each farm sample detrended equation are not signif- icantly different but that the intercept coefficients, the ai's, do differ. The three hypotheses tested indicate that these assumptions are fulfilled for the sample yield data for the seven crops studied here. The LSDV approach to pooling time series and cross-section data is appropriate in this case. The equations estimated are presented below: Corn: Y = -47.32+1.981-_5.240]+2.7002+14.14D3~4.7804i-S.21D5 (3.43) (9.42) (.95) (.50) (2.57) (-.85) (.92) R2 = .35. Navy beans: + .440 + 2.310 Y = 2.85 + 14T + 4.5901 + 3.8102 3 4 + 4.590 (-.31) (.05) (1.30) (1.39) (1.39) (1.39) (1.39) R2 = .04. 5 -~_wr—-b-_’~.. V‘w‘-‘ -"M_”pvn—v~‘A-J‘A--H h where: U 11 175 Soybeans: Y = -4.17 + .401 + 7.0701 + 12.4902 (-.31) (2.01) (2.71) (4.78) R2 = .06. Sugarbeets: - 3.3602 - 1.850 - .37D4 - 1.450 Y = 5.94 + .21T - 4.840.I 3 (2.12) (.04) (1.02) (1.02) (.99) (.96) (1.02) R2 = .12. 5 Oats: Y = —12.32+-1.36T- 1.3101- 19.4102- 10.4503- 12.4804- 6.9105 (-.91)(6.61) (.24) (—3.42) (-1.88 (-2.25) (-1.22) R2 = .21. Alfalfa: Y = -1.80 + .07T + .8901 + 1.3602 + 1.1303 + .2304 + .3605 (-2.72)(7.28) (3.05) (4.60) (3.86) (.81) (1.23) R2 = .24. Wheat: Y = 19.1 + .91T + 1.3001 - 1.3502 - 3.2903 + 12.6304 + 14.9105 (-2.50)(7.84) (.43) (-.44) (-1.05) (4.10) (4.65) R2 = .21. Yield; Time in years; and -4 -< 11 Dummy variable. _.—s.-«_ w“— ’hfie—fulnlgun I‘ -’"Vo’ar“f.'-r‘-fl—v.~—~‘fi“fiv~‘J.“w ~ APPENDIX F COMPUTATION OF CORRELATION COEFFICIENTS USING AGGREGATED VERSUS DISAGGREGATED DATA APPENDIX F COMPUTATION OF CORRELATION COEFFICIENTS USING AGGREGATED VERSUS DISAGGREGATED DATA The estimated correlation coefficients among yields computed and employed in this study are considerably lower than those computed from state or county data and used in other studies. Most other studies, e.g., Halter and Dean, 1960; Heady, 1952, used correlation coefficients derived from aggregated data. Such yield . figures represent a weighted average for a particular geographic area. In order to obtain an aggregate figure, reported farm yields are com- bined by an averaging or weighting scheme. where: W. 1 weight; and x. observation. 1 The above expression is a generalized formulation for such an aggregation scheme. The literature on aggregation of linear models (Theil, 1971) suggests that if there are N economic phenomena, each characterized by an equation of the type, Yi = XiBi + e, 176 177 where Y1 and Ei are n (i= 1, ... , n) element column vectors and Xi is by, and if the parameter vector (Bi’ ... , 8“) are all equal, then the macro relation can be expressed as: —- 1 Y - N-i The estimated coefficient vector for the macro relation is the same as for the micro relation and, more importantly, the disturbance term for the macro relation is equal to the average of the disturbance terms of the micro relations. These assumptions are met in the present situation regarding yields. As presented in a previous appendix, it was shown that the hypothesis 6] = 82 = ... = 8n could not be rejected for any of the form sample detrended equations for any of the seven crops. The difficulty is that although the 8i of the aggregate equation represents an unbiased estimate of the average 6i for the micro relations, it has been shown that the variance of an aggregated 5i is inversely proportional to the number of micro units in the aggregation. The proof from Carter and Dean, 1960, is presented here for convenience. th The yield per acre on the i farm may be written as: Yit = a1 Yit = oi + Bit + Eit where t is time, a and B are parameters, c is the residual and 'i=1, ... , N farms. - _ 2 = 2 It 15 also assumed that E(Eit) - 0 and E(Eit) oj . Aggregating overall farm units results in 178 Since E(Eit) = 0, the variance of E} is: N 2 1 2 o. o = —-2 (E o. + 2 2 p13 0.0.) 8t N 1 3:1 1 j i>j ~ 2: 2 —-2 - , Assuming Oi oE, oEt may be written. 02 (L:— =—N—+202 Z P..2 t i>j ‘3 where Pij is the correlation among random yield components for crOps i and j. Simplifying gives: 0% = 02/N[1+ (N- l) o) This equation illustrates that the variance of'E in the macro relation is inversely related to the number of micro agents comprising the macro relation. If oZE- and oZE- are greater than 1, then as >»ozE t i i t. In computing a correlation coefficient among the random elements of farm level yields, use of an aggregated series will overestimate the corre- lation coefficient if covariance remains unchanged. The effect of aggregation on covariance cannot be determined analytically. Thus, a Monte Carlo experiment was conducted to examine the impact of aggregation on covariance. The data used were the original data on value of the firm used by Grunfeld's and Griliches' study on the relationship between Micro and Macro variables (reprinted in Madalla, 1977). Twenty years of investment data for four firms in -‘-—a» _“.“."“.'," _—I‘_ 4"-‘r.".—lvfi—.IAQA-J‘ ... a g g —- v3 u- _. -‘. ~_’ w u .. a ”7...... .u h 179 two different industries were used. The data for the four firms, Westinghouse and General Electric in the electrical equipment industry and Atlantic Richfield and Union Oil in the petroleum industry were aggregated by averaging, creating two data series, one for electrical industry and one for the petroleum industry. The two series were detrended and a correlation coefficient was computed between the two sets of residuals. This computation is analogous to using aggregated county or regional yield data in computing correlation coefficients. The second correlation coefficient was computed by pooling the firm data for each industry using a least-squares-dummy-variable model. Correlation coefficients were computed between the residuals of the two regressions. Presented in the table below is a summary of the results of the computations. Table F.l Correlation Coefficients Between Aggregated and Pooled Data Aggregated Pooled by LSDV Electrical Electrical Petroleum Equipment Petroleum Equipment Variance 1017.89 70684.3 2051.52 93189.1 Covariance 5747.32 3740.52 Correlation coefficient .6775 .2705 "_OHP"—_~.:—1—'?—-;V“ r-o_o_-‘.-."—v-._.-.--Av._r‘ ...-.- ... m -_ V“. ..r-—.. ‘<-» w o . .- u 180 The variances behave as predicted—-the covariance of the aggregated series was higher than the pooled data resulting in a higher correlation coefficient. This exercise should not be regarded as proof that covariances of aggregated data are necessarily higher than disaggregated series. What is indicated, however, is that by aggregating, one measures a different phenomena than if data are combined in a different fashion. What has been demonstrated is, use of disaggregated data could have a profound impact on correlation coefficients among random disturbances of yield. The random disturbances, at least at the micro level, may indeed be relatively uncorrelated. Such a result could have an impact on farm planning in that diversification of crop production may be less important from an income maximization risk minimization point of view than previously believed. It is an area worthy of future research. fn_.>a~av.fla.“ 5 ...—U“ ~»_ ‘-._- vb.-.- n‘¢r- -u m"... u "i‘ufl— ,‘.9.. ~ ~v.u- APPENDIX G STOCHASTIC ANALYSIS OF ENTERPRISE BUDGETS PROGRAM .4“- “wan—r-..u'-—-.n—--—-Mfi'—r‘.‘.ag .— - v‘h H‘>——‘—H—r w. . - v.” .so‘- u . ,— APPENDIX G STOCHASTIC ANALYSIS OF ENTERPRISE BUDGETS PROGRAM The Monte Carlo model used to estimate the net return to land cumulative distribution functions (CDF's) for each crop rotation, and a brief explanation of what is computed in each portion of the program, are presented. Program SAEB. This is the executive procedure. Data for each crop in the rotation to be simulated is read in by this module. Figure 0.1 presents a sample input data for rotation 14 (O/A-A-NB-B). Rotation 14 is illustrative since the oat-alfalfa companion seeding represents joint production of three products on one field; namely, one ton of alfalfa, 80 bushels of oats, and two tons of oat straw. The values entered on the first card are: 1. The Rotation Number 2. Number of Crops--In this case six: oats, oats straw, first year alfalfa, second year alfalfa, Navy beans, and sugarbeets. 3. The Divisor--A value used internally in computation. This is the number of crop-enterprises grown. In Rotation 14, the divisor is 4 since the crop-enterprises are: oats/alfalfa, alfalfa, Navy beans, and sugarbeets. For rotation 3, C-C-SB, the divisor is 3 because first corn and second corn are considered distinct. 4. Number of Different Crops-~This value is used internally in setting up the correlation matrix. In rotation 14, the value is 4 since first and second year alfalfa have perfectly correlated prices and yields. For rotation 3, C-C-SB, the value would be 2, the number of different crops. 181 182 The information on each crop in the rotation is on the second and sixth cards. The first value is the crop number followed by ..——...—-—~——_ expected yield, yield variance, expected price, and price variance. , The last number represents a user input "key" to link all identical crops in the generation of covariances; in this case all alfalfa crOps are given the value 3. Numbering is to be consecutive odd numbers. Even numbers are generated internally to link price values of "like" crops. The values on the seventh and subsequent cards represent all non-zero correlation coefficients. The integers in columns two and four, respectively, represent the row and column values in the matrix. The third value is the correlation coefficient; the last, an integer, is a switch used internally to indicate end of data. A zero value will cause the program to read an additional card. A non-zero value will terminate the reading of correlation coefficients. i The "executive" module computes the upper and lower bounds for each distribution to be generated. The mean, variance, and upper and lower bound information is then used to compute the Beta parameters K1 and K2. The routine then calls the beta generator which returns a vector of 100 sample states of nature for each distribution. One hundred values for gross income are then computed. Calls to CASH, MACHINE, and HAULDRY return, respectively, variable cash costs, machinery and fuel cost, and finally, hauling and drying costs. Family labor is subtracted and the resultant 100 "net return to land" values are ranked lowest to highest as an estimate of distribution fractiles (see Figure 0.2, Anderson, 1977). 183 The remainder of the "executive" procedure is output formating routines. Sample output for rotation 14 is presented in Figure 6.2. Subroutine MVBETA. This routine (see Appendix A, King 1979) generates a vector of 100 draws for each probability distribution, two for each crop--a price distribution and a yield distribution. Two IMSL (IMSL, 1977) subroutines, MDNRIS and MDBETI are used to generate the normal and beta marginal distribution used in the table, look up functions, TABLIE and TABLI (Manetch and Park, Part II, 1974). Subroutine MVNOR. Generates normally distributed random numbers (Naylor). Subroutine COREL. Computes correlation coefficients among sample generated vectors. This information is printed with output as a diagnostic aid. Subroutine COEF. Generates the lower triangular matrix necessary for generating multivariate normal distribution (Naylor, Chapter V). Subroutine RORDER. A sort routine used in reordering Net Returns to Land in rank order from lowest to highest. Subroutine Cash. Generates cash costs including seed, fertilizer, herbicides, and cost of capital. This routine performs the multiplication of the coefficient matrix of application rates per acre for each crop in the rotation acre with the vector of input prices; determines cost of working capital. This is essentially the as generated the budgets presented in Appendix A, but without output formating routines. -__-._.-.______ dvu.—.- u-a“- .u-v—c -Nuv---fl_vh_.“wavm‘.-au h — V‘— v——4-‘ 184 Subroutine MACHINE. Attaches as data machinery cost and fuel usage rates for all rotations. The routine then selects the apprOpriate numbers for the rotation being simulated, computes fuel cost from fuel use rates and returns the figures to the main procedure. Subroutine HAULDRY. Computes hauling and drying costs (drying corn only) based on custom rates and expected yield of each crop in the rotation. 185 .444 co4omoom to. 434:4 .445am 4 .o mgamwu 02¢: ”SUV-HOB”...- GZHnHOnU HAN-m .HLWHOMH ma4fln.44.4u.d.44: 244.2 .. 3 4. .... 3 a. 3 .. o. o. a. 3 o. a. .- .. 4. 4.8.... .... a. o. a. a. . o. o. o. 2 8: c. 3 a. a 8 to. 22 240144.38 .. o. 4. o. o. 2 a. :4: 0.4.4.4. . 2.1.4. . 414.414.444.114.-4414.4I444141.444444444 4144444444 444444444 444441474 444444444 444 444 14-4-1.441414114114141411414.1441411414141441413411414141444.1144 4 4 4 4 4 44 4 4 4 4 4.4-4.4-414 4 4 4 4 J4 4&4N4o40 4 4 4 4w4 4 L 14. 44 1. 44:41.14 44.41414 4 4 4 1 4 44 411144 4 44 d4 4 4 4 4 4 44 4 4 4 4 4 4 4. 4.14144. 41414141440414.ng 44 4 404 4r -. 1.4 414. 4 .4414- 14. ;4 4.44.4 74141411144144.1414 4 4 4 4 44 4 4 4 44 4 4 4 14 4 44 4 414 4-4 4.4-44141141414140414M4w4c4-Q 41414111140“.- 4m. . .4 4.4 4 414 4114 I4 4 4.4.4.4 4-4-4, 41144144.. 4 4-41411.44--_4F44.411441444-4144141 4-424144141414414444-404-4NG4.4...--414-4 7-444440% 1441.14 41414114. -.4 4144-4444141 14144144144... 4- 4 4 4 4 44 4 4 4 -..-41441.44 41414141414 41414141414141.4174 4o. -4h4N4,.4-o.414.4- 154.45 .4 4 4 4 4-4.1.141-444 4-4141141444414444 414 41-414441414414141 444.414-444.41. 44 4 4 4 4 4 4 4 141414 .04 Riga-14414 4hl4m_ 14.4.4 441414141 4.41441411414141144141441414144. 41414 4141441414,; 41414 414414-:441 41414141141414.1411]. 4 -404 4T4N4.4Q.414144 4N4 .mw 4 4 4 4 4.4 4-414. 4.4141414141414.41.141414141417414,4 441414 4 4 4 4 4 444 44 4 4 4 4 414 4.4 .414.-4141j414l414404 4M4s_.4.... 4 4 4 1-4N..1..4w 1. 4 4 4 4 4.4 4. ..4 4 4.4 4-4-11414-41. 1%14141414144 _ 4 414-414.1414 -fijl..414441414114jl_j11441414j14141414 .04- 4M_&_._Q.J4|41.4I. I4N4 4T4... _ 4.4 4 4 _ 4.- 4 _ 4.4 4.4 4 41414111411414.414144-4 4 41411-414 4141414141414 414jlj;;jlfijlql.4lfllqllji—l4o4l4m;4..Q 41114 4.“. <1” .4 4 4 4 4-4 4: 4. .4 4. 4 41444-4...- 144444444 4 4.4--4141414414141... 4 4 4 4 444 414 14 4 4 4 4 4 4 4 4 4 44044—4240 41414 4.4 4m_ .4 _ 4 .4 414-1 :4: 14.414414411414141 41.41.4414 14104 — 4.1-«14111414141414.1344 414141414141....414-4-414111141141414403040444014414141 4.. ..M_ 4 4 4 4 4.-4 4- ..4 4-4-44414414414 ”4&44141414414 4 N4m444m404w41414l414h4m4w404md44441 o4w4.4m4.41.4|414414.1_d4..4N-4w.414.4-4-4l41£44414. . 4-4T _ 4 _ _ .-q 4 4 4 4-414 4.4--«11.14 41 .4M414-41-414. 414-4 QQ..4M4¥414114I414. 014wqo4N4N4 4141414.- ..XlLM—NaI—JJJJ 2041.4w4w41filfl «141414.14W41— £4 4 4 11 .4- 44, 4-44 4 ._ 1. .4 4 4-4-4.41.44. .4»..- 4 4--..-14414-4-..N4m_-.4w4.N414.4|414 .MK4LO40414|fl441m4w4n4w4J-44.|4.1#1_w444%414l414 4.414Lm4w4-4 T4 4 4 14 414 4 414 .1 ... 14 «1— 414 414-4-4- .4M_ 4. 45%-—.-4141411.~v4m1.43]|4.jl:m4k4.404V4141j411.N4Q.414141414|4141 .04: 4 414114414141rfi4w4l4 4 4 4 _ _ _ 4 414 _ 4. 114-41414-4 441441 .4N4-4 414111414141$MH4J4§1414144|41 0404.404M4:4|414141+r4m4m4 414144141411N414 4.14141414141dfim414 . 4- .4 4 ._ 4 _ _ 4.4 4 4- 141414 414 .4. 4,14 41 41.414-411.44 4.1:u4-04m41414141414141t4t..4wfi414141j1..14®4\4W-41114|J 4°42Q4mfi4. 4141 41414.4m41. 4 4 fl 4 _ _ 4 4-4.—L 41 .4 41414141414414 .4141.4-4141fi|4141.—J..4141414|4Idl4|414144.4.-4-1414414174114411}-.. 4-4-4 41414.3. 144-4&4- . w44§fiw o._..4..4:4:_t.4.:4: :4... 8434.83.48.343434343 8434843434943434341; _o.«.1.4..m:1.-_-.1u4.1..1.1.441.4fl4-L 0.4.flfl544mufig.§¥o.4ml~424m4vflo1~4wmfi~a~44m£4.44..4..1.1.._....4m.4-4.4fl1.1. o. rid-M4. 4. ...-.4 3.1.. u 5.54 .n u «3.44 .4 o 3...... .u .4 .02 a 1044.232 24: .~ 4.8 .4 on: .a z #20! . 455m 52242:... 234:6... w-upfim» 444 444: E44 4.32.. 2.4:.» 444E424 14444433 .4344; 4.434.443 .3... E440 Sue-4 .3483 24454:: CROPPING SYSYEHS MODEL VALLEY SAGINAU 10. ROYATXON NUMBER 186 O ZZNU‘CQHOONOONfiU‘fiNQQOQ-dfisbONNnFOOMNv-GFHDOBU‘OGQOmDnFU‘QO‘DonHDDNOQOn-IODCO“ I:¢¢Wfimrnut0uhd~crnnmcwncfluncdwnwcuawflhomCWOFO(Vn'unoOunhhurmawvmcnflmnmhnfiuflcOCMDCOWHBCUWV DJOOOO0.0IOIOOOOOOOOOOOO0.0.......O...00......O.....O0.0000..O...... .- Oflnvinf-HWV‘IONNNQDNwQQOOmwa‘dtflmOdNNmCO‘H—dNflhhtQQO~NOWWGNNIO|DFQCFDV>IOFNQFO U NnanCflDOFFthfimwmfifl‘OU‘U‘U‘OOOOA-‘HHH-«HNNNNNNV’F’F’HCCCCU)Lfi\D\D~D\D\DFFFOQOOO"C go unnuununuuu—unuuunnunnnnnunuunnuuuuuwudm .— "ACHINIt'RY COS 98.2Q WUCOV’U‘CfinnmflnfiflflnU‘OdU‘annnCOU‘HDCHMCQQFHnNleHDU‘CDHWWDMDNOfiCflONQNHOflHOF WIHOQU-OCNNNHOO‘NQU‘I‘HU‘COONNC\DNU‘NNOU‘anv-‘FOOWFnQWO-OWU‘DOWU‘QC‘QW.CWONO‘DC“Ono-O 00......O0.00.0000.........OOOIOOOOOOOOOOOCO.I.........OOOOOOOOCOCO. uUNHWWVDU‘UDFONCOU‘U‘OCQO‘OOwOo-Oo-ON‘DFONHHCFFfiNMHNCU‘WQDflWWOflWHOCFOOOOOT’WU‘HOQN QZNI'H'H’IC.IDIFMDFFFFFOOO00‘U‘U‘ODOOOOHuud—Ido-QNNNNNNNWWOCOOCCVIUW‘DOWKJFFFQOQOC‘O‘O‘O nwwmwwwwwwwwwwmwwmNNmwnnnnnnnnnnnnnnnnnnnnnmnnnnnnnnnnnnnnnnnnnnnno Figure 6.2 Samp1e Output Generated for Rotation #14. OU‘DOONCOCN—OFOOQDOIOOIDHOMFHU‘OFQCOONOU ovum-nut»(yawn—outrun:cnsunnwwwhmocnhhww 0.000000000000000...00000000000000 NNO‘Ohm—ONmmnwmtmDCOsDFo-INBNHNNQDQCOnU‘ oceanuwwwwnnnccwo¢w~nwo~nncmm01~a~c~oa~ NNNNNNNNNNNNNNNNNNNNNnnnnnnnnnnCCC dONMDflflonnU‘H-OFICONODQIDVDOCv-OQOOOVDOMW WHO—IOWGFQU‘F‘DFDHOCFHFU‘O'QID‘DWCIDO—OCHQQ 00000000000000.0000000000000000... NOONCJONI’MD‘DCFU-OOHOFQQNflOnnCC‘DF‘OONOO Ownuwmwmwnnnomwwooocoanncnnhhmtwo cccococcccccccccccoccnnnnnmnnnnooh 0.90 IT R61 IS 8 1609 LINES PRINY. 29 PAGES PRINY. COS? TF39057 22:37:33 10/13180 187 Figure G.2-Continued 1 ,‘OQ‘TIO. 1 O‘OQ‘VIQ. I OifiRt‘IIQ. VQ‘OR‘VQQ.’ 9‘OQ‘100. 1 Q‘OK‘7IQ.1 "C‘SVIQ. I 93OQG739. 1 2‘0‘67 .9. ‘?3.56739.J 7.3.,‘6189; 123.5‘1789oi 23‘5‘7'Qo1 ,3.“~ — — ... —. 44- ~— "- \- .— s -.-.u “C m. dug-....- -~ ~ f~cf-—-l—_vh-v—_--_w-v_p—. _-_._- ‘— FTN 4.8+508 10/13/80 188 =1 OPT 74/175 SAEB ’ 7 E S D. Y. A S ) T I 0 ’ ’ 2 6 N l. E M S P 9 v- A \1) S T 00 9 9 22 \l 5 (1 \l o 4.... TV 0 2 D. C9 2 l. A A) ( R T F0 0 A 9 92 N V 1 )9 P 9 E 00 O \I P 22 R 0 A (1 C 1 T URD9 1. I. BAN) ls T.) 9P 90 D UT )9)2 N PU 0’01)!» TP ZUQDUT UT (2 9L1E 0U L90E‘R :0 80210 9 2: 92(V1R) E6 )(0 9A0 PU ORHRVZ AB 20909( TF4 (C 9S’N 9D 29’10A 59 K)OV1.E 63 9011‘" F41. )2IDEA pE 0999C9 AP 20081) TA (ZZPRO 9T 1((0P1 T9 KCYR91 U0 C)( 0.1 IOC TE 1N UP ////(T. 0A 2345YS (T. KKKKRO B9 CCCCAR/ F49 OOOOVGU AEZLLLL 0 SPKBBBBNNI ll“. 9 (I19YIELD(I)9VARY(I)vPRICEtl)vVARP(I)9SYS(I) NOgCROPSoDIVISOR9$CROP x I R T A 0 M... o 14 N 4. o \l T. J so T 9 PN A. I 0P)L2 SS ( T.) RUDE... YY. R OUZSCR 0R8 3800 R oiPICORP IT. 0C )3P0 9,100 9 90) 0FOR14FCR211:J 21.4QP A 9/[l/00/3468911RC4416 CS: :) 04.4.4294)EP 9(C 44 I 9(T 44 PIJJQU 9(T. 0U MTl OPAMMMMMMTHNHHARYR ARTO .4 110 A9KNNNNSSNDDDDITSS ITCZO R8 OOOONN NNNN(A44P2(AUSR68T. oICAJNEl C 0 21. 9EN14T 9D R(NARR(U .4 44 C 8.602 III." .1113, . ...] 1‘1111111. ’(11 I. III. 119.19 I19|f1s1ot1fihllavcns {1111.126 ..v1rvrpbf . 222222222333333333344#444411k555555555566666666667777777777888888888899999999 2 A. 6 8 0 2 0 0 O 0 1 1. 3 3 3 3 3 3 0 0 0 0 0 0 T T T T T T 0 0 O 0 0 O G G G G G G 6 5 9 6 1. 6 9 6 A. )5748 )0280 \14375 )4384 )6333 )7. ‘1) 003.7. .0306 .03. .0506 0.5.1 .0 1.1.1 11 01 o 22 01 o 31 01. 41. 01 o 51. .1 O 61 S ...(l‘ ottit otitt ...—ti o**** o**** 0* P )\IDE)\IE\I\I\I\I E’)\I\l PL)” F4”), FL)”, E) 0 IILCIINIIIT. NIIIT. NIIT. NIIIT. NIIIT. NT. R ((EIlsl‘ 0(((( C(((( o((( 0(((l\ O(((( .1 C SSIRYP)DDEE \IDDEE )DDE )DDEE )DDEE )D T. YYYPRRILLCC ILLCC ILLCS ILLCC ILLCC IL 9 SS: :AA(EET.T. (Er-4.1.1.. (Er-4.17 (EEIT. (EEII (E 1. : 4.))VVOIIRR OIIRP OIIR o OIIRR OIIRR CI 44 )\IY.P: .4vav-PD-4NV-YPD 4NYYP54NYYPPQNYYPP1NY. IZZYPJJ))P 44 4. 44 :2P 4. 44 44 :20. .4 44 44 4.2P 44 44 44 :20. .4 44 44 4494p 44 #+JJ((YP0\I)\I\I 0),), 0‘1”) 0),), 0.))” 0) 4YP1‘NNJIURYYPPORYYPPORYYPPORYYPPORVIY-PD-ORY. BEL"MMME4L4AII'14740MSOIDMRPC11(ITDMI\IT . UZIUIUTTIAA‘(CJIUJJTCJJJJTCJJJJTCJJJJTCJJJJTCIU ....CCEERR(I\I\I\( ((((( (((l\( (11“ (((l\l\ (( RAEOOOOIIAEEEEEOSCOEOSRNOOOFOEOOFPYPOYPAAMMAAFULULOFULULOFULULOFULULOFULULOFU pTRCCCCDDDRRRRR-FIIDRFNCMDDCICRFCIHJJDJJFFAAVVIBBBBGIBBBBGIBBBBGIBBBBGIBBBBGIB 2 0 a. n14 6 «U 8 0 0 1 10/13/80 .2 FTN'4.8+508 =1 OPT 74/175 SAEB 189 ,9 999'". 2 1.9 3 08 :Io * t t ‘9), 1T9; (I‘l‘ DEE LCC EII IRRH GO TO 314 OIIR 0 GO TO 316 -BL(I)) ) ) ARAMETERS ( ) t ( D N A L 0 T. N R 0 U a T000 AEN:N TR 9) 9 YPPQNYYPZQNYYPPO. EA:E(M1EBT :(2 = .. 22D... : : :2P: : = :9. \I)’ 0),), 0),), UHIMRE(UVEMCM NS Ann-...NHN N YPPORYYPPORYYPPO T. 6(V)\IT. 8101 T. S C D H n \l R t B L L F. Y D L 0 H M F . R S B M L E \I R D T a O R S 3 S H Y. F. T. . S R V T A I \I S D R C G / B L N 9 N 9 L E I D O \I D U P o T. M... R F D. 3 T 9 H . 0 F. A B 9 TI R 9 T- .L T S C ... 0 l\ S C R V. C D. i L U V- R \I E Q E F. S M .)U FL land I 9 TF . L M H A cu9 T. A Hu.l L CT. S V N ( HS C Y. SC H N ( )CP 3 nu N T. + U9U C A 0 ) NOQ . N I M” 9NF. )Qu I 7: S ( CT 9) HE G A P C NOOT (N A T 0 N IRNS CT. S 0 R S I S9TC NTE *OR C P S 0300 IUN 9N9 ... 0 0 RPRH SOT. XT9 9 R R 60((3 CRT 7.0x X C G (REY3DR U 4R4 a. I .. RPfiRKoNGTAYI9).{I9 9 \1 E(ID39:AR2*4*6* 1. M DHHLZI)” 4.1.4040 : (ERSCU::MRR9*9*9* N22CUDAAARM(DE2(2(2( + ... NNRCHHB DFD(T(T(T ZABII LSN AEAEAEA BU/ACRE EXPECTE *9F5009* OG 9*8 T), 9/ odXt 01.08 9 G O( 92 )ED* 0 SNLNrO Dr CERF 0’10 9 RJV-Ct CJ)*$ 1(0 9 005x [.99 II 0‘ .‘cll-I' \.I I‘ll A.“ ‘1‘- (o'o9ollulull..9nl_I-I-.((99999‘“! 991111111111111111llllrrrlllllllll1111111111111111111111111111111111111111111 E CHT/ACRE *9F5009* YIELD CTED E) ’P* JXT 6.0—LU 5(t C E 9/ OCX* T12 9 R 92 OP* 0 G 9 6 998:! ad" 9 2JA* 0(E3 EDB NLY oEVE )IAC JYNI J)tR (a. 90. osx EXP BU/ACRE *QFSOU’. ) CTED YIELD J E DJP) G(Xi EEU 0C... B TI 9/ RX. 0P4 9 G 9 92 ‘19.: o oJSG 3JNF 0(A 9 EDP... NLB$ oEY \IIO luv-SF. J)... C (8 9T. OSXR TON/ACRE EXPEC *9F5009* YIELD D \IE JT QJC G(E) EP * OCXN TIEO R T 00.. I G 93* ‘1)?! 9 .JEZ QJE 0 0(86 EDRF NLA 9 0E6* ’103 JYS J). (2 9E O'DXC BU/ACRE EXPECTE *9F5.Do* NLS 2LT )IA JYO J). [(69 Dex TN98E6N98 6N98PEN9816N98 GP2(C7P2(DTP2( 7P2(R7P2( 00(411 0(TéL.9(T 0(TP 0(T JREAROREATOREADOREA UREA JJJTCJJJJTCJJJJTPTEZ : :IITLEZS3 . 03LLSTLLLLY3LTETHTHTHIJCTHPTCTHCTCTHETCTH TCTH (1“ ((((( ((((( ONT. UG(I\NLT o : :ONLLLLL TUHIRIRIR ..((T.R (IRE (IRT (IRD (IR LULOFULULOFULULOTOUOMIIZOAUOROABOABROAAAA"OF—0 ROROROJFFRO OFROPOFROCOFROEOFRO BBBGIBBBBGIBBBBGSCPDESKKCCPDGDLLDLLGCCCCCFDRPEHFUFHFJIIHFDGI HFXGIHFEGIHFTGIUF 2 1 4 1 Mu 4.0 2c M 08 C2 ..IG UA 2 4 6 OP h. 9 ... 5- 20 33 7 O Q. 5 i 2 D. 55 i 68 55 o 0 6 “.6 66 10/13/80 .2 FTN 4.8+508 =1 OPT 74/175 SAEB 189 ,‘I‘lll. 2 1.9 3 08 .10 * * * ‘1), III ((( DEE LCC EII IRR YPPQNYYPZQNYVIPPA. : = :29... = = :29. = : = :2 GO TO 314 GO TO 316 2 )7 1.9 o 03 08 81.. 01. o 0* * * * E)\I\I\l NIIII .(l‘l‘l‘ )DDEE ILLCC (EEII OIIRR ‘1), 0),), 0),), YPPORYYPPORYYPPO I 6(V)\II Ill -BL(I)) ) 9 M ARAMETERS ( ( / ) ( * E ( A ETURN TO LAND TR E 1M1. EA:E(M1EBT:(: UHIMRE(UVE"CH NS AA: ..NHN N BIOI 0‘ A 9 9 l- l 9 I 1 ‘D.-I|9'I'.'.ll.'o'u in; 99111.11111111111111111111111111111I111..111111111111111111111111111111111111.1111 T S C D H — \l R t B L L E V. D L 0 n... M F . R S B M L E \r R D T ... O R S o. S H Y E I . S R V T A I \I S D R C G / B L N 9 N ) L E I D D \l D U P O I N... R F D. 3 T 9 H . O F A B 9 T R 9 T L T S C t D ( S C R Y C D. ... L U Y R \: E Q E E S M. )U E L B I 9 Tc. . L M H A S9 T A U T L CT. S V N ( HS C v. SC H N ( )CP 3 H N I + D9U C A D ‘1 NOQ . N I M 9NE )3 I T S ( CT 9) HE G A D. C NOOT (N A T 0 N IRNS CI 3 D R S I S9TC NTE *OR C P S 0300 IUN 9N* ... 0 D RPRH SDI XT9 9 R R 60((3 CRT 70X X C G (REY3DR U 4R4. A. I : RCNR.NGTO)9)9)9 9 ) E(ID39:AR2*4*6* 1 M DHHLZI)" 4.10.040 ( E R S C U M R R 9 * 9 * 9 * N22CUOAAARM(0E2(2(2( ++NNRCHHB DFD(T(T(T ZABII L5N AEAEAEA E E D. c E T x E T C E D. C E X E p. E E D. X R X E C E E A R / C E T A R E nu I c E R C U A R C B I C A N A I * O I U 9 T U B 0 * B o 9 5 U * F O 9 * 9 5 0 * 9 * F o 9 U 9 5 0 o * F o 5 D 9 5 F L * F 9 E D 9 * I L * V. E D I L D V. E D L D I L E E Y. E I T D I Y n» E Y E) T D \l \IP* \Ic \IE ‘1 JD JXT JE JT JD ZJE sluEnl OJP) QJC BJE 5(T 5(* C 6(X* 6(E) 6(T EC E 9’ EEU ED. * EC OCE OCX* 0C*B OCXN OCE 8TIP‘I T12 9 TI 9/ TIEO TIP 7. RX* R 92 RX* R T Rx OPEU OP* a CPA. 9 UP I OPE 069*8 G9 6 6992 693* 69* T), 9’ 998:: )\l* o ‘1)?! 9 \l) 9 OJX* o-UN 9 0J36 OJEZ onux 01.08 9 2JA* 3JNF QJE 0 :.J8 G o( 92 0(E$ 0(A 9 0(86 0( 9 )ED* 0 E03 EOE... EDRF ED* SNLN6 NLY NLB$ NLA 9 NLS D. OERF OEVE OEVI OEG* OET 09.10 9 )IAC )IO )Ius \IIA RJYC* JYNI JYSE JYS JYO CJ)*$ J)*R J)*C J’* J)* I‘D 9 (A. 9D. (8 9T. (2 9F. .(6 9 .05x 05x OSXR O’DXC 06x TN 98E6N 98 SN 98PEN 98I6N 98 GP2(CTP2(DTP2( 7P2(R7P2( oD(TI 0(TE 0(T 0(TP 0(T JREARDREATDREADDREA OREA JJJTCJJJJTCJJJJTPTEZ : ..IITLE283 - USLLSTLLLLYRVLTETHHTHTHIJCTHPTCTMCTCTHETCTH TCTH ((l\ ((((l\ (((l\l\ ONT UG((NLT 0 LULOFULULOFULULOTOUOMIIZOAUOROABOABROAAAAHOEO ROROROJFFRO OFROPOFROCOFROEOFRO BBBGIBBBBGIBBBBGSCPDESKKCCPDGDLLDLLGCCCCCFDRPEHFUFUFJIIUFDGIHFXGIHFEGIUFTGIHF 2 1 H4 ue H H 40 6 O 8 2c 2 c 2 .1 : :ONLLLLL TUHIRIRIR ._((IR T6 20 UA 2 A. 6 33 OD. A. A. A. 5 In an» (IRE (IRT (IRD (IR * * * O 7 U 2‘. 6 8 0 46 A. 5 55 55 6 66 2 6 10/13/80 908*508 FTN 190 =1 OPT 74/175 SAEB (99"(‘TITIT'IITI'k‘ol 111111111111111.....1111111112222222222 $*9F6029*/BU*, TON/ACRE EXPE *9F5019* YIELD ED )T. JC ZJE) 71(P* EXN DCED T$1*T R 9/ DPX... Goéu9 9:192 OJ * o 6JA6 0(Fh. Ean9 NLA* QEFS )TEL JYA .d)*ru (AU9C DTXI BU/ACRE EXPECT *9F5009* YIELD )n. JE 7KUT 7(C EE DFXV) T;1X* REU DPtB G 99/ ))X* 0J7.9 TJ 92 o(* o EDT6 NLAF oEE 9 \41H* JYUS J)... (a. 9 DTXE EX TON/ACRE *9F5009* YIELD CTED \IE) JD. * JXN (ED E*T C 9/ .IX* R39 D. 92 9*. \AHG JAF JR 9 (T* DSS L ET IAE VIDC )*T. .79R TXD. EGN 98R6N 98CE 98 CTP2(P7P2(172( 142(R2(*2R1(X112((( 0(TR (TD+ (TI(TR(B(T9 ((TTT ROREA OREAPOEAEJOEAHEAOELEA92EEAAA I 0(T 9 9 9 X X t 9 9 o. L 9 T 9 E * S 2 U T C o F S D 6 ... D H F 9 c 9 9 X * R X 9 9 B 8 9) x L 9 ** I D 2 TN 1 R 0 RR 9 H 5 EU *9 9 F NT T*T 9 IE SDS X HR DNC 9 Ct CAL 9 A 9 *LE 2 "X 9 U o *0 X F 5 91 1:U9 pr X 9 ITT 9 8* 9*S X 9V. 1. 9C 0 *L SXD. 1 HI T9U 9 S" S 9Q 2 ) .AA nU*E o I CF CR 9 6 ( ... * *DT F D 99 988 9 N XX XAC X L 1.8 DLH 9 T) 119 1*Qu 9 .L2 9* 9 9c 2 R o *G * X 9 \r o I 97 SN E9, 16 1).? SI M 91. (F (I 9 DL 0*( D 9 D(X RU CGC NX NCT GA NNNIL9 LN9 *H IIIIT 9 TI 9 9* *YS(E2 ESZ X 9 9RDDR 0 RD 0 0X XDRN 6) R6 18 9*GLIF2D)GF)) \a99919!)TA.90NA11909. D* *I*X4E9XT 996x 0 o 8 .D8 98R 90F2 98037 7 9*E 9* 99 931 9:3 IFF PTCTHDTCTH TTHTJTTM* THBTYTMZBTTHHR (IRE (IR IRC: IR 9IRAILIR o IIRRRD OFROTOFRDDDRDEJDRDXRDLRMROGDRRODON DGIHFCGIHFEGHFPJGHFguaF...HFHFFDHHFFFE ... + + 4 + + ... ... 8 6 8 6 T T '0 '2 '4 '7 '9 D «It. .4 262... .2 10/13/80 FTN 4o8+508 =1 OPT 74/175 {VBETA 191 11111111.1122222222223333333333444.0.“44.444.3-39355...2:22:9—.EEEEEEEEEE.‘.I7.I.I.I.I.I.I.errCcCtCtCrCE 222222222222229L22222222222222222222222222222222222222222222222222222222222222 E S 9 T V: t A S : I I U R 9 B A N 9 V M 0 t I S 9 1 9 T N 99 1.. x L 0 00 9 5 U T. 22 U 9 M T (( 2 2 C TV ( o F N C 9 X 6 0 U A9 9 F F F0 9 9 N 92 0 t 0 D. 9 9 2 : P I U 00 ( 9 L U T 22 E 3 B A K (Is 9 I K R O URD9 9 t 0 E 0 BAND .2 9 0 N L 9D. 91. N X L E 9 991 0 3 G E U9nu( I 9 E L 9 2026 T 92 L R B * (2 9R U I o B 0 A S L 90A 8 (5 A F T N 302 9 I UF T 0 92(9) R B 9 C R I 9(000 T 9* L O T ORHII S 9: A X F U ZORII I I2 M I B (C 9( 9 D (K R R S 9 I 9 9 2 99N0 L 0 T N I R N 9 K90L2 9 R 8* N A 0 9( T 9 M 1 901A( T O 99 M I RL S R 9 . 921VF U F 9X R T EB I E I J 0 9 990 0 I3 0 R U 1+ 0 I = 9 20099. N S ( 9 F. 9 A B 99 9 T. I (220 9 9 R 22 R L I R9 L R 9 9 ( 1((29 N E K o N F. E US R 9I A 9 9 D J KCY(O I T 95 L , 9 F I GE T 2( N 2 J N R U1 N E 9F A1 9 I 9 NL S ZL I Z 999 . A 91. 9 M I 9 V0 9 D 4. A8 I 98 G 9 I2X 9 T 99 T A (t 0 9 + 2 IA D 1. R 1 (.9 J E ///00/ P R 1: F0 9 ) 9 RI 2) A Z XON 9 8 234220 0 A K1 00 9 J 3 TR L I H 9 (1." I V KKK((. I 9P 9K 0 9 ( Z A N A P( 9 N NP 9F(N N( N M CCCVJO ( I 2 SUF9 N ( RV M. N N 9 N (U 4..." K( PSZLM KJ M OOORR/ 0 D 0*N 0* EOE OD LN S E 9U I M T. K I8 0 99 9A NOIA 9 9R 9 EZLLL L I R 2 9M 2 9 U oInUN AK9I "M I o G 9 ( 9 T( 2X1. IT 92 9N1. 2( 1. NKBBBNNL T / 9X 9 9X L00: 9 V 9IR4OOF:0 R I L 2 E. 99: :ER 1. 9XA: : : : I 9///00A E 0 051005 EA: :93 :I(NZLDEI:EA :998 ..FBRE04I99 JB:FEE:OITI J9 EEI TI IIM 0 G o II(:.I( UV99N: 9:N0: N0 9U" III: JFD:UI( II D9FUUJI(A K UU UKNNNSSS 1.3U I +(TII(T N IZKI IILH9TAC9IN I ((9 IH9N(T6(( BHJINN (T00 2 9 NNS 0 nXUOMHw 0:.. D: nELA .ZPA9TEEE(( 19\ A viLR nu21E+=3121..UD IEIEAHTiZOXV 9DT¥£DEAHn4 213¢£12 RLMHMEEA :TTLNFDNTM59TM2TTNNN6 . N8VL(U LIITTKIKK 9 01+L 9TTMIKK oILI+TT2THLI I(+TT1 BAMMMMMTNUPL:FN:IR IIR oNALLL IL :LGRLL (NA: : :IO PLINIR : :0 L(D.NN IRL I FKNN UEOOOIIAIOOADI : NROO(R060RAAAO : AO3ARTAAOJORP012( : nu : A(0R0012 : OAJ 2 ODOROAO .. OD : 000 SRCCCDDDNNICRDKKHFDVHFFCEVVVDJVDZCASMCDRCENDZZXD. DpcxCHFDZZPDCRPCCDHFCDKDPKCCD * N NR N 2 E 00 E 05 5 I U 55 CN G 1.1. A. 25 U 2 9 U 86 0 2 0 2 33 2 20 22 10/13/80 .22 FTN 4.8+508 =1 OPT 74/175 NE MVBETA 192 Na)moamm¢m~ot~ma~OHNn¢mwhoomo—omnc-mxohcomoumn‘rmmhcom QQQO‘O‘O‘O‘O‘O‘\O‘O‘U‘O\DDDGOODDODHHHHHHHHHHNNNNNNNNNN NNNNNNNNNNNNNnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn ULTIVARIATE NORMAL RANDOM NUMBERS (D a: O ... U A U '9 > A 0- '3 H u v v _| DJ u. 0. 9 D a; A A O. h< :m '3 o d-(f) o o x 9 mm H 0. FL] (3)-(D WU D A LLt-D U)>- >-U Z 0‘ 04:2:er (0+ 9 o No: OOVH HA HLLN Guru-mo OH H u. 0- 52 H UOHOHV 7H|DLJLJLLI1J¥LIJZM oll>hJ DmDDvox>>HofimD oso+v22h :: H HZ oNmequom macaH (D Z hJ U m 0 DID \DIDU‘ 90!") NN0 HHNU U OOK UP TRANSFORM TO GENERATE VECTOR OF UNIFORM RANDOM _l In .J CL :3 x O O ...l A Lu x .1 o (I) A d: x r— S A V 9 o D x Z 0 H A H X a: 2 U) 0 9- x :3 u. < o m I A (I) H H m D 2 V In 0- O > CD .1 H I: Z ...I 9— 0 D < < (.9 Z I: ..I a: (D u < I 0 a: 0 O H a: 2 D V o (0.! Z u U >4: < H 03> m2 .1 A92 HV 3: m In 92 OH < M< HX 0 H—l O-HHI- NON llthLdllVHhJ OHM H(DmO-u—ADNVH IN a: (I) Z A O '3 H A Z 9- 2 o < 2: H > 0 II a: H I: w H 0 (I) H A m o z 0 AA 0 50 m H U OZ In H ..l H o on a. V>- o It!) 3: >- o t-A a: 0 < ~«Z ‘3 van (I) I O o LLA Av 20H HNF‘IDmd 3’. V \OHD OZO< 0A.: o ONX 0N2 HHhJ NX OOH o< H and MOLD ll 09- 'DhJODNVHV'fiv-Cd I—Z UXZVO— H OUZHO-VO- V02 OIIHLJm<¥HLJ<|nIN o Hmo>0huovomoxvom005ou«omomooa:03LLOZDHUUILLZLLD3U¢LU ID 0 NIDWFSD IDDO NN .22. 10/13/80 FTN 4.8+508 193 -———-~-—-—- EZEBZEGFBEE;&BEBG =1 OPT 74/175 VE RORDER N FQDO‘OHNFOQ'IDQF mnnmnnnnmn¢¢¢¢¢¢¢ N ¢¢¢IDIDLDIDIDIDIDID ”DWIGWMIOWHIONMHHMNW 9 nnnnnnnnnnn O a) \ 9") H \. D H m D ID 9 m 0 €- 2 y. LL \ A A A R H H I V H (9 v a: .J A < < K 0 > o A | >- A A Z x H 3; 50 VA :3 w vaH O a: <| A H 0A< O>H O. O @H. I—Uv Z d' OCV> t—l 0 <0: OA< x O H on: 0A> v 9'- " .J<: HQ 0: I— AV AHA 00 L9 0 HHH HVH «H H QA HVZ VGI OH 0. Z"~ AJH LDKH my 2 A! In co< (It!) H '9): H .- VX 920'. 22 II N 0 a \ 2H "D-Dd HOH'D xw U5 DJ 4' ZOXNLDDO hJ p—Hl A ..l ADUZD A OH m u I H k m D H > 9 D 9 A ti 0 A X A z D A U H o 2 O < H o h > O V N < t «J 9- . O t u < o 4 D o O N u. D A .J v V o 0 LL 0 d! x 0 I I A o O I m N LI. 0 3 o '3 LI. .9 D A * H J V a N D < 9 H > .J (D A 0 90" A I H 0 >> < >- 0 AN #9 I I -J 2v NA ma: V H o» A >0 ac: x u x H I2: WHO I ... v A HUD vHv xA Q 4 z >h2 UOH "H o u\ v NN i 99 AO\ 4N>>>>3432 Hmz+um2 :2ooooo~+++++zuw.z FZ>>>>hzzya ZZZHVDFD minuuun NHHHHZDOOFD :HDum>>>>D>>>>>UXDKKU I!) NE COREL 195 --—-_--—_——-——-—-—’------------——. .22 10/13/80 FTN 4.8+508 =1 OPT 74/175 MVNOR NE mwboomcu-«Nn N ¢mxor~coa~oHNna-msohmoxoammcmsor-ooaxovqmne- camcococooxmmox N mO‘O‘O‘O‘mOODOOOODDQHHHHHHHHHHNNNNN nnnnnnnnn o nnnnnn¢¢¢¢¢¢¢¢¢¢¢¢c¢¢¢¢¢¢¢¢¢¢¢¢ C no \ '0 H \ o ..q (I) > (n H O a) Z O :1 ID 0 'I' A co c: 0 N 6' v > Z on I— A u. o N O c: N U or 4 A O. N A a; A II D H N m o a) D N N A A 0 V 5 ‘3 m m 9 u v o 3 ‘3 (I) U v V O o- m o a U A O In < A t o 0 An. A In N II 0 X\ H O o I p— OA v A 48 O O D D '72: > u # N h MAF o v: v o A V I Q can I" z A H U D NADO < I a: x H H F .AWP A ah a U a: I" A ¢3I (I) O * ‘3 (I) m u 0.. HO A 0 0C) )- O A o i o w o m\wm moom ¥5H0 m o XH m a 2A 0 un>> >H > Hovv H o HOV > 5 >H A oxmw vam tfimhA s m 2H1 m A 22v «1 m UUHH HmNH fivomm H o fivo HHH “2"“. F D o o .0 O o OmUG> Q 0A 0mg) com-v Lu ZHHO H UJHH HUI-N H< 0mm “39‘: H(v Hc-Im ZZOI I O \ zcnuu MINA" "OJ-NH Illlo no." llll< HovaNw ¢ H\H70HAofi ¥§0Ao HAfi x+AMUHfia thumlD h h n Hm H £070H 5H :53: n :mHZZvZZ :2 A 0> I0 :zou+ Am. 3.22 AZ 02 ((HHm oooofionofioombfiO§OH- a: II II < LI... ILA A“ o- A fig I—m 1! I— . o A (04 200 AF) A U 0 ll 2 DO ILH '3 IA < OH 50 7 (no AU 2 x on! v U¢ I-U a: 00 D 0 hJ 9' 2H U HI— Zt 0 cm Dm H u H. H 2U on o OILO UI’) K I-H m x N H30 A>-H AA 0. On: 0 U 2' H 0 0‘! 9 ON # 1Q H Aw. < AA 7m. ...... a. 0 0 I—U 0- Z OLLI— Uncv O o- ‘5 A (DA 0 ZHln O I-‘DO Z<>- HH ‘5 c: 0.0 I- 31H a: va: H .4: HH 9 O O¢ 00. o HAOZH >-I.I.n: UV H \0 av O X 04! AOL'JH o <70: >->- H 0 DZ (.9th H 2H >-I;J H: 0< << V O UH LUZ II D <- It I)- AIUD I H 2 com 0 D42 court—c: I (D< 0 HOI- OO OKA OIIH. AZ<+5Z O‘DUDFHHH'thJI-U I-HOODV II OIAVH II XV D 0V“. OU>HHHUMZZK KUZI—I-IIJZDI-ZI-Z 5: II hozvo< IIH0 O (I) u) AI- U) H U A mm H > a: a N DU > H m o m :3 O 0))- D H DC DO 00) O a o H< n 0 ¢\ mm wH m u H >1 \ A H > H oq- “N AH. O A CIA 0:: OH > Cc; OD I-DI- I- 3 I-\D I-H I-Q H 2H NH m.w + o o D P ¢¢ UmU O A OH 0\ CA \ oo>co 0&2 oAh w: wA wk a III- oHI— IOCD Hm I- I- U) I- H mm H Um. AUU Am Aw AU m U°> .0 II >U,‘ .02 CL) CL) .>- U 2w 0N0 '- CKHK HAG NZ G'I- \D< 2 H N0 O. D C) (Oiwi 00 can 03: 04 O J\FA QUHA MC Ui'Ut OD DIDUA OZ>H 2A 2A 2A A4 (.sz . dxao motv OH OH OH HI 1‘) o UANQ Av Av Av v+ cam HHOJ Ho Ho Ho 00— mgom ovum HA HA HA Aw ZDDVOHO‘IH om ow Old mu H\.-I¢ 0 II Z>>OZHOZHOZHDHDmm HmHLLhJ II II >w I- OHDHmmea>$Q>mQ>m>ID p—v OVZI—I- I N ) o 5 0 v v - 4 74/175 Dumb-mmmoz Dzmhn oov 0v 0v 0v vuzoz oov<fluumz¢ oovQJJHD ¢IDZWNUUJFUJPUJPUJPJIDPHD mv Dowooomu (I) (I) Z V O \ H . I'- M :3 i to C H A a: A A ... O 0 H (O c N H H U ¢ H D (I) § V (I) A X LJ o A m _J A H I O. O H A Z e V 7 < V x 7 U) A > m '3 A A A D If) I 0 LL 2 Z Z 2 o A H 0 Z A: A: o A '7 H O «I. to D o ‘3 H (n H hJH (0H 0 d’ 0 V I- II U" V)" Z v HA 0 2 AH 2H UH I X A HH v u go (a 20 VAU) '3 VI 9:) I ZA HA 3A .190 0 DD #2 O (H 01H UHA (HA H v2 A\ 3: my (v XVA ZHO V +U HA 1 IX >> (IN/MO ODODWKOKOMKOQCKOGJOUZ mooowommomommowowmzuzmzzmzzmzturm O O O O In OD DD 00 O H N I’) '0 NH Q'IO \DID H H H H H APPENDIX H MULTIVARIATE PROCESS GENERATOR APPENDIX H MULTIVARIATE PROCESS GENERATOR Introduction The process generator employed in this study to generate ”net returns to land'I is based on standard computer simulation procedures (e.g., Naylor, l966; Manetsch and Park, 1974). These procedures were developed to generate observations from a multivariate, cumulative distribution function with user specified marginal distributions and correlation matrix (King, l979). Key concepts are summarized here for convenience. Multivariate Normal Anderson (l958) has demonstrated that if z is a vector of standard normal [i.e., N C(0,l)], random variables, then there exists a unique lower triangular matrix such that, x = C2 + u where x represents a vector of normal random variables with mean u and variance covariance matrix V, in which, V = CC' where C can be obtained from V by use of a recursive method given by: 199 200 C11=OU2 for 1515M n i-l = _ 2 1/2 C11 [011' kg] Cik] j-l [Oij ' k5] Cik Cij] Cu" forlHH¢JDZDQ li‘VVTTT'UIVVVTFIYU'I'UTITIIU]I'IUIU‘UfiITUTIUT" OD'I 06'0 OQ'O OL'O OQ'O OS'O Df'O OS'O OZ'O DI‘O OO'O AIIWIQUQOUd BAIIUWOHOO 205 . mbm p P P p - mmo¢\a oz¢4 ow zmzpwm sz bLhPHDbPP-Perbebh_bbPF mwlu Nonpmhom onHQZDL >Hszmo m>-¢43230 .oom .mww .omv .mhm .oom . mNN _ .omd DPRP _ .2. .0 .mb.. thP—bP-h-nbhb [jjTIIIUTUII'TVTWTW‘lfij—rli1rilUTUIIUIUUIUVT111111 OO'I 06'0 OB'O OL'O 09'0 OS'D DVD OS‘D OZ'O OI'O OO‘O AIIWIQUQOUd BAIIUWDNDD 206 IIIIrTIIIIIIrIIIITIj] 375. 450. 525. 600. 675. r I I I CUMULRTIVE DENSITY FUNCTION l 300. ROTHTION 3 C-C-SB r I I I l 225. NET RETURN TO LFlND $/FlCRE I r I I I 75. 150- 0. I I I I l I I I I [j I I I 75- ITTII11IIIIIIII'IIII'1fl111111111111T11111IITIIIII 00'106'0 09-0 OL'O 09-0 09-0 09-0 09-0 oz~o 01-0 00-0 XII'IIBUQOHA HAIIH'ImmZJ 207 . mum I b P b p mmocxe ozmg Op zmapmm hmz .oom .mmm .omv .mpm .oom .mNN .om~ .mb .o .mp- hb-b—PbFnT—IthbP-Phhl—LEb- mnmznu v zofipcpom onHuzsm >Hszmo m>HH¢43230 _ bbrhbhbh-bLLErrerbrOO OO'I DS'O 08'0 DL'O 09'0 OS'O OV‘O OS'O OZ‘O DVD 00 AIIWIQUBDUd BAIIUWONOO mmu¢\e 02¢; eh zmopmm pmz .mpm .oom .mmm .omv .mnm .oom .mNN .omd .mp .o .mp —phPPerpbb—~Ph#-bb-—Rbbb—thF—yhlbblbbunhP-IPIP-b—rbh-— mlmwlo m onpcpom onHozsm >mezmo m>HP¢JDZDQ 208 OO'I OS‘O OB'O OL‘O 09'0 OS'O OV'D 08'0 DZ'O OI'O OO'O' AlIWIQHBOfld BAIIUWONOO 208 .mp _ w .oom .mNm mmo¢\e ozcg Oh zmahmm hmz .omv .mhm .oom .mNN bbpbbPRbhPEPPbebe—bbhbHRPLLP zompuzom >przmo m>HH¢JDEDQ mimwio m onpmpom .omu - b b h — .mb .0 .mb DL-P-RPhh—bbbb— OO‘I 06'0 OQ'O OL'D 09'0 OS'O OI'D OS'O OZ'O OI'O OO'O XIIWIQUBOUd BAIIUWDNDO 209 CUMULHTIVE DENSITY FUNCTION ROTFlTION 6 C-NB-N-B l""l""I"'1l"fi'l 375. 450. 525. 600. 675. NET RETURN TO LFIND $/RCRE TIII1IIII 300- l 225. 'rj I r1 rI I I 0. 75. 150- I I I j ' I I I I 75- ITITTIIITIIIIIIIIIWI'ITIT'IIIIIIIIIIIIII‘IWIIUIITII 00-1 06-0 09-0 OL'O 09-0 090 07-0 090 02-0 01-0 00-0 AII'IIBUQDHA BAIIU‘InNnD 2lO I I I I I 1 450. 525. 600. 675. IIIr'IIIIIIITI I 375 0 Z O I-I .— L) 2 3 LL ). |._ H (D Z LLJ C3 LLJ > I—I I'— C]: _.l D E D L) RDTHTION '7 C-SB-N-B rIII'rIIT'rIII 225. 300. I 150. 75. 0. IITI'IIII'jiIII 1'75. IIIIWIIIII'IIII‘IIITjIIII]IIIIIITII'IIII‘IIII'TIII oo IOBODBOOLOOQOOSOO?0080020010000' XII‘IIQUQDHd BAIIU‘IT‘IHHS NET RETURN TO LFlND $/FlCRE 2H mmu¢\e 02¢; ow zmahmm hmz .ooo . mNm .omv . mhm .oom .mNN .omfl Pb-bb—rbpphPrDRLPbhbb—bbbb—bhrbr-th—nDuh mnmzumzno w onhqpom onhozzm >Hszmo m>HH¢JDZDQ phi-PPPPD OD‘I 06'0 OB'O OL'O 09'0 OS‘O OV'D 08'0 OZ'D OI'O OO'D AlIWIQHQOUd HAIIHWDNOO 212 mmomxe 02¢; Op zmzpmm puz .mpo .25 .8». .02 .m3 .oom .mmu 52 .2. .o .23 —DRIbb_bbhh—-bnlb—phbb—rbhbbe-b—bbbL—bh-nbbrbn—hth—LO onmwloluI¢I¢I¢\o m onhcpom zofipozsm >pr2wo m>HH¢JDZDQ OO'I 06'!) 08'!) DL'O 09'0 OS'D 0V0 OE‘O OZ'O OI'O 00' AIIWIQUBOUA BAIIUWDNOO 213 mmucxe 02¢; eh zmshum pmz .mhm .oom .mum .om¢ .mpm .oom .muu .om_ .mb .0 .mp- —b.-EL-b*bb—-PbL-rlnbb—hbnhlP-bbrbbbPbehPL—bb-bpbkbhr0 QIQIQI¢I¢I¢I¢\O OH onbchom onhozam >hHmzmo w>HH¢JDZDQ OO'I 06'0 08'0 OL'O 09’0 OS‘O Of’O OS’O OZ'O OI'O OO‘ AIITIQBQOUd BAIIUWDHDO 2T4 .mbm .oom .wNm mmu¢\e oz¢4 0H zmohmm puz .om¢ .mbm .oom .mNN .om~ —bhhb—PPPDPPPPLthbB—hbbLl—bbbbePbbp zumznolu «H zofipmpom onpozzm >pr2mo w>Hp¢42230 hLth .mb .0 .mp — b P h P h b b L h — OO'I 06'0 08'0 OL‘O 09'0 09'0 Of'O OE'O OZ'O OI'O OO'O' AllWIQUQOHd EAIIUWONOO 215 .mbw .ooo .mNm mmu¢\a ozcg OH zmzhmm Hmz .omv .mbm .oom .mNN —PPhDPPhPh—nnbb-bELL—brbprbbrb— mmIUImz N“ onhchom onhuzzm >hszmo m>~p¢43230 Il‘ .oma D b b n — .mh D-DL— .o .mh .bnhbhbblr- DD‘I DB'D DQ'D DL'D DS'D DS'D DVD DS'D DZ'D DI'D DD'D AllWIQUQDUd BAIIUWONDD 216 I I I I r I I I I1 6000 675. I 525. 450- CUHULRTIVE DENSITY FUNCTION 300. RDTRTIDN 13 C-C-NB-B IIIIITIITIIfl—rTFIIf'rIII 225' 3750 l 150. ITIITITIIj’IITI 00 75. 75- 'IIII'IIII'IIII'ITIIIIIII—IITIIIIIjI'IIITIIIIIIIIII now 06-0 09-0 ovo 09-0 03-0 09-0 02-0 02:0 oro oo-o XII'IIQHQOHd BAIIU‘InNr‘IO NET RETURN TO LHND $/F1CRE 217 CUMULRTIVE DENSITY FUNCTION ""I'T"l""l""l 450. 525. 600. 675. RDTFlT I ON 14 O/R—Fl-NB-B 1 375. I I I I lj I I I 300- ' I I I I I I I I I I 75. 150- 225- 0. FWIIIIITI -75. TIIIIII1IIIIIIIII'IIII1IIII‘IWII1IIII'IIII'IWII oo-ios ODQWDDLOOSOOSODV'DOSODZHODI 000 0' “11193908.; BAIIU'InanJ NET RETURN TO LRND $lRCRE 218 .wbm .ooo .mNm mmu¢\o 02¢; Op zmshmm Hmz .om¢ .wbm .oom .mNN .omu .mb .0 .mb —hphbPrPrb—PrbLP-bbr—hPEhbp-bp—Ekbn-bbbpprLL—DEFD— onHQZDm >Hszmo m>Hb¢43230 mnmzuo m“ onpcpom DD‘I DB‘D DQ'D DL'D DQ'D DS'D DI'D DS'D DZ'D DI‘D DD'D. XIIWIDUBDUd BAIIUWDHDD 219 umu¢\a ozqd Op zmnhmm puz . who . Dow . mum . omv . mbm . com . wNN . omu . ms. . o . mbl r-PRb—h-FP—Prbb—thb_DbPL-bDbE-thb—bbbP—PbEb—bpbh— unmzuulo|¢1¢1¢\o m“ zoabmhom zomhuzzm >hszmo m>HH¢JDEDQ DD'I DB'D DB'D DL‘D DQ‘D DS'D DI'D DS‘D DZ'D DI'D DD‘D XIIWIQUQDUd HAIIUWDNDD APPENDIX J PROBABILITY DENSITY FUNCTIONS Appendix J presents the probability density functions estimated for each crop price and crop yield. Price and yield are the random in"! variable components of gross income. Price and yield random variables were estimated as Beta distributions. Beta distributions are defined a on a zero-one [0, l] interval. The graph presents the Betas used on their standard interval. The linear transformation to the appropriate yield or price interval scale was calculated elsewhere. The oat straw yield distribution is implausible. It is believed to be mis-specified. The price distributions appear too exponential in shape. It is believed that the data used to estimate them encompassed two separate eras in agricultural price behavior. 220 221 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 UNCERTRIN QUANTITY PROBRBILITY DENSITY FUNCTION CORN YIELD .”311.0...0150..fi-..fi....T-....fi...,....,....,...., 0.00 rIIIIlIIIIIIIIIIIIIIIIIIIIIIfilIlIIIIlWIIITTIIIIjfiI 09 e zv-e to e 99 z 92 z 06 I as 1 #1 I 9L 0 98 o 00 0D rOIfixlIlIQUBDUA 222 0.90 1.00 0.80 0-70 D-BO 0.30 0.40 UNCERTAIN QUANTITY 0.20 .10 O PROBRBILITY DENSITY FUNCTION NRVY BERN YIELD \ IIII'IWITIIIII'IIjIlIIII'TIIIlIIIIlIIIIerrIlIIIj' O-SO 0.00 [mfiIIII1IWIj'IIIj'IIII'IIIIIIIII'IIII'IIII'IIII 0992» 3170299293 ZDSIZSIH IQLH'DDBEDDDD a-UIHII‘IIBUBDBd 223 0-80 0.90 1-00 0.60 0.70 0.50 UNCERTRIN OUHNTITY 0.20 0.30 0.40 0.10 PROBRBILITY DENSITY FUNCTION SDYBERN YIELD IIIIrIfiII'rITI'IIITIIIII'rIIIIIIrleIIIrrIIIlITII—l 0.00 |IIIIIIIIIIIIITIIITI‘IIITIIIIjIIIIIIWIITIflITTIIIII 09 9 av e to e 99 z 92 z 06 I as I It I 9L 0 99 o 00 0° vOI*XIIlIQUQOUd 224 fig... _ . w . 1. I115? >h0bz¢00 zHcpmmuzs 00,— 00.0 00.0 05.0 00.0 00.0 0¢.0 00.0 0N.0 070 00.0 FPD-b—hbhb—h-bIh—hbbe—-b*bpnbPL—EL-h—-nbb—Lnb-—.-rb— 0400» mem 00000 20008230 >00wzmo >0000m¢momm 0 08‘8 ZI'S ’ID'S 99'2 BZ'Z DS'I ZS‘I IVI'I QL'D QS'D DD' vOI*XlIWIQUBDUd 225 >FHF2¢00 szpmmuz: 8; 85 Sé 2.6 85 85 35 8.0 3.0 25 —nhPD—bbEbPPbbbhEththPPP-hbb—rEthth-bePLLF—bP 0.6 H > 0030030 200F029; powzmQ >H0400000mm 00. 0 'D DD'D DB'E ZV'S VD'S 99'3 DZ'Z DB'I ZS’I II'I QL'D 98 z-DI’MII'TIQUQDEH 226 >HHHZ¢00 zchmmuza 00.0 00.0 00.0 05.0 00.0 00.0 0v.0 00.0 0N.0 070 00.0 —bEbb—bth—bpbbphhbthh-b—DFREPb-npbrbbbbL—b-hb—b-Phr 0400» p00 ZOHHQZDL >HszmE ECHJqumomn. 0 08'8 2V8 ’ID'S 99'2 QZ'Z 06'! 391 II'I SL'D BS‘D DD yDI‘XlIWIQUBDUd »FHH2¢:a zHchmmoz: 8; 85 555 25 85 555 95 85 85 85 555 PblPhprhblb—ppub—Pbb-bpnrb—nphb—EPFbePbbbLbbbbbbhh—l 'I 171'! 9L'D DS’D DD'D 227 0.60» 205.0 H00 20:020.; >:02m_0 podmcmomm 08'8 ZV'S ’ID'E 99'3 DZ'Z DS'I ZS z-DI‘AII‘IIQUQDUd 228 0.70 0.80 0.90 1.00 0.60 UNCERTRIN OURNT I TY 0.20 0.30 0.40 0.50 0.10 PROBRBILITY DENSITY FUNCTION NHERT YIELD II—II'IIII'IIII'TITj'IIII'IIIIlIIIITIiTIIITIITrjII' 0.00 [IIII'IIII'IIIIIjIIIlIIIIIIIIIIITIIIIITthIIlIIII oewczvevoeeszezzos 129 In 19L09€"°0000 z-OIHII'IIQUQOUd n a a.“ .A....—~ . -..—... - I 1 .-‘A '7 "fir~ I . All n—l' 229 .. [a (Rafi/(Ni. HP... 1.1... . >FHHZ¢00 szhmmoza 00; 00.0 00.0 00.0 00.0 00.0 0v.0 00.0 0N.0 070 00.0 —th-—Pbbphb-Pb—pbup—r-bbPEhbhb-bnbbbhnb—DPEb—bkbh— {I muamm 2000 2005020.; >H002m0 >H0400000mm 0 DD'L DE'Q 09-9 06'? 02'? DS'S DD‘Z DI'Z DIV'I DUO 00‘ r01‘XlIWIQUQDUd 230 l... I121}... ....IF »prz¢:a zHchxmuz: 55; 555 85 555 85 85 95 85 85 S5 85 rrIrLE—hIr-b—P-bPPPDbb—bpbb—E-nPLLEPb—bethth—bbbbr 0 00'0 003E 20mm >>¢z 20:02:; >Hszm0 EZAHmcmomn. 00'? 09'€ DZ'S DQ'Z DI'Z DD'Z 09’! DZ'I 08'0 Di" z-DI‘XII'IIQUQDUd ZN 0.40 0.60 0.70 0.90 0.90 1.00 UNCERTAIN QUANTITY 0-30 0-20 0.10 PROBABILITY DENSITY FUNCTION SDYBEAN PRICE IIII'IIII'IIII'lI’TI'IIIrTI’I’IIIIIIIIIIIIIIIIrTIIII1 0.5 0.00 l—ITIIIIIIIIIIIIII1IIIIIfl IIllllle IIII‘IfiII III! 09 a re a 90 z 29 I 99 I 09 I I0 I 90 0 as 0 93 0 00 0° POI*AlIUIQUSOHd ‘9‘»1—7 TF‘A 1' 232 0.40 0.50 0.60 0.70 0.80 0.90 1.00 UNCERTAIN QUANTITY 0.30 0.20 .10 0 PROBABILITY DENSITY FUNCTION SUGAR BEET PRICE IIIl'IIlI'IIII'IIIIjIIIIIIIlIIIIfIIIIIIIIIIIIITII' 0.00 IIIIIIIIII'IIIIIIWIITITITITTI'IIIIIIlllllII—I—ITI III! 09 z 79 z 99 z 29 l 99 l 09 I to 1 9L 0 29 0 92 0 00 0° P01‘A111186808d 233 0.40 0.50 0.60 0.70 0.80 0.90 .00 UNCERTAIN QUANTITY 0.30 0.20 PROBABILITY DENSITY FUNCTION ALFALFA PRICE IIIlIIIII'IIIIIIIIIIIIII'IITWrTI’ITTrfiTIIlITIIIIIII D i D . IIIIIIIIIIIII11]IIIIIIIIIIIIVII11111TTII[111111111 09:2 #0-3 90-2 39-1 99-1 09-1 vo-I BL‘D 39-0 92-0 00-d° 901*X111180808d wfl‘m—Tffififi '73 I' 234 0.20 0.30 0.40 0.90 0.70 0.90 0.90 1.00 UNCERTAIN QUANTITY 0.10 PROBABILITY DENSITY FUNCTION DAT PRICE IIIIIIIIrIIIfirr'I-IIT'IIrfi1TfiII'IIIjrrIrIrfTII'rIII] 0 50 0.00 [TITIjIIITTIITIIIIIIlIWfi'IIIIlIIII‘lWIIIlITTITIjII 09v09902909209 300 3091031090017 0000 z-QIHII'IIEIHQOHA 235 >HHPZ000 zHOH00020 00.0 00.0 00.0 09.0 00.0 00.0 0v.0 00.0 0N.0 00.0 00.0 PhPLb—LbhbPbbe—Lthl—VLLPD—bbbibrbbbb—bLIpthbbP—erRb— \ J 00000 30090 p00 20090200 >900200 >FH.:000000 0 00'? 09'8 DZ'S 08'2 0V2 DD'Z 09'! DZ'I DB'D DVD 00‘ rDI¥XlI1IBUBDUd 236 00.0 »hupz¢:a zH¢p0wuzz 85 85 E5 85 85 S5 85 85 S5 85 LPb—bubD-rrrbrFELLLyEbbDLLPbRLbbbb—h-DEPRFPhPBIEER-O 00000 0.00:: 20090200 >900200 >9040000000 _ 'L 08'9 09'9 06'? 02'? DS'S 09'2 DI'Z DVI DUO 00' DD z-DI’AIIIIBUBDUJ BIBLIOGRAPHY AL:— :5 BIBLIOGRAPHY Agricultural Engineers Yearbook, l979. American Society of Agricultural Engineers. Andersen, A. L.; Robertson, L. S.; Black, J. R.; Erdmann, M. H.; and Ruppell, R. F. l975. Navy Bean Production: Methods for Improving Yields. Extension Bulletin E-854. Michigan Cooperative Extension Service, East Lansing, Michigan. Anderson, Jock R. 1974. "Risk Efficiency in the Interpretation of Agricultural Production Research." Review of Marketing and Agricultural Economics, 42:l3l-l84. ~ V Anderson, Jock R.; Dillan, John L.; and Hardaker, Brian. l977. Agricultural Decision Analysis. Ames, Iowa: Iowa State University Press. ”«Anderson, T. w. 1958. An Introduction to Multivariate Statistical Analysis. New York: EJohn—WiIey and Sons, Inc. Anderud, Wallace 6.; Plaxico, James S.; and Lagrone, William F. 1966. Variability of Alternative Plans, Selected Farm and Ranch Situations, Rolling Plains of Northwest Oklahoma. Research Bulletin l3-646, Oklahoma Agricultural Experiment Station, Stillwater, Oklahoma. Barry, Peter J., and Robison, Lindon J. l975. "A Practical Way to Select an Optimum Farm Plan Under Risk: Comment." American Journal of Agricultural Economics, 57:l28-l31. Bikel, Peter J., and Kjell, Doksum. 1977. Mathematical Statistics: Basic Ideas and Selected Topics. San Francisco: Holden-Day, Inc. Black, J. Roy, and Love, Ross. T978. "Economics of Navy Bean Marketing." Dry Bean Production--Principles and Practices. Extension Bulletin E-lZSl. Michigan State C00perative Extension Service, East Lansing, Michigan. Boussard, J. M. l97l. "A Model of the Behavior of Farmers and Its Application to Agricultural Policies." European Economic Review 2(4):436-46l. Boussard, J. M., and Petit, M. l967. "Representation of Farmer's Behavior Under Uncertainty with a Focus-Loss Constraint." Journal of Farm Economics, 49:869-880. 237 238 Carter, H. 0., and Dean, G. W. l960. "Income Price and Yield Variability for Principle California Crops and Cropping Systems." Hilgardia, 30:l75-2l8. Christensen, Donald R.; Robertson, L. 5.; and Mokma, D. L. l978. "Systems of Cropping." Dry Bean Production--Principles and Practices. Extension Bulletin E-l25l. Michigan Cooperative Extension Service, East Lansing, Michigan. ~ . Day, Richard H. l965. "Probability Distributions of Field Crop Yields.” Journal of Farm Economics, 42:7l3-74l. ‘\ Dernan, C., Gleser, L. J., and Olkin, I. l973. A Guide to Probability Theory and Application. New York: Holt, Rinehart and Winston, Inc. Doll, John P., and Orazem, Frank. 1978. Production Economics: Theory with Applications. Columbus, Ohio: Grid Publishing Company. Freund, R. J. l956. "The Introduction of Risk into a Programming Model.” Econometrica, 24:253-263. Friedman, Milton, and Savage, L. J. 1952. "The Utility Analysis of Choices Involving Risk." Journal of Political Economy, 56:279- 304. Grunfeld, Y., and Griliches, Z. 1960. "Is Aggregation Necessarily Bad?" Review of Economics and Statistics, 2l:l-13. Hadar, Josef, and Russell, William R. 1959. "Rules for Ordering Uncertain Prospects." American Economic Review, 59:25-34. Heady, Earl O. 1952. Economics of Agricultural Production and Resource Use. New York: Prentice-Hall. ‘1.Heady, Earl O. 1952. "Diversification in Resource Allocation and Minimization of Income Variability." Journal of Farm Economics, 34:482-496. Heady, Earl 0., and Jebe, E. H. l954. Economic Instability and Choice Involving Income and Risk. Research Bulletin 404. Iowa Agricultural Experiment Station, Ames, Iowa. Henderson, J. M., and Quandt, R. E. 1971. Microeconomic Theory: A Mathematical Approach. New York: McGraw-Hill. Higgs, Roger L.; Paulson, William H.; Pendleton, John W.; Peterson, Arthur F.; Jackobs, Joe A.; and Shroder, William D. 1974. Crop_Rotations and Nitrogen: Crop Sequence Comparison on Soils of the Driftless Area of Southwestern Wisconsin, l967-l974. Research Bulletin R-276l. Wisconsin Agricultural Experiment Station, Madison, Wisconsin. 239 Kelsey, Myron P., and Johnson, Archibald. 1979. Michigan Farm Business Analysis Summaryf-All Types of Farms, l978 Data. Agricultural Economics Report 364. Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. .-5King, Robert P. 1979. Operational Techniques for Applied Decision Analysis. Ph.D. dissertation, Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. Knight, Frank J. 1971. Risk Uncertainty and Profit. Chicago: University of Chicago Press. ’ Knoblauch, Wayne A. 1976. Level and Variability of Net Income for Selected Dairy Business Management Strategies. Ph.D. dissertation, Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. Kreyszig, Erwin. 1970. Introductory Mathematical Statistics: Principles and Methods. New York: John Wiley and Sons, Inc. Lin, William; Dean, G. W.; and Moore, C. Y. l974. "An Empirical Test of Utility Versus Profit Maximization in Agricultural Production." American Journal of Agricultural Economics, 56:497—508. Lucas, R. E., and Vitosh, M. L. Soil Organic Matter Dynamics. Research Report 358. Michigan Agricultural Experiment Station, East Lansing, Michigan. ~ 7 Madalla, G. S. 1977. Econometrics. New York: McGraw-Hill. Michigan Agricultural Statistics. Michigan Department of Agriculture, various years. Mitchell, Donald 0.; Black, J. R.; Ferris, John; Wailes, Eric; Christenson, Thomas; Armstrong, David; and Thompson, Stanley. 1980. MSU Agricultural Model--Quarterly_Rpport. Vol. 1, No. 1. Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. ,Naylor, Thomas H.; Balintfy, Joseph L.; Burdick, Donald S.; and Chu, Kong. l966. Computer Simulation Techniques. New York: John Wiley and Sons, Inc. Nott, Sherill B.; Johnson, Archibald R.; Schwab, Gerald 0.; Search, W. Conrad; and Kelsey, Myron P. l979. Revised Michigan Crops and Livestock Estimated l979 Budgets. Agricultural Economics Report No. 350. Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. Porter, R. Burr, and Gaumintz, Jack E. l972. "Stochastic Dominance Versus Mean-Variance Portfolio Analysis." American Economic Review, 62:438-446. 240 , Quirk, James P., and Saposnik, Rubin. I962. "Admissibility and Measurable Utility Functions.” Review of Economic Studies, 29:l40-l46. Robertson, L. 5.; Cook, R. L.; and Davis, J. R. l976. The Ferden Farm Report: l962-l970. Part I--Soil Management: Soil Fertility. Research Report 299. Michigan Agricultural Experiment Station, East Lansing, Michigan. Robertson, L. 5.; Cook, R. L.; and Davis, J. F. l976. The Ferden Farm Report; Part II--Soil Management for Sugarbeets, 1940-1970. Research Report 324. Michigan Agricultural Experiment Station, East Lansing, Michigan. Robertson, L. S.; Cook, R. L.; and Davis, J. F. l977. The Ferden Farm Report; Part III--Soil Management for Soybeans, l946-l970. Research Report 327. Michigan Agricultural Experiment Station, East Lansing, Michigan. Robertson, L. 5.; Cook, R. L.; and Davis, J. F. l977. The Ferden Farm Report, l940-l970. Part IV--Soil Management for Navy_Beans. Research Report 350. Michigan Agricultural Experiment Station, East Lansing, Michigan. Robertson, L. S.; Erickson, A. E.; and Christensen, 0. R. 1976. Visual Symptoms, Causes and Remedies of Bad Soil Structure. Research Report 294. Michigan Agricultural Experiment Station, East Lansing, Michigan. Schultz, Gary E., and Meggitt, William F. l978. Weed Control Guide for Field Crops. Extension Bulletin E-434, Michigan Cooperative Extension Service, East Lansing, Michigan.- Schwab, Gerald 0.; Nott, Sherrill B.; Kelsey, Myron P.; Johnson, Archibald R.; Helsel, Zane R.; and Search, W. C. l980. Michigan Crops and Livestock Estimated l980 Budgets. AgricuItural Etonomics Report 371. Department of Agricultural Economics, Michigan State University, East Lansing, Michigan. Scott, John T., and Baker, Chester B. l972. "A Practical Way to Select an Optimum Farm Plan Under Risk." American Journal of Agricultural Economics, 57:657-660. Shapiro, S. 5., and Wilk, M. B. l965. "An Analysis of Variance Test for Normality." Biometrika, 52:59l-6ll. Swanson, Earl R. l957. Variability_of Yields and Income from Major Illinois Crops, l927-l953. Research Bulletin 610. Illinois Agricultural Experiment Station, Champaign, Illinois. 241 ‘Y'Theil, Henri. l97l. Principles of Econometrics. New York: John Wiley and Sons, Inc. Tobin, J. l958. "Liquidity Preference as Behavior Toward Risk." Review of Economic Studies, 25:65-86. Tulu, M. Y. 1973. Simulation of Timeliness and Tractability Conditions for Corn Production Systems. Ph.D. dissertation, Department of Agricultural Engineering, Michigan State University, East Lansing, Michigan. Vitosh, M. L., and Warnke, D. D. l979. Phosphorus and Potassium Maintenance Fertilizer Recommendations. Extension Bulletin E-l342, Michigan Cooperative Extension Service, East Lansing, Michigan. Warnke, D. D.; Christensen, 0. R.; and Lucas, R. E. l976. Fertilizer Recommendations for Vegetable and Field Crops. Extension Bulletin E-550, Michigan Cooperative Extension Service, East Lansing, Michigan. I"Whitmore, G. A. l970. "Third Degree Stochastic Dominance." American Economic Review, 60:457-459. Wolak, Francis, J. l980. Development of a Field Machinery Selection Model. Ph.D. dissertation, Department of Agricultural Engineering, Michigan State University, East Lansing, Michigan. Wright, K. T. 1978. "Production Trends: World, U.S. and Michigan." Dry Bean Production--Principles and Practices. Extension Bulletin E-l25l. Michigan Cooperative Extension Service, East Lansing, Michigan.