smxsrrwzw ANALYSIS OF SELECTED LINEAR ’ V ' PROGRAMMLNG ASSHMPTIIONSV: A STUDY - or THE smmuw or AGRICULTURAL PROJECTIONS m ENE-R BASIN. RESEARCH Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY ~ 301m EDWARD HOSTETLER "i 1970 v I . I . y_. ‘ ,. . . ‘ ' ' 7. ' rcon. A . . .. m “"3- ‘m -a.'b . ~ 4 1’.- III A ('1 ‘2 j, h-‘iic .igan State THEV" U“. I o ‘ IMVCFSIC - v _ y f‘ . h’"W‘-;=.r, This is to certify that the thesis entitled Sensitivity Analysis of Selected Linear Programming Assumptions A Study of the Stability of Agricultural Projections in River Basin Research presented by John Edward Hostetler has been accepted towards fulfillment of the requirements for Ph, D , degree in Agricultural Economics (QZLAp/x A). Ari/LA. [M/ Major professor Date November 17, 1970 0-7539 I 322223:2:z:8333833338332333333332:3933::Bun-n—nflfianz382.: ma ananamoamamaoooaaaaanounamamaooauomounaamaunomama. a. a. - uaaa-unuue. no..nauu-na-auuo-unuuuuga-,can». It'll rl Hfi ~ --s-~sfinhphpp---~p_----~_--.~w-~n mam w uuvuaoumammouacanoemanageawamaouououmuumaumuaumm wannanannmmmnmmnmmwnmrmmnnmnmmmnmnmmmnmmmmmmnnmmmmm.an o'equenvavvevvvwvgvvvvvvvvvvvvvvvevvv¢vecvvqervvcv‘f unnmmmnmnnnnnnnnnmnnrmmnmnnmnnnnnnnnnnnnnnnnnnnmmnnnmm. NNNNNN------~N--N-N-N---~N---NN---~N ________..__.____________.._______—_________r_______r__ 322:2: :2 : :28338333838233331232:33:393933333323:2228:32.“ aaaeooaeoaaaeoeaueaaaaaaaaaaoeaueuo-aaauaeaaorraeaeeaea _ rll dl - . n. . Zeal...“ m.-. m. ABSTRACT SENSITIVITY ANALYSIS OF SELECTED LINEAR PROGRAMMING ASSUMPTIONS: A STUDY OF THE STABILITY OF AGRICULTURAL PROJECTIONS IN RIVER BASIN RESEARCH BY John Edward Hostetler Assumptions built into river basin linear program- ming projection models are subject to errors because of limiting timetables, funds, data or techniques, and these errors have an impact on the resulting estimation of economic potential for water resource development. This study was undertaken to evaluate the extent and direction of such errors associated with certain assumptions used in river basin projection models. Analysis centered on the sensitivity of 1980 Benchmark Model results to deviations in assumptions relating to: (l) livestock feeding relationships, (2) projected demands, (3) soil management practices, (4) minimum production considerations, and (5) the adopted level of crop producing technology. To test these five classes of assumptions required ninety-three different linear programming solutions reflecting three distinct John Edward Hostetler levels for each assumption class. Infeasibilities were encountered on eighteen of the solutions. When irrigation opportunities were added to the Basic Model, production possibilities were expanded sufficiently to remove all but one of the previous infeasibilities. ‘ Two procedures for analyzing sensitivity of Bench- mark projections were developed. The first relied on total production costs as a broad and readily available general indicator. In the first analysis of sensitivity it was found that certain alternative assumptions were more critical than others in causing variation in the Benchmark cost projections. These cost projections, serving as indicators of sensitivity, identified assumptions concerning livestock feeding relationships, projected demands and technology adoption levels as much more sensitive than assumptions about soil management practices or minimum acreage constraints. In a similar analysis, where irrigation was included in the 1980 Benchmark Model, almost identical results were produced. The essential difference was that irrigation reduced the general level of total production costs, by $2.5 to $3.2 million, by reducing the number of acres required to meet production objectives. The second procedure for analyzing sensitivity of Benchmark projections was concerned with "shift points" in the projected economic potential for irrigation. It John Edward Hostetler identified sensitivities of the Model to changes in as— sumptions as they influence the total projected level of irrigated acreage and its distribution among subareas. Primary concern centered on stability of irrigated acreage projections, both in magnitude and location. It was observed that the only crop with an economic potential for irrigation was potatoes at Benchmark demand levels. Variations in the assumptions had little or no effect upon irrigated acreage until demands were raised to medium and high levels. Livestock feeding efficiencies at low levels along with low concentrate rations caused sub- stantial increases in irrigated acreage and shifts among subareas. The influence from increasing demand from Benchmark to high levels was seen as irrigated acreage climbed from 20,000 acres to over 2 million acres and a range of crops entered the solution. Minimum acreage requirements were very effective in controlling irrigated acreage shifts among subareas. Sensitivity of the location of irrigated acreage among subareas was directly related to levels of assumed acreage minimums . Variations in technology caused moderate sensi- tivity in total irrigated acreage. Only one subarea was affected by these variations. The results of both analyses of sensitivity imply that assumptions about soil management practice levels John Edward Hostetler should be dropped from river basin models unless unusual conditions exist. Such conditions would be a large proportion of sloping soils or a predominance of row crop production. SENSITIVITY ANALYSIS OF SELECTED LINEAR PROGRAMMING ASSUMPTIONS: A STUDY OF THE STABILITY OF AGRICULTURAL PROJECTIONS IN RIVER BASIN RESEARCH BY John Edward Hostetler A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1970 ACKNOWLEDGMENTS The author wishes to express sincere appreciation to Dr. A. Allan Schmid as chairman of the guidance com- mittee and to Dr. John Brake who served as thesis advisor. Their suggestions and constructive criticisms, as well as those of the entire thesis committee, have improved the manuscript significantly. The assistance of Dr. Myron Wirth of Washington State University, who served as a sounding board for ideas and a strong critic of the manuscript, is greatly ap- preciated. The review of earlier drafts of the manuscript by Dr. Neil Cook, William Heneberry, and Carmen Sandretto, co-workers in the Natural Resource Economics Division, ERS, is also appreciated. A debt of gratitude is due Dr. Melvin Cotner, Director of NRE, and Max Tharp, Assistant Director for Field Operations, who provided administrative and technical support as well as financial arrangements for the work. The author thanks Miss Florence Wright, Mrs. Joan Roby, and Mrs. Ludonna Anderson for their untiring assistance in typing earlier drafts of the manuscript. ii Finally, the encouragement and understanding by my wife Beverly, and children Kim, Carrie, and Scott is deeply appreciated. Without their sacrifice this undertaking would not have been completed. iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION . . . . . . . . . . . l The Problem . . . . . . . . . . 1 Objectives and SCOpe of the Study . . . 4 Objectives . . . . . . . . . 4 Scope I O 0 I O O O O O O O 5 The Research Format . . . . . . 7 II. ANALYTICAL APPROACH AND FRAMEWORK OF THE STUDY 0 O O O O O O O I O O O O 9 Analytical Approach. . . . . . . . 9 Demand for Agricultural Products . . 10 Productive Capacity of Land Resources. . . . . . . . . . 11 Location of Agricultural Production . 13 The Basic Linear Programming Model. . . 14 The Linear Programming Format . . . 14 Typical Linear Programming As— sumptions and Constraints . . . . 1? Partial Matrix Example--The Southern Michigan 1980 Benchmark Model . . . 18 III. CHARACTERISTICS OF THE STUDY AREA AND BENCHMARK RESULTS . . . . . . . . . 25 General Characteristics of the Subregion . . . . . . . . . . . 25 Description of Study Area . . . . 25 Soil Resource Availability . . . . 27 Crop and Livestock Production Trends. 28 Results of the 1980 Benchmark Model . . 28 Projected Production of Major Crops . 29 iv Chapter Page Availability and Use of Cropland . 29 Subregional Demand Requirements and Production . . . . . . . 31 Cost of Production . . . . . . . 38 Basis for Development. . . . . 38 Benchmark Model Production Costs . 39 Utilization of Permanent Pasture . 44 IV. ALTERNATIVE ASSUMPTIONS AND MODEL SPECI- FICATIONS: THEIR IDENTIFICATION AND PURPOSE. 47 The Role of Assumptions. . . . . . 47 Class l--Assumptions Relating to Livestock Feeding Relationships . . . . . . . 49 Class 2-—Assumptions Relating to Projected Demands . . . . . . . . . . . 61 Class 3--Assumptions Relating to Soil Management Practices. . . . . . . . 63 Class 4--Assumptions Relating to Minimum Acreage Constraints . . . . 66 Class S--Assumptions Relating to Adopted Level of Crop Producing Technology . . . 70 V. SENSITIVITY OF THE BENCHMARK MODEL TO CHANGES IN ASSUMPTIONS . . . . . . . . 74 Procedures . . . . . . . . . 74 Part I--Sensitivity Analysis Without Irrigation . . . . . . . . . . . 75 Class l--Assumptions Relating to Livestock Feeding Relationships. . . 78 Feeding Efficiency. . . . . . 78 Deviations from Benchmark Projections. . . . . . . 79 Implications . . . . . . 80 Livestock Rations . . . . . . 81 Deviations from Benchmark Projections. . . . . . . 82 Class 2--Assumptions Relating to Projected Demand. . . . . . . . 85 Chapter Deviations from Benchmark Projections . . . . . . . Implications. . . . . . . Class 3--Assumptions Relating to Soil Management Practices . . . . . Deviations from Benchmark Projections . . . . . . . Implications. . . . . . . Class 4-—Assumptions Relating to Minimum Acreage Constraints . . . Deviations from Benchmark Projections . . . . . . . Implications. . . . . . . Class 5—-Assumptions Relating to Adopted Level of Crop Producing Technology. . . . . . . . . Deviations from Benchmark Projections . . . . . . . Implications. . . . . . . Alternative Criteria of Analysis Part II-—Sensitivity Analysis With Irrigation . . . . . . . . . . Shift-Point Analysis . . . . . Class l--Assumptions Relating to Livestock Feeding Relationships Feeding Efficiency . . . Deviation from Benchmark Projections . . . . Implications . . . . Livestock Rations. . . . Deviation from Benchmark Projections . . . . Implications . . . . Class 2--Assumptions Relating to Projected Demand . . . . . vi Page 88 89 90 92 92 94 95 97 98 100 102 103 107 111 112 114 114 114 116 116 118 119 Chapter VI. Deviations from Benchmark Projections . . . . . . Implications. . . . . . Class 3-—ASsumptions Relating to Soil Management Practices. . . . . . Deviations from Benchmark Projections . . . . . . Implications. . . . . . Class 4--Assumptions Relating to Minimum Acreage Constraints . . . Deviations from Benchmark Projections . . . . . . Implications. . . . . . Class S--Assumptions Relating to Adopted Level of Crop Producing Technology . . . . . . . . . Deviations from Benchmark Projections . . . . . . Implications. . . . . . SUMMARY AND IMPLICATIONS. . . . . . . Summary . . . . . . Implications. . . . . Limitations . . . . . . . . . . Application of Results . BIBLIOGMPHY . O O O I O C O O O O O O APPENDICES Appendix A. Irrigation in Southern Michigan--Data and Estimating Procedures. . . . . . . . B. Southern Michigan Irrigation Potential . . C. Supplemental Data Tables. . . . . . . vii Page 120 121 122 123 124 125 126 128 129 130 132 134 134 143 148 149 152 156 179 188 10. LIST OF TABLES Page Sample Partial Matrix of the Southern Michigan 1980 Model with Right Hand Side . 20 Availability of Cropland and Benchmark Projection of Use for Major Crops in 1980, by Subarea, Southern Michigan Subregion . . . . . . . . . . . 30 Benchmark Projections of Demand Requirements for 1980 Compared with 1964 Production Levels, Southern Michigan Subregion. . . 32 Benchmark Projection of Harvested Acreage for 1980 Compared with 1964, by Subarea, Southern Michigan Subregion . . . . . 34 Benchmark Projection of Major Field Crop Production in 1980 Compared with 1964, by Subarea, Southern Michigan Subregion . . 36 Benchmark Projected Yields of Major Crops in 1980 Compared with 1964, by Subarea, Southern Michigan Subregion . . . . . 37 Benchmark Projected Total Cost of Producing Major Field Crops in 1980, by Subarea, Southern Michigan Subregion . . . . . 40 Benchmark Projected Cost Per Acre of Producing Major Field Crops in 1980, by Subarea, Southern Michigan Subregion . . 42 Benchmark Projected Unit Costs of Producing Major Field Crops in 1980, by Subarea, Southern Michigan Subregion . . . . . 43 Average Feed Requirements, Including Pasture, Consumed Per Unit of Production, by Each Class of Livestock, United States, 1959-1961 . . . . . . . . . . . 51 viii Table 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Feeding Efficiencies for Livestock and Livestock Production, United States and State of Michigan, 1959-61 and Projected to 1980 . . . . . . . . . . . . Distribution of Average Ration Components Among Concentrates and Roughages in Terms of Feed Units, by Class of Livestock, United States, 1960-1963. . . Feeding Efficiencies for Livestock and Livestock Production, Benchmark and Alternatives, 1980 . . . . . . . . Distribution of Average Ration Components Among Concentrates and Roughages by Class of Livestock, in Feed Units, Bench- mark and Alternatives, 1980 . . . . . Current and Projected Demands for Production From the Southern Michigan Subregion (SMS) with Alternative Specifications for 1980. . . . . . . . . . . . Percentage of Cropland Available for the Production of Row Crops Under Varying Soil Management Practices, Southern Michi— gan Subregion, 1980 . . . . . . . . Projected Index of Selected Crop Yields Under 1980 Benchmark Level ("Low") of Adopted Crop Producing Technology, Southern Michigan Subregion . . . . . . . . Structure of Alternative Model Formulations with Respect to Assumptions, and Projected Total Costs of Subregion Production, Southern Michigan Subregion, 1980 . . . Definitions of Alternative Models with Respect to Variations in Assumptions From the Benchmark Model, and Projected Total Costs of Subregion Production, Southern Michigan Subregion, 1980 . . . Projected 1980 Total Cost of Production for Models Testing the Sensitivity of the Feeding Efficiency Assumptions, Southern Michigan Subregion . . . . . . . . ix Page 53 55 59 60 64 67 73 76 77 79 Table 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Projected 1980 Total Cost of Production for Models Testing the Sensitivity of the Livestock Ration Assumptions Under High and Low Feeding Efficiency, Southern Michigan Subregion . . . . . . . . Projected 1980 Total Cost of Production for Models Testing the Sensitivity of Demand Level Assumptions, Southern Michigan Subregion . . . . . . . . . . . Projected 1980 Total Cost of Production for Models Testing the Sensitivity of the Soil Management Practices Assumptions, Southern Michigan Subregion . . . . . Projected 1980 Total Cost of Production for Models Testing the Sensitivity of the Minimum Acreage Constraints Assumptions, Southern Michigan Subregion . . . . . Projected 1980 Total Cost of Production for Models Testing the Sensitivity of the Level of Technology Assumptions, Southern Michigan Subregion . . . . . . . . Projected 1980 Soil Resource Use by Subarea for Models Testing the Sensitivity of the Level of Technology Assumptions, Southern Michigan Subregi0n . . . . . . . . Projected 1980 Total Production of Wheat by Subarea for Models Testing the Sensitivity of the Level of Technology Assumptions, Southern Michigan Subregion . . . . . Projected 1980 Total Production of Corn by Subarea for Models Testing the Sensi- tivity of the Level of Technolggy_As- sumptions, Southern Michigan SubregiOn . Comparison of Harvested Acreage of Potatoes with and Without Irrigation, 1964, and 1980 Benchmark Projections, by Subarea, Southern Michigan Subregion . . . . . Structure of Alternative Model Formulations Incorporating Irrigation with Respect to Model Assumptions, Projected 1980 Irri— gated Acreage and Total Cost of Pro- duction, Southern Michigan Subregion . . X Page 83 93 96 101 104 106 106 110 113 Table 31. 32. 33. 34. 35. 36. Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Feeding Efficiency Assumptions, by Subareas, Southern Michigan Subregion . . . . . Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Livestock Ration Assumptions, by Subareas, Southern Michigan Subregion . . . . . . . . Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Demand Level Assumptions, by Subareas, Southern Michigan Subregion . . . . . . . . Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Soil Management Practices Assumptions, by Subareas, Southern Michigan Subregion. . Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Minimum Acreage Constraints Assumptions, by Sub- areas, Southern Michigan Subregion. . . Projected 1980 Irrigated Acreage for Models Testing the Sensitivity of the Level of Technology Assumptions, by Subareas, Southern Michigan Subregion . . . . . Estimated Acreage Being Irrigated by Crop and by Subarea, 1968, Southern Michigan Subregion, Great Lakes Basin Data Survey . . . . . . . . . . . . Irrigation of Agricultural and Miscellaneous Crops by Crop and Subarea, 1958 and 1968, Southern Michigan Subregion, Michigan Water Resources Commission . . . . . Summary of Irrigated Acreage of Agricultural Crops, 1958 and 1968, Southern Michigan Subregion, as Estimated by the Michigan Water Resource Commission Surveys and the Great Lakes Basin Data Survey of 1968. . Irrigated Acreage of Harvested Agricultural Crops, 1959 and 1964, by Subarea, Southern Michigan Subregion . . . . . xi Page 115 117 121 124 127 130 159 162 163 164 Table 3.1. Alternative Model Projections of General Field Crops with an Irrigation Potential in 1980, Southern Michigan Subregion, Technology 1 . . . . . . . . . . Alternative Model Projections of General Field Crops with an Irrigation Potential in 1980, Southern Michigan Subregion, Technology 2 . . . . . . . . . . Alternative Model Projections of General Field Crops with an Irrigation Potential in 1980, Southern Michigan Subregion, Technology 3 . . . . . . . . . . Significant Characteristics of Large Soil Management Groupings, Southern Michigan Subregion . . . . . . . . . . . 1958 Land Use Distribution by Subarea, Southern Michigan Subregion . . . . . Estimated Cropland Available in 1980, Adjusted for Minor CrOps and Nonfarm Uses by Soil Groups and Subareas, Southern Michigan Subregion . . . . . . . . . . . Estimated Pastureland Available in 1980, Adjusted for Nonfarm Uses by Soil Groups and Subareas, Southern Michigan Sub- region . . . . . . . . . . . . Estimated Percentage Distributions of Cropland and Pastureland Available in 1980, by Soil Groups Within Subareas and by Subarea Within Soil Groups, Southern Michigan Subregion . . . . . . . . Major Cropland Acreage Use, by Crop and Subarea, Southern Michigan Subregion, 1959 and 1964. D O C O I O O I 0 Production of Livestock and Livestock Products, by Type and Subarea, Southern Michigan Subregion, 1959 and 1964 . . . Benchmark Projection of Harvested Acreage for 1980 with Permanent Pasture Assumption Removed Compared with 1964, by Subarea, Southern Michigan Subregion . . . . . xii Page 180 182 183 188 190 191 192 193 194 195 196 Table Page C-9. Benchmark Projection of Major Field Crop Production in 1980 with Permanent Pasture Assumption Removed Compared with 1964, by Subarea, Southern Michigan Subregion . . . . . . . . . . . 197 C-lO. Benchmark Projected Total Cost of Producing Major Field Crops in 1980 with Permanent Pasture Assumption Removed, by Subarea, Southern Michigan Subregion . . 198 C-ll. Objective Functions of Alternative Benchmark Model Formulations with Irrigation Allowed, Southern Michigan Subregion, 1980 . . . 199 xiii LIST OF FIGURES Figure Page 1. Map of Michigan, 42 County Subregion and Five Subareas . . . . . . . . . . 26 2. Groundwater Availability in Glacial Deposits . 185 xiv CHAPTER I INTRODUCTION The Problem One of the major recommendations of the Senate Select Committee on Water Resources was that all major river systems in the United States should be thoroughly studied by 1970, and a comprehensive plan of development made for each.1 The responsibility for initiating and conducting these river basin planning efforts has been assigned primarily to the resource oriented agencies of the Federal Government with the further directive that they work closely with the state and local interests in the study area.2 1In 1959, Senator Robert S. Kerr, as Chairman of the Senate Select Committee on Water Resources, launched a two-year national survey on the nature and extent of existing and future water problems in the country. Probably greatest attention centered on the growing problem of water pollution. All interests and problem areas were covered by the voluminous hearings and reports, however. Of primary interest to anyone seeking information in this area would be the Report of the Senate Select Committee on National Water Resources, Senate Report No. 29, 87th Congress, January 30, 1961, and the thirty-two separate Committee Prints on specific issues. 2The four Secretaries most concerned with river basin planning, namely Agriculture, Army, Health, Education The United States Department of Agriculture, as one of the four departments primarily involved in river basin planning, has assigned certain aspects of each basin study to several of its component agencies. The Economic Research Service is assigned primary responsibility for conducting agricultural economic base studies and analyses of the economic potential for water resource development. Within ERS, the Natural Resource Economics Division (NRED) fulfills this responsibility. Studies are currently under way in all major river basins of the United States. The first such study (the Ohio) has just recently been completed.3 Linear program- ming techniques were used in the Ohio study and they continue to be the main tool of analysis in the other studies.4 Each new basin survey benefits from experience gained in the advanced stages of earlier surveys. and Welfare, and Interior, were requested by the President to form a Water Resources Council to coordinate the overall progress of the planning effort. They served in an Ad Hoc capacity until the passage of the Water Resources Planning Act, Public Law 89-80, July 22, 1965. 3See, U.S. Army Engineer Division, Ohio River- Cincinnati, Ohio, "Main Report of the Ohio River Basin Comprehensive Survey," August, 1969. 4Three-quarters of a million dollars have been spent in developing an input-output model at the University of Colorado which is being adapted for use in the Upper and Lower Colorado River Basin studies. Also, Battelle Memorial Institute, under USDA contract, has investigated the feasibility of computer simulation techniques for projecting future economic activity in the agricultural sector of a river basin. Estimated costs of developing a workable model were $500,000 along with a 2-3 year effort New techniques of analysis are continually being tried and evaluated by staff members of NRED in an effort to improve current procedures. Emphasis has been placed on either cost reduction through respecification of the analytical model, or on improved explanatory ability, through added realism, without greatly increasing the data development costs. Where additional assumptions or refinements in assumptions improve the realism of results, they are incorporated into the projection model. Certain assumptions are made, of necessity, where data do not exist or would be too costly in time or funds to develop and evaluate. But one of the main purposes of assumptions is to make the analytical problem more manageable by cutting down on the number of variables that must be evaluated. Assumptions built into river basin projection models are subject to errors because of limiting timetables, funds, data or techniques, and these errors have an impact on the resulting estimation of economic potential for water resource development. At this time the extent and di- rection of these sources of error is not known. Water resource development projects to alleviate various local and basin-wide problems are justified on the basis of by a team of scientists. The currently operational NRED linear programming model will continue to be the most realistic alternative as a tool of analysis for some time in view of budgetary constraints, study time limitations, and immediate need. Therefore, every effort should be made to understand and improve the current procedures. estimated economic potentials derived in part from these assumptions. If and when these projects receive Con— gressional authorization for construction, they are undertaken largely through the expenditure of public funds. Therefore, interest in the improvement of projection methodology is of public as well as professional concern. This study examines a selection of some of the most common assumptions currently in use. An attempt is made to determine the effects of these assumptions on the resulting projections. Objgctives and Scope of the Study Objectives The central concern of this study is an analysis of typical assumptions underlying the NRED river basin pro- jections, an assessment of the sensitivity of these projections to atlernative assumptions, and an analysis of the effects of these assumptions on the projected economic development potentials for irrigation. Specifically, the study objectives are: 1. To evaluate selected assumptions made in developing the basic ERS model used in pro- jecting agricultural activity in comprehensive river basin surveys. 2. Analyze the sensitivity of model projections of total costs of production to changes in these assumptions. 3. Evaluate the sensitivity of model projections of locations and acreages of potentially irrigable crops to changes in these assumptions. Realization of these objectives will provide a basis for general evaluation of some of the typical assumptions river basin investigators are required to make in carrying out their studies. It will also identify which model specifications and assumptions are most critical in river basin projection work, which assumptions require more intensive background research, and which are relatively insensitive to large variation with respect to their impacts on analysis results. Scope The "NRED 1980 Agricultural Projection Model for Southern Michigan" was chosen as the subject for analysis in this study. The model is a relatively small minimum- cost linear programming construct, readily manipulated and relatively inexpensive to operate in terms of research 5 It was designed to analyze a 42—county time and funds. study area in the lower half of Southern Michigan containing five subareas delineated on a type-of-farming basis. Each 5The Southern Michigan model has a matrix that is 212 rows by 554 vectors while, in comparison, the Upper Mississippi model is about 850 by 10,000 and the Wabash model is 2,000 by 15,000. With one of the other models, this study would have been prohibitive. subarea contained severn major soil groupings among which the model allocated twelve overall field crop requirements subject to such constraints as limitations on the full use of certain resources, minimum subarea production re- quirements, and limited potential physical development of resources. Most of the characteristics of the larger NRED models are contained in the Southern Michigan model. Thus, the relationships which develop from an analysis of this small model will have general application to the larger models currently being used and to others that may be developed which also contain the same characteristics. With the beginning of the Ohio River Basin Compre— hensive Survey in 1963, a decision was made to utilize the least-cost linear programming model.6 Considerable time and effort at the NRE Division level have gone into evaluating alternative projection techniques for use in river basin analysis.7 There continues to be interest and 6An operational linear programming model, oriented to the identification of water resource development po- tential and likely future cropping patterns in a river basin context, was first developed by NRED for use in the Texas study. For a discussion of the methodology behind this model, see, A Methodological Supplement to "Resource Requirements for Meeting Projected Needs for Agricultural Production, Texas River Basins," prepared for United States Study Commission-—Texas, by Farm Economics Division, ERS, USDA, 1962. Since the model and experience in its oper- ation had already been developed in the Division, it was logical to turn to this source for analytical tools in 1963 rather than try to develop new techniques in View of the time constraints imposed by various phases of the Ohio study. . 7See, for example: Stanley F. Miller and Albert N. Halter, "Simulation Systems in Making Water Resource effort directed toward adapting other techniques, such as input-output analysis or simulation, for use in river basin analysis. But, it appears that the current analytical tool of the Division will be in use for some time. This study focuses on potential improvements in that technique. The Research Format The overall research format of the study consists of an analysis of the results of a cost-minimizing linear programming model used in river basin planning, and the impact that variations in selected model assumptions have on those results. Projected 1980 agricultural activity in a 42-county subregion of Southern Michigan serves as a benchmark against which alternative formulations of model assumptions are examined. The Benchmark solution reflects an absence of irrigation, drainage or flood protection beyond the current level. The sensitivity to changes in Benchmark Model assumptions are evaluated in terms of the Decisions," Proceedings, Committee on Economics of Water Resource Development, Western Agricultural Economic Re- search Council, San Francisco, California, December, 1965; Albert N. Halter and Stanley F. Miller, "River Basin Planning: A Simulation Approach," Oregon Agricultural Experiment Station Special Report 224, November, 1966; Stanley F. Miller and Albert N. Halter, "Computer Simu- lation of the Substitution Between Project Size and Management," American Journal of Agricultural Economics, LI, No. 5 (December, 1969), 1119-1123; Neil E. Harl, "Research Methods Adaptable to Legal-Economic Inquiry: Linear Programming and Simulation," in Methods for Legal- Economic Research into Agricultural Problems, Agricultural Law Center Monograph No. 8, University of Iowa, 1966; Battelle Memorial Institute, "The Usefulness of Computer Simulation for River Basin Analysis," Research Report to NRED, ERS, USDA, March, 1967. impact upon total costs of meeting production objectives. Later, an irrigation development alternative is introduced into the Benchmark Model as a matrix extension and similar comparisons are made of deviations arising from model assumption variations. Additional sensitivity analysis examines the identification of economic potential for irrigation, its location and extent. In that analysis the deviations from Benchmark assumptions that cause shifts in irrigated acreage among subareas are evaluated. Because of the limited scope of this study, only agricultural irri- gation is included as a water resource development alternative. Agricultural drainage and flood protection are also important considerations and would be included in a more comprehensive analysis. CHAPTER II ANALYTICAL APPROACH AND FRAMEWORK OF THE STUDY Analytical Approach The future agricultural use of land and water resources in a particular river basin will reflect the kinds of food and fiber products that consumers demand and the competitiveness of basin farmers in meeting such demands. Basin farmers produce for both national and foreign markets and must compete with other basins and regions in the production of agricultural commodities. In so doing, the future productivity of the agricultural land base will have a major impact upon the amount and kind of agricultural production forthcoming from a river basin. Several non-agricultural uses of land, such as urban— related, recreation, and transportation development also have a bearing on land availability for agricultural production. The general analytical approach used in this study is similar to that employed by NRED in their standard river basin studies. It represents an attempt to project the output of an area by assessment of the following three components that affect output: 10 l. The determination of demand for agricultural products from the basin. 2. The determination of the quantity and p32- ductive capacity of the land resource (supply). 3. The estimation of the amount, kind and location of agricultural production in the basin, reflecting current and potential water resource developments (given demand and supply conditions). Demand for Agricultural Products The estimated demand for agricultural products is based upon national population projections and the expected per capita consumption rates of agricultural products. Trends in per capita meat, cereal, and dairy product consumption were developed from commodity studies made by the USDA. Estimated per capita consumption multiplied by projected population in addition to net export requirements provided estimated national demand.8 A portion of the national demand was allocated to the study area, a 42-county subregion in Southern Michigan. 8Demand estimates used in this study were developed by ERS. These data are reported in unpublished memoranda dated March 29, 1965, developed by the Economic Framework Section, River Basin and Watershed Branch, Resource Develop- ment Economics Division, ERS, USDA, cooperatively with the Economic and Statistical Analysis Division, ERS. Current estimates are made by the Resource Data Systems Group, Natural Resources Economics Division, ERS. 11 The allocation was thought to be consistent with productive efficiency in other parts of the country, being founded upon existing trends in regional production. Commodity specialists in the Marketing Economics Division, ERS, USDA made estimates of regional shifts in production based on relative efficiencies of production in the various regions. Given the Subregional share of national food and fiber requirements the problem was one of determining where the production would likely locate within the Subregion based on comparative advantage and resource potentials. Productive Capacity of Land Resources The soil resource provides the physical basis for the Benchmark Model. Over the length of the projection period, land in its various forms was assumed to be the only limiting resource at the Subregional level. Land resources were divided into seven soil groupings on the basis of similarities in yield response to like management practices, soil texture, fertility, and land treatment requirements (Appendix Table C-l). The Inventory of Soil and Water Conservation Needs was used in determining the productive potential of the resource base.9 This source identified the kind and 9Michigan Conservation Needs Committee, "An Inven- tory of Michigan Soil and Water Conservation Needs," Michigan State University, Agricultural Experiment Station, October, 1962. 12 acreage of soils within the Subregion and provided the base for projecting cropland available for agricultural pro- duction in future time periods. Certain reductions were made in the agricultural resource base. They reflect the impact of such nonfarm uses as urban-residential, industrial, commercial, recre- ational, and transportation needs for the land. Further reductions were made to account for land requirements of minor and specialty crops. The remaining acreage of cropland and pasture was assumed to be available to farm operators for agricultural production. Crop enterprises were developed for each soil grouping with the help of crop and soils specialists. Projections were made of the yield potential of all major crop and pasture uses of each soil grouping. These estimates were derived in cooperation with Michigan Agri- cultural Experiment Station and Soil Conservation Service specialists, and represent expected average yields that reflect the normal climatic, disease, and insect hazards expected to affect future yields. The projected yields take into account the improvements in technology applied to crop production, but do not include the gains obtainable through water resource development programs such as irri~ gation, drainage, and flood protection. The irrigation development aspects are discussed at length in a later section. Other water resource development alternatives 13 are not considered in this study, but they may be equally as important. In addition to projected yield information, pro- duction costs were developed for each crop grown on a particular soil grouping. These costs reflect all fixed and variable costs incurred in land preparation, culti- vation, and harvesting and account for such materials as seed, fertilizer, lime, twine, pesticides, etc. However, they do not account for land charges, transportation, or storage costs. They represent only the on-farm costs of production. Location of Agricultural Production Estimation of the amount, kind, and location of agricultural production was accomplished through the use of minimum-cost linear programming techniques. The demand side provided estimates of the future agricultural products required from the Subregion while the supply side indicated future crop and pasture productive capacity of the soils available for agricultural production. Given the demand and supplypotential, the Benchmark Model selected ap- propriate acreages of each soil that most efficiently met production requirements within the constraints placed on the model.10 10A much more detailed discussion of the procedures used in this methodology is available in Appendix 0-- Economic Base Study-Part IV, Comprehensive Water Resources 14 The Basic Linear Programming Model The Linear Programming Format The theoretical basis of the projection model has its grounding in the Iowa State interregional analysis work pioneered by the Egbert-Heady team and more recent modifications.ll However, the model used in river basin analysis is regional in construction while the Iowa models . . 12 are nat1ona1 1n scope. The basic model used for the Subregion in this study is concerned with 5 subareas, l2 crops, and 7 soil groupings. The objective of the basic model is to minimize Study, Grand River Basin, Michigan, January, 1966. See also Melvin L. Cotner, "The Potential Role of Agricultural Land Drainage in Economic Growth," unpublished Ph.D. thesis, Michigan State University, 1967. 11See for example: A. C. Egbert and E. C. Heady, Regional Adjustments in Grain Production, A Linear Program- mimgmAnalysis, U.S. Department of Agriculture, BfilIetin No. 1241 and Supplement, June, 1961; Egbert and Heady, Regional Analysis of Production Adjustments in the ngor Field CrOps: Historical and Prospective, USDA Technical Bulletin No. 1294, 1963; Egbert, Heady and Brokken, Regional Changes in Grain Production, An Application of Spatial Linear Programmin , Agricultural and Home Economics Experiment Station, Iowa State University, Research Bulle- tin 521, January, 1964; and recently, Whittlesey and Heady, Aggregate Economic Effects of Alternative Land Retirement Programs: A Linear Programming Analysis, ERS, USDA, in cooperation with the CAED, Agricultural and Home Economics Experiment Station, Iowa State University, Technical Bulle- tin No. 1351. 12The Resource Data Systems Group, NRED, ERS, is currently developing a national river basin model that also encompasses the entire United States and has the seventeen major river systems as its subregions. 15 subregional on farm costs of production. The objective function is: Minimize: 7 12 5 z = z 2 2 C.. x.. i=1 j=l k=l 13k 13k Subject to the following constraints: igl kgl aijk Xijk Z bj for j ‘ l, 2, ..., 12 7 ij aij xijk 1 gj’k :33 i : 1: ::.: 1g and 12 PIFJxfikifim f”i:i:?:x:§ and Xijk Z 0 for all i, j, and k Where: Z: total cost of production Ci'k cost of producing an acre of crop j on soil 3 i in subarea k i'k: the number of acres of the activity producing J crop j on soil 1 in subarea k aijk a coefficient expressing output of j in terms of an acre of soil i in subarea k 16 b.: subregional production requirements of crop 3 j g.k: minimum production requirement of crop j for 3 subarea k di.: quantity of land resource 1 used in producing J an effective acre of activity j ri k: quantity of soil group i available in sub— ’ ' area k ' Sik = rik ’ Pi,k Pi k = restriction placed on the full use of soil I group i in subarea k to reduce soil loss The optimal solution to the linear programming problem is a summation of the least costly means of producing specified quantities of twelve crops on seven soils within the Subregion's five subareas ignoring public resource development costs. The first set of constraints (bj) establish minimum Subregion production requirements for each of the twelve crops considered by the model. The model is further constrained (gjk) to ensure a minimum level of production of each crop within all subareas. Constraints of the form (Sik) establish upper bounds on the availability of soil resources within subareas. Certain crops are not allowed full use of soil resources (Pik) as a means of reducing erosion. The final constraint (X. 1jk 1 0) ensures that the solution will have positive values. 17 Typical Linear Programming Assumptions and Constraints In any linear programming problem, it is necessary to make several simplifying assumptions that reduce the problems of data collection and machine computation to a Inanageable size. It has been the opinion of most model builders that these assumptions do not detract greatly from the realism of an investigation, but allow the development of sufficiently detailed models to meet re- search objectives. The basic assumptions which have been established for most least-cost linear programming river basin models are: l. The special distinguishing characteristics of the area under study can be represented by spatially separated and independent producing regions, each of which is internally homo- geneous, whether it be major river basins in a national model, sub-basins of large basin studies or the five types of farming subareas used in this study. 2. Land within a soil management grouping within a subarea is a homogeneous factor and all crops may compete for it. 3. Cropland area is the limiting factor of pro- duction for each subarea. 18 4. Potential cropping activities for a subarea are determined by cropping history, climatic factors, and soil limitations. 5. Constant returns per acre of a given soil management grouping are assumed regardless of the output level. 6. Farm operators will minimize costs in their choice of the crops to be grown on particular soils. 7. Subregional demands for food, feed, and fiber, including domestic and foreign export re- quirements, are exogenously determined and known. 8. Resources can be used and products produced in quantities which are fractional units. 9. Resource supplies, input-output coefficients, and prices are assumed to be known. Partial Matrix Example--The Southern Michigan 1980 Benchmark Model While the presentation of model specifications in equation form is a very efficient descriptive means from the vieWpoint of the mathematically inclined reader, this method presents certain difficulties for others. Not only is a tabular representation more readily understood by non-mathematicians, it may also present a clearer under- standing of the relationships to mathematicians as well. 19 Thus, a sample segment of the matrix from the Benchmark Model is included and discussed briefly to provide a clearer understanding of its use in the study. A partial matrix of the Southern Michigan 1980 Inodel was selected to show how two subareas, three soils, and three commodity demands would appear when constrained by production mimima and faced with an irrigation develop— Inent alternative for one of the subareas (Table l). The projection year of 1980 is a nationally established target date for river basin studies and provides a time frame Within which to assess early action prOgrams. All of the characteristics of the complete model are represented in partial form by the example except for the constraints (actual right—hand side values of the 'table). This discussion may help those who are not fa— Iniliar with linear programming to visualize some of the tinternal workings of the model and how a particular program is "set up." Beginning with the left-hand side of Table 1, each irow in the matrix is identified with a specific name that IRust only appear once if the logic of the system is to be Inaintained. The center and major part of the matrix i=ontains all activities which compete among themselves in AUHAS commune Umumm>nmn uoc ugh pmpcmHm mucmmmnmmn poosconm can pmuaaa»: mmmmnom on» cmm3umn mocmnmwmap ocam 30 s.emo.a k.mma H.Hkm m.m~m «.msa 4.6m wouaaaus sflamsuoa s.smo.a a.m~a H.Hkm m.m~m ¢.msH 4.6m maanamsm musummm unmemeuma m.m~m.m o.mm~ H.moo.a o.H~m H.mav.a m.mH~ memoseonm adamsuoa m.msm.fl «.mma m.kks m.mmm o.-e k.oma emuasvmu coauoseoua sashes: o.mma.a m.m~a m.mom o.mkm m.kmo m.Hoa emuaaaua adamsuom m.kmm.m m.~mo.a m.q~m.a s.smm.a m.mas.a H.msq mmouo son now magmaam>a m.mao.s «.mom o.mso.H H.smm o.oam.H ~.m~m memuaaaus adamsuoa H.ms~.a m.smm.fl m.mmm.a m.Hmo.~ N.Hmm.H n.HHm ecmamouo manuaam>m Hmuoa monom ooo.a coammunsm m e m m H on: can Hmpos monmnsm Mafiawnmaflm>m mousomom coamonnnm savage“: anonusom .monmnsm an .omma ca mmono “ohms How on: no cowpomnoum xnmficocmm can pcmamono mo unflaflnmaflm> II.m mamma 31 Only one-third of the cropland available for row crop production would be expected to be utilized for that purpose. It is projected that Subarea 1, long an area of decline in agricultural importance, will continue the downward trend with only 44 percent of the cropland required and only half that percentage for row crops. Southwestern Subarea 5 would be relatively under-utilized because larger quantities of the lower producing soils are not required to meet the level of production specified by the Benchmark. Close growing crops would predominate in Subarea 3, which lies between 1 and 5 both physically and in terms of production; row crops would occupy 17 percent and all crops 45 percent of cropland available for these uses. Three-fifths of all acreage available for row crop production in Subarea 4 would be utilized for that purpose, significantly larger than the next most important subarea. {The proportion of all production devoted to row crops would Eilso be 1arge--about 80 percent in Subarea 4. Close growing crops would predominate in Subarea 2 where nearly 93 percent of all cropland is expected to be in production ‘Ntith intertilled crops accounting for 43 percent. igggggmggggsziigfimand Requirements Projections indicate that corn will continue to be t111€3 dominant field crop in the Southern Michigan Subregion ‘imrl .1980 as it was in 1964 (Table 3). More than a 32 TABLE 3.--Benchmark projections of demand requirements for 1980 compared with 1964 production levels, Southern Michi- gan Subregion Benchmark Percentage Crop Units 1964 1980 Change Wheat bu. 32,890,100 27,668,500 —15.8- Corn bu. 72,780,000 109,882,300 50.9 Oats bu. 26,379,500 20,233,000 -23.3 Barley bu. 1,065,700 2,697,700 153.1 Soybeans bu. 5,181,600 11,194,700 116.0 Dry Beans cwt. 7,645,400 8,202,200 7.2 Potatoes cwt. 5,470,200 11,960,000 118.6 Corn Silage ton 3,069,500 2,672,300 -12.9 .Alfalfa ton 2,279,100 1,563,600 -31.3 (Other Hay ton 289,100 337,200 16.6 Cropland Pasture AUDa 87,028,500 116,228,500 33.5 Source: Census of Agriculture 1964, and working data for the report, "Agricultural Activity in the Grand River Basin: A Projective Study, NRED, ERS, USDA, January, 1966. aOne animal unit day (AUD) is equivalent in feeding Value to fifteen pounds of corn. No attempt is made to identify permanent pasture production in 1964, although 90 million AUD' s are projected for 1980 in the Benchmark. 33 50 percent increase in production is expected to occur during that time period. Declines from 1964 levels are expected in the production of wheat, oats, corn silage (as an increasing proportion of all corn is produced as corn for grain), and alfalfa hay, while sizeable increases are expected for soybean and potato production. The pro- jections for barley production indicate a significant increase from 1964 to 1980; the extent of the increase is exaggerated by the fact that 1964 production was ab- normally low. On a subarea basis, the acreage required to meet projected needs declined in all but Subarea 2 (Table 4). Acreage required per crop increased for soybeans and potatoes and declined for all others. Subarea 1 indicates an increase in acreage of cropland pasture and also the .relative share of acreage in alfalfa. Potato acreage_ larojections show gains both relatively and absolutely in Eiubarea 5 with a general decline occurring in the harvested acreage of all other major field crops. Although the Iléirvested acreage in Subarea 4 is projected to decline Somewhat, the relative share overall shows a 2 percent Elatin because of the nearly 180 percent increase in corn acreage. Projections for barley, soybeans, and pasture acreage show increases in Subarea 3, but the relative £3hare for these crops of total major crop acreage declines EilDSDIIt 5 percent. Subarea 2 is expected to increase its 34 xfipcmmmfi mom .po>oEmH was coapmesmmm was» muon3 mGOmemmfioo How mIU manna .ucmHmnsummm ucmcmenom mo coaumNflHaus Hana magnum mcowuooflonmm .cOHusHOm xnmanocom can .vwma cuspHDOHHmm mo msmcoo "condom Nam.m mme.m mam pea moo.H amm.H Hum aem.H mee.H ~mm.H eHm ewe mus Hence «me men as eeH me mmH mam HHN we meH He me 0u50u86.mouo eHH mmH MH He «H as mH me He me e mH mam guano ame mam em meH as mmm me can mem omm mH ee aeHueHm mmH New a we MH mm Hm me be me e on mmaHHm auoo mm am e m OH AH m e mH N m m muouauom «em mam e N ea oem eH me emm emm H e maamm sub mam emm em em me Hm me am com m me am mamubmom me am e . e m N am e a e H H mmHumm new use eH He mm ea we eeH eeH eMH HH He memo Noo.H am~.H ea emm mHe Ham eeH owe me mmH me HNH cuoo oem OHe em mMH me eeH mm emu mmm mmH aH as Home: mmuom ooota omaH eemH oamH eemH eeaH eemH emaH eemH eemH eemH oeaH eemH m Hmuoa m monmnsm v mmumnnm m monmnsm N mmumnsm H mmnmnsm 0H0 an .eeaH aqu eouaesou oemH you ummmuum umuum>umg mo cofluomnouq gumsaoqmm ecoammnnsm sema30flz cumsusom .mmnmnsm .1 see 35 relative share by 15 percent as the harvested acreage of all but feed grains and pasture show significant gains. Benchmark projections show that acreages required to produce many of the major field crops in 1980 decreased in some subareas and even in the Subregion. However, the production from those acres, in many instances, increases sufficiently to more than compensate for the acreage decline (Table 5). For instance, although the harvested acreage of soybeans is projected to decline by 11,000 in Subareas 4 and 5, the production in those two areas increases by about 365,000 bushels. Corn production gains by 50 percent in the face of a 19 percent acreage decline and the production of potatoes more than doubles with only a 13 percent acreage increase. Projected yield increases of substantial magnitude :in all subareas are responsible for these production ianrovements (Table 6). In general, the largest increases occur in corn, corn silage, and potato yields. The EPINDjected 1980 yields represent the use of the most pro- Cituctive soils available which are generally more efficient than the less productive soils on a per unit cost of IPJrcmduction basis. If all soils were used in 1980, the Jr<3£sulting yield levels would undoubtedly be much lower. mCOmHHmmEOO now mIU manna xflpcommd mom .um>o&ou mm3 coaumESmmm was» muons .coflusHOm xnmecocom 0cm .vwma ousuazowumd mo msmcou .ccmH ousummm unnameumd mo coauMNHkus Hana madman mcowuoonoumm "mousom 6 3 e-.eHH mmo.em eoo.HH mmm.eH mmv.~H eme.H~ Hee.me mem.m~ mmH.MH Hme.eH meH.eH eHH.m one ousumua mono emm mmN an me on me we me new Ne NH Hm so» an: umnuo eem.H me~.~ meH emm HmH Hem mam nee New nee me emH :ou meauHa Nee.” oeo.m com ewe can mme «me see mee.H men em mmm con omuHHm :uoo mmm.HH oee.m «Hm.H emm me~.m om~.m mHe wee eme.m mam mom eme .030 60006866 ~o~.m nee.» m mH moe.~ Hmm.m ooe Hme mee.m Hoo.m Hm so .830 ucmmm mun mmH.HH ~mH.m ems mam mem.H mmH.H ome.H amm.H ~mm.m OOH oom.H Hoo.~ .an ucuonmom mae.~ Geo.H Hmm New mMH Hm aHe.H new mes «am He 04 .sn mmHumm mmm.o~ omm.e~ emH.H mom.m eme.~ mee.m mHe.e mem.e moo.m NeH.e ems mme.~ .5n auto amm.aoH .ome.~e ~oe.m NGH.~H mmm.oe eHe.mH ome.eH eme.em oeo.m oe~.~H eme.e one.e .sn :uoo mee.e~ ome.~m 6mm.H mee.e eeH.m Nem.e Hmm.e ~oe.m mee.eH cmm.e one moo.m .an been: uuHca ooo.H ommH eeaH ommH eemH ommH veaH omeH eeaH ommH eemH ommH eemH mafia: mono Hmuoa m mmumnsm v mmumnsm m monQSm N mmumnsm H moucnsm aumeuaom .amuunsu an .eeaH MCOHmoHnsm :mmw50az cvfl3,poummeoo owma ca cowuosuoum mono paowm Hohma mo coauoonoum xnmanocomll.m mamas uHsmmu m mH mHnmu on» cH po>ummno coHuMHHm> on» mchsoum ucoemumcma HHom an hum> muHmHh moch .mmmumnsm ecu mcosd mHHom mo xHE m>HumHou on» uo .mmmmuom coHusHom an coHuospoum mmumnsm Hmpou mcHuH>Hu an pm>Huoc .vme HON omocu one no .mmmmno>m coucmHo3 mum mpHon ommH anew .GOHHSHOm gynecocmm use .vmmH cusuHsoHHm4 mo newcou "condom 37 h.th o.MHH o.mnH o.MHH v.th o.MHH o.mnH o.mHH o.mnH o.MHH m.mmH o.MHH 0:4 musummm mono m.m m.H o.m m.H m.~ m.H m.~ m.H m.m m.H o.m o.H cou we: nocuo m.m m.m o.v m.m m.m H.m m.m m.N m.m m.m m.v m.~ so» MMHMMHd n.HN m.0H v.Hm m.m m.HN m.0H o.Hm m.HH m.H~ m.0H v.HN m.HH cou omMHHm cuoo e.vom m.mmH 0.5mm o.mmH m.mvm b.va o.mmm «.mmH o.mmm m.NVH m.bmm o.mmH usu mmoumuom m.mm o.mH H.vm m.w v.~m m.vH o.vm c.0H v.v~ m.NH m.¢~ o.oH #30 mamom who m.m~ m.H~ 0.0m m.hH o.mm h.mm o.m~ m.- 0.0m «.mH ~.om o.mm .sn mammnhom m.ow v.wv 0.0m «.mv o.vo m.mv o.mm v.mv o.mm h.Hm m.mm m.~v .sn moHHmm h.mm m.vm o.mn v.mv o.mn H.mv o.mm N.mm o.vm v.mm o.hh v.om .53 name h.m0H n.mm m.mm m.mv m.mHH m.hw m.HOH m.wm m.v0H m.mm o.mm o.vw .sn cuou N.Hm h.ov o.mv ~.mm v.mv v.mv o.om ~.ov o.om h.mv 0.0m m.mm .9n upon: ommH vomH ommH vomH ommH vme ommH vme ome oomH ommH vomH uHcD mono Hence m mmnmnsm q moumnsm m mmumnsm N moumnsm H mmumnsm mconmunsm cmmHnon cumnusom .mmumnsm an .vme suH3 poummeoo ommH CH mmouo Hoflms mo mprHm pouommoum 3.88683} . e mamas. 38 Cost of Production Basis for Development Current input price levels and relationships provided the basis for developing production cost data. Consequently, all costs used and reported by this study are in terms of constant 1964 dollars. Cost budgets were developed with the assistance of specialists at the Ohio and Michigan Agricultural Experiment Stations. All items of on-farm costs were included with the exception of land charges and charges for on-farm storage. Off-farm develop- ment costs were ignored. The per acre production costs for each crop and soil were aggregates of four major types of costs: preharvest costs, harvesting costs, cost of :materials and overhead charges. These costs were developed .by applying an hourly charge against the time required to 19erform each operation. Tillage operations, equipment asize, and performance rates represent better than current érverage production methods.15 These production costs and ‘tdue associated productivities of subarea soils served as tzfme basis for allocation within the Benchmark Model and all additional models developed to analyze the effects of a l ternative assumptions . ~L 15For a detailed account of equipment and labor PS308‘t:s used in these budgets, see: Melvin L. Cotner, "The Gotential Role of Agricultural Land Drainage in Economic '1?<>V9th" (unpublished Ph.D. Thesis, Michigan State Uni- verasing, 1967). 39 Benchmark Model Production Costs The projected total cost of producing the major field crops specified in the Benchmark was approximately $191.0 million in 1964 constant dollars, including an estimated charge of $14.5 million for permanent pasture (Table 7). Only the on-farm production costs of these crops are represented by this figure. Off-farm transpor— tation and marketing charges are not included nor are the production costs of livestock and minor crops a part. Nearly 38 percent of the total cost of projected production in the Subregion is incurred in Subarea 2 where about 93 percent of the resources are expected to be committed to major crop production in 1980. Other im- portant agricultural subareas are Subareas 3 and 4 where proportionate shares of 19 percent and 30 percent of the Subregion's costs would be incurred, respectively. Only about 5 percent of all costs would be accounted for in Subarea l, where 44 percent of available resources are utilized. Eight percent of the costs would be incurred in Subarea 5, although only 22 percent of those resources are used. The projected distribution of production costs among major crops is generally similar to the projected distri- bution of acreage used in the production of these crops. There are a few exceptions to this distribution however. Notable among them is the production of potatoes and 40 .mcsn xumfinocmnm HmchHHo mo puma HmnmoucH cm Hos mHo3 can cOHusHom may on umppm ouo3 mumoo ommna .HmuoE one ou cocoa umuMH .moHuH>Huom mmocu How mumoo mmmnm>m so comma mumEHpmm cm was onsummm pamcmfiumm How GOHHHHE m.VHw mo umoo Hmuou mafia .mHmHHOU ucmumcoo vomH mo mEHmu :H mum mosHm> HHm .pm>OEmH mp3 GOHumEsmmm chu mnmcz mcomHHmmEoo How OHIO mHnma prcmmmm mom .pcMH musumma ucmcmaumm mo QOHHMNHHHHS HHDM oEsmmm mGOHuomfloumm wew.owH wew.wH wHw.ew Hew.ww wHe.He www.w uwoo Hauoe newe.eH wHw.H wwH.m wow.e weo.w owe unnamed unmeasumm wwo.wH wwH.H oww.H www.w www.H wHw.H musuuaw uaaHaouo wew.e wwe ewe Hee wee.w ewH mum Hmnuo oew.wH Hee.H www.w www.w wew.w owe memeHe wwo.wH www HHe.H wwH.w wwo.w wwe mwaHHw cuoo ewe.wH mew.H www.e wwo.H eww.e wow wuoueuoe wow.wH wH wwH.e wee eww.HH He uaaum wen www.wH www New.H wHo.w woe.w eee.H unambwow wew.H wHw Hw wee www ww emHuum www.w wow sew.H wwo.w wow.e wwe wuuo wow.Hw eww.e www.ww www.e eww.e eww.w :uoo www.mw wHw.H ewe.w eww.w wwH.eH wow Hume: wuaHHoe woe.H GOHmeQDm m MOHMQDm v MOHMQDm m mmHMQSm N MOMMA—pm H mmHMQHHm QOHU mQOHmoHnsm cmmHnon snogusom .moHMQSm >3 .ommH CH mmono cHon H0mmfi mcHosponm mo umoo Hmuou pmuooflonm Humasocmmll.e mqmda 41 cropland pasture where potatoes occupy less than 1 percent of the acreage but account for 8 percent of the production costs. Conversely, cropland pasture acreage represents 17 percent of the total but contributes only 6 percent to overall production costs (Tables 4 and 7). The expected output of corn requires the greatest amount of land--about 26 percent of the acreage-~and accounts for nearly 30 percent of all production costs while potatoes occupy the smallest acreage. On a cost per acre basis, potatoes are by far the most expensive crop produced in the Subregion. Potatoes, at $470 per acre, are at one extreme of the spectrum while cropland pasture, averaging just over $18 per acre, is at the other (Table 8). One other crOp, corn silage, has a cost of $106 per acre which greatly differs from the typical cost range of $30 to $50 for most crops in the model. Comparing acreage projections (Table 4) with associated per acre costs (Table 8), causes an apparent inconsistency between the location of production and the lowest per acre costs. But, when the minimum acreage requirements are considered in light of the relative productivities of available soils, it is clear that the per unit production costs are really the important allo- cators of production among subareas (Table 9). Generally, less than fifteen cents per unit of product separates the highest cost producing area from the lowest for a .mumHHOU ucmumcoo vmmH mo mane» CH mum mmsHm> HH¢ .moHMQSm HMHSOHHHMQ m now coHuDHOm ecu manwucm masonm ucmEommcmE HHOm can an pmuanoz mono HmHsoHpHmm m mcHosconm mo mumoo mmmuo>m esp mucmmmummmm 42 ww.ee ew.we mw.Hm eH.mw Hw.ee Hw.ww mmmnm>< wH.wH Hw.wH we.eH H~.wH Hm.wH ww.wH musuwmm mono Hw.ew ww.ww ww.ww wm.ow ww.ww ww.ww was Hmnuo ww.ew ww.we ww.me ww.ee we.ww mw.we meHmeHm ww.wOH mw.wOH mm.wOH eo.wOH mm.wOH mm.w0H mmmHHm cuoo ww.oee wo.wee wH.ewe we.wwe wm.ewe ow.ewe umoumuoa wm.ee em.we ww.we em.we ww.ee mo.we mcumm mun ww.ww ow.ww Ho.ww oe.ww ww.ww ow.ww mcmmneom NH.om ew.ww ww.ew ew.ww ew.ew ww.ew meumm ew.ww we.ww mw.ww ow.oe ow.oe ww.ww memo we.Hm Hw.we ww.ww ew.we wH.ew ew.we cuoo eo.we ow.me mm.we Hw.we ow.we ow.me names mHMH HOD GOHOOHQDm m MQHMQDW v MOHMQDM m MQHMQSm N MGHMQDm H mmhmnfim QOHU mconoHnsm cmchon anocusom .mmnmnsm an .ommH cH mmono pHon momma mcHosponm mo whom Hem umoo pouomflonm xnmenocmmII.m mamma .mHMHHoc unnumcoo vmmHm 43 mmo.H mmo.H mmo.H mmo.H mmo.H mmo.H m.oD< wusummm 0H mono Hme.mH mmm.mH mmm.mH mmm.MH mmv.MH eom.NH con hum umcpo mmm.HH emm.mH mHe.HH mmm.HH mHo.HH omm.HH cou MMHMMHH wew.e wew.e eww.e wow.e www.e oww.e cop mowHHw auoo OHm.H mmm.H mHv.H mom.H mmm.H mem.H .uso mooumuom mmo.m omm.H Heo.m mmm.H mmo.m mmm.H .u30 mammm mun mHH.H omH.H MHH.H mmH.H mHH.H omH.H .sn mcmonmom eve. wow. www. ewe. www. wow. .ob euHumm mom. mHm. mme. emv. mew. HHm. .sn mumo mme. MHm. Hmv. «om. mmm. mme. .sn cuou mew. Hmm. mom. «we. mew. mom. .9Q #8033 mHmHHon COHmmHnsm m mmumnsm v mmnmnsm m mmHMQSm m mmumnsm H moumnsm uHcD mono mconoHnsw cmmHSOHz cnmcusom .mmnmndm an .ommH :H mmono pHmHm Hoflme mcHosuonm mo mumoo uHcs pmuomnoum Humanocmmll.m mqmda 44 particular crop. The least difference in per unit cost of production projections among subareas occurs in crop pasture, while the greatest occurs in alfalfa. This difference is mainly due to the choice of units (1 ton vs. 10 AUD's). Moreover, it should be made clear that the unit cost of production of these major crops may vary signifi- cantly with different alternative assumptions, especially those that bring pressure to bear on the resource base and force larger quantities of the less efficient soils into the solution. Utilization of Permanent Pasture Dropping the assumption that permanent pasture will be fully utilized, before requiring cropland pasture, to meet pasture objectives, caused several adjustments in the Benchmark solution. The total cost of production decreased by $4.8 million from $191.0 million to $186.2 million. Although pasture costs declined by over $5 million, the reorganization of soil resource use among the other crops in the model caused the costs of these crops to rise or fall slightly from their earlier values. Distribution of harvested acreage by crop shifted among the subareas in response to the increase in cropland pasture production. And most significantly, no permanent pasture acreage entered the solution. 45 What is the basis for such a response? Farm oper- ators in general have historically devoted less effort to improving the yields of permanent pasture than other crops. Usually, the land devoted to permanent pasture has had some problem, such as extreme wetness, stoniness, or steepness which has precluded its conversion to productive cropland. Farmers have thus treated such land as a neces- sary evil and the yields of permanent pasture have reflected this. The permanent pasture activities incorpo- rated into the Benchmark Model also reflect the history of depressed yields. But, improved management was considered to be applied to permanent pasture as well as the other crops. It is therefore obvious that when permanent pasture had to compete with cropland pasture the response from cropland was more efficient and that source prevailed. This is not to say that farm Operators with permanent pasture should idle that land in favor of cropland pasture. Operators who produce roughage consuming livestock will undoubtedly continue to utilize permanent pasture to some degree. But, with the concentration of livestock pro- duction into fewer and larger herds the relative use of permanent pasture must decrease of necessity. And: cropland pasture provides considerably more flexibility. As a result of the foregoing analysis it appeared unrealistic to continue to assume full permanent pasture usage. Consequently, permanent pasture activities were 46 added to the Benchmark Model as well as all other models with which it is compared. Companion Tables to 4, 5, and 7 are found in Appendix Tables C-8, C—9 and C-10 and re- flect the extent of changes brought about by the inclusion of permanent pasture in the model. '—' ‘N CHAPTER IV ALTERNATIVE ASSUMPTIONS AND MODEL SPECIFICATIONS: THEIR IDENTIFICATION AND PURPOSE The Role of Assumptions The necessity of "getting on with the job" causes researchers to adopt certain simplifying assumptions relating to their work. River basin studies and those who are responsible for their undertaking are no exception. Assumptions make the problem of explaining relationships more manageable than is possible without the assumptions. Moreover, they provide the opportunity to reduce the number of variables under consideration so they may be brought into sharper focus. Often the researcher is not completely satisfied with the assumptions he has to make and wonders how important or critical they may be to his study results. In this section, some of the assumptions that were made in the Southern Michigan Study are discussed in detail. These assumptions are either the same as, or similar to, those being made in other river basin studies. Variations in assumptions from those used in the Benchmark Model are developed for further analysis and used as a means of answering questions about the model's sensitivity. 47 48 The variations in assumptions that will be examined represent most situations found in river basin analyses ranging from the surplus resource situation to the limiting case. Additional questions about other aspects of the Benchmark Model are formulated and alternative models Specified to test them. Variations in assumptions are allowed to interact with each other to provide a broad range of answers to the questions of relative sensitivities. Thus, the results of these tests will have applicability to other river basin studies in which linear programming is being, or will be, utilized. Any insights into the sensi— tivity of certain types of assumptions, gained for this study, will have value for other researchers. The assumptions of the basic model that are subjected to sensitivity analysis have been grouped into the following classes: Class l-—Assumptions relating to livestock feeding relationships. Class 2-—Assumptions relating to projected demands. Class 3--Assumptions relating to soil management practices. Class 4--Assumptions relating to minimum production considerations. Class 5--Assumptions relating to adopted level of crop producing technology. 49 These five classes of assumptions include ninety— three linear programming solutions which reflect three distinct levels for each of the five classes of assumptions. Class l--Assumptions Relating to Livestock Feeding Relationshipg Subregional shares of the United States and export demand for livestock and livestock products are translated into requirements for feed and forage. In typical river basin studies, these requirements are incorporated into the basic model as demands for feed grains and roughages under the assumption that resulting cropping patterns will be associated with the location of livestock production. Feeding efficiencies and hypothetical rations for each class of livestock serve as the basis for converting livestock demands into feed and forage demands. In de- riving demands for feed and forage through this process, the final output of the model is subject to a major source of error. Insufficient published information on feeding efficiencies by state, for each class of livestock or livestock products, forces the researcher to rely on national data for the detail necessary in river basin studies. The procedure used requires a determination of 'average feeding efficiencies per unit of output at the national level. This is adjusted to represent estimated conditions in the region under study. Total feed 50 requirements, in feed unit terms, are subdivided into components such as feed grains and high protein, hay, other forage, and pasture based on average rations by class of livestock. While there is some basis at the national level for an average ration that represents the total feed input of a livestock class, this is generally not true at the state level. Results from various feeding trails are available, but are inadequate for accurate measurement of the total intake of all types of feed by all associated animals to produce a unit of livestock or livestock product. Average feed requirements in terms of pounds of feed units per 100 pounds of product for 1959—1961 at the national level, served as the base level for the study (Table 10). These data are derived by allocating annual feed disappearance to the various types of livestock production. In this way, the maintenance of breeding animals and young stock and the feed consumed by those animals which die during the year are accounted for. The figures are not intended as a guide to the quantity of feed needed to increase the weight of a particular unit of livestock by 100 pounds. Their purpose is as a planning tool for estimating the total amount of feed needed to meet the requirements of projected quantities of livestock and livestock products. For the purposes of this study, average feed re- quirements were converted to feeding efficiencies at the national level and adjusted to approximate the livestock 51 .msHm> mCHpoom CH CHOU mo UCDOQ mCo on quHm>Hsvm mH HHCC comm d .muHCs boom CH Ummmmumxmm .uCoswmmnsm pCm mmmH HmnEm>oz .emm .oz CHuoHHsm HmOHpmHumum 4am: .mmmHImomH meCmCOHumHmm poomlxooumo>mq pCm NmmmH .mHsb pmmH>om .mmm .oz CmumHHsm HMUHumHumum mama .mmmH unomom MHmEECm C "moCmHOHmmm ch CoHuosconm Enmm CH momCmCO How mHMHHoumE mCHxHoz Eonm pounced "mousom Hem Hom mm mmm mmvH emOH meHH vmm eOH HomH mmm mmm mm «em mmvH mmoH HNHH mme eOH ommH mHm oom mm mmm momH mmOH HVHH Hve mOH mmmH AmHmmn quHmB m>HHV uosuonm mo mpCCom OOH Hmm w w .1 iv 3. av 00 as w e e O u_L o I e.+ 2.1 I e e O 6.L m «OT. JHH H+e I 4 3 o. e Axe .+t. X 3 A.a I. 7.3 TL: enu w ww w 2.. a w s 1 P s.+ P H Honouoo m m. mCHCCHmom a Hmmw mwmxnsa mHoHHonm muoHHCm mmom mnEmH oHuumu moom meHmo muHma a mCmm a mmoCm MHmmHImmmH .moumpm pmuHCD .xooumm>HH mo mmmHo Comm an .CoHuosp Ioum mo HHCC Mom meCmCoo .mnsummm mCHusHoCH .mquEoHHsva comm ommuo>¢II.0H MHmCH 52 mix and feeding relationships of the Lake States (Table 11).16 The 1980 projected feeding efficiencies reflect expected advances in nutrition, breeding, and livestock management that continue the long-term trend.17 Feeding efficiencies for most classes of livestock in Michigan differ from the national average. Beef and veal feeding levels reflect a higher proportion of fattened dairy cattle and dairy calves than the national level. The proportion of livestock on grain fattening rations is also higher in Michigan than the national average. Milk production is a little more efficient in the State due to a higher average production level per cow which lowers the maintenance requirements per unit of production. Estimated rations, which are consistent with livestock production and feed disappearance at the national level, were used to determine feed consumption by various 16These adjustments to reflect local conditions were made in Washington by FPED, ERS, USDA production specialists based on their knowledge of regional feeding relationships. 17See Appendix O--Economic Base Study—Part IV, Comprehensive Water ResourCes Study, Grand River Basin, Michigan, January, 1966, for a detailed discussion of the assumed advances in technology and management practices used in this study. They are similar to those discussed in Project '80: Rural Michigan Now and in 1980, Highlights and Summary, Michigan Agricultural Experiment Station Re- search Report, February, 1966, and in earlier Phase I individual livestock reports. 53 .wmmH .muesCeb .moma .mmm .COHmH>HQ moHEOCoom meoHsOmem Hehsuez .wpsuw e>Huoefl0HM d .CHmem He>Hm pCmnw ecu CH MuH>Hpom HMHDHHCoHumC uuomen moCemeneuCH ecu How euep mCHMHo3 pCe .QOD .mmm .Qmam .CUCeHm pesmueuez pCe CHmem ue>Hm .COHuoem CoHuemHume>CH HHOBeEeHm OHEocoom ecu Comm weep peCmHHnsmCD "eonsom m.m m.m H.m o.v o.mH m.0H mm. .COHZ ommH e.m o.m m.m m.v o.mH m.HH oo.H .Con HmImmmH m.m o.m H.v m.m m.vH m.0H OH.H .m.D HmImmmH AucmHe3 e>HHV posponm mo quom Hem muHCC peem mmexuse mHeHHOHm mmmm xnom Coven: Hee> xHHE nee» cCe nEeH UCe meem owwH 0» umuumnoue one kuwwwH .ammHeon mo ouabw use wmumuw peuHCD .CoHuosconm xooume>HH pCe xooume>HH Mom meHOCeHOHmme mCHpeemII.HH mHmHB 54 classes of livestock and feed components (Table 12.)18 These rations are highly aggregated; the components are in terms of feed units as a percentage of the total ration by livestock class. For this study, national relationships were adjusted for use in Southern Michigan, with the same consideration being given as with feeding efficiencies, and were applied to 1980 Benchmark projections without further adjustment. Pasture requirements were divided between cropland pasture and permanent pasture. Initially all available acreage of permanent pasture was assumed to be used in partially meeting the total pasture requirement. The unsatisfied portion then became a demand for cropland pasture in the Benchmark Model. High protein feed needs were assumed to be met by shipment into the study area and, therefore, did not enter the Model. Hay and related roughages were divided between alfalfa mixtures and clover mixtures at the rate of 82.4 percent for alfalfa and 17.6 percent for clover mixtures. This roughage component contains such items as all hays and haylage. Other forage consists of corn silage, stover, and crops which are temporarily pastured. Green chop and grass silage are included in the pasture category. Feed grains in the ration are distributed among corn, oats, and barley at 18Adapted from, Livestock—Feed Relationships 1909— 1963, USDA Statistical Bulletin No. 337, November, 1963, Table 28, and annual supplements thereto. 55 .oueHeCH muCeEeHmmCm HeoCCe ucm mm eHQeB .mmmH HeQEe>oz .WMm .oz CHpeHHCm HmoHumHuepm .Como .mmmHImomH mmHCmCoHpeHem oeemlxooume>HH .Eoum oeummpm "eonsom o.ooH m.H . . . . m.H m.vm o.vm m.mm mmmm o.OOH o.m . . . . o.m H.em m.em o.mm mmexusa o.OOH . . . . . . . . H.me m.vm o.o0H mHeHHoum o.OOH o.e . . . . o.v e.om m.mm 0.0m mCeonCU 0.00H o.e . . . . o.e v.mH m.om o.mm xuom o.OOH o.Hm m.m e.m 0.0m m.v m.m o.oH Coupe: pCe nEeH o.o0H m.mm m.m m.mH m.me m.m m.mH H.H~ Hee> pCe meem c.00H m.mm m.mH 0.0m o.mm o.m o.mm o.~m xHHz uCeoHem Heuoa enzymes emeuom peumHem memesmsom CHeuoum mCHeHO meuenu mmMHo Hecuo w mew cmHm ueem ICeOCoo xooume>HH mmmHIommH meemum oeuHCD .xooume>HH mo mmMHo an .muHCo peem mo mane» CH memenmsou pCe meueHuCeoCoo mCOEe muCeComEOo COHueH emene>e mo CoHuCnHHumHQII.NH mHmda 56 82.3 percent, 16.1 percent and 1.6 percent respectively. Michigan has been a surplus producer and net exporter of feed grains and hay for some time.19 Total demands for feed grains and hay were, therefore, increased to reflect and maintain this relationship in the model.20 Several important factors must be evaluated in estimating what levels feeding efficiencies will likely attain at any point in the future. There are two major opposing forces that are always prevalent and the resulting feeding efficiency level is a reflection of the relative strengths of these forces. The first of these forces is toward less efficient production in the short-run. It reflects major production expansion efforts, requiring proportionately more breeding animals, or changes in consumer preferences toward higher quality. This force implies shifts to confinement feeding, shifts to higher levels of finish, and so on; and is encouraged by lower feed grain and concentrate prices and/or 19See Supplement for 1965 to Livestock-Feed Re- lationships 1909-1964, Statistical Bulletin No. 337, ERS, USDA, September, 1965; and Hay in the United States, ngntities Grown in a Normal YearL Surplus and Deficit Areas, Statistical Bulletin No. 349, ERS, USDA. 20It is recognized that this relationship may change over time due to expanding relative population, foreign exports, comparative advantage, etc. However, in view of the surplus magnitudes which have been as large as 45 per- cent in excess of feed requirements (1964-65), a modest 20 percent excess in feed grains and 10 percent in roughages are maintained. 57 higher livestock product prices. This force can be ex— pected to continue at least in the short-run until adjustments can be made in breeding herds, management techniques, and feeding practices. In contrast to the first, the second force is longer run in nature and is toward greater efficiency in feeding. It includes improved technical abilities for converting feed into livestock products, genetic im- provements in livestock, potential shifts in demand for different qualities of livestock products, and substitution of low cost roughages in some livestock rations. While aggregate statistics are adequate in re- flecting overall major changes, they do not measure relative strengths of these two forces. There may be considerable adjustment taking place that is masked by the aggregate data, and such adjustments would be of major concern to planners if they were aware of them. Currently, projections are based on arbitrary estimates of likely adjustments between the relative strengths of these two forces. Because these projections may also serve as the basis for public resource development decisions, their sensitivity to alternative forms of the livestock feeding relationship assumptions is important. Question: What effect would a small change in the nature of assumptions concerning relative feeding efficiencies and livestock rations used in river 58 basin linear programming studies, have on the model projections? Alternative specifications of the basin model needed to answer this question take the form of two additional levels of feeding efficiency and two variations in the composition of the livestock ration. It is believed that the projected feeding ef- ficiencies for 1980 in the Benchmark Model (Table 11) are the best estimates on the basis of current knowledge. Two alternative levels of feeding efficiency, that represent a 10 percent increase (High Efficiency) and a like decrease (Low Efficiency) from the Benchmark level are specified to represent likely deviations from this level (Table 13). Two variations were also specified in the basic ration for each class of livestock. The high concentrate ration reflects higher levels of concentrate feeding for high production, rapid gain, proportionately more animals with a high degree of finish and greater concentration of lambs and steers than the level assumed by the Benchmark Model. The low concentrate ration reflects more extended feeding, feeding to a lower degree of finish, proportionately more breeding animals and a greater use of low cost roughages at lower levels of production. It represents a deviation toward a ration with a lower proportion of concentrates than the Benchmark Model ration (Table 14). 59 .mmmH .muesCmn team: .mmm .COHmH>HD mOHEOCoom eoHCOmem Hmusumz =.mpsum e>Huoenoum m ”CHmmm He>Hm UCmuo ecu CH muH>Huoc HeHCuHsoHumct .uuomeu ecu How pemoHe>eu HeHueumE mCHxHOB pecmHHcomCD ”eousom mm.m mn.m Hv.m ov.v om.MH mm.HH «m. uCeEeHHDUem eHOZ uCeouem OH II>OCeH0Hmwm 30H ww.w ww.w we.w ow.w ow.oH we.w we. bamsmuHoemm uweH uCeOHem 0H --euamHuHeem aon ow.w ow.w oH.w oo.e oo.wH ow.oH ww. Hm>mH Hausauamm . IuwuemHuHeem soHumz HucmHeB e>HHV uospoum mo UCCom Hem muHC: ceem mwexusa mueHHoum mvmm xnom couusz Hee> xHHz moCeHOHmmm pCe cEeH pCe meem mCHceem mo He>eH ommH .me>HueCHeuHe pCe xumEcocem .CoHuooooum cooume>HH pCe xooume>HH MOM meHoCeHOHmme mCHpeemII.mH mqmca 60 Hmuoumz =.eooum m>HuumHoum a .mmmH .humsCMh .mamb .mmm .ConH>HQ moHEocoom eOHCOmem ”CHmmm He>Hm pceuw ecu CH muH>Huo¢ HmusuHso IHum<= .uuomeu ecu Mom UeQOHe>ep HeHueueE mCquoz UecmHHchCC Eoum peummcd "eoudom o.OOH o.Hw o.m o.w o.om o.v 0.0 o.OH CouuoE cce cfimq o.OOH o.me o.mH o.om o.om o.m o.mH o.om Hme> UCe meem o.OOH o.mm o.OH o.om o.me o.m o.eH o.mm xHHz eueuuCeOCou 30H o.OOH o.oe o.m o.mH o.om o.mH o.mm o.ov couusE pCe cEeH o.OOH o.om o.om o.OH o.om o.0H o.ov o.om Hme> oCm meem c.00H o.m o.om o.om o.mv o.mm o.mm o.mm xHHz eueuuceoCou cmHm o.o0H m.H . . . . m.H m.vm o.ow m.mm mmmm o.ooH o.w . . . . o.w o.ew o.ww o.ww uwmxuse o.o0H. . . . . . . . . o.me o.mm o.OOH mueHHoum o.OOH o.m . . . . o.m o.om o.mo o.mm mCeoncU c.00H o.v . . . . o.v o.wH o.om o.om xuom o.OOH o.om o.e o.HH o.me c.0H o.mH o.mm couusE pCe cEeH o.OOH o.mm o.OH o.om o.mm o.e o.mm o.mm Hee> pce meem c.00H H.Hm o.HH o.mm o.om o.mH o.mm o.ov xHHz He>eH xumEcocem eueuuceoCoo ECHuez uCeouem Hmuoe ensummm emmuom ueumHem memmcmoom CHeuoum mCHeHU meueuu mmeHo cooume>HH Hecuo ccm hem cmHm peem ICeOCoo .uCe CoHuem ommH .muHCs peem CH .xooume>HH mo mmeHo ac .me>HueCueuHe WCe cueficoCe memmcmsou pCe meueuuCeOCoo Coee muCeCo Sou COHueH emeue>e mo CoHuCcHHumHQII.vH mHmfia 61 Poultry and hog rations are already heavily weighted toward concentrate feeding and likely future adjustments would be toward more concentrates. Considerable variation may occur in the rations of roughage consuming animals within a fairly wide range. Therefore, the alternative rations under consideration affect only feed requirements for milk, beef and veal, and lamb and mutton. The basic ration assumed in the Benchmark Model was increased by 15 percent in concentrates to represent the "High Concen- trate" ration and increased by 15 percent in roughages to represent the "Low Concentrate" ration. . Class 2--Assumptions Relating to Projected Demands In the Benchmark Model projected demands for food and fiber are extrapolations of past trends in crop and livestock production. Adjustments were made to reflect the thinking of commodity specialists as to the probable shifts by 1980 in production among regions. The shares of United States production requirements coming from the Southern Michigan Subregion generally declined for all livestock and livestock product items between 1959-61 and 1980. The only commodities showing slightly increased shares were soybeans, drybeans, potatoes and non-citrus fruit. Projections were not made for feed grains and roughages Specifically since the conversion of livestock products into feed requirements, plus an allowance for export, provide these data. 62 It was, therefore, assumed that past production trends were good indicators of the location of future production; and that the only cause for deviation through 1980 from this pattern of production would be known changes taking place among regions. There are very real problems with this procedure of projecting regional requirements. One of the objectives of river basin surveys is to evaluate the capability of a region to meet projected requirements with and without the further development of the region's water resources. Since the extrapolation of production trends assumes that the factors affecting production in the past will also be acting in the future, certain biases are inherent in this process. Historically these biases have led to an understatement of requirements produced by the Great Lake States. NRED is currently working to evaluate the potential for further water resource development, but the possible biases in estimating regional demands may invalidate these efforts. In the absence of a national model that would allocate the total demand regionally, those areas that have experienced considerable water resource development in the recent past might be projected to receive a disproportionate share of the national demand. This situation could force the impression that further development in such a region would be required when production requirements might be met more efficiently in other regions. 63 Question: What effect will varying an area's projected share of United States requirements have on the projected water resource development potential for that area? To answer this question, results from the Benchmark Model were compared with two alternative models that re— flect increases of 50 percent ("Medium" demand level) and 100 percent ("High" demand level) in the Benchmark ("Low" demand level) 1980 requirements (Table 15.)21 These two alternatives to the Benchmark level may also be viewed as providing some insights into the problems that might arise from expanded exports or programs of food aid. In only one instance does a doubling of the 1980 projected requirements create an unrealistic situation, that of nearly 70 percent of the expected national requirements of dry beans. However, the export levels are not large for this com- modity, and any sizeable increases could conceivably have such an effect on the Subregion. Class 3--Assumptions Relating to Soil Management Practices In the Benchmark Model certain constraints were imposed on the resource base to account for crop rotations and improved management practices encouraged through 21The alternatives are both increases since the regional share of national requirements have recently been adjusted upward and the Benchmark Model represents a known understatement in view of current shares. .wmmH .xuesceh .como .mmm .ConH>HQ mOHEocoom eousomem Hmusuez =.>psum e>Huoeh Ioum 4 uCHmem ue>Hm uceuo ecu CH qu>Huo< HmusuHsoHum<= .uuomeu ecu How uemoHe>eu HeHHeueE uecmHHcsmCD "eouoom 64 wwe.mw eew.ww wwe.m www.eH www.w www.HH .u30 weHnuueme> wow.em wa.o~ wow.m eee.wH vww.w wHw.e .u30 uHoum wouuH0ucoz meHceueme> pCe muHsum wwe.ow www.wH wwH.w www.oH wwH.w wa.w .uzu wuouauow «ow.oH wow.~H mew.ew wow.w mew.ew wwm.w .830 women who oww.~w wwe.wH eww. wwH.HH woe. wwH.v wHeeusn memeneom www.wm wow.He «oo.H www.e~ wow.~ ww~.e~ wHoewon been: mmOHU vaOnm oww.wHe.w owe.Hoo.e ee~.w oew.eoe.e www.w oHe.www.w mucood xHHz oww.eww oww.mHe woo.H oo~.eee eww.H owH.~ew wocood Hm0> w Home ovw.~wm mow.wa wow. oe~.Hw~ ewo.H owe.wH~ wocood xuoa oow.Hw www.mm owe. owe.wH ewo.H oe~.eH weaned coups: w nauH on.ww wow.em oeH. wow.wH see. owe.ww wocooa mueHHoum ooo.ww ooo.we wwe. ooo.w~ ewH.H oeH.wH mucoom asexuoe oww.owe.w oww.eww.H wew.H oww.we~.H wwo.w oww.ww~.H unease: womm oww.oH «we.e wmw. wwH.w Hew. oov.w wocood weequco sumo vaHHUOHm xooum0>wfl oooH oooH uceouea oooH unmouma oooH Axuaecucem Axuaecucem Hauoe .m.o eo mzw Huuoe HwnwwwH uuHco oeuHovem 0>ob¢ o3on< momuemuumw .w.o we use meuHuoesoo woOHv womv e we mZm emeuCeouem UCMEQD flgfiwa 6 mm mZm mo He>eH mo He>eH He>eH uCeEeo =SOH= .cOHmz gesHuez: Hepoz xHeEcocem owwH aH beeswo euuueHouw nausea Huouoa ommH How mCoHueonHoemm 0>HuaeueuHa nuH3 Hmzwv eonmunom cmebon :ueausow 0:» some :oHuuououd Hoe mucuseu touumHoum 0cm uceuusoun.wH mamas 65 research and extension efforts. Not all of the available cropland is suited to continuous growing of certain crops. Cultivation of row crops over the growing season has a tendency to destroy soil structure and encourage soil loss on certain soils through both wind and water erosion. Consequently, restrictions were placed on the full use of these soils by certain Crops in the Benchmark Model. In general, these restrictions were based upon standard recommendations of the Soil Conservation Service to keep erosion losses within three tons per acre. This restriction implies that the percentage of soils that may be con— tinuously row—crOpped ranges from 32 to 90 percent among the different soil management groupings.22 These restrictions on soil resources were imposed as a means of creating a more realistic pattern of crop production in the program output. While the restrictions quite accurately represent how farm operators manage their soils, the benefits that may be derived by building these provisions into models may not be worth the expense neces— sary to develop them. Question: How are the projections of resource use and development potential affected by restrictions 22No re-cropping restrictions are recommended for organic soils. See "Instructions for Determining Cropping Systems for Sloping Land," Technical Guide, Sec. III—B, March 6, 1964, Soil Conservation Service, Michigan. R. H. Drullinger of SCS provided assistance in the interpretation of the guide and its application to Subregion soils. 66 placed on the full use of soil resources for the production of row crops? To answer this question, 1980 Benchmark Model results were compared with the results of two alternative levels of soil management practices. The Benchmark level designated as "Medium," reflects improved soil management practices that the average farm operator is expected to employ in 1980 to retard soil loss under more intensive cropping practices (Table 16). The alternative designated as "Low" represents how farm Operators currently are using their soil resources in the production of row crops. The other, designated as "High," represents the other extreme; no restriction to the full use of all soil resources for the production of row crops. While this second alternative represents a very unrealistic assumption, it is important to test its effect upon the models. Class 4--Assumptions Relating to Minimum Acreage Constraints During the early stages of this study, a test was made of the Benchmark Model's predictive power with respect to crop acreage. An attempt was made to reproduce the 1959 Census of Agriculture crop acreage and production data within the five subareas. The total 1959 production of each major crop grown in the 42-county area served as demand requirements for these crops. Not only did the model fail to recognize significant production patterns, 67 .vme .w cones .mIHHH mCHmmouU mCHCHEueueQ How mCOHuOSHumCHt cechOHz .eoH>Hem COHue>uemCou HHOm .mHHom Coneucsm ou CoHueoHHmmm muH pCm euHom ecu mo COHumueumueuCH ecu CH eoCeumHmme cepH>oum mum mo HemCHHHsuo .m .m .oem .euHCw HmoHCcoeB =.©CmH mCHmon How maeummm "eoudom oo.OOH oo.00H oo.OOH oo.OOH oo.OOH oo.OOH oo.oOH m oo.OOH oo.o0H oo.00H oo.ooH oo.OOH oo.OOH oo.OOH e commH .He>eH oo.OOH oo.OOH oo.o0H oo.OOH oo.OOH oo.OOH oo.QOH m ueuoHuumeHCDv oo.OOH oo.o0H oo.OOH oo.00H oo.00H oo.o0H oo.QOH m =cmHm= oo.OOH oo.OOH oo.OOH oo.oOH oo.o0H oo.o0H oo.OOH H oo.ooH mm.mm mv.mm mm.me em.mm me.mm ee.mo m oo.OOH em.me om.me we.mm oo.OOH Hm.Hm me.vm v commH .He>eH oo.OOH mm.mm mm.Hm mm.qe NH.em ow.oe om.mm m cueEcoCemv oo.o0H mm.mm me.mm om.mm oo.OOH mH.mm mm.me m essHueze oo.OOH oo.om me.vm mm.om oo.OOH mm.me oo.me H oo.OOH mm.ve mH.me ev.mv vv.em me.mv mv.em m oo.o0H mm.mm mo.mv mm.ov oo.om mm.mm em.me v cemmH .He>eH oo.OOH mm.Hm eH.mv ev.om mH.mm mm.me mm.me m uCeuusOV oo.o0H oe.vv NH.mv Hm.em oo.om vo.mm mm.mm m esoqe oo.o0H oo.mv mm.mv mm.Hm oo.om mm.Hm oo.om H uCeouem oz ocMm oc8e ocem om cem oceH meoHuoeHm eeu< uCeEemeCez mmCHmoouo uCeEemesz HHom HHom ome .COHmeuch CBchon Cuecusom .meoHuomum uCeEemMCeE HHOm mCHmue> HepCC mmouo 30H mo CoHuoscoum ecu now eHceHHe>e uCeHmouo Ho emeuCeouemII.mH MHmma 68 like the concentration of dry bean production that had developed over time, but it was extremely inaccurate in reflecting the relative distribution of output among sub- areas. Recognizing that the model was inadequate in its original form, certain adjustements were made and the model was re-tested. Tree and bush fruits, that had become concentrated in Subarea 5 because of particularly favorable climate were removed from the model along with sugar beets, which were highly oriented to the location of processing facilities in Subarea 2. Other crops were added to this list either because of small acreage or special character— istics which precluded wide distribution. It was also recognized that the influence of government programs, especially with respect to wheat, would not necessarily be identified by a model designed to minimize production costs over the 42-county area. With these considerations in mind, a 50 percent constraint on production in each subarea was chosen. This meant that a minimum of one-half of the 1959 acreage of each crop in the model was required to be produced in the same subarea. Thus, habit patterns and other non-market influences were given substantial weight in determining the location of production within the Subregion. When the 1959 Census model was tested with this minimum constraint, the results were sufficiently satisfactory that the same procedure was used in the 1980 Benchmark Model projections. 69 To implement the procedure, the relative distribution of crop acreage among the five subareas was used to distribute one—half of the 1980 Benchmark projected demand by crop to each of the subareas as minimums required in the solution. This production was converted to acreage through the use of average yields. While this procedure was logical, straight-forward, and easily understood, it is recognized that it had little scientific or statistical basis. It had produced "reason- able" results when tested against one point in time but how representative was that one point? Question: Will changes in assumptions that repre— sent minimum acreage constraints have a major or minor effect upon projected resource use and development potential? Two alternatives to the Benchmark 50 percent ("Medium") constraint were utilized in answering this question. The first alternative designated "Low," was less restrictive requiring only approximately 25 percent of the total acreage of each crop to be distributed among the subareas. The second alternative designated "High," was much more restrictive than the Benchmark level. It re— quired a distribution among subareas of 75 percent of all production before efficiency was allowed to allocate the remainder. 70 Class 5--Assumptions Relating to Adopted Level of Crop Producing Technology To develop the agricultural production potential for the Subregion in 1980, crop and pasture yields were projected on the basis of past trends and implications of current research work. Soils and crops specialists at the Michigan Agricultural Experiment Station were given a point of departure for yield projections based on ERS analysis of Statistical Reporting Service time series data. The projected yields represent the specialists' evaluation of how rapidly new varieties will be made available to farmers and a judgment of the rate of new practice adoption by average farmers.23 Average farm management capabilities and average weather conditions, assumed for the Benchmark Model, resulted in projected crop yield levels for 1980 approxi— mately 50 percent above the 1959-61 average levels. The 1980 yield estimates represent increased levels of all management inputs such as improved seed, use of insecti— cides, timeliness of operations, and approximately a 30 per— cent increase in per acre use of fertilizer nutrients. The costs associated with these additional inputs and added harvesting charges have also been incorporated into the Model. 23See "Agricultural Activity in the Grand River Basin: A Projective Study," Natural Resources Economics Division, ERS, USDA, January, 1966, for a detailed dis— cussion of this procedure. 71 Previous attempts at projecting the productive potential of a region's resources have often underestimated the rate at which new practices were developed and adopted by farm operators. The rapid increase in use of fertilizer in recent years is a case in point. Since yields on ex- perimental plots and some farms are currently far in excess of the average levels projected for 1980, it is conceivable that the average production levels assumed may also be seriously underestimated. Question: What effect will the underestimation of an area's production potential have on projected resource requirements or projected potential for resource development? There is a companion assumption implicit in this question--that additional research and extension efforts are not perfectly substitutable for land resources or land— increasing technology (i.e., agricultural irrigation). To answer this question, the technology level designated as "Low," which was assumed for the Benchmark Model was com— pared with two alternatives. These alternatives reflect technology increases of approximately 20 percent desig- nated "Medium," and 40 percent designated "High," respectively over the Benchmark basic level.24 24For a detailed presentation of the comparable yields by soil management grouping for these various levels of technology see Melvin L. Cotner, "The Potential Role of Agricultural Land Drainage in Economic Growth“ (unpublished Ph.D. thesis, Michigan State University, 1967). 72 All crops have not shared equally in the response to technology in the past and are not expected to in the foreseeable future. The 1980 projected yield index for all crops is 148, with the greatest increases in yields of wheat and dry beans and the smallest gains in alfalfa and soybeans (Table 17). The two technology alternatives are based primarily upon assumptions of equal increments of research and extension toward improving management and encouraging more wide-spread application of improved strains and varieties and near optimum use of fertilizers. The assumptions of technology adoption at the "High" level reflect yield and fertilizer use levels consistent with those obtained currently by top farm managers and from experimental plots. 73 TABLE l7.--Projected index of selected crop yields under 1980 Benchmark level ("Low") of adopted crop producing technology, Southern Michigan Subregion Indexes Crop 1959-61 Yield Levels = 100 Wheat 165 Dry Beans 163 Potatoes 156 Corn for Silage 153 Corn for Grain 152 Barley 152 Soybeans 130 Oats l4l Alfalfa 137 Other Hay 144 Cropland Pasture 138 Permanent Pasture 140 Source: Unpublished material developed for the report entitled, "Agricultural Activity in the Grand River Basin: A Projective Study," Natural Resource Economics Division, ERS, USDA, January, 1966. CHAPTER V SENSITIVITY OF THE BENCHMARK MODEL TO CHANGES IN ASSUMPTIONS Procedures The objective function of an optimal solution to a cost-minimizing linear programming problem reflects the least costly method of attaining production objectives. Its relative size under alternative model formulations can serve as a criterion of analysis. Comparison of the change in objective function provides a basis for evaluating the sensitivity of production costs to changes in model assumptions. Relative differences in the empirical results under alternative sets of assumptions serve to determine whether a particular alternative model formulation is measurably different from the specification of the Bench- mark projection model. In testing for sensitivity, the relationship of change in the objective function to change in model assumptions constitutes a relevant measure. Put differently, the method is one of assessing the relative change in output to known changes in input. To provide the basis from which to test sensitivity, thirty-one different models at three levels of technology 74 75 adoption were evaluated. The structure of all ninety- three models and their resulting objective functions represent the full range of analysis undertaken by this study (Table 18). No attempt is made to go into depth on each model variation. The results are presented in this form for those who may wish to explore particular vari— ations. A similar set of comparisons which include agricultural irrigation are presented and analyzed in the latter part of this Chapter. Within the body of Table 18 the five classes of assumptions are identified by the letters L, M, and H. These letters stand for the three levels, low, medium, and high which each class of assumption is allowed to take. They are presented in this way to facilitate understanding of the comparisons made in the table. Detailed discussion of the magnitudes represented by the three levels was provided in Chapter IV and is briefly summarized in the discussions that follow. Part I--Sensitivity Analysis Without Irrigation Because of the complexity associated with an evaluation of all ninety-three models, both in presentation and understanding, fifteen models have been selected for sensitivity analysis (Table 19). These models incorporate changes in the five classes of assumptions discussed in Chapter IV. In the sensitivity tests that follow, the 76 TABLE 18.-—Structure of alternative model formulations with respect to as- sumptions, and projected total costs of subregion production, Southern Michigan Subregion, 1980a Assumptions of the Models Projectedb Total cost of pro- Class - l Livestock Class Class Class ducion given Feeding 2 3 4 assumptions 1—4, and under the following Proportion 8011 Minimum technology assumption Feeding of Concen. Demand Management Acreage (Class-5): Efficiency in ration Level Practices Constraints Low Med. High Mil S M11 5 M11 5 M M L M M I867 178.6 171.2 H M L M M 174.6 167.5 160.5 H H L M M 175.0 167.2 160.2 H L L M M 175.9 168.8 161.6 L M L M M 198.1 189.8 182.0 L H L M M 198.1 189.5 181.6 L L L M M 200.0 191.4 183.4 M M M M M 282.6 266.7 255.0 H M M M M 262.6 249.3 238.4 H H M M M 262.0 248.6 237.6 H L M M M 266.3 251.6 240.5 L M M M M 304.3 284.2 271.8 L H M M M 298.7 282.7 270.3 L L M M M * 287.7 275.0 M M H M M * * 343.2 H M H M M * 337.2 319.6 H H H M M * 332.1 317.3 H L H M M * 344.2 323.3 L M H M M * * 369.9 L H H M M * 384.5 363.0 L L H M M * * * M M L L M 186.5 178.9 171.3 M M L H M 186.2 178.4 171.2 M M M L M 284.0 267.0 255.2 M M M H M 282.4 266.5 255.0 M M H L M * * 344.2 M M H H M * * 343.0 M M L M L 185.2 178.1 170.3 M M M M L 281.1 265.6 253.9 M M M M H 284.4 268.2 258.3 M M H M H * * 346.0 *Linear programming solution not feasible under the assumptions given. given. aThe designation L, M, and H mean respectively Low, Medium, and High. The precise meaning differs among the five classes of assumptions. definitions are given in the narrative discussions of each class of assumptions. b 1964 constant dollars. Detailed '77 xmoHoccoeu mo He>eH :cmng ecu mmeHCC COHudEsmmm Mch Mecca eHcheew uOC CoHusHOM OCHEEeHmouQ HeeCHH .mueHHou uCeumcoo vomHo .pems MH CoHudE:mme c .mcoHudEdmme mo mmeHo come Ho MCOHMMSUMHU e>HueuueC ecu CH ce>Hm eue mcoHuHCHweu peHHmueo .mcoHudEdmme mo memmeHo e>Hw ecu mCoee mueHMHu wCHCCeE emHoeum ece .cmHm uce .EsHpez .30H >He>Huoemmeu CeeE : use .2 .H COHuecmHmeu ecu.e ~.HeH : hmoHoccoeB .mH o.meH z amoHoccoeB .VH o.ovm : cm x muCHmuumCou emeeuoc .mH «.mmH H muCHeuumcou emeeuoc .NH w.wwH m newswoacuz HHom .HH w.wwH H useaemmcuz HHom .oH «.mvm : cm uceEeo .m w.~m~ : UCeEeo .m o.oom H H COHuem .h H.mmH m H COHuem .o m.meH H m CoHuem .m o.meH m m coHuem .v H.wwH H wuemHoHewm maHuumw .w w.eeH w euemuuuwwm oauomee .w mCOHuQEdmm< Hepoz xueEcocem Eouw memCeco «.mmH H z z A z z xumficosem .H HHmmquHm 0Ce>Ho hvoHoccoeB nuCHeHumcou meoHuoeum He>eH COHuem CH moceHonmm me mcoHudEsm mo emeeuo< uCeEemmcez uceseo eueuuceocoo wo oCHueem Inc ueuco coHu He>eH ECEHCHZ HHom - Comuu0doum . coHuecmHneo I09u0um mo umou m lllfllLl m m mCHueem UCe Hecssz Heuoz Heuoa ueuoenoum mmeHO mmeHo mmeHu mmeHu xooumeeHH I H nmeHO emcoHumECee< .ommH .Coneucsm Cechon Checuoom .CoHuospoua COHoeucdm uo mumoo Heuou ueuoehoum uCe .Hepoz xueecocem ecu souu mCOHudECmme CH mCoHueHue> ou uoemmeu cuH3 MHeuOE e>HueCHeuHe mo mCOHuHCHmeaII.mH wands 78 Benchmark Model is compared against alternative models under each class of assumption. Differences from the Benchmark solution, arising from alternative assumptions, are described and their implications discussed. Class l-—Assumptions Relating to Livestock Feeding Relationships The assumptions centering on livestock and livestock products can be separated into two categories: those affecting the average efficiency of feed conversion and those relating to the composition of the average feed ration. Both components vary by class of livestock and undoubtedly among subareas of a particular river basin not to mention regions of the nation. Ration composition also affects the feed conversion efficiency but it was felt that this problem would average out across the subregion. Feeding Efficiency Two alternative levels of average feeding ef— ficiency were examined. The "High" level was 10 percent more efficient than the Benchmark level ("Medium") and the "Low" level 10 percent less efficient. Evaluation of past trends suggests that errors in excess of 10 percent in projecting to 1980 would be unlikely barring unforeseen circumstances. 79 Deviations from Benchmark Preject1ons In testing the sensitivity of variations in the feeding efficiency assumption, deviations from the Bench— mark total production costs were nearly identical in both directions (Table 20). An increase of 10 percent in feeding efficiency to the "High" level resulted in a saving of $11.6 million in production costs or 6.2 per- cent below the Benchmark level. Total costs increased by nearly $12.0 million when the "Low" level of feeding efficiency was assumed. TABLE 20.-—Projected 1980 total cost of production for models testing the sensitivity of the feeding efficiengy assumptions, Southern Michigan Sfibregiona Total Cost of Differences in Level of production total cost of Model Feeding (Objective production from Number Efficiency Function) Benchmark level Mil. Dol. Mil. Dol. Percentage l (Benchmark) Medium 186.2 2 High 174.6 —ll.6 -6.2 3 Low 198.1 11.9 6.4 a1964 constant dollars. Models that compare changes in the feeding ef- ficiency assumption at the Benchmark demand level ("Low") are presented in Table 20. When demands are raised the 80 effects of "High" and "Low" levels of feeding efficiency are of greater magnitude. For instance, at the "Medium" demand level (50 percent above Benchmark) the effect of "low" feeding efficiency is to raise the total cost of production above the Benchmark by more than 63 percent. High feeding efficiency, on the other hand, limits the increase to 41 percent. Implications Variations in the feeding efficiency assumption caused substantial changes in the Benchmark total cost of production. The model is sensitive to these changes, more so as the soil resource becomes a limiting factor. Why is this so? The assumptions about feeding efficiency affect the quantities of all feed components required to produce a given level of livestock and livestock products. As feeding efficiency rises less feed is required to meet production objectives and vice versa. At higher demand levels the effects are more pronounced, especially for the "Low" efficiency assumption. In this case, the production requirements are increased because of larger demands, and the addition of lowered efficiency of feeding only means that more feed is required. As would be expected, cost increases were larger as the production problem became more difficult to solve. Additional soil resources were required which forced the 81 model to select less efficient soils after the more efficient were fully utilized. For those involved in river basin planning or other agricultural projection work, care should be exercised in the establishment of feeding efficiency levels. More time is normally given to this task is warranted. Errors in the direction of overstating feeding efficiency are less critical than errors toward understatement. The Benchmark Model should be considered highly sensitive to variations in the feeding efficiency assumption. Livestock Rations Livestock producers are influenced in the type of feed they use in the ration by such factors as weather, prices, the kinds of roughage handling equipment they have and what becomes available. They are influenced by new technology, educational efforts, and fads. Consequently, the composition of livestock rations is generally con- sidered to be more variable than feeding efficiencies. Thus, a range of plus or minus 15 percent was selected as a reasonable range to represent possible errors in esti— mating livestock rations. The national data that reflect highly generalized livestock rations by class of livestock were adjusted to derive a best estimate of the types of rations currently in use in Southern Michigan. An estimate of the likely rations to be used and a mix of feeding conditions in the 82 future were also established with assistance from Michigan Agricultural Experiment Station personnel. Deviations from Benchmark Projections In evaluating the sensitivity of livestock ration assumptions, the effect of varying ration composition with high feeding efficiencies was analyzed and compared with low efficiencies. Also, effects of maintaining high concentrate levels when efficiency varied were compared with low concentrate levels and varied efficiency. These comparisons are somewhat more complicated than those for the feeding efficiency assumption alone. "High" feeding efficiency assumptions when coupled with rations both "High“ and "Low" in concentrates yield surprisingly similar results (Table 21). Deviations from the Benchmark ("Medium") are both negative and nearly the same magnitude. The "High" concentrate ration is only slightly more efficient. Holding feeding efficiency 10 per- cent below the Benchmark and allowing concentrates to vary by 15 percent around the original assumption raised the cost of production by $12 million or 6.4 percent for "High" concentrates and nearly $14 million or 7.4 percent for "Low" concentrates. These deviations imply sensi- tivities of the Benchmark which are no greater than those induced by variations in the feeding efficiency assumption alone. 83 .muwHHoe bemuwoou ewme e.e w.wH o.oow 30H 30H e e.w o.HH H.wwH bon 30H w w.w- w.oHI w.weH 30H eon w o.ou w.HHI o.oeH aon amum e N.mmH ESHUeE EsHpeE cxHeEcOCemv H bamuumo .Hoo .HHz .Hoo .HHz He>eH cueficoCem ACOHuoCsm COHuem CH mOCeHOmem HecEdz Heuoz Eoum COHuoCuoum e>Huoehcov eueHuCeOCoo mCHpeem mo umoo HeuOB COHuonoum m0 m0 He>eH CH meOCeueHMHo mo CoHuuomoum umoo Hmuoe eConeuch Cmchon Cuecusom .moCeHOHmme mCHpeem 30H pCe cch mecca MCOHAmEommm COHueH cooume>HH ecu mo muH>HuHmCem ecu mCHumeu MHeuoE How CoHuosuoum mo umoo Heuou ommH peuoenoumII.H~ mHmHB 84 The effects of changing both feeding assumptions at once was neutralized by comparisons where the only variation was that of concentrate level. In each case holding feeding efficiency constant and either raising or lowering concentrate levels caused nearly imperceptable changes in the objective functions. When the impact of ration composition is controlled at either "High" or "Low" concentrate levels and feeding efficiency is allowed to move from "Low" to "High," nearly the same reduction in production cost occurs. At "High" concentrate levels the cost saving from a 20 percent increase in feeding efficiency is $23 million. Similarly, at "Low" concentrate levels the reduction is $24 million-— slightly larger but still approximately a 12 percent change in objective function. Implications Once the effect of feeding efficiency is accounted for, variations in concentrate content of the assumed rations has little influence on the total costs of meeting production objectives. There appears to be no interaction between feeding efficiency and ration composition with the exception that combinations of "Low" feeding efficiency and "Low" concentrate ration assumptions yield slightly larger variations. This follows since "Low" concentrate assumptions imply high roughage requirements which are 85 less efficient in the use of soil resources than are the feed grains that make up concentrate rations.25 In this analysis errors of 15 percent in concen- trate levels caused variations of about 1 per cent or less in production costs. This suggests that river basin analysis should place more emphasis on establishing reliable coefficients to represent livestock feeding efficiencies than would be the case for ration composition. The livestock feed components of total demands in the model are so strongly influenced by the total feed needs es— tablished by feeding efficiency coefficients that even large variations in the source of nutrients (roughages or concentrates) has minimal influence on the total production cost. Class 2--Assumptions Relating to Projected Demand Projected regional or subregional demands for food, feed, and fiber are based upon allocations of national demand. As discussed in Chapter IV, estimated future demands at the national level represent a logical and 25In this regard, infeasible solutions were only encountered under the following conditions: (1) Low feeding efficiency, concentrate, technology and medium demand, (2) Technology medium, demand high, and (a) medium feeding efficiency and concentrate, (b) low feeding ef-~ ficiency and concentrate, and (c) low feeding efficiency but medium concentrate, and (3) Technology and demand high but feeding efficiency and concentrate low. 86 consistent determination. However, in the absence of a national model to assess relative productivities and comparative advantages, these demands are broken down into regional shares by USDA marketing specialists, and these serve as the basis for regional demands. At the regional level, these estimates are still consistent with the national demands, but as further disaggregation takes place, the possibility of errors increases. The forty-two county Southern Michigan Subregion represents slightly more than 22 percent of the Great Lakes Region production. Great Lakes regional demands served as the basis for the allocation to the Subregion. These allocations took into consideration a number of known and estimated factors that might influence the location of production.26 Since these factors are subject to substantial errors in estimation, assessment of the effects of under- stating Subregional shares of national requirements is important. Regional shares of national demands have been influenced most strongly by the effects of irrigation development in the west. Resulting allocation of 1980 26Research on these factors included discussions with Michigan Agricultural Experiment Station personnel and evaluations of the many Michigan State University "Project- 80" reports published during the period of this study. In review of those decisions there is no additional evidence yet to refute the original choices made. By the same token, the confidence in those same choices has increased. 87 demands to the Subregion are relatively less than was experienced in the 1959-1961 period (Table 15). Raising Subregion demands in this analysis by 50 percent (demand assumption "Medium") resulted in approximately the same relative level of production with respect to the nation as would have existed had the 1959-1961 level been maintained. There were some variations; production of milk and eggs increased slightly while output of other livestock and livestock products remained unchanged or were slightly lower. With the exception of dry beans, soybeans, and potatoes which registered gains, crop production generally was unchanged. Dry bean production was influenced by Michigan's dominant position in the national market while soybeans are projected to continue the strong upward trend in which the State has not shared. The national projections were made prior to the establishment of new potato processing facilities in Subarea 4 which have stimulated increased potato production. Demand assumption "High" (100 percent above Benchmark) is used in two ways in this analysis. First, it provides a contrasting level to "Low," assuming his— toric shares of production are maintained. It also assures that the least efficient soil resources will be forced into projected production. This latter property was introduced to test its influence on the behavior of the other assumptions. 88 Deviations from Benchmark Projections Comparisons between demand levels "Low" and "Medium" are possible for all three technology levels but only at the "High" level of assumed technology adoption is it possible to evaluate "High" demand (Table 22). The "High" demand level is unattainable at the two lower levels of technology. A 50 percent increase in demand ("Medium") from the Benchmark level ("Low") brings forth nearly a 52 percent increase over the Benchmark cost of production. At the "Medium" level of technology adoption, where there is less pressure on the resource base, "Medium" demand causes slightly more than a 43 percent increase in Bench- mark costs, a saving of 9 percent. But in terms of the "Medium" demand levels a shift from "Low" to "Medium" technology results in cost savings of not quite 6 percent. At the "High" level of assumed technology adoption, it is possible to compare all levels of demand. In the comparison with "Medium" and "High" demand the effect is to raise "Low" demand production costs by 49 percent and 100 percent respectively. Had it been possible to make the same comparisons on the "High" demand level throughout, the induced changes in production costs would undoubtedly have commenced above 100 percent and declined as pressure was removed from the resource base. This influence is observed in Table 22 where "High" demand and technology 89 TABLE 22.-~Projected 1980 total cost of production for models testing the sensitivity of demand level assumptions, Southern Michigan Subregiona Total Cost Level of Level of Production Difference in Total Model of Tech- (Objective Cost of Production Number Demand nology Function) from Benchmark Level Mil. Dol. Mil. Dol. Percent 1 Low Low 186.2 (Bench- mark) 8 Medium Low 282.6 96.4 8 51.8 9 High High 343.2 157.0 84.3 a1964 constant dollars. levels are responsible for only an 84 percent increase in production costs above the Benchmark level. Implications The implication of an error in the specification of demand level is that projected production costs will also be in error by approximately the same degree and in the same direction. This error in costs increases as the deviation from the Benchmark increases. It is possible that the small number of soil groups used in this model obscure some of the diseconomies associated with forcing less efficient soils into production at higher demand levels. In that respect a model containing a more compre- hensive classification of soil resources would be far more 90 sensitive to errors in demand specification. Decreasing the numbers of soils may be a means of correcting for such sensitivity; but that is an empirical question that must be tested. The conclusion to be drawn from this analysis is that the Benchmark Model is very sensitive to variations in the demand assumption. Class 3-—Assumptions Relating to Soil Management Practices The long standing problems of erosion and sedi— mentation have been the basis for extensive efforts on the part of Federal and state governments and educational institutions to solve these problems. The establishment of the Soil Conservation Service and much of its overall program is such a response. Land grant universities, much of the early extension effort, and vocational agriculture courses concentrated on the benefits to be derived from maintaining soil conserving crops on steeply sloping land. Sod crops were also encouraged in the rotation to cut down on soil loss. These problems were also recognized as critical in the projections work being done by NRED. After a lengthy process of evaluating the degree of slope, length of slope, soil texture, and erodibility factors of the soils making up the soil management groups, a weighting procedure was devised.27 This procedure was 27This process required considerable assistance from SCS soils men and Agronomists who helped interpret 91 applied to each of the soil resource groups by subarea. The end result was the table depicting restricted cropland availability for the production of row crops (Table 16) discussed in Chapter IV. Cropland was restricted to growing no more than a specified percentage of crops requiring cultivation which increase the susceptibility of the soil to erosion. This upper limit on row crop production for each soil in the Benchmark Model was consistent with expected soil management practices in 1980, and was desig— nated the "Medium" soil management assumption. Because of the substantial effort devoted to this aspect of the study, it was possible to test two alterna— tive scil management practice levels to determine how sensitive the model was to variations in this assumption. These alternatives were designated "Low" which implied no change in soil management practices from current levels and, "High," which placed no restriction on growing row crops. An assessment of the difference between these two alternatives and the Benchmark level presents difficulties. The constraints representing current practices ("Low") are more restrictive than those for the projected 1980 Bench- mark ("Medium") level. But the no-constraint ("High") level is closer to "Medium" than "Medium" is to the "Low" level. What is most important about this test is the their Technical Guides in light of estimates of what practices would be employed by average farmers in 1980. 92 determination of whether soil management assumptions have substantial impacts on the magnitudes of projections. Deviations from Benchmark Prgjections Comparison of the Benchmark level ("Medium") and the "Low" alternative indicate increased production costs of only $300,000, about 0.2 percent (Table 23). The "High" management alternative resulted in no deviation from Benchmark level production costs. When all three demand levels were considered, a shift to "High" technology was necessary for the "High" demand level. Again very little total variation existed between the "Medium" and "High" management alternatives. Greater variation in total production costs resulted between "Medium" and "Low" management levels as had been anticipated; but the vari- ation was less then 1 percent. Implications Assumptions which restrict the full use of soil resources may cause some variation in projected total costs of production. But the data from this study indicate it to be so slight it can be disregarded. In view of the infor- mation required to derive the data to implement such assumptions these efforts do not seem warranted. While this position appears sound for the general case, it may not be warranted for studies where a large percentage of the soil resources is relatively steeply sloping. In the 93 TABLE 23.--Projected 1980 total cost of production for models testing the sensitivity of the soil management practices assumptions, Southern Michigan Subregiona Total Cost of Soil Production Difference in Total Model Management (Objective Cost of Production Number Practices Function) from Benchmark Level Mil. Dol. Mil. Dol. Percent 1 Medium 186.2 (Bench- mark) 10 Low 186.5 0.3 0.2 11 High 186.2 0 O a1964 constant dollars. Subregion only a small proportion of sloping land exists and the programming coefficients necessarily reflect this fact. Consequently, measurable changes in production costs, even though minor, were not encountered until soil management considerations were tested at higher demand levels. Typically each soil in the programming solutions was projected for production of a variety of crops. Had a larger number of soil groups been used, the tendency for a particular crop to dominate a soil would increase and the usefulness of this assumption might be enhanced. 94 Class 4--Assumptions Relating to Minimum Acreage Constraints Farm operators' long-run production decisions are influenced by many different factors, some of which are not readily measurable. In addition to the operator's image of supply and demand conditions are such factors as personal preference, local custom, government programs, and ad- ministrative regulations. The latter influences are, in many cases, more important in evaluating past production trends and locational advantages than economic conditions. Thus, in projecting agricultural activity for river basin planning purposes, it is necessary that consideration be given to such influences. In the Benchmark Model a constraint was made to the full economic efficiency of the linear programming system. This constraint arose from experience with a test of the model with the 1959 Census of Agriculture which was discussed earlier. As was pointed out, the unconstrained model produced such unrealistic results that a partial production restriction was required for each crop. This modification enabled the model to produce a satisfactory representation of the 1959 Census. As a result, for each of the five subareas, approximately one-half of each area's historic share of Subregional crop acreage was made a production requirement of the subarea. Subregional production requirements were converted to acreage through 95 1980 average yields and one—half of the acreage distributed among the subareas according to their share of 1959 acreage. These adjustments formed the basis for the minimum acreage constraints built into the 1980 Benchmark Model projections. Deviations from Benchmark Projections Levels choosen for comparison with the Benchmark were believed to reflect a sufficient range of possibili- ties to be meaningful. They range from consideration of the least restrictive to the most restrictive situations. The Benchmark ("Medium") acreage constraint is compared with the "Low" level acreage constraint at the "Low" demand level. And the Benchmark ("Medium") and "High" acreage constraints are compared at the "High" demand level. The results indicate little change in Benchmark production costs from a shift to the "Low" level minimum acreage constraint (Table 24). Total costs declined by only $1 million, or less than 1 percent from the Benchmark level. It appears that the Benchmark Model is more sensi- tive to increased levels of constraint than to reductions of a similar nature. The extreme situation of "High" levels of acreage constraint and demand required "High" technology for a feasible solution. This combination of assumptions raised production costs by 86 percent above 96 .MHMHHOU quumCoo emmHe w.ww w.wwH o.oew oon oon con wH w.o- o.HI w.wwH 30H 30H 30H wH w.wwH 30H 3oH soHooz Axumecuoowo H uaoouoo .Hoo .HHz .Hoo .HHz He>eH xumEcOCem ACOHuoCCm mmoHOCcoeB uceEeo uCHeHumCou HecECz Eoum COHuoCcoum e>Huoencov m0 m0 emeeuod Hepoz mo umoU HeuOB COHuospoum He>eH He>eH ESEHCHE CH meoceueMMHQ m0 uuoo Hauoe eCOHmeucsm cmchon Cuecusom .MCoHumEsmme muCHeuumCoo emeeuoe EsEHCHE ecu mo wuH>HOHwaow one ooHuwmu uHooos Hoe ooHuuooouo mo uwou Hmuou owwH oouuoHouoII.ew MHmae 97 the Benchmark. It is an example of the extreme situation on the high side to contrast with the earlier comparison which is the extreme on the low side. To give perspective to the high extreme it was compared with a similar model differing only in that acreage constraints were "Medium." The 25 percent increase in acreage constraint caused production costs to rise $2.8 million, less than 1 percent. Only at "Medium" demand is it possible to compare all three acreage constraint assumptions. Although vari- ations due to "High" constraints are larger than "Low" constraints they are still less than 1 percent. Even the 50 percent range in constraints from "Low" to "High" produced a cost variation of only 1.2 percent. Implications It is difficult to imagine that minimum acreage constraints of 75 percent on each subarea are only slightly more restrictive than 25 percent constraints; but with respect to total costs of production that is so. The only explanation possible is that the 25 percent constraint is sufficiently restrictive over the un- constrained model to have the major influence on whatever cost adjustments take place. Here, resources are quite efficiently organized and little additional change that affects total costs takes place. At high levels of constraint a reordering of production occurs among the 98 soils of a subarea without much relative influence on costs. This is not to say that total costs remain unchanged; they change by upwards of a million dollars. Had there been a larger number of soils among which to redistribute pro- duction is it possible that production costs may have varied to a greater extent. -It must be kept in mind that the primary purpose of the acreage constraint assumption was to assure that shifts in the location of production occur at a rate that was reasonable in light of historical trends. Although costs did not vary greatly as a result of changing acreage constraint assumptions, soil resource use within and among the five subareas shifted substantially. However, within the criteria of the sensitivity test, the Benchmark Model was not sensitive to changes in minimum acreage assumptions. Class 5--Assumptions Relating to Adopted Level of Crop Producing Technology Assumptions about the rate at which new technology will be adopted have historically suffered from under- estimation. This is particularly true of the most recent past as a base from which to project, whether it be looking back five to ten years from today, 1965, or even 1955. Technology appears to be growing at an increasing rate. As its base becomes larger, it serves as a springboard for new ideas which in turn swell the base. These develop- ments have induced some to conclude that technology will 99 undoubtedly solve our future problems because of its past performance. And, this may be partially or entirely true if it is all channeled into problem solving pursuits. However, researchers and planners are a somewhat consera— tive group, preferring to have a contingency plan to cover the possibility that new technology might not live up to expectations. In this regard initial crop yield projections were based on continuous data, where available, for twenty years or more. And, where data covering the smaller area became unavailable companion State data were developed and ex- tended to appraise the longer trends in crop yields. The longer the time series, usually the more conservative are the projected estimates of crop yield in the future. In this study the initial projections were discussed thoroughly with Michigan Agricultural Experiment Station soil scien- tists and crop specialists and also with personnel of the Soil Conservation Service. The purpose in this step was to incorporate the knowledge of plant breeders and others working in soil productivity, who were aware of research on new technology, with the knowledge of extension men in similar areas of work who also knew how rapidly farmers had adOpted available technology in the past. This blend of intelligence served as the basis for projections of crop yields used in this study. 100 The Benchmark ("Low") level of technology repre- sents the matrix of crop yields and associated production costs arising from the above process. Two additional levels of technology, "Medium" (20 percent higher) and "High" (40 percent higher), were chosen to evaluate the sensitivity of the Benchmark Model to higher crop yields that might have been estimated had a shorter historical perspective been taken or had the yields currently being attained by top managers been adopted directly as Benchmark (average 1980) yields. Deviations from Benchmark Projections Evaluation of the technology assumption was some— what restricted, as were other tests of sensitivity, by the infeasibility of models at the "High" demand level. However, the effects of technology at the "Low" and "Medium" demand levels can be evaluated. The influence of technology adoption assumption changes at "Low" demand were compared against Benchmark ("Low") technology (Table 25). An increase of 20 percent from "Low" to "Medium" technology adoption decreased Benchmark production costs by 4 percent. At the "High" level of technology costs were reduced by $15 million or 8 percent below the Benchmark. But higher levels of crop producing technology have more influence as demand rises. 101 TABLE 25.--Projected 1980 total cost of production for models testing the sensitivity of the level of technology assumptions, Southern Michigan Subregiona Total Cost of Production Differences in Total Model Level of (Objective Cost of Production Number Technology Function) from Benchmark Level Mil. Dol. Mil. Dol. Percent 1 Low 186.2 (Bench- mark) 14 Medium 178.6 -7.6 -4.1 15 High 171.2 -15.0 —8.1 a1964 constant dollars. Comparisons at "Medium" demand show production cost savings 0f 5-5 and 9-8 percent respectively. The most restrictive situation in which to test the sensitivity of all variations in the technology adoption assumption also occurred at "Medium" demand. However, a shift to "Low" feeding efficiency was an additional vari— ation from the Benchmark Model. At "Low" technology this restrictive formulation exceeded Benchmark costs by $118 million. Cost savings of 6.6 and 10.6 percent were induced by shifts to technology levels "Medium" and "High" respectively. 102 Implications Increasing levels of technology adoption caused reSponsive reductions in Benchmark production costs at the "Low" demand level. As levels of demand are raised the cost reductions associated with increased technology grow both absolutely and relatively. However, it also became evident that sensitivity to the first increment of techno- JHgy was relatively greater than to the second. At a given demand level an increase in technology from "Low" to "Medium" had a greater affect on cost reductions because it allowed sufficient increases in crop yields to shift production from less productive soils to more efficient soils. The second increment, to "High" technology, also contributed to cost reductions by increasing crop yields; but the better soils already were producing the majority of crops and the savings due to shifts from low producing soils were substantially reduced. This is why the level of cost sensitivity to changing technology rises relatively more as the level of demand rises. More of the less productive soils are forced into production and their removal from the solution through increased technology becomes more obvious in the level of total costs. The effect of the first increment of technology is relatively greater than the second. An error in estimating the future level of technology adoption is more likely to be made at the first increment level than the second. 103 Planners should, therefore, consider the Benchmark Model as sensitive to variations in the technology adoption assumption. Alternative Criteria of Analysis In the foregoing analysis of sensitivity the total cost of meeting production objectives was chosen as the criterion of sensitivity. Other criteria could just have easily been chosen as a measure of sensitivity. It is highly probable that variations in each of these criteria would differ from those of the objective function as alternative levels of the assumptions under study are tested. As an example of the type of variation one could expect from other criteria of analysis, the sensitivity of technology assumptions were tested using three alternative criteria. These are only three of many criteria which could have been chosen and are: (1) total acreage of cropland required to meet production objectives, (2) total production of wheat, and (3) total production of a major row crop-—corn. From the preceding analysis of the technology assumptions it was observed that variations in the assumption caused only moderate sensitivity. When resource use serves as the criteria of analy- sis, total Subregional acreage declines by about 18 per- cent and 28 percent as technology is increased by 20 and 40 percent respectively (Table 26). Variations in the 104 w.wow.w o.wow o.www o.wow H.wow o.wow emHm wH o.www.w e.wwe H.Hwo.H w.wwH.H w.wwe w.www soHooz eH cxHeE IcoCemv e.wee.e o.woe w.wwo.H o.wwH.H H.eHm.H o.www 30H H wou0< ooo.H COHmeuch m eeuecsm e eeuecsm m eeumcsm m meuecsm H eeuecsm MOOHoccoeB HecEdz Ho H0>mH Hmoos COHmeucsm CechOHz Cuecuoom .mCOfiWWEdmme mmoHOCcoeu mo He>eH ecu mo muH>Hu IHmcem ecu mCHumeu MHeUOE How eeuecsm mc ems eouoomeu HHom ommH peuoenoumll.mm MHmca 105 technology assumption cause far more sensitivity in Benchmark projections of resource use than in projected total production costs. Also of interest is the relative use of soil resources among subareas as the technology level is raised. Although total resource use declines, this is not true for all subareas. Subarea 1 increases acreage in crops by 23,000 acres and only Subareas 3 and 4 decline with both increases in technology. In the case of wheat as the criterion of sensi- tivity, raising technology to "Medium" and "High" levels cause marked shifts among subareas as the total production remains constant for the Subregion (Table 27). Subareas 1 and 5 increase wheat production by about a quarter while Subarea 3 experiences a rise of about two and one-half times. Production drops then rises in Subarea 2 but the reverse is true for Subarea 4. Of all the crops in the Benchmark Model corn has the largest demand and as such might serve as a likely criterion of analysis. Testing the sensitivity of corn production to increased yield levels reveals that as technology levels are raised for all crops it induces higher and higher levels of corn production in Subareas 3 and 5 (Table 28). Raising yield levels causes a sub- stantial shift of production primarily from Subarea 4 to the other subareas. These types of sensitivity are not detected by an analysis using the broad criterion of production costs as 106 m.m0H m.0H m.m0H 0.0H m.m0H m.m w.mm m.HN h.HH h.mm b.mH m.HH $.05 e.mH o.m uHoamow ooHHHHz w.w tout wH e.w sauce: eH ccueE -auomwo w.e 30H H COHmeucsm m eeuecsm v eeuecsm m eeuecsm N eeuecsm H eeuecsm mmOHoccoeB Hecfisz mo H0>0H Hoooz Coneuch cechon Cuecusom .mcoHumEsmme mmoHoccoeu mo He>eH ecu mo wuH>HuHmcem ecu mCHumeu MHepos How meumcsm wc Cuoo mo COHuosuoum Heuou ommH ueuoenoum .mm mHmCB e.hm m.N h.bm H.m 5.5m m.H m.m v.MH N.m o.OH m.m m.v m.w m.v m.mH meauom aoHHHHz w.H eme wH H.H soHooz eH ccueE IcoCemv w.o 30H H COHmeHch m eeuecsm v meuecsm m meuecsm. m eeuecsm H eeumcsm amoHOCcoea Hecadz Ho H0>0H Hmooz Coneucsm CechoHE Cuecusom .mCOHumECmme mmoHoccoeu mo He>eH ecu mo muH>HuHmCem ecu mCHumeu MHepOE How meuecsm ac ueec3 mo COHuosuoum Heuou ommH peuoenonmII.em mHmCB 107 a measure. By the same token that criterion may be more sensitive than some others that could have been chosen. It is more important to realize that the choice of cri- teria may influence the degree of sensitivity than to believe that a given criterion is an adequate measuring stick. Part II--Sensitivity Analysis With Irrigation Part I of this chapter was concerned with an analysis of the sensitivity of Benchmark costs of pro- duction to changes in the specification of five classes of assumptions. In that analysis, no irrigation activities were included in the Benchmark Model, and thus, no evalu- ation of the economic potential for irrigation development was made. The remainder of this chapter is devoted to a sensitivity analysis of the Benchmark Model which was modified to include irrigation activities. These activi— ties were added to the Benchmark Model through a sub— stantial expansion of the programming matrix. Irrigation activities were created for all major crops and they could only enter the programming solution in an irrigated state if they were economically justified in meeting production objectives. In the analysis of sensitivity in Part I of this chapter, it was found that certain alternative assumptions ‘were more critical than others in causing variation in the 108 Benchmark cost projections. These cost projections, serving as indicators of sensitivity, identified assumptions concerning livestock feeding relationships, projected demands and technology adoption levels as much more sensi— tive than assumptions about soil management practices or minimum acreage constraints. In a similar analysis for Part II, where irrigation was included in the 1980 Benchmark Model, almost identical results were produced. Projected production costs for the Benchmark Model with irrigation were less than the model without irrigation by $2.5, $3.2, and $2.5 million at the "Low," "Medium," and "High" levels of technology re— 28 At demand levels above Benchmark demand spectively. ("Low"), savings also increased and by about the same magnitude. The results of this second sensitivity analysis were, on the whole, very similar to the analysis in Part I. The essential difference was that irrigation reduced the general level of total production costs by reducing the number of acres needed to produce a given output of product. 28See Table 18 and Appendix Table C-ll for com- parisons used in this analysis. 109 Of all the crops in the Model the only crop entering the Benchmark solution with irrigation was potatoes.29 Potato production in the 1980 Benchmark Model without irrigation required 32,800 acres, a 13 percent increase over 1964 production levels (Table 29). When irrigation was added to the Benchmark Model, the same production was possible on 19,800 acres, nearly 32 percent less than were required in 1964 and about 40 percent below potato acreage projections for the 1980 Benchmark without irrigation. In 1964, the Census of Agriculture reported that approximately 7,300 acres of potatoes were irrigated, about one-quarter of the total potato acreage. But the entire crop was irrigated when the irrigation option was made available in the Benchmark Model. Comparison of potato acreage distribution among the five subareas in 1980 with that in 1964, indicates that the Model is capable of identifying the most likely areas where irrigation would take place. Moreover, it is consistent with what farmers are already doing with respect to the limited amount of potato production now under irrigation. 29Specialty crops like fruit, vegetables, and sod crops were recognized as having high irrigation potential. They, however, were removed from the basic model and are not a part of this analysis. 110 TABLE 29.--Comparison of harvested acreage of potatoes with and without irrigation, 1964, and 1980 Benchmark projections, ‘ by subarea, Southern Michigan Subregion 1964 1980 Census of Agriculture Benchmark Projections Subarea Total Total Total Irrigated Total a Irrigated Potatoes Potatoes Potatoes Potatoes 1,000 Acres 1 3.4 0.9 1.8 l 8 2 2.1 0.2 15 0 0 9 3 3.9 0.5 2 3 2.3 4 16.6 4.9 9.6 13.4 5 2.8 0.8 4.1 1.4 Total Subregion 28.8 7.3 32.8 19.8 Source: Census of Agriculture 1964 and Benchmark so- lutions. aBenchmark solution without irrigation. bBenchmark solution with irrigation--all potato acreage was projected for irrigation. 111 Shift-Point Analysis In Part I of this chapter, it was found that certain alternative assumptions were more critical than others in causing change in Benchmark Model projections. With changes from the Benchmark projections of total production costs as indicators of sensitivity, assumptions concerning livestock feeding relationships (Class-1), projected demands (Class-2),and technology adoption (Class-5) were found to be much more sensitive than the other classes of assumptions. In Part II when irrigation activities were introduced into the Benchmark Model similar sensitivities were observed. However, in comparing the two Benchmark solutions (with and without irrigation) it is clear that the introduction of irrigation caused certain shifts in the projected location of potato production among subareas. All subareas except 1 and 3 were projected to lose potato acreage while Subarea 4 indicated gains. Further shifts to Subarea 4 were precluded by the minimum acreage constraint assumption in the Benchmark Model. An important question then concerns what changes might occur in the projected economic potential for irri- gation as deviations from Benchmark assumptions are introduced. Since river basin development plans are based in part upon projections of economic potential for development, the stability of those projections is most important. Therefore, a procedure was devised for 112 evaluating the sensitivity of Benchmark irrigation pro- jections to changes in the five classes of assumptions analyzed in Part I. This procedure is essentially an analysis of "shift-points" in the projected economic potential for irrigation. More specifically, it identifies sensitivites of the Model to changes in assumptions as they influence projections for irrigated acreage and its distribution among subareas. In the analysis to follow, primary concern centers on the stability of projected irrigated acreage magnitude and location among subareas as affected by variations from Benchmark Model assumptions. Of major interest will be points at which shifts occur either in total irrigated acreage or location. The same selection of basic com- parisons among models as used in Part I was made for this analysis (Table 30). Also the same designation of the letters L, M, and H has been retained. Class l-—Assumptions Relating to Livestock Feeding Relationships In view of their effects upon resource use the assumptions that would appear to have the greatest influ— ence on irrigated requirements are "Low" feeding efficiency and "Low" concentrate rations. Both of these would require added resources to meet production objectives and might induce higher levels of irrigation. 1153 mcoem muwmmap mcwcmoa mmwomum one . .mumaaoo ucmumcoo woman .m>fiumuumc on» Ca Hammmm mcoauwcauop pwawmuoo .mQOAumesmmm uo mommmHo .cmflm can .Esfipmz .30A >Ho>wuoommmu some m can .2 .q :ofiumcmawmp ones o>fiu an» F .mwd M . 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All other assumptions are at "Low" levels. Feeding efficiency assumptions tested deviate by 10 percent above ("High) and below ("Low") Benchmark levels. Deviation from Benchmark Projections.—-When com- parison of alternative feeding efficiency assumptions were made with the Benchmark level no shifts in irrigated acreage took place (Table 31). Total irrigated acreage remained the same at both "High" and "Low" feeding ef- ficiency. The only crop entering the solution was potatoes at 19,000 acres (Appendix B, Table B-l). At the next higher demand level ("Medium") feeding efficiency as— sumptions "Medium" and "High" again produced identical results; but at a higher level. A change of 10 percent to ”Low" feeding efficiency caused total irrigated acreage to increase 47 percent and locational shifts affecting Sub- areas 2 and 4 to occur. In addition to potatoes 14,000 acres of corn silage entered the projected irrigation solution. Implications.--At Benchmark levels of demand ("Low") the alternative feeding efficiency assumptions have no influence on projected irrigated acreage. However, as demand rises, shifts do occur in total acres irrigated and among subareas. These shifts are affected most by the 115 TABLE 31.--Projected 1980 irrigated acreage for models testing the sensitivity of the feeding efficiency assump: tions, by subareas, Southern Michigan Subregion Subarea Model Feeding Total Number Efficiency Subregion l 2 3 4 5 1,000 Acres 1 Medium 1.8 0.9 2.3 13.4 1.4 19.8 (Benchmark- Irrigated) 2 High l.8 0.9 2.3 13.4 1.4 19.8 3 Low 1.8 0.9 2.3 13.4 1.4 19.8 "Low" feeding efficiency assumption. The change from Benchmark ("Low") demand to "Medium" demand is too large to identify at what point in the range shifts due to "Low" efficiency occur. It is known, however, that the potato crap, in its entirety, is irrigated at all demand levels. The irrigation of corn silage was induced by the greater feed requirements of "Low" feeding efficiency which in turn meant more acres were needed in production. Therefore, it is probable that shifts to corn silage irrigation would take place slightly before reaching demand "Medium" if other assumptions remained unchanged. Errors in specifying the feeding efficiency coefficients cause greater variation in projections of irrigated acreage if they understate 116 efficiency than if they overstate it, particularly at high demand levels. Livestock Rations "Medium" concentrate levels are assumed by the Benchmark Model. Variations under study are 15 percent more concentrate ("High") and 15 percent less ("Low"). Deviation from Benchmark Projections.-—When alter- native ration formulations are considered it is instructive to do so with feeding efficiency either above ("High") or below ("Low") the Benchmark ("Medium") level. First, com- parisons are made at "High" feeding efficiency and, second, at "Low" efficiency. Finally the effects of higher demand levels upon feeding relationships are assessed. Holding feeding efficiency constant at the "High" level while varying concentrate composition of the livestock ration caused absolutely no variation in Benchmark pro- jections of irrigated acreage (Table 32). The same was true of similar comparisons where feeding efficiency was held constant at the "Low" level. As the demand level was increased the first incidence of sensitivity was encountered with "Low" feeding efficiency and demand "Medium." Here variations in concentrate rations caused substantial shifts in total irrigated acreage and among subareas as reported. It will be remembered that, in the analysis of feeding efficiency sensitivities, "Low" efficiency and demand "Medium" caused irrigated acreage to increase 117 m.mH v.H v.ma m.m m.o m.H 30A BOA h m.mH s.H ¢.mH m.m m.o m.a 3oq some 8 m.mH v.H «.ma m.m m.o m.H Baum 30; m m.ma v.H q.ma m.~ m.o m.H Baum roam a pmummHHHH Ixnmanocmmv m.mH a.H «.ma m.m m.o m.H endow: endow: H mmuoa ooo.H coflmmu m e m m H mocmfloflmmm aoapmm ca nmnssz loom mcflpmom mumnucmocou mo Hobo: Hmuoe mmmumnsm cowumnomonm scammunom cmmflQOHz cnmcpoom .mmmumnsm an .mGOHumEdmmm cowumu xooumm>wa mnu mo mufl>fiuflmcmm on» maflumo» mamoofi How mmmmnom wmummwuuw ommH popomnonmln.mm mamas 118 14,000 acres.30 This also represented the Benchmark "Medium" concentrate assumption. When that concentrate assumption was increased 15 percent ("High") the 14,000 acres of irrigated corn silage left the solution. The "High" concentrate ration effectively removed the influ- ence of "Low" feeding efficiency on projected irrigated acreage. On the other hand, lowering concentrate in the ration by 15 percent ("Low") caused irrigated acreage to rise by nearly 600,000 acres while the relative distri- bution among subareas was considerably altered. With respect to maintaining "High" feeding efficiency as concentrate ration relationships varied, no shift-points were in evidence until "High" demand levels were reached where results were completely unrealistic. At this level, variations in the ration caused projected acreage of irrigation to range from 476,000 acres to over 2 million acres 0 Implications.--Contrary to observations made in Part I, there does appear to be interaction between feeding efficiency and ration composition. This is especially true in the direction of "Low" efficiency and "Low" levels of concentrate in the ration. At "High" concentrate levels the effects of "Low" efficiency are dampened. Similar but slightly less sensitive results were encountered when 30See Appendix B, Table B-1 for an indication of which crops were irrigated under each of the alternative model formulations. 119 feeding efficiency was held at the "High" level. Acreage shifts were not encountered at "Low" demand but increased precipitously as demand climbed. In view of these results river basin planners should consider projections of economic potential for irrigation as highly sensitive to changes in assumptions concerning ration composition. This is especially true if demands may be overstated or soil resources are in short supply. At high demand levels an error in overstating the concentrate ration component will result in an under- statement of irrigated acreage because the comparative advantage of feed grain production reduces the acreage needed for production. The reverse error of understating concentrate will have a greater effect on overstating irrigation projections, particularly if accompanied by an understatement in feeding efficiency because of the increased soil resources brought into production to meet the expanded requirements. Class 2--Assumptions Relating to Projected Demand Some of the discussion relevant to this analysis can be found in the preceding section. However, the concern there was to identify sensitivity of irrigated acreage projections to changes in livestock feeding relationships. The influence of demand was secondary. This section is concerned with shift-points between the ‘ 120 Benchmark Model demand ("Low") and models where changes occur in demand assumptions by 50 percent ("Medium") and 100 percent ("High"). Deviations from Benchmark Projections Increasing Benchmark demands ("Low") by 50 percent ("Medium") resulted in nearly a 50 percent rise in irri— gated acreage that generally followed the Benchmark sub- area distribution (Table 33). But the next 50 percent increment in demand (“High") brought forth more than a 100 fold increase in irrigated acreage that was not shared equally or proportionately by the subareas. Whereas in the previous two situations Subarea 4 contributed two- thirds of the irrigated acreage, with "High" demand that share was reduced to one-quarter. One-third of the irri- gation took place in previously insignificant Subarea 3, nearly a fourth was in Subarea 2, while Subarea 5 increased to 17 percent of the total, and Subarea 1 alone had a small relative decline. The "High" demand level caused lower producing soils to be forced into production which in turn gave crops other than potatoes a comparative advantage when irrigated and these crops entered the solution in all subareas. The increase in irrigated acreage from Benchmark demand ("Low") to "Medium" demand was due solely to increased potato requirements. At the "High" demand 121 TABLE 33.--Projected 1980 irrigated acreage for models testing the sensitivity of the demand level assumptions, by subareas, Southern Michigan Subregion Subareas Total Model Demand Sub- Number Level 1 2 3 4 5 region 1,000 Acres 1 Low 1.8 0.9 2.3 13.4 1.4 19.8 (Benchmark- Irrigated) 8 Medium 2.8 1.3 3.4 20.0 2.1 29.6 9 High 13.4 536.5 725.9 578.1 393.4 2,247.3 assumption variation, however, over 2 million acres of irrigated crops were forced into the solution. Over 1 million acres of that total were in corn and the re- mainder was made up of wheat, dry beans, hay crops, and potatoes in that order.31 Implications I The Benchmark model projection of irrigated acreage is very sensitive with respect to changes in demand as- sumptions in a positive direction. Also sensitivity increases exponentially as demands are raised. At low levels of demand the only crop with economic potential for irrigation is potatoes. Thus, errors in specifying demand 31See Appendix B, Tables B—l, B-2, and B-3 for acreages of irrigated crOps under alternative assumption formulations. 122 at low levels will cause variation in irrigated acreage in the same direction and magnitude as variations occur in potato demand. However, as the assumed level of demands are raised potatoes cease to be the only crop irrigated and sensitivity of the irrigation projections becomes a function of the relative availability of soil resources. River basin planners should, therefore, have less faith in the stability of their development potential projections in limited resource situations. In this regard, errors in disaggregation of regional demands are more likely to be made for smaller areas than for large. If funds permit additional model runs, the projected development potential should be tested for sensitivity to variations in demand assumptions, particularly on the high side. Class 3--Assumptions Relating to Soil Management Practices In the analysis of sensitivity in Part I of this chapter, the assumptions relating to soil management practices created slightly different restrictions on the model than those to be analyzed in this section. There the Benchmark level ("Medium") of projected soil management practices was closer to the "High" level (no restriction) than to the "Low" level (current management practices). In the analysis to follow the variations are approximately the same because soils with slow permeability, very high 123 water holding capacity, or steep slopes were removed from consideration. These are the same soils that caused unequal differentials to exist in the earlier analysis. Assumptions relating to soil management practices were incorporated into the Benchmark Model so it could account for crop rotations to reduce soil erosion. The Benchmark assumption ("Medium") provided 4.3 million acres as an upper bound for irrigated row crops. The "Low" assumption variation was 3.1 million acres while 5.6 million acres were possible under the no restriction "High" level. Relative availability of irrigable soils ranked by subarea is as follows: Subarea 3, 4, 5, 2, and 1. Deviations from Benchmark Projections Shift-point analysis of the deviations in soil management practice assumptions show no sensitivity with respect to the Benchmark at "Low" demand levels (Table 34.) Projected irrigation is identical for each alternative and limited to potatoes which is the only crop with a com— parative advantage in irrigation at this demand level. At demand "Medium" a slight variation occurs in Subarea 4 with the "Low" level of soil management. Irrigated acreage increased by about 2,000 acres of corn silage. More substantial shifts occur among subareas at "High" demand, however. Total irrigated acreage increased by 4 percent as the Benchmark management practice 124 TABLE 34.--Projected 1980 irrigated acreage for models testing the sensitivity of the soil management practices assumptions, by subareas, Southern Michigan Subregion Soil Subareas Model Management Total Number Practices 1 2 3 4 5 Subregion 1,000 Acres 1 Medium 1.8 0.9 2.3 13.4 1.4 19.8 (Benchmark- Irrigated) 10 Low 1.8 0.9 2.3 13.4 1.4 19.8 11 High 1.8 0.9 2.3 13.4 1.4 19.8 assumption ("Medium") was compared with the "Low" level. But Subareas l, 3, and 4 increased in irrigated acreage while Subarea 2 and 5 declined. The change from Benchmark ("Medium") soil management practices to no constraints on soil resource use ("High") caused a slight drop in irri- gated acreage. More variation occurred between Subareas 2 and 3 than in total irrigated acreage. Implications Projections of total irrigated acreage were gener- ally insensitive to variations in assumptions about soil management practice levels. However, when influenced by assumed demand increases above Benchmark levels ("Low") some sensitivity in the form of shifts among subareas occurred. This was more evident at the "Low" (current practice) level than at "High" (no restrictions) levels. 125 The relative magnitude of these shifts were only sub- stantial under the limiting resource situation of "High" demand. An apparent inconsistancy developed in comparisons involving the "Low" soil management practice assumption. This assumption was the most restrictive in the acreage available for irrigated row crops, yet at higher demand levels more acreage was irrigated under this assumption than the other variations of it. The reason for this was the partial displacement of row crops under the more restrictive situation. In the process of readjustment soils with higher unit production costs were selected which made certain irrigation alternatives more efficient a1- ternatives. As a result of the analysis in Part I and in this section also the continued use of this assumption does not appear warranted. It should be removed from use in most river basin models. Possible exceptions would be areas with a large proportion of sloping soils or a predominance of row crop production. Class 4-—Assumptions Relating to Minimum Acreage Constraints Minimum acreage constraints were developed for the Benchmark Model to insure that such extra-market con- siderations as personal preference, asset fixity, and administrative regulation would be accounted for in 1980 126 projections. Deviations from the Benchmark assumption of 50 percent ("Medium") were chosen as 25 percent ("Low") and 75 percent ("High"). These proportions of projected demand were required to be produced in the same subareas as had been the case historically. Deviations from Benchmark Projections At the "Low" demand level only 200 acres of irri— gated crops separated the Benchmark minimum acreage re- quirement ("Medium") from the "Low" level (Table 35). However, considerable variation exists in irrigated acreage among subareas. The only crop irrigated in both solutions was potatoes. And in the Benchmark solution ("Medium") they entered at the minimum acreage requirement in all but Subarea 4. It was concluded that a reduction in minimum acreage requirements would cause shifts in the location of production. .The "Low" requirement alternative verified the conclusion as the four subareas that had formerly entered the solution at the minimum potato acreage again entered at the minimum even though the constraint had been halved. 'Subarea 4 received the shifted acreage of irri- gated potatoes and accounted for nearly 85 percent of Subregion production. With respect to irrigated potatoes the Model seems to verify farmers actions in Southern Michigan. Subarea 4 contains both Bay and Montcalm Counties where most of the states' irrigated potato acreage is currently located. 127 m.mvm.m m.Hmm H.hmm H.mmm >.mmm H.NH swam comm ma m.mH v.0 m.ma H.H v.0 m.o 309 30A ma ApmummflHuH nxumenocmmv m.ma v.H. «.ma m.m m.o m.H 30A Edflpmz H mmno< ooo.H coammunsm m w m , m H Hm>mq muGHMHumsoo HmnEdz Hmuoa panama mmmmuom Hmpoz mmmnmnsm Eseflcflz coflmmnnsm cmmflzoflz cnmnusom .mwnmnsm >9 .chHMQHSmmm mucflmuumcoo mmmmnom Eseflcfle mcu mo mufl>fluflmsmm man mcwummu mampofi mom mmmmuom pmummHHHH omma pmuommoumll.mm mqmda 128 At demand "Medium," identical results occurred in the comparison between "Medium" and "Low" minimum acreage assumptions. As minimums were reduced potato acreage shifted to Subarea 4. However, when the minimum con- straints were raised to "High" (75 percent), Subareas 1 and 5 no longer produced irrigated crops and the total irrigated acreage declined 18 percent as potato production was removed from Subarea 4 and forced into the less pro- ductive subareas by the minimum acreage constraint. At the "High" demand extreme, a comparison was made between Benchmark minimum acreage ("Medium") and "High." Almost 2.3 million acres were irrigated under each alternative. There were, however, considerable shifts in irrigated acres between Subareas 2 and 3 caused by the "High" acreage constraints. Implications Very little sensitivity exists in the projected total irrigated acres under variations in the minimum acreage constraint assumption except at "High" demand. However, sensitivity of the location of that irrigated acreage among subareas does exist and is directly related to the assumed level of acreage minimums. If a particular crop demonstrates irrigation potential, as in this analysis, it is highly probable that the location of that projected potential will be completely controlled by the level of minimum acreage assumed for the 129 model. The lower the assumed minimums the less likely a small error will cause sensitivity in the location or projected economic potential for irrigation. The effect of "High" minimums is to preclude efficient location of crops among subareas but not within. This relocation within a subarea often removes the potential for irri- gating a single crop by requiring the resource for efficient production of other crops not having an irri- gation potential but forced into the subarea. It is possible that greater sensitivity would have been observed had more than one crOp exhibited economic potential for irrigation, or whatever development al- ternative might be considered. River basin planners should evaluate, or at least be aware of, this possibility where a variety of crops display similar potentials. Class 5--Assumptions Relating to AdOpted Level of Crgp ProducingiTechnology In this analysis, as in Part I, assumptions about Benchmark yield levels ("Low") are compared with projected yields that are higher by 20 percent ("Medium"), and 40 percent ("High"). Of concern in this analysis is whether variations in assumed yield levels will affect the level and location of irrigated acreage. 130 Deviations from Benchmark Projections The Benchmark Model with "Low" crop yield techno- logy projected 19,800 acres of irrigated potatoes. At "Medium" technology total irrigated acreage increased nearly three times to 56,400 acres, only 16,000 of which were in potatoes and the remaining acres were in irri— gated hay crops (Table 36). The "High" technology assumption also produced increases from Benchmark levels but not as large as the first ("Medium") alternative. With higher yields under the second alternative less acres were required for the same production. TABLE 36.-~Projected 1980 irrigated acreage for models testing the sensitivity of the level of technology assump- tions, by subareas, Southern Michigan Subregion Subareas Model Level of Total Number Technology 1 2 3 4 5 Subregion 1,000 Acres 1 Low 1.8 0.9 2.3 13.4 1.4 19.8 (Benchmark- Irrigated) 14 Medium 1.8 0.9 2.3 50.0 1.4 56.4 15 High 1.8 0.9 2.3 37.3 0 42.3 All of the sensitivity observed in total irri- gated acreage generally occurred in Subarea 4, with one exception; at "High" technology levels. The first 131 increment of technology ("Medium") raised yields enough to reduce potatoes by 3,700 acres. But in the process hay crops became economically feasible to irrigate and 40,400 acres entered the solution in Subarea 4. At "High" technology the same two crops continued in the solution; although, due to the higher yields, acreage declined to 13,000 for potatoes and 29,400 for hay crops. Because the Benchmark minimum acreage constraint ("Medium") was controlling potatoes, the same level of irrigation continued in all subareas but 4 which lost potato acreage with rising technology levels to offset the forced production elsewhere. At "High" yield technology the economic potential for irrigated potatoes in Subarea 5 no longer existed; but 1,400 unirrigated acres were still forced into the solution by acreage minimums. When similar comparisons were made at demand level "Medium" similar results were observed. Although Subarea 5 continued to produce potatoes at the "High" technology level because of higher general requirements. Somewhat different results occurred at the "High" demand level. With Benchmark technology ("Low") nearly 2,300,000 acres were irrigated including wheat, corn, dry beans, potatoes, and hay crops. When the "Medium" technology level was compared the projected total dropped to 215,000 acres of irrigated hay and potatoes. This was also the case at "High" technology where only 94,000 acres were required. 132 Essentially all of the change in these last two comparisons occurred in Subarea 4 as before. Implications The only shift-points observed in this analysis of sensitivity due to deviations in technology assumptions center on total Subregion irrigated acreage. At "Low" and . "Medium" demand levels the effect of changes in technology was to shift irrigated acreage into or out of Subarea 4 in the same amount as total acreage changed. At "High" demand, the first increment in technology above Benchmark ("Low") produced substantial irrigated acreage reductions. But at "High" technology the yields were large enough that results were similar to those observed at lower demand levels. In this analysis minimum acreage requirements tended to control shifting of irrigated acreage among subareas. If acreage minimums were changed to minimum production requirements the model might be more responsive to changes in technology or to the initial efficiency conditions in the Benchmark solution. If this were true the acreage observedunchanged in this analysis.would have decreased in response to rising technology levels and Subarea 4 would have had a larger irrigated acreage. Sensitivities observed at "Low" and "Medium" demand may have been spurious due to the unique situation that developed in relative crop yields giving hay crops an 133 irrigation advantage at technology "Medium" and "High." However, this same peculiarity might be associated with any error in technology estimation. River basin planners should be aware that such a relationship could develop for most any crop with a development potential. It must be concluded from this analysis that deviations from the Benchmark assumptions of crOp producing technology cause moderate sensitivity in total projected irrigated acreage. Variations in technology that apply equally to all subareas cause imperceptable locational sensitivity, even at high levels of demand. CHAPTER VI SUMMARY AND IMPLICATIONS Summary The Natural Resource Economics Division carries out a national and regional program of research, planning assistance, and related policy assistance on natural resource problems. A major area of concern of this work relates to development of plans to improve river basins and sub-basins, including investigations to identify and evaluate economic needs for develOpment in rural areas. Most of the investigations are applied economic research which contributes to inter-agency-interdepartment compre- hensive studies. Survey data and analyses for this area of work are prepared for use mainly by participating agencies. In carrying out this planning function, re- searchers and planners must rely to a certain extent on informed judgment and assumptions concerning certain factors of the total analysis. Such assumptions and judgments play an important role in developing the input data for the NRED least cost linear programming model used in river basin analysis. Considerable concern has 134 135 developed over the possible effects that errors in judgment or assumptions might have upon the solution of linear programming problems. This study was undertaken to: (l) evaluate selected assumptions made in developing the NRED model used in projecting agricultural activity on a range of soil resources in river basin studies, (2) analyze the sensitivity of model projections of total production costs to changes in these assumptions, and (3) evaluate the sensitivity of model projections of locations and acreages of potentially irrigable crops to changes in these as- sumptions. The 42-county Southern Michigan model was chosen for this study because it was representative of other larger models and its relatively small size enhanced the simplicity of incorporating adjustments. Five classes of assumptions were tested for sensi— tivity. They were assumptions relating to: (1) livestock feeding relationships, (2) projected demand levels, (3) soil management practices, (4) minimum acreage constraints, and (5) level of crop producing technology adoption. The Benchmark Model consists of a specific level of each of the five assumption classes. Sensitivity of the Benchmark Model to changes in these assumptions was first tested using changes in the total costs of production as the principal criterion. After incorporating irrigation into the Benchmark Model a second sensitivity analysis was made 136 of shifts in the location or total irrigated acreage projected because of changes in these same assumptions. Feeding efficiency assumptions that varied by 10 percent on either side of the Benchmark level caused a similar directional response in total cost of production but the magnitude was on the order of 6 to 7 percent. The model was quite sensitive to these changes, more so as the soil resource became limiting because assumptions about feeding efficiency affect livestock feed demands. At low efficiency more feed is required and less productive- higher cost soil resources are required to meet demands. The reverse is true for high efficiency but to a lesser degree. Thus, planners should take care in estimating feeding efficiency levels as errors that understate efficiency are more critical than those that overstate it. Livestock ration assumptions were changed by 15 percent in concentrate composition on either side of the Benchmark ration because of short run influences like weather, price, fad, or harvesting equipment. Once the effect of feeding efficiency was accounted for, variations in concentrate content of assumed rations had little influence on total production costs. Combinations of low feeding efficiency and low concentrate rations caused slightly more sensitivity since roughages were less efficiently produced than feed grains. Errors of 15 per— cent in concentrate levels caused variations of 1 percent 137 or less in production costs. These results suggest that basin planners should place more emphasis on establishing reliable coefficients for feeding efficiency than for ration composition. Three demand level models were tested for sensi- tivity; they included: (1) Benchmark 1980 projected level of demand, (2) Benchmark level increased by 50 percent, which approximated constant relative production levels with respect to the nation, and (3) Benchmark level increased by 100 percent. Results of these tests indicated that errors in demand specification would cause production costs to be in error in the same direction by approximately the same degree. The small number of soils in this analy- sis may have obscured the diseconomies of forcing less efficient soils into production at higher demand levels. Thus, a model containing a more comprehensive classifi- cation of soils may be far more sensitive to errors in demand specification than this model-—which was very sensitive. Soil management practice assumptions reflecting estimated 1980 levels in the Benchmark Model were compared with alternative assumptions that reflected, (1) current levels of soil management practices as constraints, and (2) no constraints to the full use of soil resources for growing row crops. Variation in the total costs of production occurred from assumptions that restricted the 138 full use of soil resources, but it was so slight that it can be ignored. This study indicates that efforts required to derive data to implement such assumptions are not warranted. While this appears to be a sound conclusion for the general case, it may not be true for studies where a large percentage of the soil resources are steeply sloping or a high proportion of all crops grown are row crops. Analysis of the class of assumptions dealing with minimum acreage constraints measured variations in pro- duction costs due to three levels of contraint, 25 percent, 50 percent (Benchmark), and 75 percent. These constraints required a certain percentage of 1980 Subregion demand to be produced as a minimum among the subareas according to the historical distribution. Considerable variation occurred among subareas and within subareas as a result of reorganizing resource use in response to changes in the assumptions. But only small changes occurred in total production costs. With respect to that criterion this class of assumptions caused little model sensitivity. The class of assumptions relating to adopted levels of crop producing technology reflected crop yields expected to exist in 1980 under average conditions of farm management and weather. This Benchmark level, -believed to be conservative, was increased by 20 percent and 40 percent. Since the effect of increased technology 139 is to raise yield levels it also allows cost savings by removing less productive soils from the solution. At low demand levels 4 to 8 percent cost savings were obtained from the two additional increments of technology. These savings increased with rising demand and equalled nearly 7 to 11 percent at the highest demand level. Sensitivity was relatively greater to the first additional level of technology than to the second because it induced a larger shift away from the less productive soils. Underestimating future crop yields will cause an over-statement of pro- duction costs and vice versa. However, the error in yields will be far larger than in the costs. If the situation is one of resource scarcity, the errors and the model sensitivity would be increased. When irrigation was included as an activity in the Benchmark Model, a similar analysis of sensitivities measured by changes in total production costs revealed almost identical results. Because the irrigation al- ternative was responsible for reducing the magnitude of the objective function, through lower unit production costs, it resulted in slight proportionate increases in sensitivity, but did not change any of the preceding conclusions based on that analysis. The introduction of irrigation into the Benchmark Model caused certain shifts in the projected location of potato production, the only crop demonstrating irrigation 140 potential at low demand levels. It then became important to learn what shifts might occur in the projected economic potential for irrigation as variations from Benchmark assumptions were introduced. In this approach, the focus was on shift-points in the solutions, on a subarea basis, and the assumptions that triggered such shifts. It was observed that the feeding efficiency as- sumptions had no influence on projected irrigated acreage at Benchmark demand. However, the reduced feeding efficiency assumption became extremely sensitive at higher demand levels. Shifts occurred between Subareas 2 and 4. Increased feeding efficiency caused no changes until the highest demand level was reached. There a 10 percent increase in efficiency reduced irrigated acreage by 35 per— cent but no subarea sensitivity occurred. Errors in specifying feeding efficiency coefficients are more critical if understated than overstated, particularly at high demand levels. Although Benchmark total production costs were insensitive to variations in ration composition, that was not true for projected irrigated acreage. No sensitivity was observed at Benchmark demand but at the medium demand level and low feeding efficiency an increase of 15 percent in concentrate caused a 32 percent decline in irrigated acres, selectively from two subareas. Fifteen percent lower concentrate in the assumed rations caused irrigated acreage to rise from 44,000 acres to 630,000 acres. More 141 variation occurred at higher demand levels. River basin planners should consider projections of economic potential for irrigation as highly sensitive to changes in ration composition, especially at high demand levels or where soil resources are in short supply. Shift-point analysis of the demand assumptions indicated that raising Benchmark demand 50 percent resulted in a 50 percent rise in irrigated potatoes, the only crop with an economic potential. Since the minimum acreage constraint was controlling, the increase was proportional for all subareas. However, the next 50 percent increment in demand caused a 7,000 percent increase in total irri- gated acreage and disrupted the subarea distribution. Over 1 million acres were in corn and the remainder consisted of wheat, dry beans, hay crops and potatoes in that order. This analysis indicates that planners should question the stability of projected development potentials where demands may be overstated, particularly in limited soil resource situations. If funds permit, alternative runs at different demand levels are advisable. Shift-point analysis of soil management practice assumptions revealed no sensitivity at Benchmark demand and only a slight variation in Subarea 4 when demands were increased by 50 percent. At the high demand level, where more than 2 million irrigated acres were forced into the solution, a change from Benchmark soil management practices to current management was restrictive enough to increase 142 irrigation by 4 percent. But removing all restrictions from growing row crops only reduced irrigated acreage 0.6 percent. The results of both analyses of sensitivity imply that assumptions about soil management practice levels should be dropped from river basin models unless special conditions exist. The analysis of assumptions concerned with minimum acreage constraints revealed that changing acreage constraints from the Benchmark (50 percent) to the 25 per- cent level reduced the irrigated acreage slightly but caused shifts from all subareas to Subarea 4. The only crop irrigated was potatoes which would have shifted completely into Subarea 4 had not minimum acreage con- straints been set. This was generally true at all demand levels. When minimum acreage constraints were raised to 75 percent it placed severe limits onSubareas l and 2. The effect was to preclude efficient location among sub— areas but not within. Realocation within these subareas, to provide efficient production of other crops, removed the potential for irrigating potatoes and total irrigated acreage decreased. More sensitivity might have occurred had other crops exhibited an economic potential for irrigation at other than forced conditions. The final analysis of shift-point sensitivity concerned variations in the assumed level of adopted crop producing technology. Essentially all the sensitivity 143 occurred in total projected acreage of irrigation due to increased levels of technology. Shifts of irrigated acreage did take place in Subarea 4 but only reflected the changes taking place in the Subregion total. A 20 percent increase in technology from Benchmark levels raised irri- gated acreage about 180 percent simply because 40,000 acres of hay crops became economically feasible to irri- gate. A 40 percent increase in technology above the Benchmark induced the same two crops (potatoes and hay) into the solution; although the relative increase was only about 110 percent as acreage requirements dropped sub- stantially with the yield increases. Throughout the analy- sis minimum acreage requirements precluded any shifting among subareas as yields increased. Had minimum acreage requirements been changed to production minimums the model may have been much more sensitive to technology changes. Implications This study has shown that sensitivity analysis, using aggregate criteria such as objective functions, can identify the relative importance of certain alternative model assumptions and the implications of errors or variance in these assumptions. This information is extremely useful in establishing model specifications. Yet, it is clear from the results of the shift-point analysis that aggre- gate criteria, such as the objective function, for the most part, fail to adequately identify important changes 144 in model subareas that may be masked by the more aggre- gative approach. Results from the sensitivity and shift-point analyses suggest that in future river basin models attempts should be made to more adequately account for projected livestock and livestock products. The current procedure of converting demands for livestock into demands for livestock feed creates an artificial situation in which the researcher must not only assume the livestock mix within class and appropriate feeding efficiency but the unique ration as well. If additional activities were added to the model to produce the livestock product requirements, several problems would be solved concurrently. The problem of locating livestock production is currently associated with the two-step process of convertinglivestock feed needs to crop demands and reconverting the projected cropping patterns back to livestock. This process requires ad- ditional assumptions about the mix of livestock in a particular subarea; partly tied to historical production mix and partly to the dominant ration components of the livestock class. For a feed crop exporting area the problem is further complicated; which Subarea or subareas should be considered as the exporters, and on what basis should the livestock be distributed among surplus crop producing subareas? There is also the compound problem of obtaining realistic cropping patterns among subareas. 145 Currently this process is handled through constraints to full efficiency in resource use. Minimum production requirements are placed on subareas and row-crop limi— tations are placed on certain soil resources. This process is supposed to provide sufficient quantities of the appropriate feed stuffs to accommodate a realistic distri- bution of livestock production throughout the basin. Introducing livestock activities that draw upon the crops produced for their feed requirements would tend to eliminate this problem. In the process of simultaneously meeting both the overall crop demands and livestock feed requirements, the livestock would be located in subareas that also produce the apprOpriate feed crops. Addition— ally, any excess feed grains, for export purposes, would be identified by Subarea. Conceptually, within each subarea an activity would be specified for the production of each type of livestock and livestock product required of the whole basin. Each activity would have the capability of meeting part of the overall demand for the particular livestock item. In so doing, certain quantities of feed grains and roughages Would be utilized per unit of livestock product produced. Upper and lower bounds, within fairly narrow ranges, could be placed on feed categories to allow some substitution of feed stuffs within the ration for any class of livestock. This would preclude the problems of 146 set rations and absolute crop requirements since overall demands could be set at minimum levels and determined, in the final analysis, by efficient ration selection en- dogenous to the model. Placing minimum and maximum bounds by subareas on total livestock product demands through an alternative specification of the model, would produce results quite similar to the current procedure. Since the type and location of feed production is related to livestock production, there would be added realism in the model. The projection of agricultural labor requirements would be facilitated by this process and would more nearly represent the likely future situation due to the greater corre- spondence among farm enterprises. There may also be greater reliability in the projected development potential with respect to feed crop-livestock combinations than with current procedures which identify potentials related to crop production alone. Moreover, further improvements would be expected from incorporation of transportation costs into the model if the difficult data problems associated with these costs could be resolved. The results of this analysis indicate that, of the five classes of assumptions tested, the assumption con- cerning soil management practices should be dropped from future river basin models. Practically no variation in Benchmark results was induced by deviations in this 147 assumption. The considerable effort in developing coef- ficients to implement the assumption is, therefore, not warranted. In this study the analysis of economic potential for irrigation has identified certain crops and subareas that appear to have a comparative advantage. This work needs to be extended by tracing the variability in model solutions through to their implications for agricultural population, employment, and income on a subarea basis. While the analysis of this study reflects only what is economically potential in the way of irrigation when the source of water and public development costs are not considered, it is true that there are locations in the State with much greater ground water resources than others. There is also considerable variability in the volumes of stream flow throughout the area. Thus, it is important to find answers to such questions as: What are the distri- butional consequences of a policy to expand supplemental irrigation? What are the implications of irrigation development for the large number of local communities that are dependent upon agricultural activity? If stream use is restricted by law, what are the implications if ground water is the sole source for irrigation? 148 Limitations This study looked at the sensitivity of the Bench- mark Model projections of total production costs and irrigated acreage as affected by alternative levels of five classes of assumptions. These assumptions are commonly used in NRED models to project agricultural activity for analysis in river basin studies. The brief example of variation in sensitivity due to the choice of alternative criteria for measuring sensi- tivity indicates that a variety of variables could have been chosen. Each choice may give somewhat different results and this must be kept in mind when evaluating relative sensitivities among the assumptions under study. One measure of sensitivity may indicate a low overall level of sensitivity for the entire study area while another measure may reveal substantial variation among subareas. While the assumptions and Model studied are similar if not identical to many of the NRED river basin models using linear programming techniques, the results of this study may not be directly applicable. It must be remembered that the Benchmark Model was specified for an area in Southern Michigan. Application can readily be made, therefore, to studies in the North Central region where production functions, type of farming practices, costs, and crops grown are quite similar. In other areas of the country these variables may be sufficiently different to 149 negate the direct application of these results. However, the general knowledge derived from this study will be useful in indicating the type of sensitivity that planners should remain aware of in evaluating results of projection models. Application of Results Each river basin study undertaken or participated in by USDA member agencies has, as part of the study guidelines, the requirement that data be developed to assist in-updating study results periodically. Such up- dating may be called for in several instances, for example, where particular projects within the study area are authorized for construction feasibility analysis, or where changes occur in the data upon which the study results are based. The latter situation is one that most often occurs either late in the study or several years following study completion. Usually, there is not sufficient time or funding for more than a partial analysis of the impacts associated with the changes. Sensitivity analysis, such as was carried out in this study, can readily provide the basis for rule of thumb estimates of the direction and extent of change in criterion variables due to either recognized errors in assumed levels of input coefficients or revised estimates of such controlling variables as population or regional demands. 150 Results of sensitivity analyses would make the user much more responsive to other agencies needs to analyze the effects of changes in study projections. The implications could be interpreted by NRED personnel for all users of study projections. In turn, the influence of other study participants determinations could also be traced back through the model if they happen to influence the underlying assumptions tested for sensitivity. Another direct use of the sensitivity analysis relates to the evaluation of economic potential for resource development (in this case the potential for irri- gation). Since the economic potential is expressed in terms of acres of particular soils, it is related to a particular location in addition to representing a specific level of development potential. With a soils map of the river basin under study the location of soils demonstrating an economic potential for irrigation could be identified under various assumptions. Cooperating agencies such as the Corps of Engineers, Soil Conservation Service, Bureau of Recreation, Federal Water Quality Administration, and Bureau of Sport Fisheries and Wildlife could then observe the location and type of cropping pattern associated with on-farm economic development potential. Such information would be useful to the con- struction agencies who would be able to divert planning resources from areas without a demonstrated economic potential for development to those areas that have 151 potential. Recreation and fish and wildlife interests could evaluate possible effects of changes in agricultural activity or reservoir development on their aspects of the planning process. And, possible changes in water quality due to different cropping patterns and more intensive management could be identified and planned for. Once development potentials were identified generally on a soils map and potential structure sites located, the area serviced by a particular site could be determined. By ranging upward on the on-farm costs of implementing the development activity in the linear programming model, that point where it is no longer profit— able to undertake the development from the farmers vieWpoint would be determined. The change in cost necessary to reach that point could then be compared against the costs associated with getting water to the land, in the case of irrigation. The cut-off point for economic feasibility from a particular source would then be related to to- pography and the length of transmission possible in view of the assumptions made concerning who was to bear the costs. BIBLIOGRAPHY BIBLIOGRAPHY Battelle Memorial Institute. The Usefulness of Computer Simulation in River Basin Analysis. Research Report to Natural Resources Economics Division, ERS, USDA, March 1967. Blaney, Harry F., and Criddle, Wayne D. Determining Water Requirements in Irrigated Areas from Climatological and Irrigation Data. SCS-TP-96 Bulletin, 1950. Cotner, Melvin L. "The Potential Role of Agricultural Land Drainage in Economic Growth." Unpublished Ph.D. thesis, Michigan State University, 1967. Dale, Robert F., and Shaw, Lawrence H. "The Climatology of Soil Moisture, Atmospheric Evaporative Demand, and Resulting Moisture Stress Days for Corn at Ames, Iowa." Journal of Applied Meteorology, IV, No. 6 (December 1965), 661-69. DeWolfe, Mildred R. Hay in the United States, Quantities Grown in a Normal Year, Surplus and Deficit Areas. USDA Statistical Bulletin 349, August, 1964. Dorfman, Robert; Samuelson, Paul A.; and Solow, Robert M. Linear Programming and Economic Analysis. New York: McGraw—Hill Book Company, Inc., 1958. Egbert, Alvin C., and Heady, Earl 0. Regional Adjustments in Grain Production, A Linear Programming Analysis. USDA Technical Bulletin 1241 and Supplement, June, 1961. . Regional Analysis of Production Adjustments in the Major Field Crops: Historical and Perspective. USDA Technical Bulletin 1294, November, 1963. , and Brokken, Ray F. Regional Changes in Grain Production, An Application of Spatial Linear Programming. Iowa Agricultural Experiment Station, Research Bulletin 521, Ames, January, 1964. 152 153 Fritschen, John F., and Atherton, James C. Resource Re- quirements for Meeting Projected Needs for Agricultural Production, Texas River Basins: A Methodological Supplement. Prepared by Farm Economics Division, ERS, USDA, for U.S. Study Commission, Texas, 1962. Grand River Basin Coordinating Committee. Comprehensive Water Resource Study, Grand River Basin, Michigan: Appendix O-Economic Base Study. Vol. X, January, Hadley, G. Linear Programming. Reading, Mass.: Addison- Wesley Publishing Company, Inc., 1962. Halter, Albert N., and Miller, Stanley F. River Basin Planning: A Simulation Approach. Eugene: Oregon State University, Special Report 224, November, 1966. Harl, Neil E. "Research Methods Adaptable to Legal- Economic Inquiry: Linear Programming and Simu- lation." Methods for Legal-Economic Research into Agricultural Problems. Iowa City: University of Iowa, Agricultural Law Center Monograph No. 8, 1966. Hill, Elton B., and Mawby, Russell G. Types of Farming in Michigan. East Lansing: Michigan Agricultural Experiment Station, Special Bulletin 206, September, 1954. Hodges, Earl F. Livestock-Feed Relationships 1909-1964. USDA Statistical Bulletin 337 and annual supple- ments, September, 1965. Hostetler, John E., and Cotner, Melvin L. Agricultural Activity in the Grand River Basin: A Projective Study. Natural Resources Economics Division, ERS, USDA, January, 1966. McKee, D. E.; Sundquist, W. B.; Bonnen, J. T.; Baker, C. B.; and Day, L. M. Equilibrium Analysis of Income Improving Adjustments on Farms in the Lake States DEirnyegion, 1965. St. Paul: University of Minnesota, Technical Bulletin 246, October, 1963. Michigan Conservation Needs Committee. An Inventory of Michigan Soil and Water Conservation Needs. East Lansing: Michigan Agricultural Experiment Station, October, 1962. 154 Michigan State University. Project '80: Rural Michigan Now and in 1980, Highlights and Summary. East Lansing: Michigan Agricultural Experiment Station, Research Report 37, February, 1966. Miller, Stanley F., and Halter, Albert N. "Simulation Systems in Making Water Resource Decision." Proceedings. Committee on Economics of Water Resource Development, Western Agricultural Eco- nomics Research Council, San Francisco, Calif., December, 1965. . "Computer Simulation of the Substitution Between Project Size and Management." American Journal of Agricultural Economics, LI, No. 5 (December, 1969), 1119—23. Ohio River Basin Survey Coordinating Committee. Main Report-Ohio River Basin Comprehensive Survey. Cincinnati: Ohio River Division, Corps of Engineers, August, 1969. Palmer, Wayne C. Meteorological Drought. Research Paper 45, Weather Bureau, USDC, February, 1965. U.S. Congress. House. Committee on Interior and Insular Affairs. "Water in Relation to Plant Growth." The Physical and Economic Foundation of Natural Resources I: Photosynthesis--Basic Featuresgf the Process, by Paul J. Kramer. Washington, D.C.: Government Printing Office, 1952, pp. 34-39. . "Evaporation in the Hydrologic Cycle." The Physical and Egonomic Foundation of Natural Resources I: Photosynthesis-~Basic Features of the Process, by C. W. Thornthwaite. Washington, D.C.: Government Printing Office, 1952, pp. 28-33. U.S. Congress. Senate. Report of the Senate Select Committee on National Water Resources. Sen. Report 29, 87th Cong. 1st. sess., 1961. U.S. Soil Conservation Service. Michigan. "Instructions for Determining Cropping Systems for Sloping Land." Technical Guide, Section III-B, March, 1964. VanBavel, C. H. M., and Verlinden, F. S. Agricultural onught in North Carolina. Raleigh: North Carolina Agricultural Experiment Station, Technical Bulletin 122, June, 1956. 155 ‘Whiteside, E. P.; Schneider, I. P.; and Cook, Ray. Soils of Michigan. East Lansing: Michigan Agricultural Experiment Station, Special Bulletin 402, De- cember, 1959. INhittlesey, Norman K., and Heady, Earl 0. Aggregate Economic Effects of Alternative Land Retirement Programs: A Linear Programming Analysis. ERS, USDA, in cooperation with Iowa Agricultural Experiment Station, USDA Technical Bulletin 1351, Ames, 1966. . APPENDICES APPENDIX A IRRIGATION IN SOUTHERN MICHIGAN--DATA AND ESTIMATING PROCEDURES APPENDIX A IRRIGATION IN SOUTHERN MICHIGAN--DATA AND ESTIMATING PROCEDURES Available Survey Data Specialized USDA Data One of the first tasks in any river basin study is the collection of basic data relating to the soils of each sub-study area. This is usually rather specialized data that must be tailored to the needs of the particular study. For instance, where there are tight limits on either the time or funds available for the study, wide use is made of the more general secondary data available. However, where warranted, more specific primary data is collected from the field. This frequently is the only source of such specialized information and is useful as a check against assumptions based on the more general data. Early in the planning stages of the Great Lakes Basin Survey, conducted in 1968, the Economic Research Service initiated a common soil classification system for the study area with the assistance of soil scientists of the Soil Conservation Service in each of the eight states participating in the study. Several hundred soil series were eventually grouped into twenty-three soil resource 156 157 groups (SRG's) for use in planning for the future develop— ment needs of the Basin. Each SRG represented soils with similar texture, slope, and hazard, such as wetness, erodibility, droughti— ness, or flooding. These soils were also grouped to re- spond similarly to management with relatively homogeneous crop yields and costs of production. Such groupings were intended to provide a basis to evaluate the relative pro- ductive capabilities of the soil resource in the studv area. Subsequently, a Soil Conservation Service-Economic Research Service team undertook an extensive data col- lection effort. Land use data for each of the 190 counties in the Great Lakes Study area were initially determined from the 1967-1968 Conservation Needs Inventory data. Meetings were held in central locations and in addition to District Conservationists from each county, the Area Conservationists and Regional Soil Scientiests were on hand to ensure continuity of the estimates over the broad area and to interpret particular soils groupings where required. At that point, major attention centered on cropland use. With the Conservation Needs Inventory as a point of departure, District Conservationists were asked to make whatever adjustments in reported acreages they felt were necessary to accurately represent the current situation. The adjusted crOpland acreage in each SRG category was then distributed among an array of crops normally grown 158 in each county. For each crop, the SRG acreage was further subdivided into the five following groups: (1) adequately drained or flood protected, (2) untreated drainage problems, (3) partially treated drainage problems, (4) flooding problems, and (5) combined flooding and drainage problems. For the major field crops and pasture types, estimates were made of normal yields under prevailing hazards. In the case of specialty crops, such as some fruits and vegetables, nursery crops, and sod, no attempt was made to derive a yield estimate. Instead, only the acreage grown on an SRG according to hazard was documented. In addition, estimates of the extent of irrigation in each county by crop by SRG were requested. As in the case of non-irrigated crops, no attempt was made to establish yields for specialty crops. . Table A-1 is a complete picture of the estimated extent of irrigation in the Southern Michigan Subregion by crop and subarea. These data reflect the best estimates of District Conservationists when asked to consider the crOp being irrigated and the soils upon which those crops are normally grown. Under these conditions irrigation estimates for the 42—county subregion reached slightly more than 119,900 acres in 1968, about 2 percent of available cropland. The primary crop being irrigated at that time was potatoes followed in order by sod, corn for grain, field beans, sweet corn, and strawberries. These 159 TABLE A—1.--Estimated acreage being irrigated by crop and by subarea, 1968, Southern Michigan Subregion, Great Lakes Basin Data Survey Subareas Sub- region Crop 1 2 3 4 5 Total Acres Corn, grain 730 4,007 8,000 12,807 Corn, silage 600 600 Apples 1,900 1,900 Peaches 1,200 1,200 Cherries 300 300 Other tree fruit 1,390 1,390 Strawberries 90 100 5,731 5,921 Blueberries 2,650 2,650 Raspberries 1,495 1,495 Hay 500 500 Sweet Corn 4,210 110 200 2,242 6,762 Green Peas 30 20 502 552 Tomatoes 15 4,389 4,404 Snap Beans 20 80 2,000 2,500 4,600 Asparagus 50 700 1,743 2,493 Cauliflower 200 200 Cucumbers 600 4,327 4,927 Carrots 100 100 Onions 100 1,700 1,800 Lettuce 100 100 Celery 2,050 2,050 Other vegetables 1,000 1,500 100 500 3,100 Cantaloupe, Melons 500 500 Mint 200 200 Nursery stock 800 800 Field Beans 350 10,123 10,473 Sugar Beets 800 800 Potatoes 6,300 1,000 595 19,000 3,450 30,345 Sod 6,307 4,000 4,829 1,300 16,436 Wormwood 200 200 Popcorn 300 300 Total 18,682 6,500 7,854 37,100 49,769 119,905 160 six crops accounted for nearly 70 percent of all irrigation in the study area. Subarea 5 was by far the most significant both in acreage and variety of crops irrigated. Subarea 4 was second, due to its dominent position in the irrigation of field beans and potatoes. Surprisingly, Subarea l, the five-county metropolitan area, was third entirely on the basis of specialty crops. The remaining two subareas had similar acreages of irrigation but a somewhat different array of crops grown. Michigan Water Resources Commission Data At approximately the same time as the USDA survey of Great Lakes Basin, the Michigan Water Resources Com- mission (MWRC) was completing the second phase of an irrigation study begun in 1958. This two-part study of irrigation by MWRC was an attempt to get a complete survey of all irrigators in the State for agricultural or other purposes. It was directed at the user, while the USDA survey was a poll of county and regional officials of the Soil Conservation Service. It also sought to identify the source of irrigation water used and the quantities applied both by county and river basin. Data from these two MWRC surveys, 1958 and 1968, help to indicate the shifts taking place in irrigation among crops and subareas of the Southern Michigan Subregion. There has been a general increase in irrigation over the 161 ten-year period of the two surveys (Table A-2). However, certain crops have not shared in that increase, namely pasture and hay crops, tomatoes, strawberries, raspberries, and tree fruit. The downward trend in the total acreage of most of these crops grown in the study area helps to explain such declines in the face of a general increase of nearly 60 percent in irrigation acreage. The one single crop that stands out in both periods is potatoes which was also the dominant irrigated crop in the USDA survey. Here the comparisons become a little more difficult due to the differences in reporting results of surveys (Table A—3). It is obvious that sod is also an important acreage in each survey, although it was un- reported in the 1958 MWRC survey, either because it was not irrigated at all or was insignificant and combined with some other category. Agricultural Census Data Both the USDA survey and the MWRC surveys were particularly interested in an accurate picture of the extent and location of irrigation in the State. The Census of Agriculture, on the other hand, is much more general and only recently has asked questions about irrigation from its respondents. In the 1959 Census only the total acreage irrigated is available (Table A—4). One would assume that this should coincide fairly closely with the 1958 MWRC survey. However, the Census data falls short 162 TABLE A-2.--Irrigation of agricultural and miscellaneous crops by crop and subarea, 1958 and 1968, Southern Michigan Subregion, Michigan Water Re- sources Commission Subareas Sub- Crop region 1 2 3 4 5 Total 1968 Acres Field Crops 258 395 1,121 1,783 6,543 10,100 Hay and Pasture 70 105 47 25 299 546 Total Vegetables 1,417 1,389 4,267 16,080 12,320 35,473 Melons, pickles (-) (310) .(270) (1,160) (2,369) (4,109) Truck Crops (1,177) (934) (3,277) (381) (6,407) (12,176) Tomatoes (-) (-) (-) (284) (1,430) (1,714) Potatoes (240) (145) (720) (14,255) (2,114) (17,474) Total Fruit 247 378 948 292 10,101 11,966 Strawberries (77) (65) (86) (162) (3,912) (4,302) Raspberries (-) (16) (36) (5) (690) (747) Blueberries (-) (-) . (8) (15) (2,276) (2,299) Tree Fruit (170) (297) (809) (110) (2,963) (4,349) Small Fruit (-) (-) (9) (-) (260) (269) Sod 1,615 2,187 2,569 205 1,298 7,874 Nursery Stock 381 165 722 27 2,723 4,018 Total 3,988 4,619 9,674 18,412 33,284 69,977 1958 Acres Field CrOps 203 101 510 1,395 1,637 3,846 Hay and Pasture 46 92 376 143 969 1,626 Total Vegetables 2,982 951 2,650 4,198 11,094 21,875 Melons, pickles (65) (20) (694) (1,001) (1,702) (3,482) Truck Crops (1,798) (656) (1,122) (247) (6,457) (10,280) Tomatoes (153) (3) (51) (52) (1,878) (2,137) Potatoes (966) (272) (783) (2,898) (1,057) (5,976) Total Fruit 421 113 496 241 11,456 12,727 Strawberries (111) (56) (205) (184) (4,536) (5,092) Raspberries (2) (27) (66) (13) (1,294) (1,357) Blueberries (35) (10) (8) (26) (1,651) (1,730) Tree Fruit (268) (20) (202) (18) (4,010) (4,518) Small Fruit (5) (-) (15) (-) (10) (30) Sod - - - - - - Nursery Stock 1,195 125 426 30 2,117 3,893 Total 4,847 1,382 4,458 7,006 27,273 43,967 Source: Working data 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.eHQeE qum .sme .BHo .meeuu mansuom .memmeum uuosm .soHueueoe> won use smuez .memmeuw uuosm use mmmuem .sme use EH0 .msoons .xeo mo umeu0w uoozuuex .memmesm usosm use seues .sme EH0 .wuoons .xeo mo umeuow uoo3usem .mEeHnosm sonoue usH3 use umouw .muHHHuueu .usoaeoesee H0>eH Hove: suH3 .msHeEeH useHa wo soHuHeomEooou HeHusem es» Eouu uemoH0>eu mmesonsu oHneHHe> mo euees use exosz .uoHHHu mH HHOm osu esos3 EeHnoum e mH sOHmoue usH3 .soHu IeNHHHuHew use soHuemHHuH on usommeu meeue He>eH .muHHHuueu 30H use quoemeo msHuHosIueue3 30H .uHoe mesosum .mesosH mm sesu msoE o» musem mmou hHsHe: .muosuo so mEeHnoum eue momoHe aeeum so soweoue use auH>Hssuoum 30H .mmesHusosouQ .ouesHeuu eHHsveH meHneu Heue3 sows uHHesOmeem suH3 meow .mmnocs me on as so assume ue meHo muHHm ou EeOH mH mums» memeo meow sH .HHom IQSm ueusumeu HesHm e squ musem meeoH emooH use smmo .emesHeHu Heusues noon >HeEeuuxw ou soon suH3 HesOHmmeHmeu on Ho>eH .uousHosH neese uesHeHu hHuoom esom usn .uesHeHu HHeS hHHeuesem .semHsoHZ eer msoHe messu usem suH3 .museHms >HHHs mHoseuuxe on H0>0H .uHmeH ou uoom emesHeuu eoemusn .meeue uoue IHUOmme exHHIsHmen es» sH mesmuee use mmEeSm .eeer suH3 sosou mHeEeuuxe 0s usHHHou use hHHHs ou He>eH 02 o .n .em 0 .n .e« nmoso sOnez use on: uses soHueueoe> e>Huez mEeHnoss usesemesez use mHeHseue: useues emesHeso use ueHHem emsoso uses Iemesez HHom .Hu.usoovII.HIU mHmdfi .NmmH .mueez soHue>Hemsou ueuez use HHom semHson no huousm>sH s4 "mousom 1190 Haw.wH Nhh.H he omm.H mmH mHm.VH va.H mmo.H mm wNm.m NHH.H NOH.m Heuoa mNm.m Hmm NN mmN on hhH.m hmv NmN m mmm va mem.H m mmm.v Nmm mH mmH mNH mom.v NmN oom w VHB.H mam mwh.H v Hmm.m mom VN omN N mhm.m mmH HNm m mhv vwm mON.N W mmm.N VHH v OHH o vvv.N Nm MbH N MNm med mah.H N mNo.N mmo m omw m omm.H mvN mOH on mmH om mmh H menus ooo.H Heuoe memss msIuHHsm useH Heuoa ashes msueh umsuo «Hues musumem useH eeu< seue: a sensa Heswuem sH uoz sH _ sH Imoso msMH useH uwsuo useHuooz emuensm H u a eeeeuos >uouse>sHsoz e umeuom ememsoe >uousm>sH ecsemsnsm cemsnosz caucusom .emuensm en coHuanuumse emu eceH mmmm -.~Io memes 191 .omma .mumscmn .flnmo .mmm .ommz z.mwsum m>Huowmoum m "cflmmm um>flm wcmuw may CH mufl>wpom HMHSuHDOHHm¢= \unommu may MOM mpmw mcflxuoz "mousom nmm.mvm.> mmv.nmm.a mvm.mmm.a mmm.amo.m mmm.amm.a omn.aam Hmuoa mmh.mNH mmm.oa mam.» ono.mm mnm.ma Hon 2 Hma.amv mmv~mom mmo.mma HON.Nm Hov.mv nvo.mv m nma.mno.a mmo.mnm owm.mmm mmm.oam wmo‘mom moa.am v mwm.mmm~a mmm.>om vmn.avm omm.omm www.mvm Hom.oma m oma.moa.a mom.vv Nmm‘mmm mma.mom omm.¢mv ooo.Nm 0N hmm.mvm.m Hmo.amm www.mmv mmm.vmm Ham~mmm mah.oma N noo.hnm Hmo.mh Hmm.mma mom.NH mnm.mm vmm.aa a mmnoa Hmuoe m v m N H msouw mmHmQSm HHom scammHQSm cmmfizoflz cumnusom .mmmHMQSm cam mmsoum HHOm ma mmms Eumm Icon mam macho Hocfle mom Umumsnwm .ommH cw magmaflm>m vanamouo wmpmeflummll.mnu mqm¢a 192 TABLE C+4.-—Estimated pastureland available in 1980, ad- justed for nonfarm uses by soil groups and subareas, Southern Michigan Subregion Subarea Soil Total Group 1 2 3 4 5 1,000 Acres 1 0.0 3.9 0.0 24.6 8.0 36.5 2 28.3 41.5 90.2 74.4 17.2 251.6 2c 2.4 20.4 20.8 24.3 5.4 73.3 3 14.0 35.4 116.8 51.9 50.3 268.4 4 4.1 24.2 29.9 109.2 23.5 190.9 5 4.8 12.6 12.7 66.4 17.4 113.9 M 2.8 10.4 58.4 20.3 7.9 99.8 Total 56.4 148.4 328.8 371.1 129.7 1,034.4 Source: Working data for the report, "Agricultural Activity in the Grand River Basin: A Projective Study," NRED, ERS, USDA, January, 1966. .woma .xuoscmn .wuomnoum 4 "Samoa uo>flm pcmuo 0:» CH >ua>fluo< amuouasowum v.ON m.mm v.0a m.N : H.m m.m m.na 0.5 o.m z o.ooa m.ma m.mm N.HH o.HH N.v m v.ma m.na m.m m.m m.m m o.ooa m.NH N.nm n.ma N.NH H.N v H.ma v.mN H.m m.oH m.n v o.ooa b.ma v.mH m.mv N.MH N.m m m.mm o.oa m.mm m.mN m.vN m o.ooa v.h N.mm «.mN m.NN m.m oN H.v w.m m.m m.ma N.v oN o.ooa m.w w.mN m.mm m.wa N.HH N m.MH o.ON v.5N o.mN N.om N o.ooH m.HN v.hm o. >.oa o. H N.m w.m o. m.N o. H m v m N H m v m N A woumnzm moumasm Hmuoe moouo msouw mmmuunsm mCOE¢ Hfiom mmumnom canvas HHom cowawusumom mo cofluonauumao cadamuoummm mo cowusnauumwo o.ooH o.ooa o.ooH o.ooa o.ooa amuoa o.ooa m.m m.w o.Nn m.NH m. z m. m. m.v m. H. z o.ooa v.Nv b.5N o.oa H.0H N.m m N.mH N.m m.N o.m m.m m o.ooa v.mN o.mm w.ma H.ma m.N v o.ON v.HN H.0N w.NH H.w v o.ooa v.5N N.ma o.nm v.ma N.m m H.5m m.va N.mm H.ma v.mN m o.ooH o.v N.NN «.ma H.Nv v.m oN N.m o.wa h.m m.mN o.wa oN o.ooa n.oa H.HN N.mm m.mN 5.5 N v.ma m.mN o.mm v.om m.mm N o.ooa o.wN w.vv b.v v.0N m.v a m.m m.h o. m.m m.N a m w m N , a m e m N a Hmuoe mwumnsm moouu mmumnsm moouo mononsm @c064 HHom mmwumnom cwnuwz Haom camamouu mo coflusnfluumflo canaoouu mo coflusnwuumao coflmmnoom cmmwnon cumLuSOm .mosoum aaom casufl3 mmumndm No cam mmoumnsm CHLuH3 maooum Haom >2 .omma CH mammawm>m pcmHmnoummm pom camaaouo mo mcoflusnfiuumflo ommucmoumm vmumeummnn.mno mqmde 1534 .vomN 6cm mmma .musuNooNumd mo momcmu "condom ON0.0 NON.O OOO NOO.N ONN.N OOO.N OOO.N OON.N NON.N ONN.N NOO NNN om: Nmuoe OON NOO OON NON NON NNN NNN OON NNN NNN NO NO musummm mono OOO NOO N N ONN OON NN NO ONN ONN O O mammm NuO ON NN N O NN ON O O N N N O Omoumuom OONHN OON NON NO NO OO ON NO OO NO OO NN ON Na: umnuo OOO ONO OON NON NNN NNN OON NON ONN NON NO OO ONNONNN ONN OON ON ON NO ON ON NN O N NO NN mammnaom NN ON O . ON N N O ON N ON N O NONHOO OOO NOO NO . ONN OO NNN NON NON NNN NON NO NO Oumo ONO NNN ONN OON ONN NON NNN NNN NON NNN ON OO pawn: NON ONN ON ON ON NO NO NO NN ON ON NN mmONNO cuoo ONN.N NON.N OON ONN NNN NNN ONO OOO NON NON NNN NON cNmuo cuoo mmuud COCOA voaa mmma vmma mmma voma mmma voma mmma vmma mmma voma mmma mono deuce m mmumnsm v mmumnsm m mmumnsm N mmumnaw H omumnsm vme paw mmmN .conmanm cnmNnoNz cumnusom .moumnom can aouo mo .mms mmmouom ocmamouu Nonmzlu.ouo mamth 195 .vOmN can mmma .muouNsoHuwd mo msmcmu “wousom NNN.N Nmm OOO mom ONN NON va vNN vN NN Ov mv mocmm loos» wwwxude on NO om mN NN O ON ON O O O m mcoNN INNE mmwm ONO.v NNm.m OOO OOO ONO NOO va.N NOO.N meO.N «om OvN OON .moN .NNE NNN: mNm.v NNN.O vmm.N NNN.m vvm ONO NNO OON.N mOO OON «NM mom mncmm noon» mcwxuNsu OON OON Nm vv mm mm OON VNN ON ON ON ON mocmm mnawa loony a moonm vmm OON ONN NON NO ONN VON mom mq vm hm OO mpcmm mmNm noon» O moon ONm.N ONN.N NNN ONN OON OON vov NNN mom ONN Om om mocmw mo>amu loos» a oNuumU vOmN mmmN «OON mmmN vOmN mmON «OON mmmN «OOH mmma vOma mmma muwca mausooum xooumm>wq m mmumnow v moumnsm m moumnsm N moumaom H mwumnsm can xooumm>NA OOON can mmmN .conmunom cmmflnoNz cuonusom .mmumnom Ocm max» >n .muosooua xooumm>NN can xUOumo>NN mo coNuUsooumuu.Nuo m4m<9 .v mNnma ou manna coNcmmEoom .mcoNusNom xumenocwm paw..OOma muouasoNumd uo momcmo "mousom 1£96 OOO.O ONO.O ONO OOO OOO.N ONN.N OON.N OOO.N NNO.N NON.N NON OOO mOO Nouoa NON.N OON ONN OON OO NON ONO NNN NNN ONN ONN OO ousummm mono ONN OON NN NO NN OO ON OO NN OO O NN NOO umnuo OOO OOO ON OON OO NNN NN OON OON ONN ON NO OONOONO NNN NON O OO NN OO NN OO ON NN O ON mOONNO :noo NO ON O N ON NN N O ON N N N mmoumuom NON OOO O N OO ONN NN NN ONN ONN N O Ocmmm NNO ONN ONN ON ON OO NO NO OO OON O NO NO OcOONNoO OO NN O O N N ON O N N N N OmNumO OON OOO ON NO ON OO ONN NON NN NNN NN NO Oumo NOO ONN.N NO OON NNO NNN OON ONO OO NON OO NNN cuoo NOO ONO ON ONN NON ONN NO ONN ONN NON ON ON yams: mmuo< ooo.H omaa vOmH ommH «Oma omma vOmH ommd vOmH omma coma omma vomH Q ouU Nouoa m mmumnsm v mmumnsm m mwumndm N mmumnsm A moumndm mcoNomunom savanna: cumcusom .mmumnom >2 .OOON zuN3 ooummeoo vm>oEmu coNuaEdmmm musummm acocmeumm nuNz OOON New mmmmuom woumm>umc mo coNuomnoua xnmficocmmnu.mlu mqmda 197 .coNuDHow xumsgocmm paw .m oNnma ou mNnoe cowcmofioom .OOOH muouasofiumd mo msmcou "mousom ONN.OON ON0.00 mma.om Omm.OH MNOOOH Omh.HN Omm.mm mNm.MN ON0.0m Hmh.ma HNN.ON ONHOO 9:4 musummm mouu NNN OON ON NO ON NO OO NN NON NN NN NN sou NOO nonuo OOmOH ONN.N Hma OON NON NOO ONN MOO OOO ONO NO OON cou awamwa< NOOON ono.m OON bmv OON ONO Omv Ohm MOO.H OON Om. NNN cou ommNNm N.500 Omm.HH chv.m NHO.H NNO OON.m omN.m mam mph vmn.m OON NOO ONO .u3o mwoumuom NON.O mO0.0 m ma mOO.N Hmm.m OOv NNN OO0.0 Noo.m HN OO .uzo mammm Nun OOH.HH NON.m OMO NOO Ohm.a OONOH OOOOH mmm.a Nmm.m OOH OOMON NOO.N .sn mammnhom mmO.N OOo.H Hmm NON mma Hm ONO.H OON mvv vhm av OO .32 mmaumm MNN.ON omm.ON OOH.H OOOOM MNO.N mmO.m Nvm.ON mvm.m mmv.O Nva.m ONO va.N .on name OOOOOOH OONONO ON0.0 NONONH OO0.00 ONOOOH OO0.0H ON0.0N moo.m OON.NN vmn.v ONh.h .on. cuou OO0.0N omm.Nm Omm.a mvh.v NN0.0 Nvm.b Ohv.v NO0.0 MOOOMH vmm.b Hmm moo.m .sn anon: mafia: ooo.H OOOH OOON omma OOOH omma OOON OOOH OOON OOON VOON OOmH «OOH mafia: mono Hmuoa m moumnsm v moumnsm m mmumnsm N mmumnom H ooumnsm aconoNndm :mmNnoNz anonusom .mmHMQSm up .OOOH nuN3 wounmeoo om>o€mu coNumEdmmm ousummm uGoCMEhom nuNS OOON CH cowuoonoum mono UNoNM Momma mo coNuomnoum gumenocmmln.mlo mamma 198 .ONONNOO unnumcou OOONN .N magma ou magma :oNcmmEoum .GONNDNOO xnmenocmm "mouoom ONN.OON OOO.ON OO0.00 ONO.NN OON.OO NNO.O umoo NOOOO IOI IOI IOI lot lo... IOI mHDummm quCmEHmm OOO.NN ONN.N OOO.N ONN.ON NOOON OOO.N ONONOOO.OOONO0NO NO0.0 OOO OOO OOO ONN.N NON OOO nmnao NNN.ON NOO.N ONN.N OON.N ONO.O ONN OONOONO NOO.NN OOO NNO.N ONN.N OO0.0 ONO OOONNO auoo ON0.0N OOO.N OON.O NOO.N OON.N OOO Omoumgom OON.ON ON NON.O ONN OON.NN NO Ocmmm NNO OOO.NN ONO NNO.N ONO.N NON.O NOO.N mammnmom OON.N NNN NO OON NON ON OONHOO NOO.O OOO OON ONN.O OOO.N NNO Oumo OON.NO OON.O OON.NN OOO.N NOO.O NNN.N cuoo NNO.NN ONO.N NOO.O ONO.N ONO.NN NOO ummgz ONONNOO OOO.N coflmmunsm m mwnmnsm O mmumnsm m mmumnsm N mmnmndm N mmumnom mouu Q .mconmH IQSO cmmNnoNz cumgusom .mmumnom an Omm>OEmH QONumEommm musummm ucmcmENmm QuNB OOON cN mmouo UNONO Hohme chUSUOHQ mo umoo Nmuou pmuomnoum xnmenocmmnl.ONlo mqmde 199 TABLE C-ll.--Objective functions of alternative Benchmark Model formulations with irrigation allowed, Southern Michi- gan Subregion, 1980a Technology Level *Infeasible. a1964 constant dollars. Model 1 2 3 Dollars Dollars Dollars 1 183,774,370 175,325,090 168,675,550 2 172,200,420 164,358,270 158,015,490 3 172,620,540 164,336,190 157,922,990 4 173,450,025 165,559,780 159,131,510 5 195,637,590 186,459,150 179,420,970 6 195,642,280 186,435,830 179,269,680 7 197,533,790 187,897,370 180,798,630 8 278,549,160 261,365,860 250,965,930 9 258,674,110 244,222,510 234,490,090 10 258,063,980 244,040,730 234,092,590 11 262,246,860 246,332,730 236,462,810 12 300,112,370 278,672,690 267,592,330 ‘ 13 294,706,780 277,796,340 266,609,740 14 309,387,160 281,859,270 270,463,820 15 411,863,890 356,782,890 337,090,270 16 371,295,140 328,711,540 313,959,280 17 355,136,240 325,499,200 312,295,480 18 388,992,690 335,391,190 317,426,420 19 459,600,070 387,581,240 362,465,050 20 424,557,550 376,319,419 357,574,380 21 * 401,494,530 369,848,440 22 184,014,030 175,590,440 168,772,420 23 183,718,718 175,190,460 168,628,530 24 279,832,610 261,482,950 251,079,530 25 278,345,990 261,243,090 250,912,890 26 414,316,430 357,822,500 337,844,310 27 411,511,400 356,524,340 336,851,390 28 182,896,540 174,422,640 167,242,010 29 277,220,320 260,024,470 249,013,170 30 281,123,000 265,399,100 257,035,850 31 417,821,620 362,291,700 343,511,690 Source: Alternative model solutions.