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Filmed as Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 I I 75-20,861 LEE, Yung-chang, 1929" ADJUSTMENT IN THE UTILIZATION OF AGRICULTURAL LAND IN SOUTH CENTRAL MICHIGAN WITH SPECIAL EMPHASIS ON CASH-GRAIN FARMS. Michigan State University, Ph.D., 1975 Economics, agriculture Xerox University Microfilms, Ann Arbor, Michigan 48106 ADJUSTMENT IN THE UTILIZATION OF AGRICULTURAL LAND IN SOUTH CENTRAL MICHIGAN WITH SPECIAL EMPHASIS ON CASH-GRAIN FARMS By Yung-chang Lee A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1975 ABSTRACT ADJUSTMENT IN THE UTILIZATION OF AGRICULTURAL LAND IN SOUTH CENTRAL MICHIGAN WITH SPECIAL EMPHASIS ON CASH-GRAIN FARMS By Yung-chang Lee The main objective of this study was to determine profitable adjustments in the organization and use of land by cash-grain farms in response to the increasing demand for agricultural products. Emphasis was placed on estima­ tion of the marginal value productivities for various inputs and investments which would provide an objective and reliable basis for evaluating the efficiency of current farm organizations and serve as a guide in planning the necessary changes in farm organization. Further, the general land use situation and the factors affecting the utilization of land in a Miami/Conover soil area were studied. The data used in this study were obtained from 61 cash grain farms in south central Michigan for the operating year 1972. Linear programming was used to determine optimum farm plans with (1) farm resources fixed at initial level, (2) Yung-chang Lee labor, land and machinery investment variable and (3) pro­ duct prices variable. Investment/disinvestment theory was incorporated into situations (2) and (3). Farmers were stratified by age of operator and net worth as a major determinant for setting up four representative farms. The former was used to indicate their willingness and the latter their ability to make adjustments. The analysis was first presented for Model I with cropland and associated durable resources fixed at initial levels. Secondly, the optimal organization was given for Model II which permitted varia­ tion in land resources and associated durable assets. A production function of the Cobb-Douglas type was employed in deriving the estimates of marginal value pro­ ductivities of inputs and investments. An effort was made to examine returns to scale by dividing the sample farms into two size groups. Examination of results lead to use of the third equation which forced constant returns to scale. Estimated coefficients were adjusted in a rough "Bayesian" way. Profitable reorganizations of farms were studied using the adjusted regression coefficients. A comparison of linear programming and Cobb-Douglas techniques was made so as to be able to exploit fully their complementarities. In addition, an attempt was made to distinguish the more or less pseudo MVPs of linear program­ ming from the MVPs of continuous function, which are partial derivatives of such functions. Yung-chang Lee The programmed solutions indicated that farms in this area similar to the representative cash-grain farms could profitably adopt a wheat-beans rotation under price condi­ tions which existed in late 1973. Also, a c o r n - c o m - c o r n - corn-soybeans rotation entered the optimal solution on larger farms. Land was the most limiting resource for each representative farm, were restricted. so long as off farm work and migration All farms had some members with off farm work, which agrees with what cash grain farmers were doing in south central Michigan area in 1973. Maximization of returns for representative farms in the studied area used all initial capital and considerable credit indicating that cash grain farmers are currently not fully utilizing their capital resources. Furthermore, capital and labor were not fully utilized in Model I where farm resources were fixed at initial levels. Thus, the representative farms studied were not completely organized so as to maximize p r o f i t s . The results of the functional analysis showed that marginal value product for land was comparatively high, indicating the desirability of a moderate expansion in acre­ age per farm. Operating expenditures and machinery invest­ ments were high relative to the other inputs, as reflected by the low returns to these input categories. This suggests that (a) more care is needed in handling operating expenses and machinery investment, and (b) the need to expand farm size in order to use machinery and operating expenditures Yung-chang Lee more effectively. The earning power of farm labor was still not high enough to compete with industrial wage rates even at favorable 1973 farm product prices. and/or migration was justified. Thus, off farm work The low earning power of labor indicated the desirability of reducing its use rela­ tive to land and other inp u t s . An increase in the use of land would tend to reduce its earning power at the margin but at the same time would increase the marginal earnings of machinery, operating expenditures and labor. Consequently, higher farm income would be generated due to better farm resource combination involving more land relative to machinery and, especially, labor. Near constant returns to scale beyond 150 tillable acres were found empirically in the functional analysis, but were assumed in the linear program; thus findings of the functional analysis confirm the assumptions of the linear programming analysis. Both functional and programming analyses indicated high returns to land and low returns to other inputs and investments. The implications of the study were drawn in such a way as to exploit the complementarities between the linear pro­ gramming and Cobb-Douglas analyses. Judging from the existence of considerable amounts of unused cropland and potential cropland found in the area studied and the fairly high returns to land, it was concluded moderate increases in farm size should be expected to continue in a foreseeable Yung-chang Lee future. The continued development and rapid adoption of larger and efficient machinery will probably give additional momentum to this trend, and creates some pressure on land prices. However, without limit. farm size should not be expected to expand The programmed results indicated that labor (including managerial labor) sion of farm size. is a major restriction on expan­ In addition, the trend toward increasing farm size would be offset by continual increasing inputs costs for machinery, fuel, herbicides, labor, and fertilizer e t c . ; reduced availability of both skilled labor and entrepreneurs; and product price uncertainty. The results of the study imply that the possibility of establishing new farms is low due to: involved in establishing a new farm, (1) the cost (2) low returns to labor, cash expenditures and machinery even at 1973 farm product prices, (3) the scattered location of unused land, and (4) nonexistence of economies to scale beyond 150 till­ able acres. As such, a continual decrease in the number of farms would be expected, larger and more efficient, as average farm size becomes larger machinery is substituted for increasingly expensive labor in the production process. ACKNOWLEDGMENTS My appreciation is extended to all those who have so generously given of their time and experience to assist me with various phases of this study and made its completion possible. My greatest appreciation and indebtedness is to Professor Glenn L. Johnson for his guidance and inspiration throughout the course of the study. My appreciation is extended to the other members of my guidance committee, D r s . L. J. Connor, L. R. Kyle, S. B. Nott and K. T. Wright for their generous assistance and constructive criticisms. I also wish to thank Dr. J. R. Black for his valuable assistance in developing the linear programming model. Thanks are due to Dr. L. V. Manderscheid and Dr. H. Riley for arranging the financial resources which made the study possible. Appreciation is also expressed to County Extension Directors William S. Pryer and James W. Pelham of the Cooperative Extension Services of Ionia and Clinton counties and their staffs for assistance and counseling in conducting the investigation. The cooperation of the farmers inter­ viewed was greatly appreciated. I also wish to express my appreciation to Joseph Greene and Douglas Lewis, fellow students, and interest in this investigation. for their help Thanks are given to Mrs. Enid Maitland for typing the first draft and Nita Campbell for final typing of this thesis. Finally, the author wishes to thank his wife, Yeh-owe (Rose) and children, Anne, May and Martin for their patience and sacrifice. Any errors in this manuscript are the responsibility of the author. TABLE OF CONTENTS Chapter I II Page INTRODUCTION............................... 1 Statement of the Problem ............. Objectives of the S t u d y ............. Organization of the Thesis ........... 2 5 6 M E T H O D O L O G Y ............................... 8 Sources of D a t a ...................... The S a m p l e ............................. The Survey Schedule and Interviewing . Processing of D a t a .................... Defining Representative Farm ......... III 9 10 11 12 13 THE ANALYTICAL M O D E L .................... 16 Linear Programming Model ............. 16 Structure of Linear Programming T a b l e a u ............................. Resource Restrictions ............. A c t i v i t i e s ........................ 20 26 27 Crop A c t i v i t i e s ............... Credit Activities ............. Labor A c t i v i t i e s ............... Land A c t i v i t i e s ............... Machinery Activities ........... 27 29 30 31 32 Discrete Investments ............. 33 ........... 35 The V a r i a b l e s ...................... 38 A Comparison of Cobb-Douglas and Linear Programming Analyses ......... 40 Cobb-Douglas Analysis ............. Linear Programming Analysis . . . . 40 45 Production Function Model iv Chapter IV V Page OPTIMUM ORGANIZATIONS FOR THE REPRESENTATIVE F A R M S ...................... 53 Optimum Organizations with Fixed Land Resources (Model I) ............. Optimum Organizations with Variable Land Resources (Model I I ) ............. Optimum Organizations Under Various Levels of Land Supply (Model II) ... Optimum Organizations Under Various Price Combinations (Model I I ) ......... Application and Limitations of the M o d e l ................................... S u m m a r y ................................. 88 92 FUNCTIONAL ESTIMATION OF RESOURCES PRODUCTIVITY ............................... 94 The D a t a ............................... Fitting the Production Function . . . . 94 97 54 57 72 83 The First E q u a t i o n .................. 97 The Second E q u a t i o n .................. 107 The Third Equation, Assuming Constant Returns to Scale ......... 116 The MVP of the Usual Combinations of Land, Labor, Operating Expenditure, and M a c h i n e r y .......................125 Reorganization and Development of Farms on the Basis of Estimates . . . . Summary and I m p l i c a t i o n s ......... 134 VI PROJECTED CONSEQUENCES OF ALTERNATIVE WAYS OF ORGANIZING THE USE OF MIAMI/CONOVER SOILS IN SOUTH CENTRAL MICHIGAN ......... Evaluation on the Results of the Linear Programming and Cobb-Douglas Function Analyses ...................... Land Use on Miami/Conover Soils . . . . Major Factors Affecting Utilization of L a n d ............................. 149 Land Policy Implications ............. Projected Consequences of Alternative Ways of Organizing the Use of Miami/ Conover Soils ........................... v 126 138 139 143 151 155 Chapter VII Page CONCLUSIONS AND I M P L I C A T I O N S ............ Linear Programming--Summary of F i n d i n g s ............................... Functional Analysis--Summary of F i n d i n g s ............................. Findings of the Land Utilization S u r v e y .................................. Implications ........................ Future Study Indicated ............. 162 164 168 172 175 179 APPENDICES A Supplementary Tables .................... 181 B Optimum Farm Organization forSmall, Medium and Medium* Size Representative Farms (Model I I ) ........................ 203 Questionnaires Used in Personal I n t e r v i e w s ............................... 220 C B I B L I O G R A P H Y .......................................... vi 241 LIST OF TABLES Table 2.1 Page Number of Farms in Each Age-Net Worth Classification ............................... 14 3.1 Structure of the Input-Output Matrix . . . . 23 4. 1 Optimum Organizations and Shadow Prices for Selected Resources for Representative Farms Under Fixed Land Resources (Model I) . . . . 55 The Levels of Potential Land Rentals and Purchases for Each Representative Farm . . . 58 4.2 4.3 Optimum Organizations and Credit Acquired for Each Representative Farm (Model I I) ......... 59 4.4 Investments and Disinvestments Required to Attain Optimum Farm Organization with the Range (Model II) ............................. 61 Shadow Prices for Selected Resources on Each Representative Farm (Model II) . . . . 68 Shadow Prices of One Unit of Excluded Crop Rotations (Model II) ........................ 70 The Levels of Potential Land Rentals and Purchases Used in Each Case in Model II. . . 73 Summary of Optimum Land Use, Resource Trans­ actions and Shadow Prices Under Various Levels of Land Resources on Large Cash Grain Farm (Model II) ............................. 76 Shadow Prices of a Unit of Excluded Crop Rotations Under Variable Land Resource Level on Large Cash Grain Farm (Model I I ) . . 82 Levels of Product Prices Assumed in Each Cash (Model II) ............................. 84 4.5 4.6 4. 7 4.8 4.9 4.10 vii Table 4.11 4.12 5.1 5.2 5. 3 5.4 5.5 Page Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Large Cash Grain Farm (Model II) ............................. 85 Shadow Prices of One Unit of an Excluded Rotation Under Various Price Combinations-Large Farm (Model II) ...................... 89 Regression Coefficients and Related Statis­ tics of the Estimated Production Function (61 Far m s ) .................................... 98 Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) .................................... 101 Comparison of Estimated b^'s and b^'s Necessary to Yield Minimum Marginal Value .................................... Products 104 Simple Correlation Coefficients Between Each Input Category ........................ 106 Regression Coefficients and Related Statistics of the Estimated Production Function (61 Farms) ......................... 108 5.6 Sums of Regression Coefficients and Related Statistics of the Estimated Production Func­ tions for Large Farms (30) and Small Farms (31).......................................... 111 5.7 Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) .................................... 5.8 5.9 114 Comparison of Estimated b ^ 's and b^'s Necessary to Yield Minimum Marginal Value Products .................................... 115 Regression Coefficients and Related Statistics of the Estimated Production Function (61 Farms) with £b. Forced Equal to 1 .........................1 ................ 117 viii Table 5.10 5.11 Page Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties)...................................... 118 Comparison of the Estimated b^'s and the b^'s Necessary to Yield Minimum Marginal Value P r o d u c t s ......................... 5.12 5.13 5.14 5.15 5.16 5.17 6.1 6.2 6.3 119 Adjusted Estimates of Marginal Value Products of Typical Organization Farms in 1972 and 1973 (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) . . . 123 Adjusted Estimated Regression Coefficients and Marginal Value Products of Typical Organization Farms in 1972 (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties)................................ 127 Changes in MVP and Gross Income Resulting from Increasing Land Area From 142 Acres to 250 A c r e s ............................ 128 Marginal Value Products of Labor at a Different Level of Tillable Acreage . . . 129 An Alternative Organization of Typical Farms Studied in Clinton and Ionia Counties, 1972 ............................. 131 Estimated Marginal Value Products--Existing Organization and an Alternative Organ­ ization for a Farm Studied in Clinton and Ionia Counties, 1972 ...................... 133 Use of Land in Clinton and Ionia Counties in 1972 (Miami/Conover Soils)--by Acreage. 145 Use of Land in Clinton and Ionia Counties in 1972 (Miami/Conover Soils)--by P e r c e n t a g e .............................. 146 Reasons for Putting Cropland Idle on Miami/Conover Soils in 1 9 7 2 ............ 150 ix Table A-l Page Initial Resource Restrictions for Representative Farms ........................ 181 A-2 Soybeans (2 years rotation)--Estimated Annual Costs and Returns Per A c r e ......... 182 A-3 Soybeans (3, 4, 5 years rotation)--Estimated Annual Costs and Returns Per A c r e ......... 183 A-4 Corn (No Cash Crop Preceded)--Estimated Annual Costs and Returns Per A c r e ......... 184 A-5 Corn (Preceded by Cash Crop)--Estimated Annual Costs and Returns Per A c r e ......... 185 A-6 Wheat (No Cash Crop Preceded)--Estimated Annual Costs and Returns Per A c r e .........186 A-7 Wheat (Preceded by Cash Crop)--Estimated Annual Costs and Returns Per A c r e ......... 187 A-8 Oats--Estimated Annual Costs and Returns Per A c r e ......................................188 A-9 Field Beans--Estimated Annual Costs and Returns Per A c r e ............................. 189 A-10 Assumed Fertilizer Requirements for Specified Cash Crop Enterprises by Soil Group, Southern Michigan .................... 190 A - 11 Estimated Labor Requirements Per Acre Per Month for Selected Cash C r o p s ............. 191 A - 12 Estimated Annual Machine, Power, and Labor Requirements Per Acre for Specified Crop Enterprises, Southern Michigan ............. 192 A - 13 Critical Planting and Harvesting Periods and Losses in Yield Resulting From Late Planting and Harvesting...................... 193 A - 14 Assumed Crop Yield, Fertilizer and Herbicide Requirements, and Other Production Practices for the Synthetic Cash-Grain Farm in Southern M i c h i g a n ..................194 x Table Page A-15 Time Available for Field Work by Calendar Period for Well Drained S o i l s ................ 195 A - 16 Number of Days Lost in a 6-Day Work Week Due to Inclement W e a t h e r ....................... 196 A-17 Factors Used to Estimate Machine, Power, and Labor Requirements for Specified Field Operations in Southern Michigan ........... 197 A - 18 Estimated Hours of Field Operation Time Required for Harvesting Corn with Selected Mac h i n e s .........................................199 A-19 Estimated New Costs, Description, Years and Hours of Use of Specified Power and Machinery Items, Southern Michigan . . . . 200 The Original Observations Obtained from Sixty-One Cash Grain Farms ............... 201 A-20 B-l Summary of Optimum Land Use, Resource Transactions and Shadow Prices Under Various Levels of Land Resources on Small Cash Grain Farm (Model II) .................. 203 B-2 Summary of Optimum Land Use, Resource Trans­ actions and Shadow Prices Under Various Levels of Land Resources on Medium Cash Grain Farm (Model I I ) ......................... 204 B-3 Summary of Optimum Land Use, Resources Transactions and Shadow Prices Under Various Levels of Land Resources on Medium* Cash Grain Farm (Model II ) ............205 B-4 Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Small Cash Grain Farm (Model 11)206 B-5 Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Medium Cash Grain Farm (Model I I ) ...................................... 207 B-6 Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Medium* Cash Grain Farm (Model I I ) ...................................... 208 xi Table B-7 Page Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Small Cash Grain Farm (Model II) . 209 B-8 Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Medium Cash Grain Farm (Model I I ) . 210 B-9 Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Medium* Cash Grain Farm (Model II) 211 B-10 Shadow Price of One Unit of an Excluded Rotation Under Various Price Combinations-Small Farm (Model I I ) .......................... 212 B-ll Shadow Price of One Unit of an Excluded Rotation Under Various Price Combinations-Medium Farm (Model I I ) ........................ 213 B-12 Shadow Price of One Unit of an Excluded Rotation Under Various Price Combinations-Medium* Farm (Model II) ......................214 B-13 Enterprise Levels by Representative Farm in 1 9 7 2 ........................................ 215 B-14 Initial and Optimum Inventories of Machinery-Small Farm (Model I I ) ............. 216 B-15 Initial and Optimum Inventories of Machinery--Medium Farm (Model I I ) .......... 217 B-16 Initial and Optimum Inventories of Machinery--Large Farm (Model II) ......... 218 Initial and Optimum Inventories of Machinery--Medium* Farm (Model II) 219 B-17 ......... LIST OF FIGURES Figure 5.1 Page Effects of different level of acreage on marginal value productivity of labor . . xiii 130 CHAPTER I INTRODUCTION Farmers in Michigan as well as farmers in the rest of the world have been facing a problem of adjustment in the use of production resources due to an ever changing prices, institutions, technology and people. As a result, farms have been changing rapidly in resource usage and in struc­ ture. Average farm size is becoming larger and more capital has been substituted for labor in the production process as agricultural wages increase. Some farmers have become part-time farmers or rural residents while renting or idling part of their farmland. Others are altering their resource use to enterprises requiring new and different skills and equipment with some uncertainties. This adjustment problem on the part of the individual farmer has been aggravated recently as the demand for many agricultural products, both domestic and abroad, has increased significantly. The demand for agricultural products is expected to increase further in the future. This coupled with the exhaustion of government stocks of feed grains causes agricultural economists and policy makers to seek ways to increase agricultural production to meet the new demands • 1 2 One of the several possible ways to increase agricul­ tural production would be to bring more cropland into cultivation. This research is designed to investigate (1) the possible economic adjustments related to increased land utilization in response to the increase in product prices and (2) the possibilities of increasing agricultural pro­ duction through crop acreage expansion at the farm level. Statement of the Problem It has long been recognized that there has been over­ investment in the agricultural sector in the United States. The overinvestment in the sector has resulted in supplying an abundance of cheap food to consumers, on the one hand, and the incurring of a capital loss for farmers, on the other.“ Two problems loom large at this juncture. been the failure of marginal returns to capital, One has land and labor to cover their acquisition cost and, the other, low income levels in the agricultural sector relative to those in the nonagricultural sector. While the marginal value products of labor and land have been lower than those in the nonagricultural sector, it does not always pay farmers to migrate or disinvest because of high moving and liquidation costs. Though a large out-migration of young agricultural ^Johnson, Glenn L. , and Quance, L e r o y , The Overproduc­ tion Trap in U.S. Agriculture, (Baltimore: The Johns Hopkins University Press, 1972) p. 3. 3 labor has taken place, the marginal value product of farm labor has tended to equalize with the low salvage wage rate of middle-aged farmers lacking industrial skills and without labor union seniority. The marginal value product of farm land, on the other hand, has been so low that some central Michigan farm land has been abandoned for farming and some crop land has been diverted by government production control programs. The result until recently has been the prevalence of excess production capacity, low earnings in farming, high cost of government programs and economic instability in the agricultural sector. These are symptoms of excess resources. Since the middle of 1972, however, the demand for agricultural products has increased rapidly and since current production plus carryover stocks were less than this demand, the prices of farm products have increased rapidly. This significant increase in the demand for agricultural products, both abroad and domestically, gives rise to problems of adjustment in the agricultural sector. Among these, the problem of more efficiently utilizing farm land to satisfy expanded demand has received increasing recent attention. Many agricultural economists, as well as policy makers, have been seeking ways to expand agricultural production to alleviate the rapid increase in food prices. Conceptually, there are three possibilities to increase food, roughage, and feed grain production. Firstly, more farm products could be produced by reallocation of cropland, 4 i.e., through the regional and farm to farm specialization. Another solution is to increase yields from present crop­ land through more intensive cultivation. Lastly, food pro­ duction could be increased by bringing more cropland into production. Unoperated tillable land can be pulled into production if there is sufficient economic justification. The question is how high farm product prices have to be in order to give incentive to farmers to bring presently unused land into production with increasing costs for machinery, labor. energy and The cost of bringing unused land into production bears on the feasibility of cultivating land now unused. Farmers are encountering many perplexing problems due to rapidly changing demand conditions. relevant questions are: Some of the (1) what are some of the possible economic adjustments related to land utilization? (2) what are the key factors that limit the utilization of more agricultural land? (3) how do farmers respond to changing demand conditions and government programs? e.g., how much unused crop land can come into production if the set-aside program is eliminated and if prices stay high? (4) what are the effects of price changes on land utilization and operation of the farm--more specifically, to what extent must output price rise in order to bring unoperated crop­ land back into production? prices likely to persist? (5) how long are favorable 5 With the recent expansion in demand for agricultural products, the series of questions listed above becomes extremely important and they need to be answered in order to assist in planning on the part of participants in the farm sector and to assist in developing relevant public policy for the sector. The present investigation attempts to answer some of the above mentioned questions. Objectives of the Study In response to the problem identified above, the objectives of this study are as follows: 1. To determine the profit-maximizing organizations by using linear programming techniques on repre­ sentative farms in this selected area, and further to examine the competitive position of alternative crop rotations covered in the model. 2. To determine the effect on gross margin, resulting optimum organization and changes of crop rotations caused by variations in the levels of land resource availability. 3. To provide information about the probable effect of product prices on land utilization and opera­ tion of the farm under 1973 price relationship. 4. To estimate the marginal revenue productivity of the resources as presently utilized under 1972 price relationship and to determine the implica­ tion of those estimates for cash grain farms in south-central Michigan. 6 5. To identify the main factors limiting the utiliza­ tion of more agricultural land and to estimate potential land supplies in the Miami/Conover soils of a selected area in south-central Michigan. 6. To determine policy implications and consequences for alternative ways of organizing the use of Miami/Conover soils. Since linear programming and Cobb-Douglas function are employed in this study, emphasis is placed on a compar­ ison of these two techniques, so as to be able to exploit fully their complementarities. Furthermore, an attempt will also be made to distin­ guish the more or less pseudo MVPs of linear programming from the true MVPs of continuous function which are partial derivatives of such functions. Organization of the Thesis Chapter II is devoted to the discussion of methodology. The research procedures, sources of data, the sample and defining representative farm are main topics in this chapter. The analytical model used to determine the best combination of enterprise and land use is discussed in Chapter III. Also a comparision of the linear programming and Cobb-Douglas analyses is presented. Chapter IV discusses optimum farm organizations and land use for the four representative farms. Chapter V is devoted to the procedures used in deriving estimates of 7 regression coefficients and value productivity of input categories. In Chatper VI projected consequences of alternative ways of organizing the use of Miami/Conover soils in south-central Michigan are presented. chapter, the agricultural land utilization, In this factors limiting the utilization of more agricultural land, and the estimation of potential land supplies in the Miami/ Conover soils are discussed. Chapter VII provides a summary of findings drawn from both the linear programming and functional analyses. survey, The results of the land utilization implications deriving from the body of the thesis and areas for future research are also presented. CHAPTER II METHODOLOGY The analytical techniques employed in this study involve the use of linear programming analysis and CobbDouglas analysis. As the cost of programming each farm would be prohibitive, it is necessary to define representa­ tive farms in carrying out the linear programming analysis. The procedures involved in carrying out the study include: (1) surveying cash grain farms located on Miami/ Conover soils in a selected area in south-central Michigan; (2) using the data collected in the field survey to define four representative farms in terms of net worth and operator's age; (3) constructing a linear program for each of the repre­ sentative farms; (4) specifying assumptions about input and output prices; (5) evaluating the result of the study and (6) estimating the productivities of resources from the data collected in the field survey by fitting and analyzing Cobb-Douglas function. The linear programming analysis in this study will be carried out under the following situations: resources fixed at initial level; (2) land, (1) farm labor resources and machinery investment variable and (3) prices variable. Investment/disinvestment theory will be used in analyzing situation (2) and (3) in such a way as to determine 9 endogenously whether resources are fixed or subject to investment and disinvestment. The investment/disinvestment theory'*' used states that an asset or resource becomes fixed when marginal value product of the resource is bounded by the acquisition costs and salvage or disposal values of the resource. When the marginal value product of the resource is less than its disposal price, it is profitable to disinvest. On the other hand, when marginal value product of the resource is larger than its acquisition price, it is profitable to invest. By incorporating this theory in the linear programming model it determines an activity where the resource restric­ tions can be endogenously rather than exogenously determined. It should be realized that the conception of this model would not be useful for a particular firm situation where all resources with Px.A > Px.,, are known ahead of time to iA iS have Px^g £ MVPx^ £ P x ^ for all possible reorganizations. 2 Sources of Data Since linear programming and functional analysis are employed in this study, data are required on farm resources, organization and production. Major reliance has to be placed on field survey because this is a necessary source ^Johnson, Glenn L. , "The State of Agricultural Supply Analysis," Journal of Farm Economics, May 1960. o Px^ stands for acquisition price of vage value of X^. and Px^g sal­ 10 of enough current data for both fitting production functions and constructing the representative farms of the specified universe of farms with the required accuracy. The information related to the farm organization, resources and production were obtained by conducting the field survey in Clinton and Ionia counties (see b e l o w ) . Technical production and coefficients and enterprise budgeting information for a specific area are usually difficult to obtain by survey, therefore, the main sources of such data used in this study are published articles and bulletins and unpublished research reports in Michigan. In case the required data were not available, guesstimates were obtained from well-informed persons working in that specific field. The data used in the linear programming and functional analyses were summarized in Appendix A. The Sample The data used in this study were obtained from sixty3 one cash grain farms in Clinton and Ionia counties for the operating year 1972. Sampling procedures were divided into two steps. (a) A random sample of twenty predominantly Miami/Conover areas (two mile square area containing four square m i l e s ) , 10 areas for each county, was drawn from the 85 such areas 3 Cash grain farms defined in this study were the farms deriving 50 percent or more of their farm income from the sale of corn, soybean, field beans, wheat and small gr a i n s . 11 of Miami/Conover soil in the two counties. cash grain farmers, (b) Sixty-one 30 in Clinton county and 31 in Ionia county in the 20 areas were interviewed. Detailed farm management and crop production information was secured. The records on livestock production were not obtained. Livestock and all other farmers whose farmsteads fell in selected areas were also interviewed. However, only information related to their farm land use in 1972 was obtained. The cash grain farms sampled in Clinton and Ionia counties indicated a substantial range in gross income and factor input categories. The lowest gross income was $2,131 and the highest was $189,396. The acreage involved ranged from a low of 22 to a high of 1,800 acres. A considerable range also existed in the amount of labor used-the smallest amount being one month and the largest 32 months. Machinery investments ranged from a low of $3,100 to a high of $93,375, while operating expenses ranged from a low of $438 to a high of $53,170. The wide range in inputs and investments made it possible to estimate the separate influence of various input categories on gross income. The Survey Schedule and Interviewing Two kinds of survey schedules^- were developed. One was "farm management" schedule which was designed to collect 4 Copies of the schedules used in this research are included in Appendix C. 12 the information on production, organization and farm resource inventories and applied to cash grain farmers. The other was "land utilization" schedule which was designed to collect the land utilization information in selected areas in 1972 and applied to all farmers in the area. The data were collected by personal interview with the farm mana ge rs . The interview was conducted by the author and two other graduate student assistants in the Department of Agricultural Economics at Michigan State Uni­ versity in the fall of 1973. personally at his farm. Each farmer was contacted During this visit, the purpose and nature of the study was explained and a tentative appoint­ ment was made. Though most farmers cooperated, a refusal rate of approximately 6 percent was experienced. Farm sizes for farmers who refused ranged from 120 to 155 acres, which was not significantly different from average of those visited (i.e., 142 acres). Of the 61 farms investigated, 30 farms (49 percent) were full-time farm and 31 (51 pe r ­ cent) were part-time farm."* Processing of Data After completion of the field survey, first coded, the data were tabulated and punched for IBM card operations. The information concerning production, inventory, expenses and investment was used in performing production function ~*The part-time farms defined in this study are those where the operator has 90 or more days of work off the farm. 13 analysis. The classification of farms was made on the basis of net worth and operator's age information. The resource inventory and financial data were used to deter­ mine the initial resource constraints for representative farms. The derivation of production function and the compu­ tation of linear programming were both carried out on the CDC 6500 computer at Michigan State University. CDC Apex I together with the Harsh-Black routine were used for the linear programming computation. Defining Representative Farm Since the cost of programming every farm would be prohibitive, it was essential to set up a representative farm in carrying out the linear programming analysis. In setting up the representative farms, essential that it was the farms in a class should be sufficiently homogeneous with respect to the key variables that affect farm adj us tment. In this study, the different groups of the repre­ sentative farms consisted of farms and farmers who were sufficiently homogeneous in terms of willingness and ability to make farm adjustments. by the following: One variable, These were indicated age of operator, was used to represent homogeneity with respect to willingness to make adjustments. Generally speaking, it is widely accepted as true that the younger farmer is more willing to make changes because the probability of realizing 14 personal gains in the future is greater. Farm operators were classified in terms of age of operator into two groups, 24 to 55 years and over 55 years. Another variable, net worth, was used to represent homogeneity in terms of ability to make changes. worth is needed to acquire land, machinery, operating expenditures. Net labor and make A farmer can hardly make the necessary adjustments even under most favorable conditions unless he has considerable net worth to provide credit and/or cash on hand. In this study, farmers were stratified by age of operator and net worth as a major determinant for setting up representative farms. The age-net worth classification for all qualifying farms is shown in Table 2.1. Table 2.1. Number of Farms in Each Age-Net Worth Classification Net Worth Age of Operator $30,00080,000 24 to 55 years Over 55 years $80,000150,000 10 17 21 2 7 4 From the above classification of farms, sentative farms: were developed. Over $150,000 small, medium, four repre­ large and medium* farms The medium* farms refer to the farms with net worth $80,000-150,000 and operator's age over 55 years. Each representative farm stratum consists of at least seven farms as shown in Table 2.1. The resources of the farmers in these strata were used as the initial resource fL restrictions for each representative farm. The levels of the initial resources in each case except machinery were based on farm averages of those making up the net worth-age strata. machinery, In the case of the restrictions were determined on the basis of the kinds and amounts of machienry that majority of farms had in the strata. The initial resources for representative farms are presented in Table A-l in Appendix A. It is assumed that the input-output coefficients are the same for all representative farms, however, the initial resources are different for each farm. CHAPTER III THE ANALYTICAL MODEL Two analytical models are used in this study. One is a linear programming model which is used to analyze the optimum organization of the farm. Another is a pro­ duction function model which is used to measure the pro­ ductivities of inputs and investments. In this chapter the two models are explained in order. Linear Programming Model Linear programming deals with the problem of optimum allocation of scarce resources among competing activities. In this sense, it is often called "activity analysis." The allocation problem arises whenever one must choose the level of some activities which compete for certain limited resources essential to perform the activities. Three important components are involved in a linear programming model: (1) objective function, constraints and (3) activities or processes. (2 ) resource The mathema­ tical model is as follows:^ ^Dorfman, R . , Samuelson, P. A. and Solow, R. M . , Linear Programming and Economic Analysis, (New York: McGraw-Hill, 1958). Maximize Z(X) = C-.X, + ,. . . , + C X 11 ’ ’ n n (3.1) Subject to restrictions (3.2) X^ > _ 0 In matrix form, i = 1 ,2 ,. . .,n (3.3) the model can be formulated as follows: O Maximize Z = C'X Subject to restrictions: AX < B X > 0 Where: C = nxl vector of prices X = nxl vector of activity A = mxn matrix of input-output coefficients B = mxl vector of resource levels restrictions It is required to find n numbers X-^, X 2 , . . . ,Xn which make Equation (3.1) as great as possible, where C^,. . -,Cn are given constants subject to the restrictions that no X 2 Heady, Earl 0., and Candler, Wilfred, Linear Programming Methods, (Ames, Iowa: The Iowa State University Press, 1955) p. 416. 18 shall be negative and that the X's shall satisfy the m inequalities, i.e., Equation (3.2). In order to have a precise solution, the problem under consideration must meet several assumptions in the 3 model. These assumptions are: 1. Additivity and linearity of the activities. 2. Divisibility of activities and resources. 3. Finiteness of alternative activities and the resource restrictions. 4. Single-value expectations--!.e., resource supplies, input-output coefficients and prices are known with certainty. It is also required to assume that maximization of Z is the only motivation for entrepreneurs or farmers in order to fit the problem in linear programming scheme. Very few problems in the real world can precisely fulfill all the assumptions built in the linear programming model. The assumptions of additivity and linearity, divi­ sibility and single-value expectations are of particular concern. However, as a technique of linear programming has been improved combined with the availability of high­ speed electronic computers to a solution of the linear programming routine, some of the difficulties in applying the model have been alleviated. A model can more easily be modified in such a way that it can nearly approximate ^Ib i d . , pp. 17-18. 19 the conditions of the particular problem under consideration. To add special constraints on resource use in handling the risk and uncertainty problem is one example. The model used in this study consists of many activi­ ties and equations which are usually used in studying the resource allocation problems at the firm level. However, the structure and size of matrix are rather complex and large and need explanation in some detail. This is especially true for the credit and asset acquisition activities, because they involve some aspects peculiar to this model. In order to explain the model the whole structure of the model which includes activities, constraints and input output coefficients is presented in Table 3.1. equations Sixty-two (i.e., resource restrictions) and 92 variables (i.e., activities or processes) are included in the model. The incorporation of investment/disinvestment theory into a linear programming framework requires the addition of one or more acquisition and salvage activities for each of the resource categories to be incorporated into the m o d e l .^ ^For an application of the theory to a linear program­ ming model see: Johnson, G. L . , o£. c i t .; Smith, V. E. "Perfect vs. Discontinuous Input Markets: A Linear Program­ ming Analysis," J ournal of Farm Economics, Vol. 37, August 1955, p. 538. ; Edwards, C l a r k ,"Resource Fixity, Credit Availability and Agricultural Organization,"unpublished Ph.D. dissertation, Michigan State University, 1958; and Hildebrand, Peter E.,"Farm Organization and Resource Fixity: Modifications of the Linear Programming Model," unpublished Ph.D. dissertation, Department of Agricultural Economics, Michigan State University, 1959. 20 Structure of Linear Programming Tableau The activity set used in the model is denoted by: Pl ’* ' ‘,Pm ; Sl» * ’ ‘,Sw ; ^ 1 ’ ' ’ ',(^6; N 1 ’ ‘ ‘ ',Nt N 2.h m f- N 1 sf j * * * >N Sf > N 1 Sm j * * * »N t S m 9- L 1 pl T ri L4 , ro ’ L5 T wc ’ L6 T pc ’ 7 b M b 9 ; L 2pm * L 3 S s s ; M1 ’• • ->Mr ; M! »■ • ‘-’^u Where: Pl ’’ ’ ,,Pm are act^-v ^t;i-es associated with m crop rotation producing activities wheat-bean, S-, , . . .,S (e.g., corn-bean-soybean, etc.). are activities involving selling W crop outputs for cash. Qf,. . •>Qg are activities associated with credit borrowing and selling. sent chattel mortgage, mortgage, to repre­ real estate land contract, land mortgage and machinery dealer credit, respectively and Qg represents a saving account. . . . ,Nt^ are activities involving hiring seasonal unskilled labor. hm N-^ is an activity associated with hiring managerial labor. sf , . . . ,Nt sf are activities involved in selling family labor for nonfarm work. N-^s m , . . . ,Nt sm are activities associated with selling operator labor for nonfarm work. 21 r ^, L^r o , k£W C , L 7^ C represent L-j^, I ^ ™ , land purchase by land contract, and mortgage, land selling, land rent-in, land rent-out, woodland clearance and pasture clearance activities, respectively, b M-^ , . . b are activities involving purchase of r machinery. s , . . -,M s represent selling u machinery. The model assumes income maximization as the only objective for farming. Therefore, the Z in the objective function would represent the total returns of owned assets. The C j 's in the objective function represent either unit cost (negative) or unit net on thenature activities, of activities. price (positive) depending In the case of crop producing the C b 's (negative) are the per unit acreage variable cost (i.e., CE + R = cash expenditures and repairs) for crop production (per unit acreage may be 2 acres or 3 acres depending on a type of crop rotation). The C ^ 's (negative) in the land clearance activities are the per acre cost of owning land (real estate tax) plus per acre cost of clearance including tiling amortization principle.^ cost computed by the In the land purchasing activities ^The formula of computation i s : r _ P (l+r)t L — o Where: C = current cost; r = rate of interest; life and P = initial cost, o t = usable 22 the C j 's are the amount of real estate tax payment per acre. In the credit (borrowing) activities the C^'s (negative) are the interest charges per dollar of credit. The C j 's in the machinery purchasing activities reflects the cost to the farm of owning the asset. That is, the annual depreciation and taxes that incur by owning ma ch ­ On the other hand, i n e r y .6 the profit equation coefficients for machinery sales activities are the savings depreciation) (taxes plus to the farm of not owning the asset. Thus, Z in the objective function represents returns to fixed resources (i.e., gross income less variable costs) from each of the producing activities. In the producing activities the X . 's show the level of the different acti1 vities, including production, disinvestment and investment, and other activities to which the resources may be allocated. All crops produced are first transferred into crop transfer equation so that crops can be sold through selling output activities. This scheme is used because it was desirable to study the effect of changing output prices. The 's represent the quantity of various farm resources available on the farm and/or some other restric­ tions which limit the use of farm resources. Farm labor is divided into five seasons according to the seasonal pattern of cash crop production. December through March ^There are no taxes on farm machineries in Michigan. Therefore, machinery tax is excluded in the objective function. 23 Tableau 3.1 Structure of the Input-Output Matrix* Activities Crop Production Sell Output Credit (Borrowing) Restrictions Revenue or cost -(CE+R) Cropland Woodland Plowable Pasture Cash (CE+R) - d - U 'im Seasonal Labor Annual Labor liV Crop Transfer Managerial Labor ‘im Operator's Off-farm Work Family Labor's Off-Farm Work Real Estate Mortgage Land Contract Land Mortgage Credit Machinery [ Dealer Credit Land Purchase Limit I Land Rent-ir Limit Tractor Capacity im Machinery Capacity Plowing Discing Cultiva­ ting Planting Harvest­ ing 1im Saving Unskilled Labor Hiring 24 Tableau 3.L. Continued Selling Family Labor Land Purchase Pasture Clearance Purchase Machinery Sell Machinery -C. -(DfT) (DfT) pm Restrictions^ Revenue or cost -T, -T. Cropland Woodland Pluwable Pasture -.25P. A'ij Seasonal Labor Annual Labor Crop Transfer Operator's Off-Farm Work Fmnily Labor' £ Off-Farm Work Real Estate Mortgage Land Contract Land Mortgage Credit .50P- -.5a, -.5a, -.75P, -. 50P' Machinery Dealer Credit Land Purchasi Limit_______ Land Rent-In Limit Tractor Capacity Machinery Capacity Plowing Discing Cultivnting Harvesting and positive signs indicate incomes, while negative signs proceeding ’in tableau negative signs proceeding the coefficient in profit eauation indicate costs the production coefficients indicate adding to the resource labor is considered as one resource as at this time period, a cash crop fanner does not work much on his farm. 2 (April and May) Season and season 3 (June and July) make up the planting, cultivating and wheat harvesting period. Season A (August) is considered as a slack period. 5 (September, October and November) Season is a harvesting and fall planting period. Tractor services, measured in hours, are broken down into five periods and their availability for field time usage is determined by the following factors: number of work days in the period; (1) the (2) the percentage of days suitable for field w or k and (3) the maximum number of hours each day that the tractor can be expected to be in the field. The availability of the field time for machinery services is determined by the specific time period in which the machines are needed. The number of acres that can be covered by a machine in a 10 -hour day in a specific time period are used as a measurement of machinery services. By specifying the objective function with constraints, the programming model selects the X J s at a level that does not exceed the prespecified restrictions. The set of X^'s in the programming result indicates an optimum combin­ ation of production activities, investment and disinvestment activities, credit and other activities. 26 Resource Restrictions In the model all resources except net worth (land to some extent) were limit to production. variable and therefore presented no Resources could be purchased once it was exhausted and if it was profitable to do so. They could also be sold once their value in use is less than their salvage value. The most limiting resources for all repre­ sentative farms was the capital resources which were deter­ mined by credit available and net worth. The annual cash resource included cash on hand, near cash assets, and crop inventories valued at current p r i c e s . Debts against crop inventories were deducted from the annual cash resource. The initial level of real estate mortgage resource was defined as the funds that farm operators thought they could borrow from public credit institutions taking into account the current value of land and other assets less outstanding debts against such assets. The initial amount of the chattel mortgage resource was estimated at 50 percent of the current value of the machinery inventory minus any outstanding debts against such assets. Cost of credit varies with the source. Money could be borrowed at 8 percent per annum using real estate mortgage or 9.5 percent per annum using a chattel mortgage whereas dealer credit costs 14 percent per annum. The initial cash on hand could be saved at 6.5 percent per annum. A further explanation of the credit resources will be given in the next section. 27 The determination of the initial levels of the potential land rentals and land purchases were based on the data collected on the field survey. During the survey, were questioned as to the quantity, farmers location and quality of land available for rent and for purchase in the area of three miles square around the farm. Also, an effort was made to eliminate all double counting. This information was used to determine the prices and quantities of land for purchase and rent for representative farm situations (see Table A-l in Appendix A ) . Activities The model includes several major activity groups such as crop production, activities. credit, labor, land and machinery The activity groups in the model are explained as follows: Crop Activities In the model, twenty-one rotations are provided as cropping alternatives with an additional five selling out­ put activities. Each crop rotation is composed of two or more of the following crops: wheat (W), field beans i . e . , corn (C), soybean (S), (B) and oats (0).^ As the yields, herbicide costs and level of fertilization differs for the same crop with different crop rotations, separate crop ^The letters in the parentheses are used to denote the crop rotation. budgets were developed taking into account the different g crop rotations. The crop budgets used in the model are presented in Table A - 2 to Table A-9 of Appendix A. Levels of crop yields, fertilization, capital, labor input and machinery required for each rotation apply to a unit of rotation, the rotation. containing one acre of each crop in For example, a unit of CCBW rotation (corn- corn-bean-wheat) includes two acres of corn, one acre of field beans and one acre of wheat. In the tableau the negative sign preceeding the coeffi­ cient in the profit equation indicates variable costs and no sign indicates income, while negative signs preceeding the production coefficients indicate adding to the resource and no signs refer to consuming resource. No institutional restrictions were imposed in the model since there would be no government set-aside of land in 1974 for feed grains, soybeans and wheat. It is worth noting that the income from sales of products does not add to cash to be used in crop production. The reason for this is that crop sales income is received after most of crop expenditure has been spent. However, the inventories of last year's crop are added to cash for crop production. g The crop rotations and input-output coefficients were developed through consultations with Lynn Robertson of the Soil Science Department and Milton Erdman and S. C. Hildebrand of the Crops Department, Michigan State University. 29 Credit Activities In the model, a group of credit activities are included so that additional credit could be obtained against present chattel assets and real estate as well as from dealers for buying machinery or other assets. The group of credit alternatives includes: mortgages chattel (Q-^) , real estate mortgage (Q2 ) > land contracts (Q3X obtaining credit on newly acquired land (Q^), machinery dealer Q credit (Q^), and savings account for surplus cash (Q^)• The chattel mortgage credit costs $0,095 for each dollar borrowed, limit. adds $0,905 to cash, and uses $1 of the credit Real estate credit costs $0.08 per dollar, furnishes $0.92 to cash and uses up $1 of the real estate credit limit. Purchasing land or new machinery furnishes additional credit for farmers. These credits are available only with the purchase of land or machinery. However, the model would not force the use of credit, unless it was profitable to do so. The land contract credit costs $0.09 per dollar of credit and adds $0.91 cash while using up $1 of credit limit. land is purchased on real estate mortgage, When an additional land mortgage credit activity is allowed to be activated. This activity costs $0,085 per dollar borrowed and furnishes $0,915 to cash while using up $1 of the credit limit. 9 The notation in the parentheses are used in Table 3.1. Machinery credit costs $0.14 per dollar borrowed and adds $0.86 to cash while using up $1 of the dealer credit limit. In the model the credit acquisition activities handled all interest costs. The cash saving activity (Q^) provide an opportunity cost of 6.5 percent for the initial cash on hand. This implies that capital used on farm, either for asset purchase or production, have to bring at least 6.5 percent returns or the resources will not be used on the farm. Labor Activities A perfectly elastic supply schedule for labor was a s s u m e d . S e a s o n a l unskilled labor and managerial labor could be hired without limit in any of the five time periods whenever family labor were insufficient to meet all labor requirements on the farm. On the other hand, two off-farm alternatives were added to provide the opportunity of off-farm work for operator and family labor. Operator and family labor may be hired out at $5.75 and $2.55 per hour, respectively. Restrictions on the quantities of off-farm work for operator and family labor were based on the average hours of off-farm labor obtained in the year covered by the field survey. Hiring managerial labor activity (N^ tun ) costs $5.80 ■^Farmers interviewed indicated that they could hire enough labor in the five time p e r i o d s . 31 per man hour, uses $5.80 cash, adds one hour to annual labor which was distributed by periods, and contributes one hour to the managerial labor restriction. The wage rate of $5.80 per hour was based on a 40-hour week with an annual income of $ 1 2 ,000 . Land Activities The model provided alternative activities such that capital could be used to purchase land as well as for the clearance of land or renting of land. Land could be purchased either on a land contract basis (L^P^) or on a mortgage basis (L2 ^m ) . The former requires a 25 percent down payment furnishing 75 percent land contract credit while the latter needs 50 percent down payment providing 50 percent mortgage credit. The prices and quantities of land available for rent and for purchase were determined b y the data collected on field survey. 184, 131, The estimated quantity of land for rent was 134, respectively for small, and the potential quantities medium and large farms for purchase were 117, and 54 correspondingly for small, 82 medium and large farms. The rental rate was estimated at $30 per acre, while the purchase price was estimated at $500 per cropland a c r e . ^ 11 In analyzing the effect of land availability on the optimum organization, it was further assumed that a sub­ stantial quantity of high priced land could be purchased and/or rented at a higher price in order to approximate the empirical assumption that the supply of land is not per­ fectly elastic. (This is not shown in the Tableau.)This 32 The model also provided alternatives for selling land at price of $500 per acre and r e n t i n g annual rental rate of $30 per acre. out land at an Two land clearance activities were incorporated in the model. One is clearance activities for woodland requiring $500 clearance cost per acre of woodland and the other is for plowable pasture land requiring $395 clearance cost per acre. The CL's in these two activities were the annual clearance cost computed by the amortization principle, i.e., P . d + r )1 C = - T ---Where C is the current cost, P o the initial land clearance cost, r, the interest rate and t is the usable life. By permitting land and associated durable resources to vary in the model, one could observe the effects of varying land area on the optimal organization of a farm. Machinery Activities The linear programming model provided for acquisition and disposal of machinery and equipment. Economic theory states that a profit-maximizing entrepreneur will employ a variable productive service until the point is reached at which the marginal value product equals its marginal factor cost. 12 Likewise, a profit-maximizing entrepreneur was defined as land B in the model. The costs to obtain control of an acre of land B were $600 and $35, respectively for purchasing and renting. 12 Ferguson, C. E . , Microeconomic Th eo r y , (Homewood, 111., Richard D. Irwin, I n c ., 1969) p. 404. 33 would not acquire an additional unit of machinery unless the annual marginal value product of the machinery exceeds its annual marginal factor cost. The annual marginal factor cost of an asset includes depreciation, taxes, interest and repair. Consequently, the annual marginal value product of the machinery purchased has to be at least equal to the sum of depreciation, interest, repair and taxes of the asset. Since repairs are basically a variable cost in nature, they are charged as variable cost in the crop producing activities. 13 Furthermore, as stated previously the credit acquisition activities handled all interest costs. There­ fore, the profit coefficients in the machinery acquisition activity represented only the depreciation and taxes (EH-T) which is the cost of the annual flow of services from the asset. By the same token, the profit coefficients for machinery sales activities were the savings to the farm of not owning the machinery. It is assumed that a 25 percent of down payment was required when machinery was purchased providing 75 percent of machinery dealer credits. Discrete Investments There is a problem in interpreting the results of linear programming due to the divisibility assumption made 13 This study does not consider the user cost problem which deals with the economics of deciding on the optimum rate at which to generate service from durable assets. 34 in the model. In linear programming, resources and products are assumed to be infinitely divisible. Therefore, the results of linear programming will include the fractional unit of activities and resources. to solve this problem. There are several ways Integer programming which is being developed at Michigan State University will partially overcome this problem. 1 A- The other alternative is to fix the discrete invest­ ment to the nearest unit higher than and lower than the fractional unit present in the optimal solution with all assets assumed to be infinitely divisible. The program is then re-run twice, once using higher value restrictions and once using the lower value restriction, and select the plan giving a higher p r o f i t . ^ The selected organization is less profitable than the previous organization since purchasing whole unit of assets impose a greater capital restriction on the farm. First, This procedure has two pitfalls. this integer solution may be infeasible. this solution may be too far from optimality, is feasible. Secondly, even if it In order to reach the optimal integer solution, it may require a much more drastic realignment of the decision variable values than merely rounding off. 14 CDC Apex II routine which is designed to solve the integer programming problem is being developed on the CDC 6500 computer at Michigan State University. "^Hildebrand, P.E., o£. c i t ., Chapter II. 35 Another alternative is to deal with d i s c r - e t e as a flow rather than a stock. In this case, considered as a continuous input. ii_ tn For e x a m p l e „ can provide many hours of service which can b e as a continuous input. Also, the fractional assets c a n be a tractor considered u x i i t s of machines can be interpreted as purchasing m a c b i _ x i . e s which embody different amounts of services by a c q u i i r i n g different sizes or ages, or simply viewed as those of torn service hired. In this study, no effort was made to s o l v e of the fractional unit of activities and r e s o u . optimum plan for two reasons. First, the c e s problem in the the a p p r o a c h adopted -| by Hildebrand could not handle the problem s l cfL uately. Secondly, Apex I routine used in this study g i v e s of a machine over which the optimal solution the range r e m a i n s By using this information a program can be r o u n d e d activities produced to the nearest whole u n i t causing serious decision making errors. stable. to include v^rdLtliout In c s l s that the rounding is beyond the range, we allow the f r a c t i o n a l of inputs and could be viewed as custom s e r v i c e units hired. Production Function Model One of the approaches to the problem of o timum resource allocation is to estimate a p r o d u c t i o x x function from which the elasticity coefficients of p r o d x x c t i o n the marginal value products of factors can b e ^ Ib id ., Chapter II. e and s timated. 36 The estimated marginal value products of each input can then be compared with the estimated marginal factor cost of respective variable i n pu t s . If the comparisons show that the ratio existing between marginal factor cost and marginal value product is substantially different for each variable factor used by the farm, a proposed reor­ ganization for applying different levels of inputs until the ratios are equal for each variable input would increase net farm income. All inputs combined in optimum proportions can be increased until the ratio between marginal factor cost and marginal value product for each variable input becomes equal to one. Under this condition, the high profit point is reached and the optimum level of resource use is determined. There are several algebraic forms which can be used to fit the production function. used are: The ones most commonly Cobb-Douglas, Spillman, quadratic, square root functions. power and Many factors should be considered in order to select the appropriate functional forms. The basis for selection of alternative formulas include ease of fitting and manipulating, statistical goodness of fit, empirical evidence and economic theory. In this study, the Cobb-Douglas type f u n c t i o n ^ will be chosen because of ^ E a r l 0. Heady and John L. Dillon, Agricultural Production Functions (Ames, Iowa, Iowa State University Pr ess, 1961) pp. 73ff. 37 its goodness of fit to the data, efficient use of degrees of freedom and computational feasibility. The equation is of the form b, b9 Y = AX± LX2 . . . . b Xn n Where Y represents output, X p . . .,X (3.4) the dependent variable, and represents the independent variables that determine output. The exponents b^ (i = 1,. . .,n) are the elasticities of the independent inputs . . .,n) with respect to the dependent variables X^ (i = 1 , (Y). The values of these exponents indicate percentage change in output associated with a one percent change in the respec­ tive input factors while keeping all other inputs constant. If they are not forced to one, E b. < 1 indicates decreasn ing E b. > 1 indicates increasing returns to scale. i=l The model can be expressed in logarithmic form as follows: Log Y = log A + b-^ log X^ + b 2 log X 2 + , . . . , + b m log Xn (3.5). The function is linear and is easily fitted to empirical data by the least squares regression technique. sion coefficients The regres­ (b^) are in natural numbers and the only transformation required where the function is to be written in exponential form is the conversion of the constant "A" back to the natural numbers. The power function permits the phenomenon of decreasing marginal returns to appear without using up many degrees of freedom. 38 The marginal value productivities for each factor b± Y input can be estimated by using the equation MVPx^ = where Y is the estimated gross income of the factor inputs, and is the amount of the factor used in the prediction equation. The Variables One of the main problems encountered in the applica­ tion of a Cobb-Douglas function to the analysis of farm data has been that of classification of inputs into homo­ geneous categories. The ideal situation in input classi­ fication is to have the inputs within each category combined in the proportions dictated by the scale line. Since this ideal situation is difficult to reach, Johnson 1R developed a set of rules which insure that it is at least approximated the ideal situation. 1. That the inputs within a category be as nearly perfect substitutes or perfect complements as possible, 2. That categories made up of substitutes (a) be measured according to the least common denominator (often physical) causing them to be good sub­ stitutes and (b) be priced on the basis of the dollar value of the least common denominator unit, 18 Johnson, Glenn L . , "Classification and Accounting Problems in Fitting Production Functions to Farm Record and Survey Data," Resource Productivity, Returns to Scale, and Farm Size, The Iowa State College Press, 1956, Chapter 9. 39 3. That categories made up of complements (a) be measured in terms of units made up of the inputs combined in the proper proportions (which are relatively unaffected by price relationships) and (b) be priced on an index basis with constant weights assigned to each complementary inputs, 4. That the categories of inputs be neither perfect complements nor substitutes relative to each other, 5. That investments and expenses be kept in separate categories, (The reason for this suggestion is that returns expected from these two types of inputs are different. The expected returns of cash expenses are at least one dollar for the last dollar spent. However, investment categories are expected to return enough to cover maintenance, depreciation, interest and taxes for a given year and are usually less than one dollar per dollar of investment.) 6. That maintenance expenditures and depreciation be eliminated from the expense categories because of the difficulty encountered in preventing duplication. This means that the earning of the investment categories must be large enough to cover maintenance and/or depreciation. According to the rules developed by Johnson, this study uses total value product (Y) including the sum of all cash sales, home consumption and inventory changes, measured by 40 gross income as the dependent variable. Such sources of income as grant payment for diverted acreage, the rental value of the farm home and investments in nonagricultural sector is not included. (causal) variables are: acres; (X2 ) , labor, in dollars Classifications of the independent (X^) , land, measured in tillable in months; (X^), operating expenses, (interest and taxes are considered as nonpro­ ductive since no return is expected to accrue from these items); (X^), machinery investment, in dollars; (X^) , buildings,in dollars. A Comparison of Cobb-Douglas and Linear Programming Analyses In general, the problems of resource allocation and the issues associated with supply responses and adjustments in agriculture can be analyzed using several different techniques. analysis, Among techniques commonly used are: simulation, budgeting, aggregate time series. functional linear programming and Cobb-Douglas function analysis and linear programming were employed in the present study. This section compares these two techniques. Cobb-Douglas Analysis As a power function, the Cobb-Douglas function has some unique mathematical characteristics; mental, others useful. some are detri­ The following are some shortcoming inherent in the function: (1 ) it is monotonously increasing and never reaches a maximum, (2 ) it cannot simultaneously 41 handle more than one stage of production as it has constant elasticity coefficients for inputs. On the other hand, advantages. the power function has several The more important advantages are as f ol l o w s : (1) it is linear in logarithmic form and easily fitted to empirical data, (2 ) it immediately gives elasticities of production with respect to factors of production, (3) it yields diminishing marginal returns estimates for each productive factor separately without using up too many degree of freedom, and (4) if the errors in production data are small and normally distributed, a logarithmic transforma­ tion of the variables preserves normality to a substantial degree.^ In addition to the limitations and advantages listed above, the following characteristics should be noted. 1. The Cobb-Douglas function can be used both in estimating parameters of production functions and in find­ ing optima. In practice, parameters of production function can be obtained by fitting the production function directly to the data. The derivatives with respect to inputs obtained from the Cobb-Douglas function are estimates of the marginal value product of each factor and have the advantage of being computable for any level of the 19 and Y within the range Tinter, Gerhard, "A Note on the Derivation of Production Functions From Farm Records," Econometrica, XII, No. 1, January, 1944, p. 26. 42 of the data from which the function was derived. more, Further­ the estimated marginal value product of each input can be used with the marginal factor cost of the respec­ tive variable inputs to determine optimal resource alloca­ tions. Therefore, the Cobb-Douglas function can be used: (1) to estimate parameters and (2) to locate optima, while linear programming can only be used to locate optima. 2. The Cobb-Douglas function can deal with the problems of enterprise combinations and resource allocation. However, farms. it is difficult to use on multiple enterprise In other words, the function is more difficult to use in analyzing farms having diversified enterprises. This is due to the fact that the effect on gross income obtained from one enterprise of an input category may be substantially different than in another and the proportion of the two may vary greatly from farm to farm. However, this problem can be avoided by choosing a group of farms producing similar products, or w it h adequate enterprise accounting for both outputs and inputs. 3. In practice, 20 the Cobb-Douglas function is best used when it involves imperfect complements and substitutes among broad input categories with high complementarity and 20 Beringer analyzed individual enterprises on multiple enterprise farms wi th adequate accounting of outputs and inputs. (See: Christoph Beringer,"A Method of Estimating Marginal Value Productivities of Input and Investment Categories on Multiple Enterprise Farms," Unpublished Ph.D. dissertation, Michigan State University, 1955.) 43 only substitutability among inputs left within input categories. A problem encountered in the application of CobbDouglas functions in the analysis of farm data has been that of classifying inputs into categories. Johnson^l through analytical reasoning developed rules which proved useful in this study. The rule is to group good comple­ ments together and good substitutes together, measuring the complements in terms of "sets" and the substitutes in terms of the common denominator which makes them good substitutes. The resultant sets of complements and sets of substitutes can sometimes be grouped into larger cate­ gories on the basis of the same rules. Consequently, input categories defined should be neither good substitutes nor good complements for each other. This avoids much of the specification bias with which Griliches was later concerned. 4. The Cobb-Douglas function can be used to investi­ gate increasing or decreasing returns to scale. When the sum of the elasticities is larger than one (£b^ > 1 ), increasing returns to scale are indicated; when the same sum is less than one (£b^ < 1), decreasing returns to scale are evidenced; and when the sum is equal to one (£b^ = 1), constant returns to scale are indicated. 21 22 72 Johnson, Glenn L . , o£. c i t . , Chapter 9. Griliches, Z v i . "Specification Bias in Estimates of Production Function," Journal of Farm Economics. Vol. 39, 1957, pp. 8-20. 44 5. Some effects of change in the amount of supporting inputs and investments on the estimates of the marginal value products of an input category can be measured. The function is capable of measuring some of the effects of interaction of different levels of inputs and investments on their respective value productivities„ Although linear programming has such capability if enough activities are used in the model, the cost of including enough activities is often prohibitive in terms of additional complexity and computing. 6. The Cobb-Douglas function permits estimates of the marginal value productivity of one input category to be made without arbitrarily assuming the earning power of other input categories as in accounting work. 7. The Cobb-Douglas function can indicate which resources are economically fixed and which are candidates for investment or disinvestment by comparing the estimated marginal value products of specific resources to both salvage value and acquisition price of corresponding inputs and investments. However, stock-flow conversion problems arise because of the unsolved user cost problem in economic theory. 8. Statistics can be used to provide measures of significance of the parameter estimates for a Cobb-Douglas function; however, some of the tests of the significance of the difference between MVP and MFC are of questionable 45 validity due to the difficulties involved in estimating the variance of marginal value p r o d u c t i v i t y . ^3 Linear Programming Analysis As an optimizing model, linear programming can be applied to the great variety of situations including farm planning, minimum-cost feed formulation and transportation planning. The main advantage of this technique is that it provides computational simplifications not present in analysis of curvilinear production functions due to the smooth, continuous and frequently nonlinear nature of such production functions which make it difficult to work with them mathematically. Linear programming can deal with certain aspects of highly complex enterprise interrelation­ ships by using different activities within and among enter­ prises . Activities can be set up so that the marginal value product of inputs are bounded by acquisition price and. salvage values. In these cases, capital acquisition and disposal activities and the credit activity become very important. 2A However, care has to be taken not to confuse the linear programming MVPs with the partial derivatives ^ F o r a discussion of these see: Carter, H. 0. and Harley, H. 0., "A Variance Formula for Marginal Productivity Estimates Using the Cobb-Douglas Function," Econometrica, 26 pp. 306-313. ^ I n this study the linear programming model dealing with the endogenous determination of fixed resources is applied. 46 from a continuous production function because the former are not synonymous with the latter, as will be made clear in Chapter IV. Linear programming has several unique characteristics. 1. In linear programming, parameters can be easily changed or adjusted with information beyond time series and cross-sectional data. In Cobb-Douglas analysis similar adjustments can be made but with somewhat greater difficulty.^5 In addition, a linear programming model can be modified by adding additional activities so that it can nearly approx­ imate continuous production relationships reflecting imper­ fect complementarity and substitutability; however, the cost involved in such modification may prove to be prohibi­ tive. Programming is more efficient in locating optimum enterprise combinations. 2. The linear programming model concentrates on perfect complementarity among input categories and either covers up imperfect complementarity and perfect substitu­ tability among inputs within each category or handles them with additional activities. In general, in linear programming the restrictive resources should be classified according to the following rule: Resources which are perfect or near perfect substi­ tutes should be grouped together leaving as much complementarity 25 In this study, the reorganization of farms was based on the adjusted regression coefficients as dis­ cussed in Chapter V. 47 between resource categories. If imperfect complementarity among inputs creates difficulties, it can be handled by introducing more activities while separately handling the complements. These rules were developed to handle the often contrary to fact linear programming assumption of comple­ mentary relationships among inputs. 3. Linear programming can be used to analyze problems of farm adjustment and to estimate supply functions. One of the important advantages of programming is that it permits one to examine the consequences of alternatives within short time period. if. The question, what would happen . .? can be posed repeatedly and answered quickly. Thus the analysis of farm adjustment problem and the estima­ tion of supply functions can be conducted in an environment where no time series of data exist. However, syntheses of macro supply response estimates from micro data using linear programming has not worked well due to inadequate modeling of investment and disinvestment decisions which when modeled destroy weights needed to aggregate micro-economic results into macro-economic relationships. It is difficult to build realistic group restrictions into a linear program­ ming model of the individual firm without unrealistically limiting the firm's adjustment potential. 26 Programming models Beneke, R. R. and Winterboer, R . , Linear Program­ ming Applications to Agriculture (Ames, I o w a : The Iowa State University Press, 1973) p. 4. 48 do permit assumptions concerning structural changes to be built into the system. 27 Moreover, they are able to anti­ cipate such changes using recursive programming and/or dynamic programming. 4. One advantage of linear programming is that the sensitivity of the optimal organization to changes in the relative prices, costs and resource levels can be studied. Linear programming can easily answer important questions such as: What is the ranges of prices, resource levels or costs over which a recommended plan remains stable? By definition, sensitivity analysis is a method of examin­ ing the changes in the optimal organization due to changes in p r i c e s , costs and resource levels of the activities appeared in the optimum solution. The importance of sensi­ tivity analysis is found in examining how much prices, costs or resource levels must change before the optimum solution changes. 5. One of the important values in linear programming is that the shadow p r i c e s ^ of excluded activities can be estimated. The shadow prices of the excluded activities indicate the income penalties of forcing an extra unit of an activity into a solution. Therefore, the shadow prices o7 Colyer, Dale and Irwin, George D . , Beef, Pork and Feed Grains in the Cornbelt: Supply Response- and Resource Adjustments, Missouri Agricultural Experiment Station, Research Bulletin 921, p. 35, August 1967. 28 More detailed explanation about shadow price will be presented in Chapter IV. 49 of the excluded activities indicate the competitive posi­ tions of these activities in the optimal solution. This information has great value in making enterprise combin­ ation decisions because it not only indicates what acti­ vities are not profitable but how much personal preference might cost if he forces an excluded activity into a plan. 6. Linear programming model handles more resource categories but fewer activities than functional analysis. The cost of extra activities is often prohibitive in addi­ tional complexity and computing. Moreover, a priori infor­ mation about productivity coefficients is required before the actual processes involved in the linear programming is undertaken. Therefore, the resultant productivity estimates are dependent on coefficients of productivity obtained independently of linear programming. As such, the evalua­ tion of the appropriateness of estimates of productivity has to be external to the actual programming procedures. In contrast, productivity coefficients for functional analysis are obtained by fitting the production function directly to the data, this raises questions about data adequacy not ordinarily raised explicitly in linear pro­ gramming analysis. 7. To use statistics to provide measures of significance of the results or to examine elements of risk in the farmer's environment is difficult, if not impossible 50 with linear programming. If statements about the statisti­ cal significance oftheprogrammed results could be offered, the value of optimum solutions to practical farm problems would be largely enhanced. In constrast, the Cobb-Doublas function being linear in logarithmic form can use statistics to offer limited measures of significance of results. 8. 29 Linear programming concentrates on the opportunity cost principle and can handle investment and disinvestment problems when acquisition and salvage activities are incor­ porated in the model. Linear programming addresses itself primarily to allocating fixed resources among alternative uses. Since a resource is fixed when its marginal value product is bounded by the acquisition costs and salvage values of the resource, the use of the opportunity cost principle is essential to insure adequate allocation of the use of the services generated by the fixed resources. By incorporating one or more acquisition and salvage activities into the model for each resource category, the levels of investment and disinvestment can be determined in the optimal solutions. 29 30 However, For a discussion of these see: Harley, H. 0., 0£. c i t ., pp. 306-313. 30 the power of linear Carter, H. 0. and In this case the resources are allocated according to opportunity costs, salvage values, and acquisition cost, and the model is capable of determining endogenously which resources are fixed and variable. The inadequacy of the usual neoclassical presentation stems either from an assumption that acquisition costs are 51 programming to deal with investment and disinvestment pr o ­ blems and, hence, farm growth and deterioration is limited by the difficulties encountered in solving the user cost problem. ^ 9. There is a difficulty in understanding the meaning of the so-called marginal value products obtained in linear programs. The difficulty comes essentially from the assump­ tion of perfect complementarity among inputs used in an activity within a linear programming model. assumption, Under this it is obvious that the partial derivative of production function with respect to an input does not exist. Thus, the pseudo linear programming MVPs ( MVP, p ' s ) arise only when other resources are available for use with the resource whose marginal value productivity is being estimated. As such, the MVPpp of an additional unit of the limiting resource is generated by combining it with other nonrestricting resources. Its value can be very "erratic" depending on how many other resources are unrestricted and in what amounts. The distinction between the two will be examined in more detail in the next chapter. In order to find a solution by applying linear pro­ gramming, the problem under consideration has to meet several equal to salvage values or from a hidden unrecognized assumption that acquisition costs can exceed salvage values. (See Johnson, Glenn L. and Quance, Leroy, o£. c i t ., p. 34.) 31 User cost problem could probably destroy the independence of activities and thus reduce its power in handling the investment and disinvestment problem. 52 linear programming assumptions. Very few problems in the real world can precisely fulfill all the assumptions built into a linear program. The assumptions of divisibility, additivity and linearity and single-value expectations are of particular concern. However, as techniques of linear programming such as integer programming, nonlinear program­ ming, recursive programming and dynamic programming have been improved combined with the availability of high-speed electronic computers to handle linear programming routines some of the difficulties in applying it have been alleviated. CHAPTER IV OPTIMUM ORGANIZATIONS FOR THE REPRESENTATIVE FARMS This chapter presents the programming results of representative farms under (1 ) fixed land resources, (2 ) variable land resources and (3) different price combinations. In the first place, the optimal solutions will be given for Model I with cropland fixed at 1972 levels. Secondly, the optimal organizations will be presented for Model II which permits variation in land resources and associated durable assets. In Model II, the farm size is allowed to change through the renting and/or buying land activities. Lastly, the resulting solutions are given for Model II under a number of different price combinations. The optimal farm plans for the representative farms given in this chapter are based on 1973 product and input prices. corn; The product prices per bushel were: $5.50 for soybeans; $2.25 for $4.25 for wheat; $1.25 for oats ; and $15.00 per cwt. for dry beans. The initial farm resources used in the program are based on field survey data in 1972 as presented in Table A-l of Appendix A.^ Budgets for ^The initial resources used in this model do affect the programmed solution, because the initial resources would be kept in use so long as their shadow price (i.e., value in use) is larger than their salvage value. In other words, their value in use, combining with additional new assets 53 54 individual crop which are used in developing the budgets for each crop rotation are presented in Tables A - 2 to A - 9 of Appendix A. Optimum Organizations with Fixed Land Resources (Model I) As previously noted, change in Model I. farm size is not allowed to Managerial labor, machinery and land are assumed to be fixed at the 1972 levels. No alternatives are provided for selling durable assets or selling family labor off the farm but the model permits hiring of unskilled labor to replenish the farm labor when the family labor is used up. The model also includes credit borrowing and cash saving activities. Table 4.1 presents the optimum organizations (includ2 ing optimum land use) and the shadow prices of specific resources for the representative farms. In all farm situations, the four optimum plans call for the same crop rotation which gives the maximum produc­ tion of wheat and field beans. All the WB rotation in the optimal organizations are operated up to the acreage or other initial assets, must have shadow price larger than their salvage value. Otherwise, the initial assets would be disinvested and an entirely new type of business brought in if such alternatives are permitted in the model. Shadow price of limiting resource indicates the amount by which the income would be increased by increasing a unit of resources. Only resources which are scarce have positive shadow p r i c e s . More explanation about shadow price will be given in the subsequent section. Table 4.1. Optimum Organizations and Shadow Prices for Selected Resources for Represen­ tative Farms Under Fixed Land Resources (Model I) Repres entative Rotation Acres F a r m Cash <$) Labor ($/hour) Net 1 Return ($) 141 .065 0 13,410 395 141 .087 0 22,306 Saving Real Estate A c c o u n t M o r t g a g e ($) ($) 1,428 ---- -- Shadow Prices Cropland ( $ / a c r e ) Small W B 93 Medium W B 156 Large W B 438 307 — 141 .065 0 62,737 Medium* W B 211 2,827 — 141 .065 0 30,397 — ------------------------ The net return is the farm income above the variable cost. to owned land, capital, labor and machinery. It represents return 56 restrictions. The level of the rotation varies with the different farms because of variations mainly in land resources. The level of net return varies directly with farm size, i.e., net return increases as farm size increases. Labor and capital are not limiting factors as reflected by a zero shadow price for labor and low shadow price for cash. No seasonal labor is required. The provision of saving account alternative in the model furnishes an off-farm opportunity cost or salvage value of at least 6.5 percent for the initial cash on hand. This salvage value is reflected by the shadow price of cash in small, large and medium* representative f a rm s . The results show that cropland is in short supply as revealed by the shadow price of $141 per acre which is much higher than its marginal factor cost. The high shadow price of cropland indicates that expansion of farm size would be profitable under the assumed yields and prices. It would appear from this model that the provision of supply of land is a crucial factor in increasing the scale of operation and the level of farm income. An increase in the use of land would tend to reduce its marginal value productivity at the margin but at the same time would increase the marginal earning of labor and capital. Consequently, higher farm income would be generated due to a better farm resource combination involving more land relative to labor and capital. Accordingly the Model 57 II is designed to examine the potential contribution of varying the levels of land resources on the level of farm income, scale of farm operation and optimum crop rotation. Optimum Organizations with Variable Land Resources (Model II) Model II deals with a situation which permits variation in land resources. The model allows a farm to expand or to contract through buying or selling land and associated resources. Model II differs from Model I mainly in that labor, land and machinery are permitted to vary. Acquisi­ tion and salvage activities of labor (including managerial labor), land and machinery are added to Model I . In order to model investment and framework, disinvestment in a linear programming the addition of these activities becomes essential The inclusion of such transaction alternatives, the optimum level of resources can be determined endogenously within the model instead of arbitrarily assuming them fixed. The structure of Model II is presented in Table 3.1. The initial levels of resources in Model II were the same as those of Model I. The levels of the potential land rentals and land purchases for each farm were determined on the basis of the data collected in the field survey. The estimated quantities of land for rent and land for purchases for each representative farm are shown in Table 4.2 The annual rental rate was estimated at $30 per acre while the land price was estimated at $500 per acre. These prices are based on what farmers thought they would have to 58 pay for the land that was available for rental or purchases at the time of interview. Table 4.2. The Levels of Potential Land Rentals and Purchases for Each Representative Farm Representative Farm Land (Acres) Renting Limit Buying Limit Small 134 117 Medium 184 82 Large 131 54 Medium* 213 114 By providing the opportunity to rent and/or purchase additional land and associated main durable resources, one can observe the effect of additional land supplies on optimal farm plans. The prices of outputs and inputs used in the Model II are the same as those used in Model I. The programming results indicating the optimum land use and the credit acquired for each representative farm are presented in Table 4.3. The results show that W B rotation dominates all other crop rotations covered in the model in all farm situations. All the crop rotations appeared in the optimal plans are operated up to the acreage restrictions. The levels of the W B rotation increased above the Model I levels for all farm situations. Consequently, the levels of credit used and net returns increase in all farm situations. Farmers obtain all Table 4.3. Optimum Organizations and Credit Acquired for Each Representative Farm (Model II) Representative Farm Rotation Acres Credit Acquired ($) Total Chattel Mortgage Real Estate Mortgage Others Net Return ($) 1 Small W B 344 63,678 4,418 18,600 40,660 44,725 Medium W B 422 49,376 --- 31,176 18,200 54,559 Large W B 496 CCCCS 127 34,380 --- 34,380 W B 422 C B 116 75,306 5,270 25,714 Medium* --- 44,322 83,783 62,057 ^Other credits include land contract credit, machinery dealer credit and land mortgage credit beyond that owned initially. 60 the land available for purchase and rent, which allows the expansion of their crop activity levels. It is worth noting that more crop rotations enter the optimal solutions as more land is obtained. on the large farm, For example, 127 acres of CCCCS rotation enters the optimal solution together with the expansion of W B rotation from 438 acres to 496 acres as more land is obtained. The levels of the activities vary with different farms due to the variations primarily in land resources. As compared with Model I the provision of land rental and purchase opportunity, not only resulted in increased net returns but also changed the optimum combination of crop rotations. The results show that additional resources have to be obtained or sold in order to achieve optimum farm organiza­ tions. Table 4.4 reveals the quantities of specific resources obtained or sold in order to attain the optimum plan for each representative farm. As shown in the table, some additional unskilled labor is hired in all farm situations. There is no managerial labor requirements for the small and medium* farms but approximately 100 and 130 hours of managerial labor is required for the medium and large farms, respectively. All farms have some members with off-farm work, which agrees with what cash grain farmers were doing in the south central area in 1972. Except for small farms, the family had off-farm work up to the limit of the off-farm work restric­ tion. All farms rent and purchase all the available land 61 Table 4.4. Investments a n d Dis i nvestments Required to A t t a i n O p timum Farm Organization w i t h the R ange (Model II) Representative Farm Unit Resources M edium Large Me d i u m * ... 103 130 ... 1,125 Small Managerial labor hired hours U nskilled labor h ired m a n hr 380 647 366 M a nagerial labor sold hour 1,052 904 587 389 Family labor sold hour 268 565 411 365 Land rented acre 134 184 131 213 L and purc h a s e d acre 117 82 54 114 W ood l a n d cleared acre ... ... ... --- Plowable pasture land cleared acre --- ___ --- -- No. --- --- M achinery p urchased 4-bo t t o m d Io w 1. 72 (1.72-1.72) .75 (0-.75) No. .03 (.03-2.01) .21 (.21-2.06) 1. 70 (0-3.32) .74 (0-3.62) No. . 79 (.31-.79) --- .97 (.58-.97) --- .26 (.10-. 26) .84 (. 58-1. 54) No. .55 (0-.55) .45 (0-.45) 4-bot t o m plow No. . 21 (0-.21) .03 (0-.03) Cultivator No. .06 (.06-1.97) .08 (.08-1.98) No. 1.00 (0-1.75) 1.00 (1.00-1.61) Combine (2 row) Pull type No. . 18 (0-.18) Spring tooth (12') No. .27 (.27-2.07) Tractor 2 (70 H.P.) No. -- -- Planter No. -- -- No. -- -- Disc 2 (16') Grain drill Combine (16'-17") (10', 2 row) No. . 10 (0-.12) --- --- .30 (0-.36) - - Machinery sold Tractor Com (53 H . P . ) (4 row) p i cker (2 row) (6 row) Spring tooth (16') ... .34 (.34-1.88) .20 (.20-1.92) - .04 (0-.33) .35 (.08-1.70) ... .10 (0-.10) .40 (.40-.50) . 71 (.71-1.15) .49 (0-1.30) -... ■''Data in p a r entheses show the range over w h i c h the o p t i m u m sol u t i o n remains unchanged. 62 and increase crop acreages. Neither the woodland nor the plowable pasture land was cleared in the optimal solutions. This indicates that it is not economical to convert wood­ land and/or pasture land into cropland at the cost of $500 per acre and $395 per acre, respectively under assumed yields and product conditions. However, some pasture land would be cleared under more restricting land resource and/or higher product price condition. This situation will be shown in the next section. Purchase of some equipment and sales of some machinery are necessary to achieve the optimal farm p l a n s . in the lower part of the table. show This is shown The data in parentheses the range over which the optimal solutions remain stable. It should be noted that the kinds and amounts of machinery bought or sold depend on the kinds and levels of crops that enter the optimal solution. For example, corn does not enter the optimal organization on the small and medium farms, farms. and thus corn pickers are sold out on these On the other hand, corn pickers are retained on the large and medium farms due to the inclusion of corn enterprise in the optimal solution. Original and optimum inventories of machinery for each representative farm are presented in Appendix B. One of the important values in linear programming is that the shadow prices of scarce resources and excluded 3 activities can be observed. Shadow prices are sometimes 3 Excluded activities are the activities that do not enter the optimal solution and are sometimes called "non­ basis activities." 63 called the marginal value products or the marginal costs depending on whether they are referring to the slack (or disposal) activities or the real activities. In general, the shadow prices of the limiting resources indicate the marginal contribution to income of the last unit of resource. It reveals the pressure to expand or contract the use of particular resources. In this sense, it would appear analogous to the marginal value product derived from a continuous function. However, care has to be taken not to confuse the linear programming MVP (MVP^p) with the MVP from a contin­ uous function (MVPc £) because the former is not synonymous with the latter. By definition, the marginal value product of an input is the addition to total value product attri­ butable to the addition of one unit of the variable input to the production process, other inputs remaining unchanged.^ It is quite obvious that such a marginal value product of an input does not exist in linear programming due to the assumption of perfect complement relationship among all inputs in the model. In linear programming, resource (i.e., the imputed values to a shadow price or MVP^p) is estimated at the margin with no other resource restricting.^ 4 Ferguson, Consequently, C. E . , o£. c i t ., p. 119. ^Lard, C. H. "Profitable Reorganizations of Repre­ sentative Farms in Lower Michigan and Northeastern Indiana with Special Emphasis on Feed Grain and Livestock." Unpub­ lished Ph.D. dissertation, Department of Agricultural Economics, Michigan State University, 1963, p. 80f. 64 the MVP^p a res°urce is generated by an additional unit of the limiting resource combined with other nonrestricting resources. This type of MVP holds only for an additional unit of resource when all other resources are not restric­ tive and its value may be very "erratic" for further addi­ tional unit of resource. The magnitude of its value depends on which other factors become limiting as an additional unit of the resource is used. The essential nature of corner solutions of linear programming contributes to the "erratic" behavior of the linear programming MVP, i.e., the optimal solutions remain stable for a specific range until one of the other resources becomes restricting, then MVPs of resources change erratically due to change in optimum basis. The distinction between MVP^p and M V P cf would become more obvious if they were expressed in mathematical form. Consider the production function: y = fOp- • • ,xd , x d + l ’ - • - ’X g) Where: y represents total value product; X p , . . ., x^ are variable inputs and hence for all X i (i = 1 ,. . . ,d) , 0 _> Px A = Px >_ 0 where i i P X •a* = acquisition price of X. and P X •s = salvage value 1 l l Of X.; X d+i«. . .,Xg are the inputs which are fixed separ­ ately for firm as a whole but allocable 65 among enterprises and hence for all X i (i = d+ 1 ,. . .,g), 0 < P — x^s < MVP x^ < P x^A• —< 00. Then MVPT x = 4^ LP(xd+1)y dX Where: ^ is a total derivative of y with respect to X, and X = (x1 ,. . .,xd , X d + 1 > . .,xg ) while all x_L (i = 1, . . . ,g) are combined in fixed proportion, i.e., all x^ (i = 1 ,. . .,g) are perfect complements as assumed in linear programming under which assump­ --- vani s he s. d+1 MVPT P / \ > 0 when x,,-. is a limiting Lir xd_j_d^y utI tion input and x d+ 2 ’‘ ' ’,Xg are not restrictinS inputs. MVP t p /' '> Li^ xd+l'y = ® when x,., is a limiting input and ciTi simultaneously one of x^ (i = d+2 , . . .,g) is a restricting input or xd+^ is a nonrestricting input. In comparison, marginal value product from a continuous function is as follows: MVP cf(xd+1>y = iX. 3xd+1 W he re : 3X is a nonvanishing partial derivative of y with 9xd+l respect to x d+^ 66 It is apparent that: W ^ L P C x ^ y > Where ” 0 > ° It should be noted that when is not a restricting resource, the MVPtp/>. is 0. Only under this condition 'x d+l ^ MVP^p is synonymous to the meaning of marginal value product from continuous function. In order to avoid the confusion between MVP^p and MVPc£, the term "shadow price" rather than MVP^p is used to indicate the marginal contribution to income of the last unit of resource in linear programming. Only resources which are limiting in use or those which have positive salvage prices have positive shadow prices. Hence the shadow prices of resources indicate which resources are restricting and the potential gains in income through acquiring one unit of limiting resources. It should be noted that the shadow prices of resources indicate the pressures to expand or contract the use of a specific resource. Moreover, these pressures tell how far adjustments should be made and the range over which these shadow prices hold. The shadow prices of the excluded activities indicate the income penalties of forcing one unit of non-basis 67 activities into the solution. The shadow prices of excluded activities are always positive because if the excluded acti­ vities were brought in with the given resource constraint, they would have to replace some higher earning activities already in the program. The shadow prices for selected resources are presented in Table 4.5 for each representative farm. These values are the amount of income which the firm would gain or lose by purchasing or selling respectively one unit of the resource. As mentioned before, values. only scarce resources have positive The shadow prices for the cropland is much less than that in Model I. This result is to be expected as variation in restricting resources is allowed. In all farm situations, land is the most limiting resource as reflected by its high shadow price. The values range from $92 to $109 per acre for cropland and $62 to $79 per acre for rented land. The high shadow prices of cropland and rental land indicate that it would be profitable to expand farm size under assumed yields and price conditions. The rental rate for cropland in the area was estimated to be around $30 per acre. The shadow prices of purchased land range from $38 to $50 per acre which are higher than a land rental rate. This indicates possible expansion in farm size through purchasing land at the price of $500 per acre under assumed product condition. The labor in season I (December to March) and in season 2 (April to May) is 68 not exhausted. limiting. The labor in other seasons are most often However, an increase in the use of labor in these seasons would not be profitable except on the large and medium* farms. Table 4.5. Shadow Prices for Selected Resources on Each Representative Farm (Model II) Resources Unit Representative Farm Small Medium Large Medium* Cropland $/acre 101 95 92 109 Rented land $/acre 71 65 62 79 Purchased land $/acre 40 38 38 39 December, January, February, March Labor $/hour April, May Labor $/hour --- --- June-July Labor $/hour .50 1.51 August: Labor $/hour .50 1.51 September, October, November Labor $/hour .50 1.51 3.26 3.49 Cash $ .11 .09 .09 .16 Chattel Mortgage $ .01 $ $/hour .02 .01 2.85 3. 81 Real Estate Mortgage Managerial Labor --- --- 3. 26 --- --- 3.49 3.49 --- .05 --- .07 4.94 --- One of the limiting resources in the optimal solutions is the operating cash. However, the increase in cash beyond the initial amounts would not be profitable for all farms except medium* farms as its shadow price ranges from 9 cents 69 to 16 cents per dollar. Managerial labor is a limiting factor in the optimum solutions except on medium* farms. But the increase in the use of this factor is undesirable as its shadow price ranges from $2.85 to $4.94 which is lower than its marginal factor cost. In short, the shadow prices for resources indicate that land is the most limiting resource as reflected by its high shadow price. This indicates the farmer would likely find it profitable to expand farm size under the assumed prices and output conditions. At this point, it should be remembered that an expansion of land would not increase for all succes­ sive unit of land, since some other inputs might become limiting resources. The shadow prices of an excluded activities indicate by how much income would be penalized were they forced into the final solutions. Therefore, the shadow prices of the non-basis activities indicate the competitive positions of these activities in the optimal solution. shadow prices of a non-basis activity, The lower the the higher is its competitive position in the optimal farm plan. trary, the higher the shadow prices, On the con­ the lower is its competitive position in the optimal organization. In order to examine the effects of rotations on economic potential of all crop activities included in the model, shadow prices of the excluded (or non-basis) the crop rotation activities are presented in Table 4.6. As shown in the table, COW, CCCBW and CCCCS rotations 70 Table 4.6. Crop Rotation Shadow Prices of One Unit of Excluded Crop Rotations (Model II) Representative Farm Unit Small Medium Large Medium* ------ Dollars----CB $/2 acres 8.85 13.25 7.18 CS $/ 2 acres 36.54 24.64 32.76 WB $/2 acres NA 1 WS $/2 acres 26.21 10.15 24.42 30.35 CBW $/3 acres 1.99 9.20 2.93 3.60 CBS $/3 acres 17.94 .77 12.38 3.02 COW $/3 acres --- --- 3.26 1.91 BCO $/3 acres 25.08 21.65 29.16 12.76 CBO $/3 acres 20.06 16.66 24.19 7.61 SCO $/3 acres 22.20 --- 24.98 14. 29 CCB $/3 acres 14.18 25.15 12.61 8 .72 CCS $/3 acres 7.14 --- 5.15 4.20 CCCB $/4 acres 6.57 25.45 6 .87 .71 CCCS $/4 acres 3. 57 3.68 2.57 2.10 CCBW $/4 acres 3.57 17.99 5.44 6 .78 CCOW $/4 acres .25 3.25 --- CCBS $/4 acres 18.57 8.67 14.20 5.42 CCCBW $/5 acres --- 21.67 2.86 4.68 CCCCS $/5 acres --- 7. 36 CCCBS $/5 acres 15.83 ■*"NA denotes does not apply. NA 13.11 NA NA 12.20 NA 32.52 NA --- --- 3.97 71 are in the most competitive position in the optimal plan on the small farm as reflected by the near zero shadow prices for these activities. On the other hand, CS rotation is in the weakest competitive position as reflected by its shadow price of $36.54 per unit (2 acres) of crop rotation. value is a net marginal cost (i.e., This the excess of marginal cost over marginal revenue) indicating that the income would be reduced by $36.54 if one unit (2 acres) of CS rotation was forced into the final solution under assumed prices and yield conditions. It is worth noting that the competitive position of the same crop rotation changes as farm size changes. For example, CCCBW rotation is in the most competi­ tive position on a small farm, but it becomes less competitive on the medium farm. On the medium farm, COW, SCO and CCS rotations are in the most competitive position as revealed by the near zero shadow prices of these activities. CS rota­ tion still remains in the weakest competitive position as it was on the small farm. On the large farm, CCOW rotation is in the most competitive position while CS rotation is in the weakest competitive position in the final organization. This information is very important to a farmer in making decisions about selecting rotations because it not only indicates what rotations are not profitable but how much personal preference might be worth if a farmer preferred to force an excluded rotation into the solution. 72 Optimum Organizations Under Various Levels of Land Supply (Model Il)~ From the previous discussion, it appears that crop production is limited by the supply of land as reflected by the high shadow prices of cropland, rented land and pur­ chased land. The resulting optimal solutions for all farm situations call for expansion of farm size up to the limit of land restriction permitted in the model. To further investigate the effect of variable land supplies on optimal land use, the opportunity to rent and purchase additional land is considered in this section. At the same time, two cases in which less land is available for rent and purchase are also considered in order to examine how optimum land use changes under more restricted land supply conditions. The initial levels of resources are the same as used in the Model II in the previous section. Five cases are involved in the model based on the assumptions made in terms of potential land resources avail­ able for a farmer to rent and/or to purchase. The levels of potential land rentals and purchases assumed for each case in Model II are shown in Table 4.7. In this table, land A is defined as land which can be purchased at price of $500 per acre or can be rented at the annual rate of $30 per acre. These prices are based on what farmers thought they would have to pay for the land that was available for rental or purchases at the time of interview. The price of land B, on the other hand, was set at $600 per acre or can be rented Table 4.7. The Levels of Potential Land Rentals and Purchases Used in Each Case in Model 11^ (Unit: Acres) Case I2 Cas e II Case III Case IV Cas e V S M L M* S M L M* S M L M* S M L M* Renting Limit 30 30 30 30 50 50 50 50 134 184 131 213 134 184 131 Buying Limit 30 30 30 30 50 50 50 50 117 82 54 114 117 82 Renting Limit NA5 NA NA NA NA NA NA NA NA NA NA NA 200 Buying Limit NA NA NA NA NA NA NA NA NA NA NA NA 200 S M L M* 213 134 184 131 213 54 114 117 82 54 114 200 300 200 1200 1500 2000 1500 200 300 200 1200 1200 1300 1200 Land A^ Land B4 ^The levels of land A in Case III, IV, V are determined by the field survey data in 1972 while the others are assumed quantity. S stands for small; M stands for medium; and L stands for large. O Land A: land which can be purchased at the price of $500 per acre or can be rented at the annual rate of $30 per acre. 4Land B: land which can be purchased at the price of $600 per acre or can be rented at the annual rate of $35 per acre. ■’NA denotes does not apply. 74 at the annual rate of $35 per acre. The levels of land resource restriction in all cases were set by assumption except the quantity of land A in Case III, IV and V which were obtained from data collected from the field survey. In Case IV, and V, land B restrictions and activities were added. The levels of land B restriction in Case IV and V for each category of representative farms are shown in the table. The purpose of this relaxation on the land resource restriction is twofold: (1) to examine the effect of change in land resources on the optimal crop rotation and (2) to figure out what resources would become restrictive on expansions in farm size. In this section, only the results for the large size representative farm in each case are presented. The program­ ming results of the other representative farms in each case will be placed in Appendix B. Table 4.8 presents the summary of optimum land use, the resource transactions and the shadow prices of farm resources for large farms under various levels of land resource avail­ ability. It is easily seen that the increase in land avail­ ability results in an increase in farm size and farm income and changes the optimum combination of crop rotations, although product prices are unchanged. The increases in farm size and net return are moderate in Cases I, II and III in which land is more restricted. However, farm size and net return increased considerably in Case IV and V as more land was assumed. In all cases, the WB rotation dominates in the optimal solutions with levels of WB rotation increasing as more land was obtained. Also other crop rotations entered the optimum plan as more land was acquired. For example, CCCB rotation entered the optimum solutions in Case I and II but moved out of the optimum organization when more land was allowed. The CCCCS rotation appeared in the optimum plans in Case III and IV while CCS rotation entered the optimum solu­ tion in Case V. The amount of credit varied directly with farm size. The amounts of credit used increased as more land was obtained except in Case V in which case the amount of credit acquired decreased as farm size increased. The main reason for this is that the optimal solution in Case V did not call for the land purchasing activities which require more borrowed credit. As shown in the upper part of the table, land is acquired through renting 131 acres of land A and 700 acres of land B but no land is purchased. A comparison of the optimal use of specific resources for five cases is also given in the table. There was no m a n a ­ gerial labor requirements in Case I and Case II but a substan­ tial managerial labor was required when more land was obtained (see Cases IV and V ) . In all cases, some unskilled labor was required. The amount of hired seasonal labor increased as more land was acquired. The resulting optimal plans in all cases indicated that both family members and the operator took off-farm employment up to the limit permitted in the model. The 76 Table 4.8. Summ ar y of O p t i m u m Land Use, Reso urce Transact io ns and Shadow Prices Under Various Levels of L and Resource s on Large Cash G rain Fa rm (Model II) Unit Net Return $ Cas e I Case II Case III Case IV Case V 74,164 77,195 83,783 460 41 460 78 496 --- 127 - __ 253 -- 271 12,284 24,734 -- 100,586 117,926 701 998 34,380 95,076 86,445 - 130 1, 793 3, 339 20 161 366 1,041 1,946 587 411 30 30, NA1 NA - 587 411 131 54 NA NA 587 411 131 54 300 31 587 411 131 -- 587 411 50 50 NA NA -- _ 700 - 3 -- -- -- - 119 89 66 NA NA 117 87 64 NA NA 92 62 38 NA NA 82 52 14 47 Crop Ro tation WB CCCB CCCCS CCS acre acre acre acre Credit Used $ --- _ -- Resources Obt ained or Sold Manager ia l Labor Hired Unskilled Labor Hired Managerial Labor Sold Family Labor Sold Land A Rented Land A Purch ase d Land B Rented Land B Purch as ed Wo odland Cleared Plowable Pasture Cleared hour m a n hrs hour hour acre acre acre acre acre acre - Shadow Prices Cropland Land A for Rent Land A for Purchase Land B for Rent Land B for Pur chase April-M ay Labor June-July Labor August Labor Septem be r-N ove mb er Labor Cash Chattel Mo rtg ag e Real Estate Mo rtgage Managerial Labor Woodland Plowable Pasture ^NA denotes $/acre $/acre $/ acre $/acre $/acre $/hour $/hour $/hour 3. 26 -- $/hour $ $ $ $/hour $/acre $/acre ------ 2. 38 .09 the ite m is not applicable. 3.26 3. 26 .09 ---- - 3.26 -- 3.26 .09 - 4.94 --- _ 35 5 - 1.04 3.46 3.46 4.83 5.00 5. 00 3.46 .15 .04 .06 4. 713 5.00 .67 .51 .53 6.36 --- - 77 operators were allowed 587 hours of off-farm employment while the family members were permitted to work off the farm 411 hours per year at the wage rate of $5.75 per hour for an oper­ ator and $2.55 per hour for family members. The optimal plan in all cases rents and purchases land A up to the land rental and land A purchase limits except in Case V where no land is purchased. When more land is avail­ able for rental in Case V, both land A and land B are rented in the optimal solution but no land is purchased. clearly This indicates that renting land is more profitable than purchasing land for agricultural use if abundant land is available for rent. However, result is applied. care has to be taken when Land may have other values that considered in the model. this were not These values include purchasing land for inflation protection, capital gains, urban or industrial uses or simply for prestige. No woodland is cleared in any case investigated. This indicates that converting woodland into cropland at the cost of $500 per acre is not economically justified under the assumed prices and product conditions. This result is con­ sistent with the real situation in the sense that most farmers visited indicated that they had no intention to clear woo d­ land due simply to the high clearance cost. However, they also indicated that the woodland could be cleared if the government could subsidize a part of the clearance cost. — The annual rental rate of $30 per acre used in this study is low compared to the land price of $500 per acre. The 78 amount of subsidies desired varied between $200 and $300 per acre depending on the amounts of initial clearance cost. The programming results show that no plowable pasture land is cleared in all cases except in Case I in which only 60 acres of land is permitted to be rented and purchased. This indicates that some plowable pasture land or low-costwoodland^ is likely to be cleared at the cost of $395 per O acre for cropland if product prices remain high and little land is available for rental and for purchase. This result is consistent with the current trends on a south central Michigan farm. In many cases, plowable pasture land and low- cost woodland were cleared at costs below $395 per acre in 1972 by a farmer who had little opportunity to acquire land by renting and/or through purchasing. The shadow prices for selected resources are presented in the lower part of Table 4.8. Reading across the table, one can observe the effect of changing the levels of land resource availability on shadow prices of various resources. The shadow price of land decreases without exception as more land is ob ­ tained. For example, when the level of land availability was fixed at 60 acres in Case I, cropland had a value in use of ^Low-cost woodland is defined as woodland which can be cleared at the cost of $395 or less per acre. ^Among the $395, the clearance cost accounts for $245 per acre and tiling cost $150 per acre; thus drained and cleared plowable pasture can be brought into crop production merely by covering the opportunity cost of using it for pasture which is not more than $20 per acre. (See R. L. Me e k h o f , L. J. Connor and S. B. Nott, "Field Rental Rates in Michigan," Extension Bulletin, E-683-Rivised May 1974). 79 $119 per acre but its shadow price dropped all the way down to $35 per acre in Case V where land was more abundant. On the other hand, the shadow prices of other resources increased consistently as more land is acquired. ous that in linear programming, It is obvi­ the shadow price of a restrict­ ing resource increases as the amount of another resource is increased. It should be remembered that the shadow price of a resource indicates the contribution to optimum income of the last unit of resource. Thus the twofold effect of the opera­ tion of the law of diminishing returns is demonstrated in linear programming. The same phenomena can also be observed on other representative farms (see Table B-l to B-3 in Appendix B ) . Examination of the shadow prices of various resources in Case V where land was abundant, revealed several conclu­ sions about potential expansions in farm size. The very low shadow prices on rental land and zero shadow price for purchased land indicate that it would not be profitable to expand farm size along the extensive margin. It also implies that land resource is no longer a limiting factor in the optimal solution. On the other hand, the high shadow price on credit indicates that it would be profitable for a farmer to borrow such credit if further sources of credit were made available at the prevailing rate of interest. The comparatively high shadow price of labor (includ­ ing managerial labor) indicates the desirability of increasing 80 in the use of labor in optimal solution. It also indicates that labor is in short supply. Judging from the high shadow prices of labor and capital in Case V, it is obvious that these two factors are the main 9 resources that restrict the further expansion of farm size. The desirability of expanding farm size as shown by the programmed solutions imply that (1) land values in the studied area will continue to be bid up as farmers are seeking more land for farming; (2 ) inasmuch as farm sizes tend to be stable, the land price of $500 per acre and the annual rental rate of $30 per acre used in this study was too low for land for farm­ ing purposes and (3) more unused cropland, and plowable pas­ ture land are expected to be brought into cultivation if product prices remain high with stable input prices. Since quite a few acres of land were either diverted by government set-aside programs or simply idle in 1972, an increase in crop area by expanding the extensive margin of cultivation was indicated as likely to occur after the termination of the government production control programs. In fact, this has taken place. However, the programmed results indicate that farm size in the studied area would not be expected to expand without limit even under conditions of plentiful land supply. with the rise in land values, Along labor (including managerial labor) and capital would eventually become the main restrict­ ing resource to limit the further expansion of farm size. ' g The same analysis can be applied to the other repre­ sentative farms (see Table B-l to B-3 of Appendix B ) . 81 The shadow prices of a unit of excluded crop rotations in each case are presented in Table 4„9. It should be noted that the value imputed to excluded or non-basis activity indicates the amount by which the opti­ mum income would be reduced if one unit of that activity were forced into the optimum solution. Therefore, one can easily identify close competitors to those activities in the optimal organization. The nearest competitive rotations in Case I are CCOW and CCCCS as shown by their near zero shadow pri ce s. Reading across the table, one can observe the change in competitive position of a unit of each crop rotation as more land is acquired. It is interesting to note that the competitive posi­ tion of a crop rotation changes as farm size increases. However, the direction of change is not the same for each crop rotation. Some crop rotations become more competitve while the others less competitive when a farm is permitted to acquire more land. For instance, CB rotation loses its competitive position consistently as more land is obtained. This is indicated by its increasing shadow price as more land is supplied. In contrast, WS rotation becomes more competitive as more land is obtained. This is shown by its consistently decreasing shadow price as farm size increases. Also, one can observe that CCOW rotation remains the most competitive position while CS rotation appears the least competitive position in all cases. 82 Table 4.9. Crop Rotation Shadow Prices of a Unit of Excluded Crop Rota­ tions Under Variable Land Resource Level on Large Cash Grain Farm (Model II) Case I Case II Case III Case IV Case V CB .74 .82 7.18 5.23 11.31 CS 33.98 33.99 32.76 30.58 32.35 WS 32.09 32.01 24.42 23.31 12.15 CBW 2.71 2.67 2.93 4.11 7.12 CBS 6 .79 7.06 12.38 6.15 3.81 COW 3.53 1.90 3.26 6.00 12.53 BCO 15. 03 15.60 29.16 26.21 43.33 CBO 10.06 10.63 24.19 21.09 36.99 SCO 17. 93 18.55 24.98 21.04 27.01 CCB 5.95 5.99 12.61 14.13 40.98 CCS 5.58 5.66 5.15 3.13 NA 6.87 7.00 16.86 CCCB NA 1 NA CCCS 2.79 2 .83 2.57 1.57 .09 CCBW 5.01 4.92 5.44 7.92 14.00 CCOW --- --- --- --- --- CCBS 8.37 8.59 14.20 8.25 .93 CCCBW 2.22 2.09 2.86 6.35 14.09 CCCCS CCCBS --- 6.18 --- 6.36 NA 12.20 NA 8.14 'NA denotes the item is not applicable. .18 10.34 83 Optimum Organizations Under Various Price Combinations (Model II) This section presents the resulting optimal solutions of representative farms under a number of different price combinations. Model II is used to investigate the effect of change in prices on land use, scale of operation and farm income. The initial resources are the same as those previously used in the Model II except the assumption made for the land availability for rental and/or purchase. The assumed quantity of land for rent was 50 acres and the quantity for purchase was 50 acres. Five different product price combinations were studied for corn, soybean, wheat, oats and field beans as presented in Table 4.10. In each case, price ratios among products are different as the same optimum plans would result if constant price relationships were maintained among products and inputs. Results are presented here only for the large size representative farm situations. The results of the other representative farms are in Appendix B. Table 4.11 presents a summary of optimum land use, resource transactions and shadow prices of selected resources for large farms for the five price combinations. Reading across the table, one can observe the effects of price variations on the optimum farm organization in terms of net r e t u r n s , levels of specific crop rotations and credit used. Table 4.10. Product Levels of Product Prices Assumed in Each Case (Model II) Unit Case I1 (Low Price) Case II (Fall 1973 Price) Case III2 (High Price) Case IV3 (Low Wheat Price) Case V (Fanner's Desired Price) Com Bu. $ 1.80 $ 2.25 $ 2.48 $ 2.25 $ 2.34 Soybean Bu. 4.40 5.50 6.05 5.50 5.34 Wheat Bu. 2.13 4.25 4.25 3.00 4.03 Oats Bu. .90 1.25 1.38 1.25 1.49 Field Beans cwt. 12.00 15.00 19.50 15.00 18.09 ^"Prices of com, soybean, oats and field beans are 20 percent lover and wheat price is 50 percent lower than those in Fall 1973 price. ^Prices of com, soybean, oats are 10 percent higher, and field beans 30 percent higher than those in Fall 1973 price. 3A11 product prices are the same as those in Fall 1973 price except wheat price at $3.00 per bushel. Table 4.11. Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Large Cash Grain Farm (Model II) Price Combination Net Return CBS CB WB CCCB Credit Used Unit Case I (Low Price) 51,068 (FallC 1973Iprice) Case III (High Price) 77,195 96,500 --- __ Case IV (Low Wheat Price) Case V (Farmer1s Desired Price) $ acre acre acre acre --- $ 30,288 24,734 34,072 33,309 34,072 hour --- -- -- -- -- 446 92 460 78 -- 72,248 284 269 --- 280 258 87,928 -—— -- 284 269 Resources Acquired Managerial labor hired Unskilled labor hired Land rented Land purchased Woodland cleared Man hour acre acre acre -- 334 50 50 -- 161 50 50 301 50 -- 50 -- 404 50 50 301 50 50 -- P lowable pasture cleared ... acre ——— 15 15 Off-Farm Employment Managerial labor Family labor Shadow Prices hour 587 587 587 587 587 hour 411 411 411 411 411 70 40 17 117 87 64 135 105 82 91 61 37 129 99 75 Cropland Rented land Purchased land $/acre $/acre $/acre April-May Labor June-July Labor August Labor September-November Labor Cash Chattel Mortgage Real Estate Mortgage Managerial Labor Woodland Plowable Pasture $/hour $/hour $/hour --- $/hour $ $ -- $ $/hour $/acre $/acre ----- 3.26 -3. 26 .09 -- -- ------ 3.26 3.26 .09 -- 3 .26 -- 3 .26 .09 -- 3.26 .09 -- --- -- 3.26 3.26 3 .36 16 -'— --- -- 3.26 3.26 .09 -2.09 -- 1.67 9.53 86 In Case II (i.e., under Fall 1973 prices), the optimal solution includes 460 acres of WB rotation and 78 acres of CCCB rotation. However, wheat is not in the optimal solu­ tion for Case I where wheat price is relatively low. In Case III where field beans have a strong price advantage, CB and WB rotations enter the optimum plan. Wheat leaves the optimal organization at $3.00 per bushel with other crop prices constant at Fall 1973 prices as shown in Case IV. The need to borrow to attain optimal organizations is also shown in the table. One of the interesting price combinations is the farmer's desired price as indicated in Case V. the survey, As part of data were collected from the farmers concerning the product prices that would induce farmers to bring more unused land (including woodland and plowable pasture land) into cultivation. At this price combination, the program­ ming results show that plowable pasture land was cleared up to the limit permitted by the model. This result tends to justify what farmers thought to be appropriate prices to give them an incentive to bring more land into cultivation. Specific resources acquired and their shadow prices for the large farm are also presented in the table. No additional managerial labor is acquired in any case; however, some seasonal labor is required to attain the optimum solu­ tion. The amounts of unskilled labor required range from 161 to 404 man hours. 87 In all cases, the farmer rents and purchases all the available land and increase crop acreages„ is cleared; however, No woodland 15 acres of plowable pasture land is cleared at the cost of $395 per acre in Case III (i.e., high price) and Case V (i.e., farmer's desired price). This indicates that under higher product prices and more restricted land supply conditions, plowable pasture land and low-cost woodland would likely be cleared and converted to a c r o p l a n d . ^ Both family members and operator worked off-farm up to the limits of the restrictions. The results are consis­ tent with what cash grain farmers were doing in the south central area in 1973. The shadow price of land varies directly with the change in product price, i.e., shadow price of land increases as product prices increase. The shadow price of land indi­ cates that it would be profitable to expand farm acreage under the assumed prices and output conditions. In most cases, June-July labor and September-November labor were limiting resources, but August labor was not exhausted. In all cases, the capital is not a restricting resource under the assumption that up to 50 percent of real estate assets may be mortgaged. This is reflected by the zero shadow prices of chattel mortgage and real estate mortgage credit. ^ T h i s result is consistent with the real situation. In many cases, this has actually occurred on farms in south central Michigan. 88 The shadow prices of a unit of an excluded rotation under various price combinations are presented in Table 4.12. Reading across the table, one can observe the change in competitive position of a unit of each crop rotation when product price changes. In Case I where all product prices are lower than 1973 fall price, WB and CBO rotations are in the most competitive position as reflected by the near zero shadow prices for these activities. The shadow prices for WS rotation is $37.77 indicating that it is in the least competitive rotation. In contrast, in Case III where all product prices except wheat are higher than the 1973 fall price, CBS and CBO rotations are on the verge of coming into the program as indicated by the near zero shadow prices for these acti­ vities. The shadow price of CS rotation is $50.96 which indicates that the rotation is the most expensive to force into the optimum plan. The shadow prices of the other crop rotations can be interpreted in a similar way. Application and Limitations of the Model Some remarks should be made concerning the application of the results derived from this study. place, In the first the assumptions concerning credit supplies in the model are based on the usual practices of institutional lenders. No provisions were made in the model for internal credit rationing due to uncertainty. In reality, farmers may prefer a much lower ratio of debts to total assets than Table 4.12. Shadow Prices of One Unit of an Excluded Rotation Under Various Price Combinations— Large Faun (Pbdel II) Crop Rotation Case I (Lew Price) CB CS WB WS CBW CBS OOW BCO CBO SCO CCB CCS CCCB CCCS OCBW CCOW CCBS CCCBW CCCCS CCCBS Pggp TT (Fall 1973 Price) NA1 32.47 — 37.77 13.45 NA 14.48 4.97 — 13.29 15.95 20.99 20.74 28.94 26.48 34.80 6.23 34.43 34.77 20.86 .82 33.99 NA 32.01 2.67 7.06 1.90 15.60 10.63 18.55 5.99 5.66 NA 2.83 4.92 — 8.59 2.09 — 6.36 Case III (High Price) NA 50.96 NA 49.80 19.30 Case IV (Low Wheat Price) NA 34.20 -- NA 46.10 NA 44.94 16.74 26.18 4.97 33.16 9.68 NA 6.94 4.97 — — — 19.17 21.80 32.70 32.44 46.50 38.22 52.42 18.77 52.02 66.52 32.57 9.52 12.18 13.46 13.20 17.64 18.95 23.50 4.58 23.13 22.10 13.33 16.61 19.24 27.58 27.33 38.83 33.10 44.75 16.21 44.35 56.29 27.46 — - ^NA. denotes does not apply. Case V (Fanner's (Desired Price) ....... -1 — 21.07 4.97 90 the limits imposed by lending agencies. These facts were repeatedly indicated by the farmers interviewed. quently, Conse­ the actual demand for land and associated durable assets may be much less than those indicated. Secondly, the model does not consider the overall aggregate effects of large scale adoption of the results on product and input markets. The optimal solutions in the model call for expansion of farm size and associated durable assets to produce specific crops. farmers bid for resources, However, if all land and associated input prices would increase while product prices would likely decrease. This trend would limit the expansion of farm size. Thus, in reality the farm size would be smaller than that indicated in optimal p l a n s . Lastly, knowledge. the model assumed that farmers possess perfect However, as perfect knowledge does not exist in the real world, risk and uncertainty would affect adjust­ ment of land use, enterprise levels and farm size. Some of the limitations of this study should be noted. Problems concerning the stock and flow characteristics of resources are not sufficiently handled by this model. was shown in the model, As the acquisition and salvage of dura­ ble assets are measured in terms of stock unit. However, the productivity of the stock stems from the flow of services generated by the stock. The objective functions for acqui­ sition and salvage activities are for services per production 91 period with the ratio of flow to stock determined by the utilization of the flow in production activities. The stock and flow conversion problem is closely related to the user cost problem which was not handled in this study. Solution of the user cost problem could p r o­ bably destroy the independence of activities to make it impossible for a linear programming to handle investment and disinvestment. The unrealistic assumptions such as perfect divisi­ bility, linearity in the input-output coefficients and single-value expectations built in the model continue to be a problem. The optimal solutions obtained from a linear program are restricted to the particular activities or alternatives covered in the model. As previously mentioned, the deter­ mination of the factor combinations within each alternative is exogenous to the model. Erroneous combination of factors within the alternatives would result in erroneous solutions from the model. The land price of $500 per acre and annual rental rate of $30 per acre assumed in the model are considered too low. 11 As such, the consequent program­ ming result is the expansion of farm size for all represen­ tative farms by renting and/or through purchasing land up to the limit permitted by the model. Land often becomes "^The land price reported by farmers were probably lower than what they would have actually to pay when they purchase land for farming p u r po se s. 92 the most limiting resources as reflected by its high shadow price. On the other hand, the plowable pasture clearance cost ($395 per acre) used in the model is too high. As a result, plowable pasture was cleared only under high product price and more restricted land supply conditions. Age of an operator and his desire to increase farm size are not adequately handled in the model. No provision was made to limit the expansion of farm size for an old operator. Wage rate of off-farm work for old farmers was assumed as same as that of young farmers which did not correctly reflect the real situation to some extent. The optimum solutions are affected by the assumptions made relative to available off-farm employment. The model assumes off-farm employment is available only for a specified number of days in five seasons. Full-time off-farm employ­ ment should be permitted so that one could investigate which farms would go out of business. In applying the results of this study, the above mentioned limitations have to be kept in mind and the careful interpretation must be made. Summary The objective of this chapter was to ascertain pro­ fitable adjustments in the farm organization and land use for cash-grain farms in south central Michigan in response to the increasing demand for agricultural products. Linear programming was used to determine optimum farm plans under (1 ) farm resources fixed at initial level, (2 ) 93 land, labor and machinery investment variable and (3) product prices variable. Investment/disinvestment theory was incorporated into situations (2) and (3) though the user cost problem remained unhandled. Cash grain farmers were classified by their desire (or willingness) and ability to make farm organization adjustments. One variable, age of operator, was used to represent homogeneity with respect to willingness to make adjustments. Another variable, net worth, was used to represent homogeneity in terms of ability to make changes. Thus, farmers were stratified by age of operator and net worth as a major determinant for setting up representative farms. Two age classifications were: over 55 years. 24 to 55 years and Three net worth classifications were $30,000 to $80,000, and $80,000 to $150,000 and over $150,000 which were defined respectively as small, medium and large farms. The analysis was first given for Model I with crop­ land and associated durable resources fixed at 1972 levels. Secondly, the optimal organization was presented for Model II which permits variation in the land resources and asso­ ciated durable assets. Emphasis was placed on the effects « of change in land resource availability on optimal land use, farm organization and competitive position of each crop rotation. Lastly, the programmed solutions were given for Model II under a number of different price combinations. Application and limitations of the model were discussed in the last part of the chapter. CHAPTER V FUNCTIONAL ESTIMATION OF RESOURCES PRODUCTIVITY This chapter presents the statistical results of fitting the production function and the resulting estimates of re­ sources productivity. As previously mentioned, the Cobb- Douglas function was employed to estimate the value produc­ tivity of the various categories of inputs and investments. Three separate functions were fitted to the data gathered from sixty-one cash grain farms. In each case, somewhat different estimates of value productivity resulted for each category of inputs and investments. However each fit provided valuable information which was used to obtain more realistic estimates of marginal value productivities for,various inputs and investments. The Data The data obtained from each of the sixty-one farms for the calendar year of 1972 were as follows: The dependent variable was Y, or gross income, independent variables were: X-^, land, in tillable acres, X 2 , labor, in months, X^, productive operating expenses, X^, machinery investment, X^, buildings, in dollars. 94 in dollars, in dollars, and the 95 Gross income (Y) included all crop income from produc­ tive resources for the year 1972. was excluded; Income from livestock however, crop production utilized by livestock was credited as gross income. Land and pasture rent, custom work or machinery rent were also included in gross income since they represented a return to productive factors on a farm. Such sources of income as government soil bank pay­ ments, subsidies, rental values of the farm home and invest­ ments in other business were not included. The landlord's share was credited to gross income in the case of crop-share renting and the corresponding input share on the part of the landlord was included in the appropriate input categories. In the case of cash rent no charge to expenses was made as the rented land was included in the tillable acres. The prices used in computing the value of farm products were the average prices for each crop in Michigan in 1972.^ These prices per bushel were: soybeans; were: $1.12 for corn; $3.27 for $1.62 for wheat and $.76 for oats. Other prices $10.53 per cwt for dry beans and $29.96 per ton for hay. Land (X^) was measured in actual tillable acres used in crop production. Diverted tillable acres, land, unoperated cropland, soil bank land for pasture, woodland, ditches and farm building lots were excluded. ^Sources of Data: Michigan Agricultural Statistics, Michigan Department of Agriculture, July 1973, pT 40. 96 Labor (X2 ) was measured in man-month equivalents used on the farm with regard to crop production including custom work, machinery maintenance and crop storage. furnished with hired machine custom work, connection with livestock, Labor labor used in and unproductive labor was excluded as its value is in productive operating expenses. Productive operating expenses (X^) included all inputs that would be expected to yield at least one dollar return for each dollar spent. or machinery hired, These inputs included custom work fertilizer and lime cost, power and machinery and seed cost, etc. In order to avoid double accounting, machinery depreciation and machinery mainten­ ance charges such as tire purchases and major overhauls were excluded from operating expenses. insurance, Furthermore, interest and tax charges were excluded, they were not considered productive expenses. that the earning power of machinery, expenses must cover such charges. cost, since This means land and operating In computing fertilizer the residual values were subtracted from 1972 expenses if these expenses were much larger than those for a normal year. Machinery and equipment investments (X^) were valued at what a farmer thought they were worth in farming in early 1972. Values to farmers are ordinarily greater than salvage or sale values, but less than the replacement costs of m a c h ­ inery of the same age, quality and condition. Machinery 97 and equipment used for livestock production was excluded as was livestock income. Building investment (X^) was estimated in a similar method as used in measuring machinery investment. Buildings idled or those used for livestock were excluded. Fitting the Production Function The data gathered from the sixty-one sample farms were used as a basis for three regression analyses. The first equation includes five variable input categories, i.e. land, labor, operating expenses, machinery investment and buildings. In the second equation, buildings were omitted in an attempt to obtain more reliable estimates of the remaining production coefficients. In the final equation, a restriction was imposed which made the sum of the regression coefficients equal to one; this restriction imposed constant return to scale. The First Equation The data collected from the farms were first summarized in the categories of gross income and the variable inputs described previously. the logarithm form, These figures were then converted to and fitted to a Cobb-Douglas production function. The estimated regression coefficients, together with the relevant statistics, are shown in Table 5.1. In the logarithmic form, function w a s : the estimated Cobb-Douglas 98 Table 5.1. Regression Coefficients and Related Statistics of the Estimated Production Function (61 Farms) Regression Coefficients (fii) Standard Error of Coefficients T-Statistic for Testing H : b. = 0 0 1 1.28665 0.25522 5.0414 0.51261 0.08834 5.8024 0.25830 0.06589 3.9203 Operating expenses, Dollar (X3) 0.24728 0.11443 2.1610 Machinery investment, Dollar (X^) 0.09279 0.08910 1.0414 Buildings, Dollar (X.) 0.06343 0.04727 1.3418 Variables Constant terms Land, acre (xx) L ab or , month (X2 ) Multiple correlation coefficient, R = 0.9601 Coefficient of determination, R = 0.9217 Sum of regression coefficients, 1.17441 Log Y = 1.28665 + .51261 log X ]_ + .25830 log X 2 + .24728 log X 3 + .09279 X 4 + .06343 log X 5> The estimated regression coefficients, b^, indicate the percentage change in gross income associated with a one percent change in factor inputs. For example, one percent increase in cropland is accompanied by a 0.51261 percent increase in gross farm income; a one percent increase in farm labor is associated by a 0.25830 percent increase in gross farm income. 99 The sum of the regression coefficients was 1.17441, indicating increasing returns to scale, i.e. with an increase in all factors by one percent, gross income would increase by more than one percent (1.17 percent). A test of significance indicated that the results differ signi­ ficantly from 1.00 (constant returns) at a five percent probability level. A significance test of the sum of the regression coefficients will be discussed in more detail in the following section. The multiple correlation coefficient was 0.9601, indicating that the correlation between the dependent variable and the combined independent variables was fairly high. The coefficient of determination (R ) was 0.9217, which suggests that 92.17 percent of the variation in the logarithm of the estimated gross income was associated with variation in the independent variables included in the analysis. The remaining 7.83 percent of variance unexplained by the independent variable was likely due to such factors as weather conditions, timing, aggregation or index number problems, and differences in the appraised value of investments. /*V The estimate of the logarithm of gross income (log Y) at the geometric mean was found to be 4.16800, or in natural numbers, 14,723 dollars. The standard errors of estimate (S) of the dependent variable (log Y) was 0.11866. This implies that under the production conditions prevailing in 1972, the logarithm of the actual average gross income (log Y) of the typical (geometric mean) farm would be expected to fall between 4.16800 + 0.11866 in 68.27 percent of the sample, or in natural numbers, between $11,203 and $19,349. This also indicates that one farm out of three farms with the geo­ metric mean organization would be expected to have a gross farm income of less than $11,203 or greater than $19,349. The marginal value productivity of each factor input for a typical farm is computed from the equation /N MVP = b. 2xi 1 Xi W h er e: MVP b^ X • = the marginal value products of input X . ; X = the regression coefficient of log X ^ ; A Y = geometric mean of gross farm income; and = geometric mean of factor input, X ^ ; and are shown in Table 5.2. From the equation of computing marginal value products, it is apparent that the reliability of marginal value products n The term "typical farm" is used to indicate a farm having geometric mean quantities of the input categories for the farms included in the study. A geometric mean is better than an arithmetic mean for studying a group of farms because it gives proportionately less weight to the few large farms included in the sample and tends to be more representative of the majority. 101 estimates are closely related to the level of significance of the regression coefficient. Table 5.2. Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) Input Category Quantity of Input (Geometric Mean) Regression Coefficient Marginal Value Product (Dollars) X^ Land 142.08 acres .51261 53.12 X2 Labor 7.36 months .25830 516.71 X^ Operating Expenses $5,265 .24728 .691 X^ Machinery Investment $16,886 .09279 .081 X^ Buildings $6,619 .06343 .141 One way to test the regression coefficients for signi­ ficance is to test the coefficients against zero as a null hypothesis using t-test. The regression coefficients were significantly different from zero at the .05 percent level for land (b-^) and labor ^ 2) , five percent level for opera­ ting expenses (b^), and were not significantly different from zero at the five percent level of significance for machinery (b^) and building (b^) investments. A better way to test the significance of the coeffi­ cients is to compare the estimated coefficients with the coefficients necessary to yield marginal value products equal to a set of minimum reservation prices or returns for those factors. 102 On the basis of observation and discussion with farmers, extension workers and farm management specialists, the following were considered as reasonable minimum expected reservation prices or returns:^ Land medium quality good quality $41.00 per tillable acre $50.00 per tillable acre Labor family labor operator's labor Entrepreneurial labor $400.00 per month $500.00 per month Operating Expenses $833.00 per month $1.04 per $1.00 of expense Machinery Investment 25 percent Building Investment 10 percent The minimum expected return to medium quality land was based on an eight percent interest charge for land valued at $400.00 per acre, plus seven dollars for taxes and two dollars for maintenance. Good quality land was valued at $500.00 per acre with the same interest rate, plus eight dollars for taxes and two dollars for maintenance for a reservation price of $50.00 per acre. The minimum expected return to family labor and operator labor was based on a wage rate of $ 2.00 per hour for the former and $2.50 for the latter using eight hours a day, 25 days a month, 3 as a basis for computation. Dr. Glenn L. Johnson of the Department of Agricultural Economics of Michigan State University was very helpful in developing these minimum expected reservation prices. 103 The expected return to entrepreneur was based on a yearly income of $10,000.00. For operating expenses, a return of one dollar plus four percent interest (eight percent for an average investment period of six months) on current crop expenses was expected. The return to machinery investment must cover maintenance, interest on investment, insurance and taxes. depreciation, It was estimated that a twenty-five percent return on machinery investment was reasonable consisting of ten percent for depreciation, two percent for insurance, maintenance and ten percent for interest. three percent for The minimum return to buildings must cover five percent of deprecia­ tion and maintenance and five percent interest on investment. The estimated minimum expected return was substituted A bY for the MVP in the equation MVP = These equations xi xi i were then solved for the coefficients which would yield these minimum expected returns. Table 5.3 compares these coefficients with the estimated regression coefficients. As shown in the table, the estimated coefficients were lower than the coefficients required to yield minimum return for operating expenses, machinery investment and entrepreneurial labor. The differences were large enough to fall beyond the 68.27 percent confidence interval for cash expenses and the 95 percent confidence interval for machinery investment. On the other hand, the estimated coefficients were higher than the coefficients required to yield minimum 104 Table 5.3. Comparison of Estimated b^'s and b^'s Necessary to Yield Minimun Marginal Value Products Variable Estimated bi Standard Error of Estimated b. r b^ to Yield Difference Minimum Return Land, acre , *L 0.51261 0.08834 0.39566 (MFC^. = 41) 0.11695 0.48251 (MFC^ = 50) 0.03010 0.19996 (MFCj^ = 400) 0.05834 0.24995 (MFC^ = 500) 0.00835 0.41642 (MFC^ = 833) -0.16342 Labor, month, *2 Operating Expenses, Dollar, Machinery Investment, Dollar, X. 4 Buildings, Dollar, X,. 0.25830 0.06589 0.24728 0.11443 0.37191 (MPC^ = 1.04) -0.12463 0.09279 0.08910 0.28673 (MFC^ = .25) -0.19394 0.06343 0.04727 0.04487 (MPC^ = .10) 0.01856 105 return for land, operator and family labor and buildings. The differences, however, are small enough to fall within the 68.27 percent confidence intervals for land (compared at MFC^ = $50.00), operator and family labor and buildings. The estimated coefficient for labor was lower than the coefficient required to yield the reservation price (entrepreneurial labor valued at $833.00 a month), that coefficient falling beyond the 95 percent confidence intervals. The reliability of the estimated regression coeffi­ cients is affected by the correlations among the independent variables, the range of the independent variables and the sample size.^ Such influences are accounted for in the standard errors of the regression coefficients. Quite often, system of errors may exist, due to the high intercorrelations among the independent variables. In such cases, if the marginal value product of one input is overestimated the MVP of another is underestimated. The simple correlation coefficients were computed as in Table 5.4. It is easily seen that the correlation between land (X-^) and operating expenses (X^) is high. Lower degrees of correlation were found between operating expenses (X^) and 4 Notes taken on lecture of production economics given by Dr. Glenn L. Johnson, Michigan State University, 1967. For a detail discussion see: Ezekiel, Mordecai, Methods of Correlation Analysis. New York: John Wiley and S o n s , I h c : ~ r 9 4 9 7 p'- 5U2 .---- 106 machinery investment (X^), between land (X^) and machinery investment (X^), and between labor ( ^ ) and operating expenses (X^) . Table 5.4. Simple Correlation Coefficients Between Each Input Category X3 X2 X5 Buildings X4 Machinery Investment Operating Expenses Labor X-^ (Land) .50612 .77689 .8860 .50500 X 2 (Labor) .41233 .55585 .67783 Xg (Operating Expenses) .53894 .82816 X, (Machinery Investment) Therefore, .66347 the estimated coefficients may involve compensatory errors for the above-mentioned pairs of inputs. In other words, for any set of inputs mentioned, one of the coefficients may be overestimated and the other underesti­ mated compared to the true regression coefficients with corresponding errors in the marginal value product estimates obtained from the coefficients. The estimated marginal value product for cash expenses appears low.^ In view of the fairly high correlation exist­ ing between land and operating expenses (.89) and between ^The low earning power of cash expenses might be partly attributed to the high percentage (51 percent) of part-time 107 land and machinery investment (.78), it appears that the regression coefficient for land is overestimated with com­ pensating underestimation of the coefficients for cash expenses and machinery. Thus the estimated marginal value products of cash expenses and machinery are regarded as low while the estimated marginal earning of tillable acres of land as high. By the same token, the correlation between labor (X2) and current expenses (X^) may have caused the estimated marginal value product of labor to be high and the estimated marginal value product of operating expenses to be low. In using the results of this study to find profitable farm reorganization, these likely errors have to be taken into account. The Second Equation The reliability of the estimated marginal value produc­ tivity for building investments (X^) was not high as indicated by the high standard errors of its coefficient (b^). This is probably due to difficulty in measuring the value of buildings. The amount of farm building investment is not proportional to farm size though building investments were correlated with other inputs at simple correlations of .41 farms among 61 farms interviewed. Generally, a part-time farmer tends to spend more cash for inputs in order to have more time for off-farm work. 108 or higher. The correlation between farm gross income and buildings was comparatively low (y = .587). yx5 In an attempt to obtain a better fit with greater con­ fidence in the estimates of the regression coefficients, buildings (X^) were then excluded. omitted, When buildings were the multiple coefficient of determination was reduced by only .0025, an insignificant amount. The esti­ mated coefficients (b^'s) for the other inputs and the relevant statistics are shown in Table 5.5. Table 5.5. Regression Coefficients and Related Statistics of the Estimated Production Function (61 Farms) Regression Coefficients (b^) Standard Error of Coefficients T-Statistics for Testing H: b. = 0 1 1.32195 0.25567 5.1706 xi 0.51541 0.08895 5.7945 Labor, month, X 2 0.26672 0.06605 4.0379 Operating Expenses , Dollar, X^ 0.23763 0.11501 2.0661 Machinery Investment, Dollar, X^ 0.14711 0.07994 1.8403 Variables Constant Terms Land, acre Multiple correlation coefficient, R = 0.9587 Coefficient of determination, R^ = 0.9192 Sum of regression coefficients, 1.16687 109 The results of the t-test performed on the regression coefficients indicate that the estimated coefficients were different from zero at level of significance of .05 percent for land and labor, 5 percent for operating expenses and 7.1 percent for machinery investment. coefficient is 0.9587, The multiple correlation indicating the correlation between the dependent variable and all the independent variables is fairly high. The coefficient of determination (R^) is 0.9192, implying that the four explanatory variables specified in the model taken together explain 91.92 percent of the vari­ ation in gross farm income. The sum of the regression coefficients was 1.16687, indicating increasing returns to scale since gross income would increase by more than one percent if all factor inputs were increased simultaneously by one percent. A significance test suggests that the sum differ significantly from one at fi a five percent probability level. In the Cobb-Douglas production function Y^ = 3 -^ + &2^i2 + £ 3X ^3 + where Y = log ou to ut , and X ^3 = log capital input, = l°g labor input, the hypothesis of constant $2 + ^3 3 . + ft, = a can be returns to scale is equivalent to the hypothesis H Q : = 1. tested In general, the hypothesis H : O by noting that (3j+ 3^ Sg + g = /Sg2 + S g 2 j k j k J - a)/Sg + g j + 2 Est.Cov“T B ~ 3^) • K ^^ - k w ^ ere k This test can be 110 Based on the sums of coefficients of factor inputs and the result of statistical tests, increasing returns to scale seem to prevail in the sample studied. However, an attempt was made to further examine the result by dividing the sample farms into two size gro u ps . A large farm was defined as one with 150 acres or more of cropland. versely, Con­ one with less than 150 acres was classified as a small farm. The typical farm among the 30 large farms had a gross income of $38,279. of labor, It had 352 acres of land, 11.80 months $12,210 in operating expenditures and $35,700 in machinery investment. On the other hand, the typical organization among the 31 small farms earned a gross income of $ 8 ,866 . land, The associated inputs included 85 acres of 7.97 months of labor, $3,302 in operating expenses and $10,692 in machinery investment. Cobb-Douglas produc­ tion function was then fitted separately for each group of farms. The sums of estimated regression coefficients, together with the relevant statistics for two groups of farms, are shown in Table 5.6. It is interesting to note that the sums of coeffi­ cients of the large and small farms reveal very distinct extended to a sum of more than two regression coefficients. See J. Kmenta, Elements of Econometrics. New York: The Macmillan Co ., 1971, p"! 372. Table 5.6. Farm Cateogry Sums of Regression Coefficients and Related Statistics of the Estimated Production Functions for Large Farms (30) and Small Farms (31) Sum of Coefficients Zb. l Standard Error of Eb-s Degree of Freedom T-Values for Testing H : Zb. = 1 O 1 Results of Test (57o) Large Farm Average 352 Acres $38,279 11.8 months With Buildings Without Buildings 1.02892 .097978 .08089 24 .35749 Accept H q .07824 25 -.25847 Accept H q Small Farm Average 85 Acres $ 8,866 7.97 months With Buildings 1.15895 .13529 25 1.17492 Reject H J o Without Buildings 1.15403 .061264 26 2.51425 Rej ect H J o 112 differences between the two groups. In the large farms group (without buildings), the sum of the elasticity coeffi­ cients is a little smaller than unity indicating a slight tendency to diminishing returns to scale. However, in the small farm group, the sum of the regression coefficients is larger than unity, scale. suggesting increasing returns to Increasing all factors by one percent will be associated with an increase in gross income of 0.98 percent in the large farms group and 1.15 percent in the small farms g roup. A test of significance indicated that, percent probability level. at a five The results do not differ signi­ ficantly from linear for the large farms group. However, the results differ significantly from constant returns for the small farms group. Judging from the sums of coefficients of factor inputs and the results of significance test, constant returns to scale seem to prevail at the farm firm level for large farms and increasing returns to scale prevail for small farms in the region studied. This can be explained partially by the fact that small farms have a high degree of part-time farming and consequently rely more on nonfarm income. often than not, these farmers cultivate their land in their spare time from off-farm occupations. Labor and machinery would not be used efficiently on the smaller More 113 farms under this condition due to acreage limitations and time constraint imposed on labor. of labor, With increased amounts land, machinery investment and operating capital, the greater volume could permit farmers to devote more time to farming and do a better job of using their resources. The estimated gross income for all farms, at the geometric mean, was computed by inserting a constant term (log A = 1.32195), the estimated b^'s and the logs of the geometric means of the input categories in the pre­ diction equation. It was found that log Y = 4.16883 (or / N A Y = $14,751) with a standard error of estimate (S) of 0.11950, i.e., under the production conditions prevailing in 1972, log Y would be expected to fall between 4.16883 + 0.11950 for typical farm organization in 68.27 percent of the sample, or in natural numbers between $11,203.00 and $19,424.00. The marginal value products of land, labor, opera­ ting expenses and machinery investment for typical farm organization were computed as in Table 5.7. A comparison between the estimated regression coeffi­ cients and the coefficients necessary to yield minimum expected returns is shown in Table 5.8. The estimated coefficients were lower than the coefficients required to yield minimum return for operat­ ing expenses, machinery investment and labor when considering 114 Table 5.7. Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Casn-Grain Farms in Clinton and Ionia Counties) Input Category Quantity of Input (Geo­ metric Mean) Regression Coefficient Marginal Value Product (Dollars) X-j^ Land 142.08 Acres .51541 53.51 X 2 Labor 7.36 Months .26672 534.60 X~ Operating Expenses $5,265 .23763 .67 X^ Machinery Inves tment $16,886 .14711 .13 entrepreneur's return as a minimum return. The differences are large enough to fall beyond the 68 percent confidence interval for operating expenses and machinery investment, and the 95 percent confidence interval for entrepreneurial labor valued at $833 per month. On the other hand, the estimated coefficients were higher than the coefficients required to yield minimum return for land, operator and family labor. The differ­ ences, however, were small enough to fall within the 68.27 percent confidence intervals for better land (MFCV = $50) 1 and operator labor (MFCy = $500). 2 The estimated coefficient for labor was lower than the coefficient required to yield a return of $833 for entrepreneurial labor that the coefficient falling beyond the 95 percent confidence intervals. 115 Table 5.8. Comparison of Estimated b^'s and b^'s ISfecessary to Yield Minimum Marginal Value Products Variable Land, Acre Labor, Month Estimated b. 1 Standard Error of Estimated b. 1 0.51541210 0.08894869 0.26672362 0.06605426 *2 b^ to Yield Difference Minimum Return 0.3949074 (MFC^ = $41) 0.1205047 0.4815944 (MPC^ = $50) 0.0308177 0.1995796 (MFC^ = $400) 0.06714402 0.2494746 (MFCj^ = $500) 0.01724902 0.4156247 (MPC^ = $833) -0.14890108 Operating Expenses Dollar, 0.23763110 0.11501469 0.3712019 (MFC^ = 1.04) -0.1335708 Machinery Investment Dollar, 0.14710564 0.07993501 0.2861839 (MPC^ = .25) -0.13907826 116 The Third Equation, Assuming Constant Returns to Scale From the previous discussion, we have noticed that the sums of elasticity coefficients for the large and small farms reveal distinct differences between these two sizes. The sums of the regression coefficients are 0.98 and 1.15 for large and small farms, respectively. The former indicates a slight tendency to diminishing returns to scale, while the latter suggests increasing returns to scale. As estimated returns to scale for the large farms were not significantly different from one the data for all farms were fitted to a Cobb-Douglas production function imposing the restriction of constant returns to scale. The resulting estimated regression coefficients, with relevant statistics, together are presented in Table 5.9. The standard error of the regression coefficients was comparatively small for the constant term and land, resulting in a considerably large value of T-statistics. The results of the t-test indicate that the estimated coefficients were different from zero at levels of signi­ ficance of .05 percent for land, 5 percent for labor, one percent for operating expenditures and were not significantly different from zero at the 5 percent level of significance for machinery investment. 117 Table 5.9. Regression Coefficients and Related Statistics of the Estimated Production Function (61 Farms) with Z b . Forced Equal to 1. Variables Regression Coefficients (b±) Constant Terms 1.56313 .26180 5.9706 .45118 .09296 4.8537 Labor, Month X2 .15446 .05954 2.5944 Operating Expenses, Dollar, .32905 .11948 2.7541 Machinery Inves tment, Dollar, .06531 .08113 .8050 Land, Acre, Standard Error of Coefficients T-Statistics for Testing H: b± = 0 xi Multiple correlation coefficient, R = .9513 Coefficient of determination , R 2 = .9051 Forced sum of regression coefficient, 1.00000 The multiple correlation coefficient (R) is .9513, indicating that the correlation between gross income and all factor inputs specified in the model is quite high. o The coefficient of determination (R ) is .9051, suggesting that 90.51 percent of the variation in the logarithm of the estimated gross income was explained by the independent variables included in the analysis. 118 A The standard error of estimate (S) of the dependent variable (log Y) was .12836. This indicates that under production and price conditions prevailing in 1972, the logarithm of actual gross income would be expected to fall between 4.16881 + .12836 in 68.27 percent of the sample, or in natural numbers between $10,976 and $19,823. The marginal value products of each factor input for typical organization were computed as in Table 5.10. Table 5.10. Estimated Marginal Value Products of Typical Organization Farms (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) Input Category Quantity of Input (Geome­ tric Mean) Regression Coefficient Land,X^ 142.08 Acres .45118 46.84 L a bo r, X 2 7.36 Months .15466 309.57 Operating Expenses, $5,265 .32905 .92 $16,886 .06531 .06 Marginal Value Product (Dollars) X3 Machinery Investment, X4 The estimated regression coefficients were compared with the coefficients necessary to yield minimum expected return. The results of the comparison are shown in Table 5.11. 119 Table 5.11. Comparison of the Estimated b / s and the b / s Necessary to Yield Minimum Marginal Value Products Variable Estimated b. l Standard Error of Estimated b^ to Yield Difference Minimum Return bi Land, Acre .45118 .09296 xi labor, Month .15446 .05954 *2 .39491 (MFC^ = $41) .05627 .48159 (MPC^ = $50 -.03041 .19958 (MFC^ = $400) -.04512 .24947 (MFC^ = $500) -.09501 .41562 (MFC^ = $833) -.26116 Operating Expenses, Dollar, .32905 .11948 .37120 (MPC^ = $1.04) -.04215 Machinery Investment, Dollar, .06531 .08113 .28618 (MFC^ = $.25) -.22087 The estimated regression coefficients were lower than the coefficients required to yield minimum return for all input categories except land at the low price (MFCV X1 $41). The differences are large enough to fall beyond the 68.27 percent confidence interval for operator labor, 95 percent confidence interval for machinery investment and 99 percent confidence interval for entrepreneur (MFCV = $833). 2 120 The difference, however, is small enough to fall within 68.27 percent confidence intervals for land at the high price, family labor (MFCV = $400) and operating expenses 2 (MFCV = $1.04). 3 On the other hand, the estimated coefficient was higher than the coefficient required to yield minimum return for land at the low price, but the difference is small enough to fall within the 68.27 percent confidence interval. It is worth noting that the estimated coefficient for labor was lower than the coefficient required to yield a return on entrepreneurial labor of $835 a month, that coefficient falling beyond the 99 percent confidence inter­ vals. This suggests that the return in the agricultural sector in 19 72 was not high enough to provide an incentive to most potential entrepreneurs from the nonagricultural sector to enter cash cropping in central Michigan. Land yielded fairly good returns in the typical farm organization as shown in Table 5.10. On such a farm, the estimated marginal earning of tillable land was estimated to be around $47 per acre, so that an increase of one acre in crop area would result in a $47 increase in gross income. However, in view of the fairly high correlation existing between land and operating expenses and between land and machinery investment, it appears that the regression 121 coefficient for land is overestimated with compensating underestimation of the coefficients for cash expenses and machinery. Thus the estimated marginal value products of machinery investments and productive cash expenses are regarded as low while the estimated marginal value product of tillable acres of land as high. In the writer's judg­ ment, estimated marginal earning of tillable acres of land was actually between $37 and $45 per acre. The comparatively high return to land indicates the desirability of a m oder­ ate expansion in acreage, at least within the constraints imposed by available labor and equipment. The amount of labor used on the "typical" farm was found to be 7.36 man-months per year with an estimated marginal value product of about $310 per month. This implies that gross income would have increased about $310 a month had additional labor been used beyond the 7.36 months used. Labor earnings can be increased by additional investment in land and other inputs or by using less labor relative to other inputs. Operating expenditures amounted to $5,265 on the usual or typical farm studied. in a year's operation, Since cash expenses are used up they should be expected to return at least a dollar for the last dollar spent, plus interest on the money from the time it was spent until recovered. The estimates indicate that the last additional dollar 122 expended for this input category returned only 92 cents to the farms. However, operating expenses were used in amounts rather closely related to the land inputs and the chances of error in the estimate are increased due to this close relationship. There appears to be some reason for suspecting that part of the return to operationg expenses is reflected in the estimated marginal value product of land inputs. Therefore, it is concluded that the marginal value product of operating expenses was slightly over a dollar ($1 .01 ) for a dollar spent in 1972. The estimates indicate that machinery on the typical farm was earning low returns. However, the high correlation between land and machinery may have caused the estimated marginal value product of land to be high and the estimated marginal value product of machinery to be low. It is the belief of the author that the marginal earning of machinery was between 12 and 21 cents per dollar per year. return hardly covers depreciation, interest, This insurance, and maintenance which usually amount to about 25 cents per dollar investment. The low return to machinery reflects a large machinery investment of $16,886 which might pro­ fitably be reduced both relatively and absolutely. fore, There­ further investment in machinery seems unlikely to be profitable unless land and other supporting inputs are substantially increased. 123 It should be remembered that the estimates of marginal value productivity are based on 19 72 prices and weather conditions. In order to update the estimates, these value productivity estimates were adjusted for changes in product and factor prices in 1973. The separate marginal value productivities of invest­ ments and inputs for the typical farm at 1973 prices together with the 1972 MVP's at the "usual" farm organization are shown in Table 5.12. Table 5.12. Adjusted Estimates of Marginal Value Products of Typical Organization Farms in 1972 and 1973 (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) Input or Investment Usual Amount (At 1973 Prices) Marginal Value Product (1972 Prices) Marginal Value Product (19731 Prices) Land, 142.08 acres $37 to $45 per acre $66 to $80 per acre Labor, X 2 7.36 months $310/month $554/month Operating Expenses, $ 6,002 $ 1 .01 /dollar $1.58/dollar 12 to 21 percent 20 to 35 percent X3 Machinery $18,237 Investment, X4 19 73 price indexes used in this computation are: 178.65 for farm products, 108 for machinery investment and 114 for operating expenditure, where 1972 = 100. Source: Computed from Agricultural Pric es , USDA, 1972, 1973. 124 The adjustment technique used in this study is based on the following formula 7 b.E(Y). n 1 v 't—0 . IV4_ Yt=n MVP X i(t=n)Y t=n X i(t=o) Ixi(t=n) Where: ^Yt=n = Pr ^-ce index of farm products at n Iv = price index of inputs at n year; year; i (t=n) b 1 b 1 b r. E(Y) = A X ]_ 1 . . ..Xi 1 .......... Xn X i(t_0 ) = geometric mean period (i = 1 ,. b^ ; input of X^ at the base . .,n ) ; = regression coefficients of X^ (i = 1 ,. . . .n)^ At 1973 prices, the return to land indicates the desirability of an expansion in acreage. Use of more land would maintain the earnings of larger amounts of labor and operating expenditures. Larger land investments would also increase the earning power of machinery investments. The return to machinery investments, is low compared to depreciation, even at 1973 prices, interest, repair and tax costs, which amount to at least 25 percent. Trant, G. I., "Adjusting for Price Levels in Produc­ tion Function Studies," reprinted in Resource Productivity, Returns to Scale, and Farm S i z e . Edited by E. 0. Heady, (T L~! Johnson and L. Hardin, The Iowa State College Press, Ames, Iowa, 1956, p. 164. 125 Thus, even at 1973 prices, machinery investments should not be increased unless supporting inputs and investments (particularly land) are increased substantially. The earning power of farm labor was probably still not high enough to compete with industrial wage rates even at 1973 farm product prices; hence, few farms could consider expanding their use of really reliable, high-paid, skilled labor. The MVP of the Usual Combinations of Land, Labor, Operating Expenditure, and Machinery Since the amounts of land, machinery investment and other expenses used tended to change together from farm to farm, it is worthwhile to estimate the combined marginal value productivity of these inputs and investments. The study shows that these four inputs and investments yielded low returns when considered jointly. With a usual "batch" of inputs used, an additional acre of land, combined with 1/20 months of labor, $37 opera­ ting expenses and $119 machinery investment, would add about g $104 to gross income. The corresponding additional cost of using these additional inputs and investments in 1972 was around $119 labor; (i.e., $30 for rent/acre; $20 for 1/20 months $39 for $37 operating expenses and $30 for a $119 machinery investment). Apparently, the typical farmer would incur losses by using an additional $119 inputs. It should be noted that all these estimates apply to 1972 prices and production conditions. ------- g---------- This figure is computed from Table 5.10. 126 What would the combined marginal value productivity of these four inputs and investments be under 1973 price conditions? To answer this question, the farm product 9 price index for 1973 was computed using 1972 as a base year. The index was found to be 178.65, indicating farm product prices were increased by 78.7 percent compared to 1972 prices. Also in 1973, corresponding costs of the additional resources increased to $141 (i.e. for 1/20 months labor; $40 for rent/acre; $25 $40 for $37 operating expenses and $36 for a $119 machinery investment). Thus, at 1973 prices, a farmer could obtain $193 additional gross income of $52 additional net income using an additional $141 more inputs. For the typical farm, gross income would have increased from $14,751 in 1972 to $26,353 in 1973, an increase of $11,602. This indicates quite favorable conditions for farmers in 1973. Reorganization and Development of Farms on the Basis of Estimates One of the objectives of this study was to provide an objective and reliable basis for evaluating current 9 The prices used in computing the price index of 1973 were as follows: prices per bushel: $2.25 for corn; $5.50 soybean; $4.25 wheat; $1.25 oats; $15 per cwt. for dry beans and $40 per ton for hay. 127 farm organization and to serve as a guide for reorganizing farm business. Judging from the considerably high correlation exist­ ing between land and productive cash expenses and between land and machinery investment, some estimated coefficients were believed not reliable enough for use in estimating gross farm income and marginal value products for different combinations of factor inputs. Therefore, an effort was made to adjust the estimated coefficients in a rough "Bayesian" way. The adjustments were based on information and data obtained from nonsurvey sources and according to the author's judgment. Table 5.12. The adjustments are summarized in The adjusted regression coefficients and the consequent marginal value products of each factor inputs for a typical farm were presented in Table 5.13. Table 5.13. Input or Variable Adjusted Estimated Regression Coefficients and Marginal Value Products of Typical Organization Farms in 1972 (Based on 61 Cash-Grain Farms in Clinton and Ionia Counties) Quantity of Input (GeoMetric Mean) Constant Terms Land, X-^ Labor, Operating Expenses, 142.08 acres 7.36 months $5,265 *3 Machinery $16,886 Investment, X4 Nonadjusted Regression Coefficient Adjusted Regression Coefficient 1.56313 1.37096 Adjusted Marginal Value Product (1972) .45118 .3550 $37/acre .15446 .1520 $305/month .32905 .3600 $1.01/dollar .06531 .1330 12 percent 128 In this section, the reorganization of farms was based on the adjusted regression coefficients and on the 4 assumption that constant returns to scale (i.e. Z b. = 1) prevail in the region studied. 10 The first case to be considered is to examine the effect of increasing an input (land) having a higher rate of return on gross income and marginal value products. The effects of increasing land area from 142 acres to 250 acres while using typical quantities of the other input categories are shown in Table 5.14. Table 5.14. Changes in MVP and Gross Income Resulting From Increasing Land Area From 142 Acres to 250 Acres Input Category Quantity of Inputs Land, X-^ 250 acres 37 26 Labor, X 2 7.36 months 305 372 Operating Expenses, $5,265 1.01 1.23 X3 Machinery Investment, $16,886 .12 .14 X4 Estimated Gross Income Original MVP and Gross Income ($) $14,751 New MVP and Gross Income ($) $18,027 Under the assumption of constant returns to scale, the optimum size of a farm does not exist. However, once one or more factors were fixed, their subfunctions,would be subjected to diminishing returns and thus an optimum farm size could be determined. 129 All marginal value products were increased by the expansion of tillable acres except the marginal value product of land, which decreased from $37 to $26. gross income increased from $14,751 to $18,027. Estimated The increase in gross income was due not only to increased revenue from the expanded land area, but also to increased marginal productivities of other factor inputs when used in combination with more of the input (land) earning a higher rate of return. This phenomenon illustrates the twofold effect of the law of diminishing r e t u r n s . The effect of increasing tillable acres on labor productivities is shown in Figure 1 and in Table 5.15. Table 5.15. Marginal Value Products of Labor at a Different Level of Tillable Acreage Labor (Month) Acreage 142 200 250 300 ------ ---- Dollar----- -------- 7 318 359 389 415 10 235 265 287 306 13 188 212 230 245 16 158 178 193 206 19 136 154 167 178 22 120 136 147 157 25 108 122 132 141 Marginal Value $500 - Products of Labor Typical Organization (142 Acres) With 200 Acres With 250 Acres With 300 Acres 400 - 300 200 4 100 Figure 5.1. Effects of different level of acreage on marginal value productivity of labor 131 It is apparent that when the amount of labor employed increases, the marginal value product of labor decreases rather rapidly at first, labor are increased. then less rapidly as months of It is also noticed that the marginal value product of labor shifts upward when tillable acreage is increased. The amount of the shift decreases as more land is used. This is again due to the effect of the opera­ tion of the law of diminiishing r e t u r n s . For the purpose of explaining how the estimates may be used in finding more profitable input combination, an alternative organization, along with the resultant estimated marginal value product and gross income, is shown in Table 5.16. Table 5.16. An Alternative Organization of Typical Farms Studied in Clinton and Ionia Counties, 1972 MVP (Dollars) Input Category Quantity of Inputs (X.) Log X. Regression Coefficient (bp Land, 350 2.54407 .3550 .90314 24.09 8 .90309 .1520 .13727 451.21 Labor, ^ Operating Expenses, 8,000 3.90309 3 Machinery Investment, 16,000 4.20412 .3600 .1330 X4 Log Constant (A) = 1.37096 I Log ‘ b^ + Log Constant (A) = 4.37563 Log ^ 4.37563 = $23,748 = Estimated Gross Income (Log X.) -(b,)1 1.40511 1.07 .55915 .20 132 The input category given most emphasis in developing this particular organization from the original one was the land category, since it was generating higher returns. As the amount of land was increased, its estimated marginal value product decreased from $37 to $24. Although amounts of machinery investment and labor were not signifi­ cantly changed in this organization, their estimated marginal value products increased from $.12 to $.20 per dollar and from $305 to $451 per month, respectively. This is a result of using relatively more supporting inputs, i.e. land and operating expenses. Gross income for the typical organization increased from $14,751 to $23,748 resulting in a net increase in gross income of $8,99 7 under production and marketing conditions prevailing in 1972. To illustrate a further application of the results of this study, a large farm in the sample was selected and an alternative organization constructed. The quantitites of inputs used on this farm with their estimated marginal value products are shown in Table 5.17. Examination of the estimated marginal value products shows that marginal return to labor for this particular farm was substantially higher than the average ($309.57) with lower than average return ($1.01) to operating expenses. The high earning power of labor on the farm suggests the 133 Table 5.17. Input Category Estimated Marginal Value Products--Existing Organization and an Alternative Organization for a Farm Studied in Clinton and Ionia Counties, 1972 Existing Organization Alternative Organization Quantity MVP ($) Quantity Land, 1,386 acres 28.44 1,500 acres Labor, X 2 27.85 months Operating Expenses, $45,980 .87 $40,000 Machinery Investment, $93,375 .158 $93,375 606.04 40 months MVP ($) 27.16 436.05 1.03 x3 .163 X4 Gross Income $111,040 $114,750 desirability of an expansion in the use of labor. other hand, On the the low return to operating expenses reflected a large amount of cash expenses which might profitably be reduced. Accordingly, an alternative organization was developed. Labor was increased while operating expenses were reduced. Land was moderately increased while machinery investments remained unchanged. As a result, the marginal returns to land and labor decreased and the earning power of cash expenses and machinery increased. This illustrates the twofold effect of the operation of the law of diminishing returns. The expected gross income increased from $111,040 134 to $114,750, resulting in net increase in gross income of $3,710. The estimates show the relationship between each cate­ gory of input and gross income derived from the 61 sample cash-grain farms in Clinton and Ionia counties during 1972. The results of the study provide a basis of estimating returns that might have been realized under the same condi­ tions had different farm organization been adopted. However, it is worth noting that the future return depends much on future prices of inputs and outputs. It is believed that the typical organization in this study was not too far from optimal organization. However, some adjustment is considered necessary in order to raise farm income. The main adjustments seem to be: (1) to moderately increase farm size by expanding tillable acreage, (2) to reduce the use of labor, and (3) to be more careful in handling current operating expenditures and machinery investments.^ Summary and Implications The purpose of this chapter was to estimate marginal value productivities for various inputs and investments in cash grain farm business of south central Michigan. ■^The model does not consider off-farm work as a way of using farm operator labor. 135 Functional analysis was employed in this chapter because of its capability to measure the effects of i nter­ action of different levels of inputs and investments on their respective value productivities. The data obtained f r o m the 61 sample farms were used as a basis for three regression analyses. The first equation includes five variable input c a t e ­ gories, i.e. land, labor, operating expenses, machinery investment and buildings. In the second equation, buildings were omitted to obtain a better fit with greater confidence in the estimates of the production coefficients. In the third equation, constant return to scale was assumed. A tentative conclusion from examining the typical organization of cash-grain farms on Miami or better soils in the two counties in 1972 was that marginal value product for land was comparatively high, indicating the desirability of a moderate expansion in farm acreage. Since much cropland was either diverted by government set-aside programs or simply idle in 1972, an increase in crop area by e xp a nd in g the extensive margin of cultivation was indicated for 1972 and 19 73 conditions. Operating expenditures and machinery investments w e r e high compared to other inputs, as reflected by the low returns of these input categories. This implies that m o r e 136 care in handling operating expenses and machinery investment is desired, and expanded farm sizes are needed in order to use machinery and operating expenditures more effectively. Some ways of reducing machinery investment have been noted, but much improvement in this direction cannot be assured because of indivisibility of machinery. Farm labor studied was earning a low rate of return in 19 72. The estimated marginal value product of labor was found to be $309.57 per month, indicating that an increase of one month's work on the farm would be accompanied by an increase of $309.57 in gross income, holding other factor inputs constant at their respective geometric mean levels. This implies that most cash-grain farms in the area studied are not able to compete with industry for hired labor. The low earning power of labor also indicated the desirability of reducing its use relative to land and other inputs. An increase in land use would tend to reduce its marginal earning power, but at the same time would increase marginal earnings of machinery, operating expenditures and labor. Consequently, farm income would be higher due to a better farm resource combination involving more land relative to machinery and, especially, labor. The results of the study provide a basis of estimating returns that might have been realized under the same condi­ tions but with different farm organizations. However, future 137 returns depend on future conditions of prices, institutions, weather conditions, technology, and human factors. applying the results of this study, In these factors together with the limitations of the study previously mentioned must be taken into account. CHAPTER VI PROJECTED CONSEQUENCES OF ALTERNATIVE WAYS OF ORGANIZING THE USE OF MIAMI/CONOVER SOILS IN SOUTH CENTRAL MICHIGAN In this study, static linear programming has b e e n , employed to investigate the profit-maximizing o r g a n i z a ­ tions and land use for representative farms in the s e L e c t i area. In addition, a Cobb-Douglas analysis has been u s to estimate the marginal value productivity of the r e s o r x r r t on the selected farms. The purpose of this chapter is to relate the r e s u l t s of the study to the micro, as well as macro aspects o f decisions regarding land use programs and policies whi_ ctln. could lead to more efficient and wise use of land r e s o u r c t In the first place, an evaluation will be made of the of linear programming, analysis. Secondly, r e s i in light of the results of f u n c t i o r the general land use situation a n d tl: factors affecting the utilization of land will be d e s c r i b e Thirdly, land policy implications based on the study w i l d be presented. Lastly, the projected consequences of a l t e i native ways of organizing the use of Miami/Conover s o i 1 s will be presented. 138 139 Evaluation on the Results of the Linear Programming and Cobb-Douglas Function Analyses The results of linear programming have to be examined in light of the results drawn from the functional analysis. Both locate optima but different optima and in different ways. In linear programming, a priori information about pro­ ductivity coefficients is required before the actual process is undertaken. (i.e., Thus, the resultant productivity estimates shadow price of a resource) are dependent on coeffi­ cients of productivity obtained independently of the program. The results of the functional analysis indicated (1) fairly high returns to land, (2) low returns to farm labor, (3) low returns to cash operating expenditures, returns to machinery. and (4) low Near constant returns to scale beyond 150 tillable acres were found empirically in the functional analysis but were assumed in the linear program. The findings of the functional analysis confirm the assumptions of the linear programming analysis. Both functional and programming analyses indicated high returns to land and low returns to other inputs and investments. The functional analysis indicates the desirability of a moderate expansion in farm size to more fully utilize family and operator labor and machinery due to comparatively high returns to land. The programming results indicate the profitability of expanding farm size by renting and/or through purchasing land up to the limit permitted by the model (Table 4.4). In the linear programming analysis some 140 additional unskilled labor is required, seasonally, in conjunction with the expansion in land use. The programmed results are based on several assump­ tions which require evaluation before accepting these conclusions. The land price of $500 per acre and annual rental rate of $30 per acre assumed in the model are considered low. As such, the consequent programming result is the expansion of farm size for all representative farms by renting and/or through purchasing land up to the limit permitted by the model (Table 4.4). Land often becomes the most limiting resources as reflected by its high shadow price. When more land is available for rental, the linear programming analysis concentrates on expansion of land through renting probably because rent at $30 an acre is low priced relative to the purchase price of $500 per acre (Table 4.8, Case V). The optimum solutions are affected by the assumptions made relative to available off-farm employment. The model assumed that off-farm opportunities were limited in five seasons. A perfectly elastic supply schedule for labor hired was assumed. These assumptions are probably invalid as wage rates are increasing and young rural people increasingly work off farms. Moreover, the agricultural sector is increasingly affected by the increase in the price of purchased farm inputs caused by the energy crisis which were not considered in the programming model. Product 141 prices used in the programming analysis are much higher than the product prices used in the functional analysis.^ Assumptions concerning the credit supplies in the program­ ming analysis are based on the usual tutional lenders. practices of insti­ No provisions were made in the model for internal credit rationing due to uncertainty. The linear programming model does not consider the overall aggregate effects of large scale adoption of the results on product and input markets. The programmed solu­ tions call for expansion of farm size and associated durable assets to produce specific crops. bid for resources, However, if all farmers land and associated input prices would increase while product prices would likely decrease. This trend would limit expansion of farm size. Lastly, risk and uncertainty in production was not considered in the model. technology, institution, Lack of knowledge about future people and prices often cause a farmer to act more conservatively. The qualifications presented above indicate that farm size would actually be smaller than that indicated in the ^"The prices used to compute the value of farm products in functional analysis were the average price of each crop in Michigan in 1972. These prices per bushel were: $1.12 for corn; $3.27 soybeans; $1.62 wheat; $0.76 oats; $10.53 per c w t . for field beans. In contrast, the prices used in linear programming were 1973 fall prices except field bean price. These prices per bushel were: $2.25 for corn; $5.50 soybean; $4.25 wheat; $1.25 oats; $15.00 per cwt, for field beans (i.e., normal price of field beans). 142 programmed solution. The lower marginal value product of land found in the functional analysis and nonexistence of increasing return to scale beyond 150 tillable acres also support the above statement. Judging from the existence of considerable amounts of unused cropland and potential cropland and the fairly high returns to land as shown by both the functional and programming analyses, it is con­ cluded that the trend toward a moderate increase in farm size should be expected to continue in a foreseeable future. The continued development of larger and efficient machinery and rapid adoption of larger machines would probably give additional momentum to this trend. The desirability to expand farm size as shown by both the programmed solutions and functional analysis implies that land values in the area will continue to be bid up as farmers seek more land for farming, along with the increase in demand for land for other uses. This trend would probably discourage the establishment of new farms as more capital would be required for the land resources, combined wit h high labor cost, expensive m a c h ­ ineries and high land clearance cost. As farm size becomes larger coupled with high labor costs, larger and more efficient machines and equipment are needed in order to complete field work in time. This implies that more capital is required to replace expensive labor. On the other hand, the majority of young rural 143 people tend to leave farming as more attractive off-farm work is available for them. As old farmers retire, the total work force in agriculture is reduced while total farm land remains relatively stable or slightly increases. Farms with limited labor but with larger acreages could probably generate higher farm income. However, it takes quite a long time to make this kind of adjustment. Land Use on Miami/Conover Soils This section presents the results of the land utiliza­ tion survey on Miami/Conover soils in Clinton and Ionia counties for the operating year 1972. The purpose of this part of the survey was to examine the overall land utiliza­ tion and quantity idled on the Miami or better soils, and reasons for such land being idle. As such, the approach is descriptive with emphasis on acreages of land used for various purposes, rather than on theoretical matters. The year 1972 is selected because it was the year before agricultural product prices increased significantly. As part of the survey, data were collected from farmers concerning their 1972 land utilization using "land utilization schedule" and aerial photographs for the selected areas. As previously stated, a random sample of twenty predominantly Miami/Conover areas (two mile square area, containing four square miles) was drawn for this study. All farmers whose farmsteads fell in selected areas were 144 questioned as to the kinds and acreage of crops planted in each tract on their farms in 1972. An effort was made to distinguish between diverted cropland and idle cropland. The former is land idled by government production control programs while the latter is a land idled by a farmer for some other r e a s o n s . The results of land use survey for each area in the two counties are presented in Table 6.1 (actual acreage) and Table 6.2 (percentage). As shown in Table 6.1, most of Miami/Conover soils (68 percent) were used for crop production including corn (15,888 acres), (5,279 acres), acres), oats Also, legume-grass hay (5,369 acres), wheat soybeans 3,572 acres), field beans (1,391 acres) and other crops (3,057 (371 acres). fairly large areas were in woodland which accounts for 7.91 percent (4,049 acres), while pasture constituted 3.82 percent (1,956 acres) of the total area. Quite a few acres of cropland (4,863 acres, or 9.5 percent) were diverted by government set-aside programs, or simply idled (784 acres or 1.53 percent) by the farmer. Much of the idle cropland comprises 11.03 percent (5,647 acres) of total area investigated. The diverted cropland (4,863 acres or 9.5 percent) has probably been pulled into production since 1972 as all farmers interviewed indicated that they would like to increase crop production by bringing diverted cropland back into production after the termination Table 6.1. Area Use of land in Clinton and Ionia Counties in 1972 (Miami/Conover Soils)— by Acreage Total Com Soybean Wheat Field Beans Oats Hay Other Crops Pasture Woodland Swamp Diverted Land Idle Land Others^" 5,120 1,792.90 160.70 334.10 303.40 987.00 6.10 314.10 338.60 15.00 527.70 21.00 319.40 2 5,120 1,646.50 482.00 501.90 176.90 160.50 768.60 12.20 238.90 393.30 16.00 345.20 4.00 374.00 3 5,120 1,350.50 487.90 477.10 340.50 92.60 635.40 5.10 218.30 473.60 55.50 384.80 92.70 506.00 4 5,120 1,604.50 471.70 361.30 190.9 192.80 707.50 285.30 278.00 38.00 578.80 67.30 343.90 1,166.10 480.50 768.00 528.10 49.00 396.10 123.00 127.70 402.30 15.00 500.10 55.30 510.80 — — 5 5,120 6 5,120 1,443.60 257.50 446.60 676.15 121.50 443.90 29.20 209.20 397.80 536.80 146.60 411.15 7 5,120 1,669.60 267.60 668.00 479.90 210.80 298.40 31.50 168.70 288.30 — 528.41 59.90 446.99 8 5,120 1,790.14 447.70 424.30 258.80 26.40 365.50 78.80 91.10 428.00 _ _ _ 534.00 160.30 494.96 9 5,120 1,773.60 293.30 541.40 221.90 58.00 357.40 17.30 192.90 562.10 20.00 460.30 97.30 544.40 10 5,120 1,650.60 222.80 756.00 183.80 176.00 409.30 67.50 109.40 486.50 108.80 467.10 79.30 402.90 51,200 15,888.04 3,571.70 5,278.70 3,056.95 1,391.00 5,369.10 370.70 1,955.60 4,048.50 268.30 4,863.21 783.70 4,354.50 Total ■'"Others include land used for roads, building lot and ditches, etc. 145 1 Table 6.2. Use of Land in Clinton and Ionia Counties in 1972 (Miami/Conover Soils) -by Percentage Woodland Swamp Diverted Cropland Idle Cropland Others Total Pasture 1 70.01 6.13 6.61 .29 10.31 .41 6.24 100 2 73.22 4.67 7.68 .31 6.74 .08 7.30 100 3 66.20 4.26 9.25 1.08 7.52 1.81 9.88 100 4 68.93 5.57 5.43 .74 11.30 1.31 6.72 100 5 68.53 2.49 7.86 .29 9.77 1.08 9.98 100 6 66.77 4.09 7.77 — 10.48 2.86 8.03 100 7 70.82 3.29 5.63 -------- 10.32 1.17 8.77 100 8 66.63 1.78 8.36 — 10.43 3.13 9.67 100 9 63.34 3.77 10.98 .39 8.99 1.90 10.63 100 10 67.69 2.14 9.50 2.13 9.12 1.55 7.87 100 Total 68.21 3.82 7.91 .52 9.50 1.53 8.51 100 ■^Computed from Table 6.1. 146 Cropland Area 147 of government production control p ro gr a m s . The estimated crop acreage which could be pulled into production averaged approximately 31 acres per farm. The cost of bringing diverted cropland into cultivation was small enough to be negligible. Whether or not the other idle cropland (1.53 percent) could be pulled into production is unknown due to many factors involved in the use of such land. This point will be discussed in the next section. Pasture land (3.82 percent) and woodland (7.91 percent) could be pulled into production if there is sufficient economic justification. The cost of bringing unused land into production bears on the feasibility of cultivating land now unused. The estimated cost of clearing plowable pasture is approximately $80 per acre while clearing wo od ­ land costs about $500 per acre at 1973 prices. pasture would likely be converted into cropland, Plowable if other land is not available for renting at $30 per acre or for purchase at $500 per acre and product prices remain high. However, programmed results show that no woodland would be cleared at the cost of $500 per acre (Table 4.8). Consequently, it is reasonable to assume that sources of potential acreage expansion come mainly from diverted cropland (9.5 percent) and plowable pasture (3.82 percent). Using these figures, the potential crop acreage expansion in Miami or better soil could be estimated. To do this, 148 however, requires an estimate of the acreage of Miami/ Conover soils in the studied area. The total area of Miami/Conover soils in the two counties is estimated to be approximately 252,802 acres. 2 Therefore, the estimated diverted cropland was 24,016 acres (i.e., 252,802 x .095) while plowable pasture is about 9,657 acres (i.e., 252,802 x .0382). as of 1972, In total and approximately 33,673 acres of cropland not farmed in 1972 in Miami/Conover soils in the two counties could be pulled into production at 1973 price relationships. It should be noted that pulling 33,673 acres of cropland into production could easily be accomplished by expanding the size of existing farms. not impossible, However, it is difficult, if to bring the land into production through establishing new farms due to its scattered location and the lack of monetary incentives for new entrepreneurs. It is worth mentioning that farm size could continue to increase under the condition of constant returns to scale. The process could be accomplished through the consolidation of the existing small farms with low farm earnings and/or by buying out old farms which can not make adjustments for economic survival. In the following section, the factors affecting land utilization will be discussed. - Computed from: (1) Soil Survey-Clinton County, Michigan, USDA and Michigan Agricultural Experimental Station, Series 1936, No. 12, p. 14; (2) Soil Survey-Ionia County, Michigan, USDA and Michigan Agricultural Experiment Station, December 1967, pp. 6-8. 149 Major Factors Affecting Utilization of Land There are quite a few factors which would affect the utilization of land. In general, classified into four categories: these factors can be (1) physical factors including such factors as water supplies, terrain, geography and climate, including new varieties, soil types, (2) technological factors irrigation, fertilizers and improved technology, drainage, tiling, (3) economic factors which are based primarily on economic principles productivity or profit) resources, (i.e., that affect the use of land and (4) institutional factors including legis­ lation with regard to property rights, arrangements, planning, land tax, leasing zoning, education and safety, etc. It should be noted that no single factor could establish the pattern of land use for a given land area. Rather, combinations of many factors determine the specific use of land. It should also be recognized that it would be extremely difficult to determine the extent to which each factor influenced the intensity and efficient use of land. In other words, the determination of relative effects of those factors on land utilization is very difficult, if not impossible. This section presents the result of survey concerning factors, or reasons, why farmers left a portion of their cropland unused in 1972. Only those factors which, according to survey and observation, had a relatively important impact on land utilization on Miami/Conover soils are studied. 150 As previously mentioned, there was about 784 acres (1.53 percent of total area) left idle by the farmers in the studied area. As part of the survey, a farmer who had idle cropland was questioned as to the reasons for such idleness. Table 6.3 shows the result of the survey. The most important factor limiting the use of Miami/Conover soils is poor drainage particularly for the Conover, followed by operator's age and speculation. Table 6.3. Reasons for Putting Cropland Idle on Miami/ Conover Soils in 1972 Cropland (Acre) Reasons Percent Land is too wet and needs tiling 308.50 39.36 Operators are too old and/or no interest in renting out 228.10 29.11 Land held for speculative purposes 149.90 19.13 Summer fallow 44.00 5.61 Discarded private airport 14. 70 1.88 Land was cleared in 1972 11.00 1.40 Discarded pasture (livestock sold) 10.00 1. 28 Inaccessible due to bridge damage 9.00 1.15 Farmer was hurt by tractor accident 8.50 1.08 783.70 100.00 Total Idle Land As shown in the table, among the 783.70 acres of idle land, 308.50 acres (39.36 percent) was left idle due to poor drainage, 228.10 acres age, and 149.90 acres (29.11 percent) due to operator's (19.13 percent) due to speculation. 151 Other factors include mainly property rights, other physical reasons and a special farm practices. Apparently, physical and institutional factors are the most important reasons for idle land on Miami/Conover soils in south central Michigan. It should be noted that the cost of drainage is closely related with the outlet. If outlet exists, drainage is moderate--if it does not, the cost of costs are prohibitive. Land Policy Implications On the basis of information discussed above, and in view of the results of linear programming and functional analysis, together with farmers' options, the following land policy implications were derived to foster the more intensive or higher and better use of land resources, to encourage a farmer to get underutilized land into production, and at the same time, to discourage certain types of land 3 use. 1. The comparatively high returns to land, both functional analysis and programmed solution, shown by indicate that it would be profitable to expand farm size under the assumed conditions if one can obtain enough labor. As such, land prices in the studied area would continuously be bid 3 Both positive or nonnormative and normative informa­ tion is required to obtain a prescriptive knowledge to solve the practical problems. In this study, the positive information includes land use situation, factors affecting the land use and the results of the functional analysis. The normative information, on the other hand, includes farmers' opinion, author's judgement and the results of linear programming. 152 up as farmers seek more land for farming in competition with nonagricultural uses. The increase in the land price might have a cumula­ tive adverse effect on agricultural sector. It might encourage land speculation and idle land would be held for such purpose,^ on the other hand higher land prices would make it more expensive to hold idle land. Secondly, it would encourage a farmer to sell agricultural land once the point is reached where the salvage price of land exceeds the marginal value product of farm land. This could lead to desirable consolidation of holdings. Lastly, it would also discourage those planning to establish new farms . 2. The result of the study indicates that the demand for land for nonagricultural uses has increased signifi­ cantly in the past few years. Apparently, the trend has been toward an increase in residential uses involving encroachment on farm land. by observing the number This encroachment This trend can easily be seen of new residences in rural areas. has not yet caused serious inroads on the total agricultural production, nevertheless, it will have a cumulative adverse effect on crop production if it continues indefinitely. ^In at least one case, this has actually occurred on a farm in Clinton county. A 7.4 acres of cropland was left idle for more than 10 years and gave rise to a serious insect and weed control problem for those who have land around the idle land. 153 A sound policy under this situation should focus on the maintenance of a proper balance between agricultural and nonagricultural uses of land. The policy should be designed to preserve the intrinsically best agricultural land and protect this land from the encroachment of non­ agricultural uses while leaving agriculturally inferior land for residential and nonagricultural use. This objec­ tive can partly be attained by setting up zones of specified land use to avoid possible incompatibilities and conflicts between nonagricultural and agricultural uses of land. 3. The study shows that physical determinants, especially drainage are the most important factors limit­ ing the use of agricultural land on Miami/Conover soils. As shown in Table 6.3, of the 784 acres of idle land, nearly 308 acres (40 percent) was left idle due to poor drainage. If the objective of land policy is greater crop acreage and more profitable agricultural use, it appears that some realignment in land use policy is necessary such as subsidized tiling of the wet land and land reclama­ tion etc. to assist and encourage farmers in construction of drainage ditches and tiling wet land. Tax systems that favor private construction practices and subsidize the introduction and private acceptance of conservation measures could also be used. 4. The study shows that tenure arrangements in the studied area are not appropriate in the sense that the tenure period is too short (usually on a year-to-year basis) 154 and there are few written tenure agreements. These customary rental arrangements frequently give neither the tenant nor the landlord much reason for long term investment. Operators with limited tenure rights have little incentive for improv­ ing or maintaining the soil fertility or adopt drainage measure for long planning pe riods. The government can play an important role in overcoming this problem. Specific programs can be developed to promote leasing and tenure arrangements that encourage investments in conservation practices. Sound land tenure arrangements should provide incen­ tives and means to stabilize resource productivity, equality of access to resources among individuals and efficient resource use. 5. One possible way to encourage a farmer to get underutilized land into production is to increase incentives with higher product prices. As part of the survey, data were collected from the farmers concerning the product prices that would induce farmers to bring more idle land (including woodland and plowable pasture land) into culti­ vation.^ At this price combination, the programming results show that plowable pasture land was cleared up to the limit permitted by the model. This result tends to justify prices "*The prices for each crop are listed in Case V in Table 4.10. 155 farmers thought were needed to give them an incentive to bring more land into cultivation. It should be recognized that land policy has to be flexible to meet an inevitable change in social, political and economic conditions. Furthermore, it has to be real­ ized that no single, rigid land policy can be devised which is applicable to any region. As such, land policy has to be adapted to meet the needs of separate regions. Projected Consequences of Alternative Ways of Organizing the Use of Miami/Conover Soils On the basis of the previous discussion of agricultural land utilization on Miami/Conover soils and the results of functional analysis and programmed solution, some tentative projections of farm land uses, potential acreage expansion and consequent returns etc. can be made under some assumptions. The projected consequences are made based on the assumption that strong positive land policies such as a heavy tax on idle cropland, zoning, and subsidies are implemented by a government. 1. Agricultural production can be increased over 1972 through additional acreage of new land. By clearing and drainage, approximately 47,653 acres of additional new land could be pulled into production on the Miami/Conover soils in the two counties. Such land includes 24,016 acres (9.5 percent) of diverted land, most of which is now in production, 3,868 acres (1.53 percent) of idle cropland, 156 9,657 acres (3.82 percent) of plowable pasture land and 10,112 acres (4 percent) of woodland. expandable acreage is 23,637 acres. Thus, the present This projection is made by assuming that all diverted land has been brought back into production. Furthermore, it was assumed that about half of woodland rather than all woodland could be cleared and converted into cropland. viewed expressed the opinion Some farmers inter­ that they were reluctant to clear the woodland because it was required for recreation purpose, preserving wildlife, and wood production. It should be recognized that production would not increase in proportion of the acreage of new land because the study indicated that most of the unutilized land in the Ionia-Clinton area was poorer quality than the land normally used for row and grain crops. cussed, As previously dis- the land is unused because it is inferior first place; in the is idle because of the kind of ownership and change in value from a lower to a higher use; or has reverted due to poor drainage. Increased use of presently idle land would likely be accomplished by expanding the size of existing farms. It would be unlikely that such land could be brought into production through establishing new farm due to the scattered location of the idle land coupled with the low labor returns ^Land is inferior in terms of productivity and/or poor drainage. 157 which could not provide monetary incentives for new entrepreneurs. 2. Approximately $1,380,401 of earnings to land would be generated by bringing an additional 23,637 acres of new land into production on Miami or better soils in the two counties under 1973 price relationship. This figure is obtained b y assuming that the actual increase in produc­ tion through the crop use of idle, pasture land and w o o d ­ land is 80 percent of the land normally used for row and grain crops (i.e., 23,637 x $73 x .80 where $73 is the adjusted estimate of marginal value product of land under 1973 price relationship). 3. Uses of agricultural land would not be fixed for certain crops or even nonfarm u s e s . They are expected to undergo continual shifts depending on changes in physical, economic, technological and institutional factors. Economic considerations indicate that more acreage would be devoted to wheat, field beans, at 1973 prices. corn and soybeans on cash crop farms Dairy and fatstock farms were not studied. The programmed solution indicates the WB rotation dominates all other crop rotations on crop farms at fall 1973 price relationships. Furthermore, CCCCS and CB rota­ tions entered the optimal solution for a large farm and medium* farm respectively (Table 4.3). On the other hand, CS rotation is in the least competitive position in the optimum plan (Table 4.6). Therefore, with the assumption of profit maximization as a single goal for a farmer, the 158 trend would be more wheat and field beans production except perhaps on dairy and fatstock farms. It should be noted that the least competitive position of CS rotation does not necessarily lead to the conclusion that corn and soybean acreage would likely decrease. On the contrary, acreages of corn and soybean would tend to increase due to the com­ parative advantage of CCCCS rotation on a large crop f a rm s. Corn is probably in a stronger position on dairy and fatstock farms. However, care must be taken in applying the results derived from programming analysis, since the static linear programming model does not consider the overall aggregate effects of large scale adoption of optimal farm organization, risks and technology associated with field beans production, and internal rationing on the part of a farmer. 4. Land prices in the studied area can be expected to increase moderately due to: (a) comparatively high returns to land as indicated by both functional analysis and programmed solution, schedule, (b) inelastic nature of land supply (c) continued inflationary economy, and (d) continued demand for living space as population pressures increase. However, continual increasing production costs, reduced availability of labor and product price uncertainty might offset 5. the rate of price increase to some extent. Moderate farm size expansion would be expected as the estimated marginal value productivity of land in the studied area was found to be higher than return 159 estimated to be necessary to cover the cost of using the input. On the other hand, many acres of diverted land, idle cropland and pasture land could be brought into p r o ­ duction as described in the previous section. Since returns to the labor, operating expenditure and machinery were low as indicated by the functional analysis, an increase in the use of land would tend to increase the marginal earnings of machinery, operating expenditures and labor but at the same time would reduce the earning power of land at the margin. Consequently, higher farm income would be generated due to a better farm resource combination involving more land relative to mach­ inery, and especially labor. However, continual increasing input costs such as fertilizers, machinery, wages, reduced availability of both etc.; skilled labor and entrepreneur; product price uncertainty; and nonexistence of economies to scale beyond 150 tillable acres would probably level off the trend of increasing farm size to some extent. 6. low due to: farm, The possibility of establishing new farms is (a) the cost involved in establishing a new (b) low returns to labor, cash expenditures and mach­ inery even at 1973 farm product prices, (c) the scattered location of unused land, and (d) nonexistence of economies to scale beyond 150 tillable acres. As such, a continual decrease in the number of farm would be expected as average farm size is becoming larger and more efficient big machinery 160 is substituted for labor in the production process as agricultural wages increase. 7. Agricultural production can be increased through improvement of agricultural practices and intensification of cultivation on existing land in use, without the addi­ tion of new land, i.e., by selection and adaptation of crop varie t ie s, appropriate use of fertilizers, better tilage, drainage, irrigation and control of water table. This point is repeatedly expressed by many farmers inter­ viewed, though specific evidence was not obtained. Whether or not product prices would change is unknown, since this study does not consider the overall aggregate effect of large scale adoption of optimal plan on both input and output market, and thus the programming analysis provides no direct information. However, it is conceivable that the supply curve of farm product would shift to the right over time, were enforced. if some product expansion policy measures Under this condition, farm product price would be depressed with consequent decline in farm income, given the inelastic demand for farm products. On the other hand, the input price would increase as more inputs were required due to the expansion of farm size, giving rise to the cost-price squeeze in the agricul­ tural sector. As such, although land policies might be effective in inducing expansion of farm size and consequent increase in production, they often give rise some adverse effects which create additional problems in the agricultural 161 sector. Furthermore, the energy crisis induced by the oil embargo has heavily affected the agricultural sector with higher production costs. This factor also needs to be taken into consideration before adequate land policy is developed. Therefore, further studies are needed with respect to overall aggregate effect of the energy crunch, large scale adoption of optimal plan on both input and output m a r k e t s . CHAPTER VII CONCLUSIONS AND IMPLICATIONS The primary objective of this study was to ascertain profitable adjustments in the farm organization and land use for cash-grain farms in response to the increasing demand for agricultural products. Emphasis was placed on estimation of the marginal value productivities for various inputs and investments which would serve as a guide in planning the necessary changes in farm organization. Further, the general land use situation and the factors affecting the utilization of land in the Miami/Conover soils were studied. Static linear programming was used to determine optimum farm plans with (1) farm resources fixed at initial level, (2) land, labor and machinery investment variable and (3) product prices variable. Investment/disinvestment theory was incorporated into situations (2) and (3). Farmers were stratified by age of operator and net worth as a major determinant for setting up representative farms. The former was used to measure their willingness and the latter was used to estimate their ability to make adjustments. Four representative farms: 162 small, medium, 163 large and medium* farms'^ were developed. The analysis was first given for Model I with cropland and associated durable resources fixed at 1972 levels. Secondly, the optimal organization was presented for Model II which permits variation in land resources and associated durable assets. A production function of the Cobb-Douglas type was employed in deriving the estimates of marginal value pro­ ductivities of inputs and investments on the selected farms. The data obtained from the sixty-one sample farms were used as a basis for three regression analyses. The first equation includes five variable input categories, i.e., land, labor, operating expenses, machinery invest­ ment, and buildings. were omitted. In the second equation, buildings An effort was made to examine the returns to scale by dividing the sample farms into two size groups. Examination of results lead to use of the third equation which forced constant returns to scale. Estimated coeffi­ cients were adjusted in a rough "Bayesian" way. Profitable reorganizations of farms was studied using the adjusted regression coefficients. Since both linear programming and Cobb-Douglas func­ tion were used in this study, emphasis was focused on a ^The medium* farm refer to the farms with net worth $80,000-$150,000 and operator's age over 55 years. 164 comparison of these two techniques, so as to be able to exploit fully their complementarities. In addition, an attempt was made to distinguish the more or less pseudo MVPs of linear programming from the true MVPs of continuous function which are partial derivatives of such functions. The remainder of this chapter presents the major findings obtained from both the linear programming and functional analyses. In addition, results of the land utilization survey are also summarized. The implications of the study were drawn in such a way as to exploit the complementarities between the linear programming and CobbDouglas analyses. Lastly, suggested future studies are presented. Linear Programming--Summary of Findings The major findings of this part of the study may be summarized as follows: 1. The operators of representative farms in this area used all their initial capital and a considerable amount of the credit to make the indicated adjustments (Table 4.3). This implies that cash grain farmers were currently not fully utilizing their capital resources. As such, the representative farms studied were not organized to maximize profits. 165 2. The operators of representative farms in this area could profitably adopt a wheat-beans (WB) rotation under price conditions which existed in late 1973. The programmed solutions for Model I and Model II indicated that a WB rotation dominated each of the representative farm situa­ tions. However, CCCCS and CB rotations enter the optimal solution for the large farm and the medium* farm, respec­ tively (Table 4.3). Even so, the corn-soybeans (CS) rota­ tion was the least competitive in the optimum plans (Table 4.6) .2 3. The programmed results indicate that land is the most limiting resource so long as off-farm work and migra­ tion are restricted. The high shadow price of land indi­ cates that it would be profitable to expand farm size under assumed prices and output conditions if enough labor is fixed on the farm. The results also show that returns to land in the studied area were high, especially when O compared with an annual rental rate of $30 per acre. Furthermore, capital and labor were not fully utilized in 2 This result does not necessarily imply that corn and soybean acreages likely decrease. It merely indicates that CS rotation is in the weakest competitive position on cash crop farms among the crop rotations covered in the model and prices assumed. Acreages of corn and soybeans tend to increase due to the comparative advantage of CCCCS rotation on larger farms. Furthermore, corn is in a rela­ tively stronger position on dairy and fatstock farms. 3 The annual rental rates reported by farmers were pro­ bably low compared to what would actually have to be paid for farming purposes. 166 Model I where farm resources were fixed at initial levels (Table 4.1, 4.5). 4. No full-time hired worker was employed on the representative farm since family labor (including operator labor) was either adequate to meet all supervisory require­ ments or could not be paid for. However, some amounts of seasonal labor were employed in the optimal solution to supplement the family labor when it was completely used. The moderate increase in the use of unskilled seasonal labor was due primarily to expansions of farm size (Table 4.4). 5. In the optimum solution, all farms had some members with off-farm work, which agrees with what cash grain farmers were doing in the south central area in 1973. As opportunity cost of farm labor was high in the south central area of Michigan, it would be profitable for family members and operators to work off the farm as indicated in the pro­ grammed solution (Table 4.4). However, the constraints on off-farm work prevented the program from selling out the business to permit the farmer to accept full-time off-farm work. 6. The levels of land resource availability affected optimal farm organization and the competitive position of crop rotations. More crop rotations entered the optimum solutions when more land was acquired. As compared with 167 Model I, the provision of land rental and purchase oppor­ tunity not only resulted in increased net returns, but also changed the optimum combination of crop rotations (Table 4.3, 4.6, 4.8, 4.9). 7. Farm size would not be expected to expand without 4 limit even under conditions of abundant land supply. The results indicate that labor (including managerial labor) and capital are major restricting resources limiting expan­ sion in farm size (Table 4.8). 8. More woodland and plowable pasture land would be cleared at the cost of $395 or less per acre and converted into cropland, if product prices remain high (fall 1973 price), with stable input prices and/or limited land were available for rental and purchase. Of the $395, clearance accounts for $245 per acre and tiling $150 per acre; thus drained and cleared plowable pasture can be brought into crop production merely by covering the opportunity cost of using it for pasture, which is probably not more than $20 per acre. However, no woodland would be cleared at the cost of $500 per acre in any representative farm situations studied. This indicates that converting woodland into cropland at the cost of $500 per acre is not economically justified, under the assumed prices and product conditions (Table 4.4, 4.8, 4.11). ^The farm size expanded from 438 acres to 1,269 acres for a large farm (Table 4.8) under conditions of abundant land supply. 168 9. use. Product prices affect optimum farm plans and land The results indicate that wheat would leave the opti­ mal organization if its price should fall to $3 per bushel with other crop prices constant at 1973 levels. CB and WB rotations enter the optimum plan to expand field bean production when field beans have a strong price advantage (Table 4.11, B-4, B-5, B - 6 ) . 10. The programming results tend to justify what farmers thought were prices needed to provide an incentive to bring more land into cultivation. The prices are pre­ sented in Table 4.10. This study considers the optimum individual farm organizations. Macro analysis of the impact of widespread adoption of results was not considered. Functional Analysis--Summary of Findings On the basis of this phase of the study, the following statements can be made about Clinton-Ionia County cash-grain farms under the prevailing 1972 and 1973 marketing and production conditions. 1. Land on Clinton and Ionia county farms earned a fair rate of return during 19 72. The unadjusted estimated marginal value product of tillable land was $46.84 which is higher than required to cover its marginal factor cost. adjusted marginal earning of land was between $37 and $45 per acre in 1972 and $66 and $80 in 1973 (Table 5.12). The 169 Since much cropland was either diverted by government set-aside programs or simply idle in 1972, an increase in crop area by expanding the extensive margin of cultivation was indicated for 1972 and 1973 conditions. An increase in the use of land per farm would tend to reduce its earning power at the margin but would, at the same time, increase the marginal earnings of machinery, operating expenditures, and labor. 2. 1972. Farm labor was earning a low rate of return in The estimated marginal value product of labor was found to be $309.57 per month, indicating that an increase of one month's work on the farm would be accompanied by an increase of $309.57 in gross income, holding other factor inputs constant at their respective geometric mean levels. This indicates that most cash-grain farms in the area studied are not able to compete with industry for hired labor and that off-farm work and/or migration was justified. Results of this study also indicate that the earning power of farm labor was still not high enough to compete with industrial wage rates even at the most favorable 1973 farm product prices. As such, few farmers could consider expanding their use of really reliable, high-paid, skilled labor. The return to labor can be increased by additional investments in land or using less labor relative to other inputs. 3. Cash operating expenditures were too great relative to the other categories of inputs, as reflected by the low 170 returns of this input category. This conclusion holds despite indications that the analysis somewhat underestimates the marginal value product of operating expenditure. The adjusted estimate of the marginal value product of operating expenses was slightly over a dollar ($1.01) for a dollar spent in 197 2 which does not cover interest on the use of working capital for an average of six months. This suggests that care must be exercised in handling operating expenditures. The low earning power of productive cash expenses might be partly attributed to the high percentage (51 percent) of part-time farming among the 61 farms interviewed. Generally, a part-time farmer may tend to spend more cash for inputs in order to have more time for off-farm work. 4. The results of this study indicate that machinery was not used efficiently on farms in Clinton and Ionia counties during 1972, as reflected by the low returns found for this input category. Though the estimated marginal value product of machinery was probably biased downward, returns are still believed insufficient to cover the cost of using the input. The adjusted estimate of the marginal earning of machinery was between 12 and 21 cents per dollar per year in 1972 and 20 and 35 cents in 1973. hardly covers depreciation, interest, This return insurance, and main­ tenance which usually amount to at least 25 cents per dollar invested in machinery. The comparatively low return to 171 machinery reflected a large machinery investment of $16,886 for a typical farm which might profitably be reduced both relatively and absolutely. Therefore, further investment in machinery seems unprofitable unless land and other supporting inputs are also increased. 5. The empirical evidence indicates that economies to scale do not exist beyond 150 tillable acres at the farm-firm level^ but that increasing returns to scale pre­ vail for farms with less than 150 acres. 6. The results of this study show that the typical farm is not extremely maladjusted; however, improvement may often be obtained by some adjustment in the use of resources. The main adjustments needed seem to be: (1) to moderately increase farm size by expanding tillable acreage, (2) to reduce labor use, and (3) to be more careful in handling cash expenditure and machinery investment. An increase in the size of farm would tend to reduce the earning power of land at the margin, but at the same time would increase the marginal earning of machinery, operating expenditures and ^The results of this study did not indicate that other than constant returns to scale prevail at the farm-firm level beyond 150 tillable acres. This fact does not neces­ sarily lead to the conclusion that farm size would not grow beyond that level. Theoretically, increasing sizes of farms are possible under constant returns. However, the problems of consolidating small farms and buying out old farms at high acquisition costs for reliable labor are an important real world constraint on farm size. 172 labor. Consequently, higher farm income would be generated by larger size due to a better farm resource combination, involving more land relative to machinery and, especially, labor. Some ways of reducing machinery investment have been noted, but much improvement in this direction cannot be assured because of indivisibility of machinery. An alterna­ tive organization of typical farms based on the adjusted regression coefficients and on the assumption of constant returns to scale was presented in the last part of Chapter V. The results of the study provide a basis of estimating returns that might have been realized under the same condi­ tions , but with different farm organization. However, future returns depend on future conditions of prices, nology, tech­ institutions, weather conditions and human factors. In applying the results of this study, these factors together with the limitations of the study previously mentioned must be taken into account. Findings of the Land Utilization Survey One of the objectives of this study was to identify the main factors limiting the utilization of more agricul­ tural land on Miami/Conover soils in south-central Michigan. Another was to estimate potential land supplies and a third was to develop policy implications and consequences for alternative ways of using Miami/Conover soils. The approach 173 was descriptive with emphasis on acreages of land used for various purposes, rather than on theoretical concepts. The major findings of this phase of the study may be summarized as follows: 1. Most Miami/Conover soils for crop production, wheat, (68 percent) were used including corn, legume-grass hay, soybean, field beans, oats and other crops. fairly large areas were in woodland, Also, accounting for 7.91 percent of the total area while pasture constituted 3.82 percent. 2. The most important physical factor limiting the use of Miami/Conover soil is poor drainage (particularly for the Conover), followed by operator's age, high off-farm wage rates and speculative investment. Other factors include property rights, other physical reasons and special farm p r a c t i c e s . 3. Several land policy implications were derived from this study. They involve land prices, land utilization between the agricultural and nonagricultural sectors, utilization in agriculture, product price policies 4. land institutional arrangements and (see Chapter VI for details). Agricultural production could be increased through additional acreage of new land. By clearing and draining, a total of approximately 23,637 acres of Miami/Conover soils could be pulled into production in the two counties.^ ------ z------- This figure does not include 24,016 acres (9.5 percent) of diverted land, most of which is now in production. 174 Such land includes 3,868 acres (1.53 percent) of idle cropland, 9,657 acres (3.82 percent) of plowable pasture land and 10,112 acres (4 percent) of woodland. 5. Approximately $1,380,400 of earnings to land would be generated by bringing an additional 23,637 acres of new land into production on Miami or better soils in the two counties under 1973 price relationships. This figure is obtained by assuming that the actual increase in production through crop use of idle, pasture land and woodland is 80 percent of that for land normally used for row and grain crops. 6. Uses of agricultural land will not be fixed for certain crops or even among nonfarm uses. Those are expected to undergo continual shifts depending on changes in physical, economic, technological and institutional factors. 7. Land prices in the studied area can be expected to increase moderately due to: (1) comparatively high returns to land as indicated by both functional analysis and programmed plans under 1972 and 1973 price relations, (2) the inelastic supply of land, tionary economy, (3) a continued infla­ (4) continued demand for living space and population pressures increase and (5) loss minimizing on labor and equipment now fixed in agricultural use. 8. Moderate farm size expansion would be expected as the estimated margional value productivity of land in the 175 studied area was found to be higher than return estimated to be necessary to cover the cost of using the input. This trend may continue as larger and more efficient machines were developed and their adoption of these machines takes place. 9. Agricultural production can be increased through improvement of agricultural practices and intensified cul­ tivation on existing land, without the addition of new land, i.e. by selection and adaptation of crop varieties, appropriate use of fertilizers, better tillage, drainage, and control of the water table. Implications The results of this study reveal important implications about the utilization of land and associated inputs for cash grain production. The programmed results indicated that it would be profitable to expand farm size under assumed restraints on off-farm work, output conditions. results, assumed prices, and assumed The functional analysis showed similar indicating that a moderate increase of farm size would be profitable if labor is available. The desirability of expanding farm size as shown by both the linear programming and functional analyses imply that, given labor availability, higher farm income would be generated if more land were used relative to machinery, productive cash expenditure and especially labor. Probably 176 land values in the studied area will continue to be bid up as farmers seek more land for farming along with the increase in demand for land for residential and industrial purposes. More unused cropland, and plowable pasture land can be expected to be brought into cultivation if product prices remain high with comparatively stable input prices. Since quite a few acres of cropland (about 11 percent of total area) on Miami and Conover soils were either diverted by government set-aside programs or simply idle in 1972, an increase in crop area has probably occurred since the termination of government production control programs. Adjustment in the utilization of agricultural land would be reflected in the structure of land use. land will probably be removed by residential, Some farm industrial and other nonfarm uses, but the relative decline will be small due to the considerable amount of potential cropland in the area studied. At the present time, the encroachment on farm land has not yet caused serious inroads on total agricultural production. Nevertheless, encroachment will have a cumulative adverse effect on crop production if it continues indefinitely. Under this situation, land-use policy should focus on the maintenance of an adequate balance between farm and nonfarm uses of land. The policy should be designed to preserve the intrinsically best farm land and protect this land from the encroachment of nonfarm uses while leaving agriculturally inferior land for residential and other uses. 177 Labor availability and use also affected expansion of farm size and adjustment in the utilization of farm land. Both the Cobb-Douglas study and the programmed results indicate that earnings to labor are lower than obtainable from off-farm employment. The study also indicated that the earning power of farm labor was not high enough to compete with industrial wage rates even at the most favorable 1973 farm product prices. As such, few farmers could con­ sider expanding their use of really reliable, high-paid, skilled labor. On the other hand, programmed results indicated that it would be profitable for family members and operators to work off the farm. functional analysis. The same results were obtained from the Under this situation, the majority of young rural people have been attracted by higher earnings of nonfarm work, and have left farming. This trend coupled with the continual retirement and other forces cause the total farm labor force to decline. Larger farm sizes and high labor costs imply that more capital is needed to replace labor. This indicates that there will be demand for capital to expand if labor is available (Table 4.3). In an economic environment characterized by a strong demand for labor saving technology, the industrial sector responds by developing and producing a stream of such new machines. As larger, and more efficient machines are 178 developed and adopted, impetus to increase farm sizes develops and creates some pressure on land prices. With reduced amount of total labor, an increase in the use of larger machines, the trend of increasing farm size may continue. However, farm size should not be expected to expand without limit. The programmed results indicates that labor (including managerial labor) would eventually become a major restriction on expansion of farm size (Table 4.8, B-l, B-2, B - 3 ) . The trend toward increasing farm size will be offset by continual increasing inputs costs for machinery, fuel, herbicides, fertilizers etc.; reduced availability of both skilled labor and entrepreneurs; and product price uncertainty. One question still remains to be answered. That is: the possibility and profitability of establishing a new cash grain farm in the area studied. The results of this study imply that at prospective farm product and input prices, a farmer should not expected to receive simultaneously marginal earnings of $50 per acre on $500 an acre land to cover taxes, depreciation, interest and repairs on fences, for labor of the operator; tile, etc.; $9,600 per year 25 percent on machinery investment to cover interest, depreciation and repairs; per dollar expended on fuel, lubricants, and a $1.06 fertilizer, 179 herbicides, etc., plus interest on the use of the committed money for an average of six months. Thus, the farm reorgan­ izations suggested above are mainly for those who have substantial unrecoverable investments in their farms and for those who have committed their lives to cash crop farming on Miami or better soils in Clinton and Ionia counties and in similar central Michigan areas. Those cap­ able of earning over $9,600 annually elsewhere should be extremely careful about leaving such employment to risk an investment of, say, $300,000 in land and machinery to establish new cash crop farm businesses unless they can find substantial tax management benefits, product markets, labor, fuel, special stable or access to stable cheaper supplies of fertilizer and/or other agro-chemicals and are able to obtain much higher yields than the typical farmer without increasing expenditures much beyond typical levels .^ Future Study Indicated This study centered on the problems of resource pro­ ductivities, farm organization and land utilization on the "heavy and lower" soil associations including Miami and ^Lee, Yung-Chang and Johnson, Glenn L . , "Are Central Michigan Cash Crop Farmers Getting Rich?" Michigan Fann Economics. Department of Agricultural Economics, Michigan State University, June, 1974, No. 377, p. 3. 180 Conover soils. Similar studies are needed on other loca­ tions in southern Michigan and on the "lighter and higher" soil associations including Hillsdale, Bellfontaine and Coloma. Emphasis should be placed on economic, physical, technological and institutional determinants of land use along with supply and demand considerations for farm products and farm i n p u t s . The study would have to be multidiscip­ linary taking into account the utilization of advanced bio-chemical, irrigation and other technologies and the technical problems of roughage, and livestock production. food grain and feed grain APPENDICES APPENDIX A Supplementary Tabl 181 Table A-l. Initial Resource Restrictions for Representative Farms Operators Age Initial Resource Unit Over 55 yrs Medium* 24 - 55 years Medium Large 93 156 438 211 1,144 1,236 2,024 1,268 583 632 1,072 703 703 Small Cropland acre Farm Labor In Season I man hrs Farm Labor In Season 2 11 Farm Labor In Season 3 If 637 660 1,101 Farm Labor In Season 4 It 286 324 516 317 Farm Labor In Season 5 ft 572 618 1,058 706 2,904 3,024 3,650 3,257 13,714 9,286 Managerial Labor Op. hrs Annual Cash Account $ 4,275 4,412 Chattel Mortgage $ 5,394 8,616 19,120 5,600 Real Estate Mortgage $ 18,600 31,176 43,952 25,714 1,728 1,402 587 389 Family Off-farm work It 384 565 411 365 Land Rented in Limit acre 134 184 131 213 Land bought in Limit tt 117 82 54 114 tfoodland tt 9 22 25 12 Pasture land tt 1.03 Cperator Off-farm work Hours 5.54 14.53 8.17 280 280 280 280 Power capacity (period 2) ii 390 390 390 390 Power capacity (period 3) it 180 180 180 180 Power capacity (period 4) it 170 170 170 170 200 200 200 Power capacity (period 1) Power capacity (period 5) Hours a 200 ; 182 Table A-2. Soybeans (2 years rotation) - Estimated Annual Costs and Returns Per Acre Item I. Price or Cost/Unit ($) Quantity Value or Cost ($) bu. 5.50 25 137.50 8.50 Inccme Yield per acre II. Unit Variable Cash Costs Seed bu. Fertilizer (n -p 2o 3-k 2o ) bu. Herbicide (Amlben) lb. 4.83 1 4.83 acre 5.86 1 5.86 acre 3.56 1 3.56 .10 25 2.50 .2H-.19-.067 .83 30+50+15 7.06 17.71 Power & Machinery Costs (Preharvest) | Power & Machinery Costs (Harvest) Hauling III. bu. Total Variable Cash I Cost J $ - ....... 41.52 Sources! (l) Costs and Returns for Major Cash Crons in Southern Michigan. revised by R.L.Meekhof, L.J. Connor and S. B. Nott, Dept, of Agri. Econ. M.S.U. September 1974-, (2) Fertilizer Reconendatio-is for Michigan Vegetables and Field Crops, by D. R. Christenson, R.E. Lucas and E.C. Doll, Crop and Soil Sciences Dept., M.S.U., Nov. 1972, and (3) Weed Control in Field Crops, by W.F. neggitt, Dept, of Crop and Soil Sciences, I’i. S .U . , January 1974-. 183 Table A-3* Soybeans (3, 4, 5 years rotation) - Estimated Annual Costs and Returns Per Acre Item I. Price or Cost/Unit ($) Quantity Value or Cost (&) 30 165.00 Income Yield per acre II. Unit bu. 5.50 Seed bu. 8.50 Fertilizer (n - p 2o 5-k 2o ) Ib. .24-.19-.067 Herbicide (Amiben) lb. 4.83 1 4.83 acre 5.86 1 5.86 acre 3.56 1 3.56 bu. .10 30 3.00 Variable Cash Costs .83 7.06 40+25+25 16.02 Power & Machinery Costs (preharvest) Power Machinery Costs (Harvest) Hauling III. Total Variable Cash Cost $ Sources< Same as Table A-2. 40.33 184 Table A-4. C o m (No cashcrop preceded) - Estimated Annual Costs and Returns Per Acre Unit Item I. Quantity Value or Cost ($) 90 202.50 Income bu. 2.25 Seed bu. 25.00 Fertilizer (n - p 2o 5- k 2o ) lb. .24-.19-.067 Herbicice Atrozme lb. 2.30 2 4.60 acre 4.81 1 4.81 acre 4.40 1 4.40 bu. .10 90 9.00 Yield per acre II. Price or CoBt/Unit ($) Variable Cash Costs (80W) .21 5.25 100+50+50 36.85 Power & Machinery Cost (Preharvest) Power Machinery Cost (Harvest) Hauling III. Total Variable Cash Cost $ Sources> Same as Table A-2. 64.91 185 Table A-5. C o m (preceded by cash crop) - Estimated Annual Costs and Returns per Acre Unit Item I. Quantity Value or Cost ($) 90 202.50 Income bu. 2.25 Seed bu. 25.00 Fertilizer (N-PgOg^O) lb. Yield per acre II. Price or Cost/Unit ($) Variable Cash Costs .24-.19-.067 .21 5.25 100+50+25 35.18 Herbicide Bladex + Lasso lb. + gal, 2.85 + 13.50 1 1 / 2 + 2 qt. 11.03 Power & Machinery Cost (preharvest) acre 4.81 1 4.81 acre 4.40 1 4.40 .10 90 9-00 Power & Machinery Cost (harvest) Hauling III. Total Variable Cash Cost Sourcesi Same as Table A-2. 69.67 186 Table A-6. Wheat (no cash crop preceded) - Estimated Annual Costs and Returns per Acre Item I. Unit Quantity Value or Cost ($) Income Yield per acre II. Price or Cost/Unit ($) bu. 4.25 bu. 4.50 45 191.25 Variable cash costs Seed Fertilizer (n -p o o 5-k 2o ) lb. .24-.19-.067 1.75 7.88 45+75+25 26.73 Power & Machinery Cost Preharvest acre 4.06 1 4.06 acre bu. 2.06 .10 1 45 2.06 4.50 Power & Machinery Cost Harvest Hauling III. Total Variable Cash Cost Sourcesi Same as Table A-2. 45.23 187 Table A-7. Wheat (preceded by cash crop)— Estimated Annual Costs and Returns per Acre Item I. Quantity I Value or Cost ($) bu. 4.25 bu. 4.50 lb. .24-.19-.067 60+75+50 32.00 Power & Machinery Cost Preharvest acre 4.06 1 4.06 Power & Machinery Cost Harvest acre 2.06 1 2.06 bu. .10 45 4.50 45 191.25 Variable Cash Cost Seed Fertilizer (n - p 2o 5-k 2o ) Hauling III. Price or Cost/Unit ($) Income Yield per acre II. Unit Total Variable Cash Cost $ Sourcesi Same as Table A-2. 1.75 7.88 50.50 188 Table A-8. Oats - Estimated Annual Costs and Returns per Acre Item I. bu. 1.25 bu. 3.50 Quantity Value or Cost ($) 81.25 65 Variable Cash Costs Seed Fertilizer (n - p 2o 5+ k 2o ) lb. .24-.19-.067 2.25 45+50+15 7.88 21.31 1.50 Herbicide (2,4-D) lb. 6.00 Power & machin­ ery cost Preharvest acre 6.39 1 6.39 Power & machin­ ery cost Harvest acre 2.05 1 2.05 bu. .10 65 6.50 Hauling III. Price or Cost/Unit ($) Income Yield per acre II. Unit Total Variable Cash Cost $ Sourcesi Same as Table A-2. .25 45.63 ______________ 189 Table A-9. Field Beans - Estimated Annual Costs and Returns per Acre Item I. II. Incane Yield per acre Variable Cash Costs Seed Fertilizer (n -p 2o 5+k 2o ) Herbicide (Eptcm) Price or Cost/Unit ($) cwt. 15.00 bu. 45.00 lb. .24-.19-.067 Quantity Value or Cost ($) 14 210.00 •67 4CB-25+50 30.15 17.70 lb. 2.41 2 4.82 Power & Machin­ ery cost Preharvest acre 11.08 1 11.08 Power & Machin­ ery cost Harvest acre 3.56 1 3.56 bu. .10 Hauling III. Unit Total Variable Cash Cost $ Soucesi Same as Table A-2. 23.30 2.33 69.64 190 A-iO. Ass umed Fer tilizer Requirements for Specified Cash Crop Enterprises by Soil Group, Southern Michigan!/ Soil Group Crop S1 (Loam-Clay Loam) S2 (Loam-Clay Loam) 120+60+50 100+50+50 80+ 25+50 70+0+50 Wheat 60+75+50 60+ 75+5 0 60+25+75 60+25+75 Oats 40+50+50 40+50+50 40+25+75 40+ 25+50 Soybeans 10+50+30 10+25+25 10+0+50 10+0+25 Field beans 40+50+50 40+ 25+50 0+50+75 0+50+75 Corn for grain Alfalfa^ 40+75+100 Sugar beets 1/ S4 (Loamy Sand) — 0+25+75 — 0+25+75 — -- The actual pounds of N+P gOg+K^O are specified. Inputs are based on the assumed yie lds in App endix Table 2 ana rec ommendations in:- Fertilizer Recommendations for Michigan Vegetables and Field Crops, Mic higan State Uni versity Extension Bulletin #-550, Nov ember -972. When the assumed yield did not coincide, Interpolations wer e res pectively made. Fer tilizer inputs w e r e based on the following soil test assumptions: N - No legumes or manure P - 20-39 pounds available per acre for loam-cl ay loams - 40-59 pounds available per acre for sandy loams and loamy sands ICj 2/ — S3 (Sandy Loam) Annual topdressing. 120-159 pounds available per acre for loam-clay loams 120-169 pounds available per acre for sandy loams and loamy sands. Seeding fertili zer is charged to oats enterprise. Sourcej R.L. Meekhof,L.J. Connor and S.B. Nott, Costs and Returns for Ma.ior Cash Crops in Southern Michigan. Agri. Econ. Report No, 277. Dept, of Agri. Econ, M.S.U. P. 2 6 , 191 Table A - 11. Estimated Labor Requirements Per Acre Per Month for Selected Cash Crops Crop L a b o r N (Hrs) Com Soybeans Wheat Oats Field Beans March .1 --- --- .4 April 1.2 .8 -- 1.8 .4 May 2.1 1.6 -- --- 1.2 June .7 -- .4 1.6 July .9 -- 1.1 .8 1.9 Augus t -- .9 -- 1.6 .5 September -- .8 .4 -- October November 1.3 .8 -- Total Annual Labor 6.5 5.6 Source: .9 1.8 -- --- .8 2.4 -- --- .4 --- 4.5 5.0 8.0 Unpublished data, Department of Agricultural Economics, Michigan State University. 192 T&ULe A^12, Estimated Annual Madhiner, Power, and Labor Requirements Per Acre for Specified Crop Enterprises, Southern Michigan Crop and Operations Times Over Dates Machine Time (hrs.) Power Time (hrs.) Labor Time (hrs.) .46 .45 .35 .85 2.11 .07 .46 .45 .35 .85 2.18 .09 .47 .59 .36 .94 2.45 .46 .29 .13 .26 .63 1.77 .07 .46 .29 .13 .26 .63 1.84 .09 .47 .36 .16 .27 jJO 2.05' .46 .18 .17 .44 .47 .18 .19 .52 Corn - S^ Soils Fertilize (bulk spreader) Plow (moldboard) Plant, fertilize, and spray Cultivate Harvest (combine) Total Requirements Corn - S2 , S 3 and 3/15- 4/30 4/1 - 5/15 5/1 - 5/31 5/25- 6/25 10/10-11/30 Soils Fertilize (bulk spreader) Plow (moldboard) Plant and fertilize Spray Cultivate Harvest (combine) Total 'Requirements Wheat, Plow (moldboard) Disc (tandem) Harrow (spring-tooth) Drill and fertilize Harvest (combine) Total Requirements' Oat? Plow (moldboard) Disc (tandem) Harrow (spring-tooth) 4)rill and fertilize Spray Harvest (combine) Total Requirements 3/15- 4/30 4/1 - 5/15 5/1 - 5/31 5/10- 6/10 5/25- 6/25 10/10-11/30 8/1 8/158/159/107/10- 8/31 9/15 9/15 9/25 7/30 10/1 -11/20 3/153/154/1 6/1 7/10- 4/15 4/15 5/1 6/15 8/10 Soybeans Plow (moldboard) Harrow (spring-tooth) Plant, fertilize, and spray Cultivate Harvest (combine) Total Requirements 4/1 - 5/15 5/1 - 5/20 5/20- 6/10 7/1 - 7/25 9/15-10/15 Field Deans Plow (m^lddoard) Disc and spray (tandem) Plant and fertilize Cultivate Full and windrow Harvest (c ombine) Total Requirements- 4/155/206/1 7/1 8/258/25- Source! 1 1 1 1 1 5/31 6/10 6/15 7/30 9/25 9/25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 1 1 1 1 1 1 1 1 2 1 1 .46 .ia .17 .44 .40 1.65 .40 .44 1.65 1.80 .46 .18 .17 .44 .13 47 18 .19 .52 .16 .46 .18 .17 .44 .13 .40 1.78 .40 .44 1.78 1.96 .46 .17 .45 .35 .55 1.98 .46 .17 .45 .35 .55 1.98 .47 .19 .59 .36 .61 .46 .46 .21 .21 .39 .70 .39 .55 2.70 .39 .70 .39 .55 2.70 2.22 .47 .23 .48 .72 .43 .61 2.94 L.J, Connor, Costs and Returns for Ma.jor Cash Crops in Southern HlcMfr*n. Agricultural Economics F c r r t Ho, 87, Dept,'of Agri, Econ, Michigan State University, 1967. ?• Table A-13. Critical Planting and Harvesting Periods and Losses in Yield Resulting From Late Planting and Harvesting Crop and Maximum Yield Corn 85 bu. Navy Beans 23 bu. May 1-10 May 15-25 June 1-10 Oct. 5-15 Oct. 1-10 Aug. 25-Sept. 15 Late Operations Causing Reductions in Yield Yield Reductions Number of VJeeks Operation is Late 1 *2 planting harvesting 5 1 10 2 planting harvesting 1 1.5 2 3.5 planting harvesting 1 1.5 planting harvesting 2 2 k It 3 1U 3 5 (bushels) 6 7 8 9 10 15 20 25 5 7 5 6.5 13 11.5 17.0 2 3.5 5 6.5 13 11.5 20 20 23 It 8 9 16 20 35 1*5' 193 Soybeans 28 bu. Critical Period to Obtain Maximum Yield Harvesting Planting Uheat It5 bu. Source: Sept. 16-25 July 10-20 Unpublished data, Department of Crop Science, Michigan State University. Table A-l4. Crop Com (38 in. rows) Assured Crop Yields, Fertilizer and Herbicide Requirements; and Other Production Practices for the Synthetic Cash-Grain Farm in Southern Piiciiiran Maximum Assumed Possible Yield Seed Require­ ments (bu./acre) (bu.) Fertilizer Requirements n -p 2o 5(lbs./acre) Herbicide Require­ ments (lbs./acre) 80-0-0 85 .21 Other Production Practices Critical Time Times Period for Maximum Operation Over Possible YieldsfL/ (dates) bulk spread fertilizer plow plant & fertilize 10-50-25 2 lbs. atrazine 28 .83 Navy beans (28 in. rows) 23 .67 Wheat 30-50-15 45 1.75 Source: 30-50-15 45-75-25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Mav 1 - May 10 Oct. 5 - Oct. 15 May 15 - Hay 25 Oct. 1 -"Oct. 10 June 1 - June 10 Aum. 25 - Sept. 15 Sept. 16 - Sept. 25 July 10 - July.20 Larry J. Connor, Costs and Returns for Major Cash Crops in Southern Mlchlp-an, Apricultural Economics Report No. 87, Department of Arricultural Economics, Michipan State University, 1967. G,L, Beniamin and L.J. Connor, Economies of Size of Machinery Systems on Southarn j i ' n M C a s h - O r a l n Farms. Agri, Econ. Report No, llz, uept/oi Agrit^con. 194 Soybeans (20 in. rows) spray cultivate harvest plow harrow 1 lb. amiben plant, fertilize spray cultivate harvest plow 2 lbs. eptan disc & spray plant & fertilize cultivate pull & windrow harvest plow disc harrow drill & fertilize harvest 1 1 1 195 Tame A-15.- TIME A V A I L A B L E FOR FIELD WORK BY C A L E N D A R P E R I O D FOR WELL DRAINED SOILS Period Calendar days % Good Days 16 i* 5 my 11 - 18 8 37 MAY 1 9 - 2 6 8 65 MAY 27 - J U N E 3 8 70 SEPT, 27 - OCT. 17 21 53 OCT. 18 - NOV. 7 21 33 april 26 - my 10 Nov. 8 - 2 8 19 Good days available depict the percent of days that historically have been available in 7 out of 10 years for well drained soils. In two years out of 10, fewer days will be available than depicted. Fall field days can be adjusted upward 10* for combining and picking operations. Sourcei Unpublished Data,' Department of Agricultural Economics, Michigan State University, 196 Table A-l6.* Climatic Week Calendar Period Nunfcer of Days Lost in a 6-Day Work Week Due to Inclement Weather No. Ten Year Average Precipitation1 (inch) April 1-17 April 8 -lU April 15-21 April 22-28 April 29-May 5 May 6-12 May 13-19 May 20-26 May 27-June 2 June 3-9 June 10-16 June 17-23 June 2U-30 July 1-7 July 8 -lU July 15-21 July 22-28 July 29-Aug. k Aug. 5-11 Aug. 12-18 Aug. 19-25 Aug. 26-Sept. 1 Sept. 2-8 Sept. 9-15 Sept. 16-22 Sept. 23-29 Sept. 30-0ct. 6 Oct. 7-13 Oct. 1^-20 Oct. 21-27 Oct. 28-Nov. 3 Nov. 1+-10 Nov. 11-17 Nov. 18-2U Nov. 25-Dec. 1 Number of Ten Hour Days Lost Per Neek^ (days) Number of Hours Lost Per Week (hours) 1 .75 1.3 2 .2 8 .6 6 .8 1 .6 1 .8 1 .0 18 8 16 18 10 1.7 17 1 .0 .8 .8 10 8 8 3 1+ 5 6 7 8 9 .73 .1*0 .6 8 .1+2 .30 .33 Average Number of Hours Lost Per Day (hours) 2.51 1.11+ 2.29 2.57 1.1+3 2.1+3 1.1+3 1 .11+ 1 .11+ Number of Days Lost in a Six-Dpy Work Week^ (days) 1.5** .68 1.37 1.51+ .8 6 _ %* 1 .1+6 .8 6 .6 8 .66 10 11 12 1 .1 6 2.7 27 3 .8 6 2.32 .91 2 .2 22 .6 0 .36 1.5 .9 15 9 1 .8 8 1 .2 8 13 lU 15 16 11 16 .57 .50 .75 .56 .61+ .81+ .70 .1+1 .63 .99 .69 .50 .1*5 .37 .1+2 .1*3 .1+7 1 .6 1 .1 1 .1+ 1 .2 1 .8 1 .1+ 1 .6 2 .0 3.1U 2 .11+ 1.29 2.29 1.57 lit 2 .0 0 1 .2 0 16 20 2.29 1.7 17 1 .0 10 1.5 2 .1+ 1.7 15 1 .2 1 .1 12 11 2.1+3 1.1+3 2 .11+ 3-1+3 2.1+3 1.71 1.57 1.29 1.1+3 1.57 1.71 2 .1 U 1.37 1.71 1 .1+6 .86 17 18 19 20 21 22 23 2k 25 26 27 28 29 30 31 32 33 3U 35 .6 6 .1+1* .6 0 .2 6 .58 .9 •U 1.37 .91+ ll» 2 .0 0 1 .2 0 12 18 1.71 2.57 1.03 1.51* 2k 17 9 1 .0 1 .1 1 .2 10 * 11 12 1.5 .7 1.5 15 7 15 2 .8 6 ' 1 .0 0 2 .11+ 1 .2 8 2 .0 6 1 .1+6 1.03 .91* .77 .86 .91+ 1.03 1 .2 8 .6 0 1 .2 8 ^■Data pertains to the years 1958 to 1967- The information was obtained from the U.S. Weather Bureau, East Lansing, Michigan. 2 Based on the regression line; Days Lost = .0l+ + 2.31+ (In. of Precipitation). ^Values in column 5 are 6/10 of the values in column U. Multiply by 6 to get the number of hours lost in a 6 -day work week and divide by 10 to convert hours lost into days lost. Sources G.L. Benjamin and L.J. Connor, Economies of Size of Machinery Systems on Southern Michigan Cash-Graln Farms. Agricultural Economics Report No. 112, Dept, of Agri, Econ. , Michigan State University. P. Table A-17.' Factors Used to Estimate Machine, Power, and Labor Requirements for Specified Field Operations in Southern Michigan Operation Table continued on next page. 120 78 56 Operating Speed (MPH) 3.0 Fieid Efficiency— (percent) 70 Acres/ Machine Hour 2/ (acres) 2.52 Han Hrs. as Percent of Power Hrs. (percent) 111 Man Hrs./ Acre/Time Over (hrs.) .44 .63 .85 .55 111 111 111 .70 .94 .61 .68 111 111 111 102 1.02 '1.10 Hrs./Acre /Time Over— (hrs.) .40 70 70 65 1.60 1.18 112 3.0 3.0 2.5 76 56 56 64 3.0 3.0 3.0 4.0 65 65 60 85 1.48 1.09 2.18 .92 .99 .46 152 3.8 3.8 60 60 3.47 2.55 .29 .39 124 124 .36 .48 3.6 3.6 3.3 3.1 55 55 65 60 3.01 .33 .45 .44 .51 132 132 119 127 .44 .59 .52 .65 3.0 3.0 4.5 4.2 5.0 4.0 4.0 3.0 85 85 85 80 80 80 80 75 .26 .35 .18 104 104 .27 .36 .18 .23 .19 112 152 112 105 105 152 112 144 144 144 144 84 112 1.82 1.01 2.22 2.25 1.95 3.88 2.86 5.51 4.84 5.76 4.61 2.69 2.52 .21 102 110 .17 108 .22 100 100 110 .37 .39 .75 .47 .22 .41 .43 197 Combine small grain (10 ft.) Combine corn (two-row): 38" rows 28" rows Combine soybeans and field beans Pick corn (two-row): 38" rows 28" rows Harvest beets (two-row) Plow (4-16") Plant 6 fertilize (four-row): 38" rows 28" rows Plant, fertilize 6 spray (four-row): 38" rows 28" rows Drill and fertilize (15-7") Drill, fertilize, and spray (15-7") Cultivate (four-row): 38" rows 28" rows Disc (12 ft.) Disc and spray (12 f t .) Harrow (12 ft.) Windrow (12 ft.) Mow (7 ft.) Pull and windrow beans (four-row) Width of Machine (inches) Tabje A-l?.' continued Operation Top beets (three-row) Bale hay Mow-condition Spray (six-row): 38" rows 28" rows Spread fertilizer (30 ft.) Width of Machine (inches) 84 168 84 228 168 360 Operating Speed (MPH) 5.0 4.0 3.8 5.0 5.0 5.0 Field Efficiency!/ (percent) 85 75 75 65 65 80 Acres/ Machine Hour 2/ (acres) 3.57 5.04 2.39 Hrs./Acre /Time Over— (hrs.) .28 7.41 5.V6 14.40 1/ Man Hrs. Mart Hrs./ as Percent Acre/Time of Power Hrs., Over (hrs.) (percent) 100 .28 .20 111 .22 .42 105 .44 .13 .18 .07 125 125 133 .16 .23 .09 — Field efficiency refers to the percentage of field time remaining for effective production after "lost time" has been deducted for such items as an adjustment, repairs, lubrication, and turning at ends. 2/ — The capacity of field machines in acres per hour was computed as follows: (Machine width in inches) (Speed in MPH) (Field efficiency) 100 3/ Hours of machine and power time required to cover one acre. Sourosi L.J. Connor, Costs and Returns For Ma.ior Cash Crops in Southern Michigan. . Agricultural Economies Report No. 87, Department of Agricultural Economics. Michigan State University, 1967, pp. 32- 33.' * 199 Table A-18. ESTIMATED HOURS OF FIELD OPERATION TIME REQU I R E D FOR H ARVESTING CORN WITH SELECTED MACHINES. 2/ M a c h i ne Hours R eq uired to Type of Harvesting Equipment Harvesting Field Speed. M.P.H. Efficiency Acres H a r v e s t :________ per Hour 100 A cr es Your Crop (40-Inch Row Spacing) 1-Row Picker 3.00 2-Row Picker 3.00 2-Row Pic ker-Sheller 3.00 2 -Row Picker-Grinder 3.00 2-Row Combine (Shell) 3.00 2-Row C o m bine 3.00 3-Row C ombine (Shell) 3.00 3-Row Combi ne (Grind) 3.00 4 -Row Combine (Shell) 2.75 4 -Row Combine (Grind) 2.75 .67 .65 .67 .65 .70 .67 .70 .67 .65 .62 .80 1.56 1.61 1.56 1.68 1.61 2.52 2.41 2.86 2.73 125 65 63 65 60 63 40 42 35 37 (30-Inch Row Spacing) 2-Row Picker 3.00 2-Row P i c k e r - S h e l )er 3.00 2 -Row Picker-Gr indor 3.00 3-Row C on.bine (Shell) 3.00 J-Row Combine (Gri nd) 3.00 4-Row Combine (Shell) 2.75 4 -Row Combine (Gri nd) 2.75 6 -Row Comb ine (Shell) 2.50 2.50 6-Row Combine (Grind) .65 .67 .65 .70 .67 .65 .62 .65 .62 1.17 1.21 1.17 1.89 1.81 2.15 2.05 2.93 2.79 86 83 86 53 56 47 49 35 36 (20-Inch Row Spaci up.) 6 -Row C o m b i n e (Shell) 2.50 2.50 6-Kow Combine ( Gr i nd) 2.50 8-Row Combi ne (Shell) 2.50 8 -Row Combi no (Gr ind) .65 .62 .65 .62 1.95 1.86 2.60 2.48 52 54 39 41 2/ Estimates based on 100 bushel corn yieids. For yields of 125 bushels and over, increase the time for h ar vesting 100 acres by 10 per cent. For yields of 75 bushels or less, discount the time for harvesting 100 acres by 5 per cent. Sources “Field Efficiency Guides" by R,G. White, Agricultural Engineer­ ing Department, Michigan State University, April, 1966, Table A-19. Estimated New Costs, Description, Years and Hours of Use of Specified Power and Machinery Items, Southern Michigan Item Description New, , Cost1 ' Years of 2/ Use1 ' (dol.) Diesel, 105 HP (PTO) Diesel, 64 HP (PTO) 12 ft. SP, with grain platform Four-row Two-row, mounted Size 14x18, PTO, twine tie 11,593 9,305 11,500 4,508 3,713 2,491 787 8,450 Two-row 4,432 6-16", semi-mounted, automatic Eight-row with fertilizer attachment 6,767 2,193 16-10" with fertilizer attachment Eight-row 2,367 1,657 12 ft. 403 12 ft. 1,709 12 ft. (PTO) 825 Four-row Eight-row, pulltype with tank 622 Four-row 250 Four-row, double drum, rubber & steel flail 5,000 2,870 7 ft. 702 7 ft. 765 Grain box with tires, 8 ton of 3/ Use1 Hours of Use Per Yeai (yrs.) (hrs.) (hrs.) 10 10 10 10 10 10 10 8 10 10 12 10 12 15 8 10 10 10 10 8 10 10 6,500 6,500 2,000 1,000 1,000 2,000 2,000 1,200 1,500 1,000 804 1,500 1,200 1,500 1,200 1,000 1,200 1,200 1,200 1,600 1,500 2,500 650 650 200 100 100 200 200 150 150 100 67 150 100 100 150 100 120 120 120 200 150 250 V Estimates of new costs and descriptions were obtained from machinery companies, local dealers, and from National Farm and Power Equipment Dealers Assoc., Official Guide, Tractors and Farm Equipment, Fall, 1974. 2/ Estimates were obtained from farmers enrolled in Michigan State University Telfarm Project. 3/ Years of use times annual hours of use. Source. R.L. JJeekhof, L.J. Connor and-S.B. Nott, Costs and Returns For M a W l £ p t° im. fian-‘ Agri* Ec0n* Cash G r o m **1°* N°. 2 77, Dept, of Agri. Econ. M.S.U. 200 Tractor Tractor Combine Corn Head Corn Picker Baler Bale Thrower Beet Harvester Plow Corn & Bean Planter Grain Drill Cultivator Tandem Disc Spring-tooth Harrow Windrower Bean Puller Sprayer Spray Attachment Beater-Topper Mower-Conditioner Mower Grain Wagon Total Hours 201 Table A-20. Farm No. The Original Observations Obtained from Sixty-One Cash Grain Farms *i Gross Income *2 Land (Acre) *3 Labor (Months) X4 Expenses ($) X5 Machine Investment (?) X6 Buildii ($) 1 2 3 4 5 21,318 47,351 39,531 2,691 2,238 205 368 358 38 29.40 5.90 9.80 14.00 1.00 2.50 5,520 15,997 12,541 438 801 32,083 50,388 30,853 3,100 6,155 15,500 36,000 23,000 2,800 1,200 6 7 8 9 10 2,922 48,158 13,685 6,880 11,415 46.30 476 110 78.20 117 2.00 20.00 8.00 7.50 11.00 1,125 11,480 3,480 2,423 3,188 6,350 33,600 17,800 6,530 6,365 7,500 16,500 5,000 9,250 3,200 11 12 13 14 15 2,267 4,279 9,383 12,572 5,324 49.30 51.60 110.70 145.60 94.60 1.70 2.00 4.00 8.00 9.00 1,736 1,767 5,420 3,315 4,697 3,632 5,930 17,700 7,250 2,730 3,150 2,500 10,000 2,800 150 16 17 18 19 20 13,546 5,190 7,280 10,521 21,927 112 49.50 100.30 57.50 251.48 6.00 6.00 4.00 6.00 11.60 4,813 1,535 2,453 3,677 6,834 17,800 7,305 7,750 14,150 23,605 3,000 2,700 6,000 3,000 15,400 21 22 23 24 25 23,317 10,672 10,896 5,518 7,338 298 83.60 110 60 80 12.00 10.00 8.00 7.00 7.00 8,806 3,773 4,296 2,842 4,525 27,580 17,000 19,175 6,100 16,200 10,800 4,000 17,500 3,800 2,000 26 27 28 29 30 55,456 17,553 24,543 19,116 24,870 336.60 136 145 234.50 303 10.00 7.10 12.00 8.00 10.00 15,321 3,512 5,566 6,904 8,613 62,100 10,050 8,702 17,259 29,250 12,000 4,500 7,500 7,500 18,500 31 32 33 34 35 17,566 29,544 7,209 11,134 2,131 135 206 45 76 22 11.00 6.00 2.00 8.00 2.50 4,905 9,957 1,870 3,200 600 15,275 44,100 7,900 11,150 12,500 8,500 30,500 2,000 3,500 3,000 202 Table A-20. Farm No. Continued. *i Gross Income h Land (Acre) X3 Labor (Tfonths) X4 Expenses ($) X5 Machine Investment ($) X6 Buildings ($) 36 37 38 39 40 8,025 4,799 23,203 6,911 47,953 139 64 253 95.40 525 6.00 2.70 14.20 3.00 12.00 4,010 3,390 10,182 6,475 12,945 10,992 7,700 34,267 13,850 20,650 3,800 4,500 10,800 13,100 1,950 41 42 43 44 45 27,799 12,551 22,533 39,200 15,649 200 116 154 365.30 186 4.00 2.00 8.00 12.50 12.00 6,740 3,790 7,048 11,248 3,683 21,267 7,900 11,618 29,267 16,850 14,500 1,000 5,700 18,000 8,500 46 47 48 49 50 7,424 15,373 18,593 42,075 21,782 75 198 185.60 365 194 3.00 15.00 6.00 15.00 13.00 3,038 8,486 6,658 11,902 9,216 12,800 62,500 34,525 55,333 16,303 4,000 6,000 21,000 10,600 29,000 51 52 53 54 55 33,057 189,396 16,441 20,614 20,275 244 1800 163.10 207 192 13.00 32.00 6.00 8.00 8.00 8,634 53,170 9,680 4,572 7,432 31,629 91,019 18,850 15,750 20,117 10,500 8,000 6,500 20,400 3,700 56 57 58 59 166,492 10,388 19,827 21,493 1386 140 163 245 27.85 9.50 12.00 10.00 45,981 5,722 11,337 8,195 93,375 23,613 30,243 27,400 61,700 8,000 16,500 6,890 60 61 30,486 25,531 10.00 8.00 12,801 14,419 29,262 59,979 15,150 3,500 272.55 232 APPENDIX B Optimum Farm Organization for Small, Medium and Medium* Size Representative Farms (Model II) 203 Table B-l. Summary of Optimum Land Use, Resource Transactions and Shadow Prices Under Various Levels of Land Resources on Small Cash Grain Farm (Model II) Net Return Crop Rotation WB Credit used Resources obtained ££..2Qld Mgr. labor hired Unskilled labor hired Mgr. labor sold Family labor sold Land A rented Land A purCX •c.■ 7*: "C . ci i 6 . r - ; * 205 Table B-3- Sunmary of Optimum Land Use, Resource Transactions and Shadow Prices Under Various levels of lend Resources on MediunmCash Grain Farm (Model II) Unit Net Return Crop Rotation WB CB CCCCS CCS Credit Used $ acre It Case I case II 'Case III I Case IV Case V 40,820 44,480 62,057 | 71,445 78,079 279 319 422 116 570 666 If 107 II 114 $ Resources obtainec J 3? sold Mgr. labor hired hour Unskilled labor IWAtt hw hired Mgr. labor sold hour Family labor sold hour Land A rented acre ff Land A purchased II Land B rented It Land B purchased Woodland cleared f f Plowable pasture It cleared Shadow Prices Cropland $/acre Land A for rent $/acre Land A for punJtW I I If Land B for rent Land B for purch« I I Aprd.1-May labor $/hr. If June-July labor If August labor 1? Sept.-Nov. labor Cash $ ff Chattel mortgage ft Real Estaiemortaafle Mgr. labor 4 ' i/hr. Woodland h/lcrf tf Plowable pasture 14,129 26,962 75,306 J— 59,184 42,791 570 1,071 389 49 389 1,125 389 1,430 389 1,723 389 365 30 30 NA NA 365 50 50 NA NA 365 213 114 NA NA 365 213 53 200 365 U'”'U 213 356 8 8 _ 126 96 73 NA NA 109 79 I / 39 NA NA 78 48 35 c 0 — 137 107 84^ NA"' NA 43 ~ ^—. — 3.26 3.26 3.49 3.49 3.49 .09 .16 •05 .07 .09 _ 18 7 1.80 5.17 5.17 5.17 .22 .10 .12 5.20 .72 oc .59 7.12 — . ~^NA denotes does not apply. 18 • XU 3.65 3.65 3.65 ~ ■ — 206 Table B-4. Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Small Cash Grain Farm (Model II) Case II (P*ilm3 (Low Price) Price) Case I Price Combination C o m Price Soybean price Wheat price Oats price Field beans price Net Return CBS CB WB Credit used Unit $/bu. ff ft ff $/cwt. 1.80 4.40 2.13 .90 12.00 $ acre ff ft 25,338 193 $ 18,5^7 Resources acquiree Mgr. labor hired hour Unskilled labor man lie hired Land rented acre ff Land purchased Woodland cleared ff Plowable pasture If cleared Off-farm employing Mgr. labor hour ti Family labor Shadow prices Cropland $/acre ff Rented land ff Purchased land April-May labor $/hr. ff June-July labor If August labor Sept.-Nov. labov fl Cash $ ff Chattel mortgage Real Est. mortjoje ff Mgr. labor $/hr. Woodland $/acre ff Plowable pasture 2.25 5.50 4.25 1.25 15.00 35,426 ------- 50 50 Case III (High Price) 2.48 6.05 4.25 1.38 19.50 41,525 — ---- — ---- Case IV (Low wheat Price) 2 .2 5 5 .5 0 3.00 1.25 15.00 Case V (Farmer's Desired Price 2 .3 4 5.34 4.0 3 1.49 18.09 38,649 32,913 45 148 ------- 193 15,811 194 16,320 19,543 194 16,320 ---- ---- ---- ---- 50 50 50 50 50 50 50 50 ---- — — — — — 1 1,666 54 1,724 77 54 24 107 77 53 .68 .44 .44 — — — — — 138 108 85 2.99 2.99 2.55 2.55 .09 .09 — 1,719 75 .44 .44 — 1,605 42 1,719 75 92 62 36 124 94 7C — — — — .09 — 2.56 — — — — — — 19 — .09 — .01 2.56 — 2.56 .44 .44 .47 .47 .09 — — 2.56 1 — 2 .56 — 4.26 207 Table B*5. Summary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Medium Cash Grain Paim (Model II) Price Combination C o m pride Soybean price Wheat price Oats price Field beans price Net Return CBS CB WB Credit used Unit. $/bu. $/bu. ft ff April-May labor June-July labor August labor Sept.-Nov. labOV Cash Chattel mortgage Real Est. mortg<^)€ Managerial labQY" Woodland Plowable pasture 1.80 4.40 2.13 .90 12.00 i/cwt. $ acre tf It $ Resources acquired Mgr. labor hired hour Unskilled labor hired iran hour Land rented acre M Land pur. It Woodland cleared Plowable pasture It cleared Off-farm employ m.?nT Mgr. labor hour Family labor hour Shadow prices Cropland Rented land Purchased land Case I (Low Price) 29,546 234 22 — 23,050 — — 50 50 — Case IV (Low Wheat Price) 2.48 6.05 4.25 1.38 19.50 2.25 5.50 3.00 1.25 15.00 42,768 51,112 ---- ---- 262 21,514 79 183 22,212 39,686 82 174 Case V (Fanner's Desired Frice) 2.34 5.34 4.03 1.49 18.09 47,132 69 193 22,095 ---- 25,149 — — — — — _ 50 50 50 50 5 50 50 50 50 ____ _ — 6 6 __ 6 1,402 166 1,402 258 1,402 179 1,402 87 1,402 190 66 36 12 120 90 67 152 122 98 94 64 41 137 107 84 $/hr. If If ff 3.10 2.83 2.38 2.38 $ .22 .22 — — .09 ti If 2.25 5.50 4.25 1.25 15.00 Case III (High price) ____ $/acre tf tf $ $/hr. $/acre Case II (t=*ii m 3 price) — — 2.56 — — *2.77 2.77 2.55 2.55 .09 ---- — ---- — _ _ _ 1.00 .09 .09 _ ---- 1.78 ___ 33 2.77 2.77 2.55 2.55 ---- .09 — .71 .44 — _ — T- . 17.66 208 Table B-6. Suimiary of Optimum Land Use, Resource Transaction and Shadow Prices for Selected Resources on Medium* Cash Grain Farm (Model II) Price Combination C o m price Soybean price Wheat price Oats price Field b e a m price Net Return CBS CB WB Credit used Unit $/bu. II II ff i/cwt. * acre II II $ Resources acquired Mgr. labor hired hour Unskilled labor hired rtifwhour Land rented acre II Land purchased II Woodland cleared Plowable pasture tf cleared Off-farm employment Mgr. labor hour I! Family labor Shadow prices Cropland Rented land Purchased land April-May labor June-July labor August labor Sept.-Nov. labor Cash Chattel mortgage Real Est. mortj^C. vIanagerial labor Woodland Plowable pasture Case I (Low Price) 1.80 4.40 2.13 .90 12.00 28,649 195 116 — 28,660 Case II (Fall m 3 Price) 2.25 5.50 4.25 1.25 15.00 44,480 -- Case III (High Price) Case IV (Low Wheat Price) 2.48 6.05 4.25 1.38 19.50 2.25 5.50 3.00 1.25 15.00 55,155 178 141 29,197 319 26,962 2.34 5.34 4.03 1.49 18.09 50,185 _ 178 141 29,197 41,337 311 — 31,848 _ Case V (Farmer's Desired Price) — — — _ — 68 50 50 49 50 50 — 84 50 50 -- 13 50 50 — 13 50 50 -- 8 8 - 8 339 365 389 365 389 365 389 365 389 365 $/acre II It 76 ab 20 126 96 73 161 131 105 110 80 53 $/hr. II N II — — — 146 116 90 __ 3.28 $ II II $/hr. $/acre II — 3.28 _ 3.26 3.26 — .09 — — .09 — .01 — — * 3.28 — — 3.28 3.28 .09 — .09 -- .01 __ —— __ — __ _ 41 — 6.97 — .09 — .01 — _ .01 25.85 209 Table B-7. Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Small Cash Grain Farm (lyfodel II) Crop Rotation Case I Case II Case III Case IV Case V CB CS ws CBW CBS 4.52 36.68 31.00 1.97 13.54 14.70 26.15 10.30 8.56 3.48 8.85 36.54 26.21 1.99 17.94 7.06 33.14 22.98 3.80 9.75 15.51 31.10 5.14 11.15 .11 OCW BOO CBO SCO CCB .63 15.95 10.98 17.28 9.00 ___ _ __ 22.48 17.52 25.76 25.08 20.06 22.20 14.18 8.27 29.05 23.74 23.41 18.38 5.16 37.31 30.69 12.75 53.27 CCS CCCB CCCS CCBW CCCW 7.05 2.31 3.53 3.53 25.66 3.06 16.70 5.95 7.14 6.57 3.57 3.57 .25 CCBS CCCBW CCCCS GCCBS — 13.55 --- --- 11.45 -- 10.08 19.76 6.12 14.57 18.57 — 4.17 7.87 2.08 7.17 — 12.07 5.09 — — 15.83 10.89 --- 28.62 3.82 21.84 -- 4.81 25.65 7.63 14.37 210 Table B-8. Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Medium Cash Grain Farm (Mndel II) Crop Rotation Case I Case II Case III Case IV Case V CB CS ws CBW CBS 4.06 36.66 31.44 1.97 13.09 8.63 27.72 17.93 6.54 1.45 13.25 24.64 10.15 9.20 .77 7.75 29.49 19.56 4.66 6.54 13.51 31.82 8.23 9.02 2.35 COW BCO CBO SCO CCB .69 15.09 10.12 16.91 8.53 «...— 1.51 25.75 20.60 16.37 17.53 5.44 37.63 31.08 17.22 48.17 CCS CCCB CCCS CCBW CCOW 7.06 1.84 3.53 3.53 2.09 10.57 1.04 8.91 NAa 22.47 1.75 17.63 — -- CCBS CCCBW CCCCS CCCBS — 13.46 ----- 10.99 14.39 9.43 21.65 16.66 -- ---- 17.68 25.15 ____ 15.56 1.04 12.68 3.88 25.45 3.68 17.99 3.25 6.39 13.73 2.09 8.51 8.67 21.67 7.36 13.11 aNA denotes the item is not applicable. 9.94 7.86 — 9.60 7.82 19.38 3.50 12.41 211 Table B-9. Shadow Price of a Unit of an Excluded Crop Rotation Under Various Land Resource Levels on Medium* Cash Grain Farm (Model II) Crop Rotation Case I Case II Case III Case IV Case V CB CS ws CBW CBS 1.92 30.53 27.45 4.71 4.66 28.12 22.29 5.33 .25 m a 32.52 30.35 3.60 3.02 7.44 30.65 20.31 4.53 7.10 12.94 31.84 9.22 8.53 2.71 COW BCO CBO SCO CCB .33 4.97 1.91 12.76 7.61 14.29 8.72 2.92 27.26 21.99 19.00 18.99 7.00 38.76 32.27 19.35 46.06 4.20 .71 2.10 6.78 2.63 9.77 1.31 8.68 NA 21.07 1.35 16.68 — 8.88 3.91 ------- .71 9.13 — CCS CCCB CCCS CCBW CCCW 1.59 5.17 .79 9.00 2.64 .34 9.17 .17 10.25 2.94 CCBS CCCBW CCCCS CCCBS 3.46 8.20 4.33 10.08 — 12.49 5.42 4.68 — — 3.38 — 4.87 3.97 aNA denotes the item is not applicable. — — 10.31 7.37 NA 9.75 7.29 18.02 2.70 11.89 T a b l e B - i O . S h a d o w P r i c e o f O n e U n i t o f a n E x c l u d e d R o t a t i o n U n d e r V a r i o u s P r i c e Combinations--Small Farm (Model II) Crop Rotation 2.16 23.75 --- 29.63 6.87 NA 4.17 4.97 --- 2.46 11. 53 5.67 9. 74 7.04 13.39 10.88 2.67 14.76 5. 37 7. 70 aNA denotes does not apply. Case II (Fall 1973 Price) Case III (High Price) Case IV (Low Wheat Price) 14.70 26.15 NA 10.30 8.56 3.48 -57.55 NA 56.39 25.36 NAa 31.39 --- 39.87 4. 97 30.25 6.77 NA 8.30 4.98 --- --- --- 25.20 27.87 44.82 44.57 64.69 50.31 68.24 19.83 70.18 84.56 44.70 6.70 9.48 7.63 7.35 8.88 13.20 14.92 5.57 14.45 11.79 7.49 20.28 22.95 34.98 34. 73 49.93 40.47 53.48 18.48 55.42 64.88 34.86 22.48 17.52 --- 25.76 --- 25.66 3.06 16.70 5.95 10.08 19.76 6.12 14.57 --- --- Case V (Farmer1s Desired Price) — _ — 50.16 NA 49.00 20.44 --- 35.64 4.97 212 CB CS WB WS CBW CBS COW BCO CBO SCO CCB CCS CCCB CCCS CCBW CCOW CCBS CCCBW CCCCS CCCBS Case I (Low Price) Table B-ll. Shadow Price of One Unit of an Excluded Rotation Under Various Price Combinations--Medium Farm (Model II) Crop Rotation Case I (Low Price) ci NAa 27.02 --- 35.41 8.01 NA 5.52 4.97 --- 7.92 10.51 10.11 9.86 12.62 15.67 18.62 --- 18.18 11.99 9.98 NA denotes does not apply. Case III (High Price) Case IV (Low Wheat Price) Case V (Farmer1s Desired Price) 8.63 27.72 NA 17.93 6.54 1.45 NA 59.78 NA 58.62 27.27 --- 43.68 4.97 32.11 8.63 NA 12.02 4.97 --- --- --- 27.12 29.77 48.63 48.38 70.40 54.13 76.09 22.10 75.90 93. 70 48.51 8.54 11.13 11.36 11.11 14.50 16.92 20.50 7.11 20.06 19.30 11.24 24.31 26.96 43.02 42.77 61.99 48.52 65.49 19.29 67.49 80.95 42.90 14.39 9.43 --- 17.68 --- 15.56 1.04 12.68 3.88 6.39 13.73 2.09 8.51 --- NA 33.15 --- NA 54.41 NA 53.25 24.46 --- 38.07 4.97 213 CB CS WB WS CBW CBS COW BCO CBO SCO CCB CCS CCCB CCCS CCBW CCOW CCBS CCCBW CCCCS CCCBS Case II (Fall 1973 Price) Table B-12. Shadow Price of One Unit of an Excluded Rotation Under Various Price Combinations--Medium* Farm (Model II) Crop Rotation Case I (Low Price) CB CS WB ws CBW CBS COW BCO CBO SCO CCB CCS CCCB CCCS CCBW CCOW CCBS CCCBW CCCCS CCCBS NAa 33.53 --- 36.40 14.41 NA 23.57 4.98 --- 14. 30 17.11 22.90 22.63 31. 79 28.43 37. 75 7.94 37.32 40.13 22. 76 aNA denotes does not apply. Case II (Fall 1973 Price) 4.66 28.12 NA 22 .29 5.33 .25 --- 8.88 3.91 --- 12.49 .34 9.17 .17 10.25 2.94 4.33 10.08 --- 4.87 Case III (High Price) Case IV (Low Wheat Price) 38. 65 14.47 NA 53.11 NA 51.88 22.94 --- --- 16.49 4.98 40.63 4.98 --- --- 14.36 17.18 23.03 22.76 31.99 28.57 37.95 9.35 37.52 42.45 22.90 22. 79 25.64 39.96 39.69 57.38 45.46 63.27 22.40 62.88 76.30 39.82 NA 86.41 NA 85.17 27.86 31.08 50.47 4.98 NA 39.89 --- 58.80 30.56 80.88 49.53 103.22 55.30 78.03 58.40 77.64 127.06 80.75 Case V (Farmer's Desired Price) — 215 Table B-13. Crops Enterprise Levels by Representative Farm in 1972 Operator's Age Unit Over 55 Years 24 to 55 Years Small Medium Large Medium* Corn Acre 18 45.29 136.24 38.14 Soybeans Acre 25.30 15. 71 37.29 15.43 Wheat Acre 13.40 15.47 55.00 40.14 Oats Acre Field Beans Acre 10. 70 31. 76 102.14 68.57 Hay Acre 3. 60 12.06 22.86 5.71 Other Crops3 Acre 2.10 10.06 7.71 0 4.00 23.57 aOther crops include sugar beets, cucumber, 3.14 0 etc. 216 Table B-14. Initial and Optimum Inventories of Machinery-Small Farm (Model II) Item Initial Inventory Tractor 1 (53 H.P.) 1 Tractor 2 (70 H.P.) 1 4-bottom plow 1 Disc 1 (12') 1 Disc 2 (16') Purchased Sold Optimum .55 .45 1 .21 .79 1 .03 Planter (4 row) 1 Cultivator (4 row) 1 Grain drill(13 holes) 1 Grain drill (16*-17") .03 1 .06 .94 1 .79 .79 Corn picker (2 row) 1 Combine (2 row) pull type 1 .18 .82 Spring tooth 12' 1 .27 .73 1 0 217 Table B-15. Initial and Optimum Inventories of Machinery-Medium Farm (Model II) Item Initial Inventory Tractor (53 H.P.) 1 Tractor (70 H.P.) 1 4-bottom plow 1 Disc 1 (12') 1 Disc 2 (16') 0 Planter (4 row) 1 Cultivator (4 row) 1 Grain drill (13 holes) 1 Grain drill (16’-17") 0 Corn Picker (2 row) 1 Combine (pull type) 1 Spring tooth 12' 1 Purchased Sold Optimum .45 .55 1 .97 .03 1 .21 .21 1 .92 .08 1 .97 .97 1 0 1 .34 .66 218 Table B-16. Initial and Optimum Inventories of Machinery-Large Farm (Model II) Item Initial Inventory Purchased Sold Optimum .10 .90 Tractor (70 H.P.) 1 Tractor (115 H.P.) 1 1 6 bottom plow 1 1 4 bottom plow 0 Disc 1 (12') 1 Disc 2 (16') 0 Planter (6 row) 1 .40 .60 Cultivator (4 row) 1 .20 .80 Grain drill (16’-17") 1 Combine (13',4 row) 1 Spring tooth (16') 1 Combine (10',2 row) 0 1.72 1. 72 1 1. 70 1. 70 .26 1. 26 1 .71 .10 .29 .10 219 Table B-17. Initial and Optimum Inventories of Machinery— Medium* Farm (Model II) Item Initial Inventory Purchased Sold Optimum .30 .70 Tractor (53 H.P.) 1 Tractor (70 H.P.) 1 1 3-bottom plow 1 1 4 bottom plow 0 Disc (12') 1 Disc (16') 0 Planter (4 row) 1 Cultivator (4 row) 1 Grain drill (13 hole) 1 Grain drill (16'-17") 0 Corn picker (2 row) 1 Combine (pull type) 1 Spring tooth (12') 1 .75 .75 1 .74 .74 1 .04 .96 1 .84 .84 .35 .65 1 .49 .51 APPENDIX C Questionnaires Used in Personal Interviews 220 Land Area_ Farm No. Tel. No.__ Enumerator Date Confidential Michigan State University Department of Agricultural Economics East Lansing, Michigan Farm Management Survey About what percent of your 1972 gross farm sales (income) from the farm came from: Cash grain________ % Other Sales %_____________ Kind______________ Livestock________ % If "cash grain" is less than 50%, use "Land Utilization" Questionnaire. I. Farm Size How many acres did you operate? Total Owned Rented Tillable (cropland) Diverted Tillable Unoperated (Cropland) Pasture Woodland Tillable acreage: Value per acre: Leased out_____________ Owned____________ Rented Pasture Woodland Rent Out Soil Type 221 Please indicate the location of each kind of land.* N r 40 NW 1/4 40 Acres J 1 1 1 _ , 40 i SW 1/4 160 Acres W - S I ' 2 miles — — — ----- — — — ----------------------- -i *Refer to "plat book." 1. Tillable_______ Acres. Diverted Tillable________ Acres. Unoperated (cropland) Acres. Pasture_________Acres. What crops did you plant within a 2 miles square in 1973? Corn________ , soybeans Drybeans L , Alfalfa , Wheat______ , Oats Woodland_____ Acres. (Acres) , Barley________ , , Others_____________________________________ 222 II. Farm Labor Force A. Family Labor Force (Man-Months on Farm) I Person Days Months Age Average Man-Month Equivalents Operator Wife Son Daughter *Hired Total 1 Labor for Livestock (subtract) Net Labor for Crops *Exclude labor furnished with hired machine custom work. B. Labor supply during rush periods. Maximum hours per week during rush periods. Operator_____________ Wife_______________ Son__________________ Daughter_____________ C. Hired Labor (Days Worked) DecemberMarch (a) Regular (b) Seasonal AprilMay JuneJuly August SeptemberNovember Total for Year Days Wages 223 D. Off-Farm Work (1) Kind Wages/hour Amount Remark (when) Operator Wife j Son I Daughter ! How many miles was your job from home? (2) If you have no off-farm work, Have you tried to obtain off-farm work? Yes No What kind of work do you think you are qualified for (1) without further training?__________, expected pay_$_____ /hour. (2) with further training______________ , expected pay (3) why d o n ’t you work off-farm?________________ $_____ /hour. 224 HI. Machinery and Equipment (Inventory Beginning of Year) - January 1, 1972 *Value to farmers > sale value and purchase cost, same quality Item Model. Year Size Number *Value Major Equipment Tractor Combine Trucks Automobile (Farm Share) Tillage Equipment Plow Harrows (Spring & Spike Tooth Disks Cultivator Other Planting Equipment Grain Drill Seeder Corn Planter Sprayer Harvesting Equipment Hay Rake Bean Harvester Hay Loader Field Chopper Hay Baler Corn Picker Mower & Conditioner Elevator & Grain Augers Lime Spreader Grain Drying Equipment « Other Major Equipment Wagons TOTAL CROP MACHINERY INVESTMENT $ 225 Sales & Trade ins Purchase* Date Item total Cost ♦Includes tires and major overhauls and repairs reflected in ending inventory Prop.Add. Date Total Value Beginning Inventory $ . dd. $ Frop" $ Prop. D ed. Total IV. Item Mach Lnery In vestment Gross Crop Income (1972) Gross Crop Income Calculation-------------------------------- $ Total Crop Income (P. 7)------------------------------------- $ Crops, Feed & Seed Inventory Increase or Decrease (P. 8 ) ------------------------------------------------ $ Gross Income, excluding livestock----------------------------$ $ Prop. Ded. 226 IV. A. Cross Income (Continued) Crop and Other Income Crop Acres Yield/Acre Unit Corn for Grain Bu. Soybeans Bu. Meat \ ♦Total Quantity Quantity Sold Date Sold Value $ Unit Price Bu. Corn for Silage Ton Cats Bu. Barley Bu. Potatoes Bu. Dry Beans Cwt. Sugar Beets Ton Grass Silage Ton Hay: Legume Ton Grass Ton Mixed Ton Others Garden Land and Pasture Rent Custom Work or Machinery Rented Other Income from Farm Sources (Exclude Gov'nt Payment for Diverted Acreage) Total (Excluding Livestock) ♦Quantity includes sold and/or used for feed and food. i ! i 227 IV. Gross Income (Continued) Inventories of Crops, Feed and Seed (January I, 1972 - December 31, 1972). Kind Bepinning Inventory Quantity Value($) Ending Inventory Quantity Value (?) Corn Soybeans Wheat Oats Barley Dry Beans Others Silage Hay Commercial Feed Others Seeds It o t a l $ $ Inventory Increase $ Inventory Decrease $ 228 V. Fertilizer and Lime Cost Total Quantity Amount Applied per acre Crop Price Cost Corn Soybean Wheat Small Grains Others TOTAL $ Residual Fertilizers & Lime: Only if very different in fertilizers and lime usage between 1972 and the normal year. N, Total lbs. x ■ ■■■«« " P„0 , Total 2s lbs. K 2O, Total lbs._______ x ' «'>■ ■■ % ss ■ 1 ■ x -... " ■I"-— C a $i iii- — ■ '■— — x C $ -------------- X**----------------T -----x X _ ________ x________ ( = $________ Total Residual. Value $__________ Total Cost of fertilizer from which residual is computed $_________ Minus residual value $_________ Current fertilizer cost $_________ Application Cost $. Total Lime Cost (Annual Charge) $ TOTAL FERTILIZER COST $ 229 VI. Other Expenses Item Quantity Co s t ($) Custom Work or Machinery Hired Fertilizer & Lime Cost (P. 9) las & Oil for Farm Use (Include fuel for Grain Dryer) Implement and Machinery Repairs (Not of an Investment Nature) Electricity (Farm Share) Automobile Operation (Farm Share)* Seed Herbicide (Weed Spray) Insecticides Dther: (Baling Wire, Sacks, Crop Sprays & Pest Control, Telephone, etc.) TOTAL CROP EXPENSES *Mileage x 10c $ 230 VII. Building Investment (Excludes Idle and That Used for Livestock). Item and Description Farmer's Estimate of Investment Value $ Granary Haystorage Corn Crib Silo Grain Bins Machinery Storage & Workshop Bucket Elevator Others Farmer's Estimate of total building Investment $ 231 VIII. Capital Position 1. Do you have any additional funds and non-farm investments of your own which you could transfer to farm use to increase your investment in your farm business? Yes If yes, what is the total amount? 2. No____________ $___________________ Do you think you could borrow additional funds from any sources? Yes_________ No______________ If yes, how much? Amount Private Credit (Friend, relative, etc.) ! Chattel Mortgage i (P.C.A.) Rate of Interest Duration Restriction of Usage ! Real Estate Mortgage! (Bank) ! 1 Land Contract Others P.C.A.: 3. Production Credit Association List the p o s s i b l e for the next year. Acres 1. 2. 3. 4. "land rental" Annual Rent opportunities in your neighborhood Kind of Contract (Cash or Crop Share) Duration of Lease 232 Please indicate the location of land.* Location 640 Acres 1 1 i i I i 1 I i t i ' / /// / ' /J , / '/ 1 1 . .. . // / '/ / I / E ’ ~ 1 / / 1 1 o > 1 i 1 \ 1 - \ i i i________ ! 1 _ I ////'■■ 1 r i .....L1 --------- — i--------- S I. . ..... A: . . - 6 miles ------------------------ The 2 miles square area where visited farm is located. *Indicate with blue ink, refer to plat book. JL 1 6 miles 233 4. List the possible "land buys" for the next year.* Acres which you know of in your neighborhood Price per Acre Contract Financing Down Kind Pymt. Yrs. % Interest L. 2. 3. i. - .. ■ 'i * Indicate the location of land on land map on Page 13, using red ink. Land Utilization 1. After the termination of set-aside program next year, are you planning to produce more cash-grains if the prices remain at current level? 2. What are the main reasons that you left a part of crop land uncultivated? (Number in order of importance.) Lack of Labor____________. Lack of Capital________________ . Yes_______ NO_________ . If yes, how much______«____________________________ Acres. Prices of output are too low or too uncertain_______________ . Cost of clearance is high_____________________ . Input prices are too high__________________ unproductive (land)_____________ . Others_______________________________________________________________________ , Speculation___________ , Lack of entrepreneur____________ . 3. What factors are more important when you are solving pulling the idle land into production? Input prices_______ , output prices Capital________ , labor the problem of , initial cost_________ , , entrepreneur__________. 234 4. Could you tell me the clearance cost (per acre) of your unoperated crop land? Clearance Cost Labor(hour) Cash($) (1) Diverted (2) Unoperated (3) Plowable Pasture (4) Woodland 5. Other Drainage Cost($) Do you have a plan to increase your production next year? Kind of cro More Intensive Cultivation Acres Corn Wheat Soybean If N o , please give the reasons. Total Yes______ No Bring in Diverted Land Bring in Unoperated Buy Land Rent Land Acres Acres Acre Acre 1 i Other 6. What price expectation would be necessary to cause you to bring unoperated crop land into cultivation or buy or rent more land? Expected Price of Crops $/bu. Corn_________ Wheat________ Soybean______ Oats_________ Drybean______ 2.36 Net Worth Statement* As of December 31, 1972. Assets Liabilities Land (p. 1) $_ Farm Mortgage Buildings (on farm, p.ll)_ Other Mortgage Machinery (Refer to p.5) Bank Notes Feed, Crops, Seed Supplies (p. 8) _ Personal Notes Livestock _ Other Notes Household Equipment _ Accounts Payable Stock, Bonds Cash on Hand Taxes, Rent, Insur. Due _ Cash in Bank Other Debts (household Installment debts, etc) Accounts Receivable House Other Assets (cars, etc)_ Total Net Worth Total Total *We want estimates of the actual values, not the book values for accounting purposes. The point is, what were these items worth to you. 2,37 Farm No. ToJ. No.__ Kmimorafor Date Confidential .Michigan State University Deparinent of Agricultural Economics East Lansing, Michigan Land Utilization Survey I. Farm Si7.cHow many acres did you operate? Total Owned Rented Till ahl-: (crop! .mil) Dive rtcd TiJ1able Unoporat. ed (Cropland) Pasture Woodland Tillable arn-ngv': Value p. r acre: Leased out____________ CP.tied_____________Rente.d Rent Out Soil Type 238 Please indicate the location of each kind of land.* N J I 40 40 NW 1/4 Acres 40 1 1 1 S'..' 1/4 I/O Acr e s 2 miles E S 2 miles I*Refer Lo "plat book." Tillable Acres. Unoprrated (cropland)^ Diverted Tillable Acres. Pasture _Acres. Acres. Woodland Acres. 239 Land IL'liU-7.-1-— -!11. After the termination of set-aside program next year, arc you planning to produce more cash-grains if the prices remain at current level? Yes__________ No____________. If yes, how much------ — 2. -------------- Acres What are the main reasons that vou left a part of crop land uncultivated? (Number in order of importance.) hack of Labor____________ . hack of Capital________________ . Prices of output are too low or too uncertain_______________ • Cost of clearance is high__________________ Input prices are too high • _______________unproductive (land)_____________ . — ’ - Others_____________________________________ Speculation_____________ , Lack of entrepreneur__________ . 3. What factors are more important when you are solving pulling the idle land into production? Input pricer. _ capital 4. _, output pric e s __ , labor ( 2)_ Could you lell me the clearance cost (per acre) of your unoperated crop land? hivej'tod_ J I ; -■>i u T . - . t e .' (3) Plowablo. _______ Part arc (4) , initial cost_________, , entrepreneur__________. Clearance Cost Labor(hour) Cash($) (1 ) the problem of VI.inj land Other Drainage Cost($) Total 240 5. Do you hive a plan to Increase your production next year? Kind of creps~^_^ More Intensive Cultivation Yes______ No Buy Bring in Diverted Land Bring in Unoperated Land Acres Acres Acre 1 Rent Land Other Acre Acrc i Acres Corn Whoa 1. Soybean i ----------If Ko, please give tlie reasons. 6. What price expectation (next five years) would be necessary to cause you to bring unoperated crop land Into cultivation or buy or rent more land? Kxpected Price of Crops $/bu. Corn_____________ Wh ea t _________ Soybean Oats _______ __ ________ D r y b e a n ________ BIBLIOGRAPHY BIBLIOGRAPHY Barlow, R. Land Resource Economics. Prentice-Hall, In c., Michigan State University, 1558. Beneke, R. R. and R. Winterboer. Linear Programming Application to Agriculture. The Iowa State University P r e s s , 1973. Benjamin, G. L. and L. J. Connor. Economies of Size of Machinery Systems on Southern Michigan Cash-Grain F a r m s . Agricultural Economics Report No. 112, Department of Agricultural Economics, Michigan State University, September 1968. Beringer, C. "A Method of Estimating Marginal Value Pro­ ductivities of Input and Investment Categories on Multiple Enterprise Farms." 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