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Application of Linear and Nonlinear Programming Models in Specifying Land Use, Spatial Equilibrium and Prices for Agriculture

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Part of the book series: Lecture Notes in Operations Research and Mathematical Economics ((LNE,volume 15))

Abstract

In this paper we deal with the application of spatial programming models to solve certain problems in interregional competition, land use and production capacity of U.S. agriculture. The studies were initiated partly because programming models and modern computers now allow the analysis of a large number of interdependent sectors represented by regions and commodities. They also were initiated for policy purposes to determine how large U.S. agricultural capacity is and the need for supply control and price support measure; to determine the amount of food the U.S. might export under different foreign aid policies and the effect of the level of output on different farm regions and rural communities; and to determine the cost of land retirement under alternative programs. In these respects, a major use of the models was in an analysis for the National Advisory Commission on Food and Fiber in its recommendations for future agricultural policy.1 /

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References

  1. Heady, Earl O. and Mayer, Leo V. Food Needs and U.S. Agriculture in 1980. Technical Papers-Vol. 1. National Advisory Commission on Food and Fiber. Washington, 1967.

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  2. In addition to the study by Heady and Mayer cited earlier, see the details in the following: Egbert, Alvin C. and Heady, Earl O. Regional Adjustments in Grain Production, A Linear Programming Analysis. USDA Tech. Bul. 1241; Heady, Earl O. and Egbert, Alvin C. Activity Analysis in Allocation of Crops in Agriculture. (in Manne and Markowitz, editors: Cowles Foundation Monograph 18. Studies in Process Analysis pp. 161–214. Wiley, New York, 1963); Egbert, Alvin C., Heady, Earl O. and Brokken, Ray F. Regional Changes in Grain Production, An Application of Spatial Programming. CAED Report 14T. Center for Agricultural and Economic Adjustment; Egbert, Alvin C. and Heady, Earl O. Regional Analysis of Production Adjustments in Major Field Crops Historical and Prospective. (bulletin forthcoming); Heady, Earl O. and Egbert, Alvin C. Programming Regional Adjustments in Grain Production to Eliminate Surpluses. Journal of Farm Economics, Vol. XLI, No. 4, 1959; and Heady, Earl O. and Egbert, Alvin C. Mathematical Programming of Regional Production Patterns, -forthcoming; Heady, Earl O. and Skold, Melvin. Projections of U.S. Agricultural Capacity and Interregional Adjustments in Production and Land Use with Spatial Programming Models. Iowa Agr. and Home Econ. Exp. Sta. Res. Bul. 539; Skold, Melvin D. and Heady, Earl O. Regional Location of Production of Major Field Crops at Alternative Demand and Price Levels, 1975. USDA Tech. Bul. 1354; Heady, Earl O. and Whittlesey, Norman K. A Programming Analysis of Interregional Competition and Surplus Capacity of American Agriculture. Iowa Agr. and Home Econ. Exp. Sta. Res. Bul. 538; Whittlesey, Norman K. and Heady, Earl O. Aggregate Economic Effects of Alternative Land Retirement Programs: A Linear Programming Analysis. USDA Tech. Bul. 1351; Brokken, Ray C. and Heady, Earl O. Interregional Adjustments in Crop and Livestock Production in the United States. (In process); Heady, Earl O. and Egbert, Alvin C. Efficient Regional Allocation of Farm Products and Programmed Supply Prices. Agr. Econ. Res. Vol. 16, pp. 1–11; Egbert, Alvin C., Heady, Earl O. and Brooken, Ray F. Regional Changes in Grain Production - An Application of Spatial Linear Programming, Iowa Agr. Exp. Sta. Bul. 521.

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  3. For discussion of aggregation bias, see the following: Barker, R. and Stanton, B. F. “Estimation and Aggregation of Firm Supply Functions.” Journal of Farm Economics, Vol. 47, pp. 701–712, Aug. 1965

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  4. Stovall, J. C. “Sources of Error in Aggregate Supply Estimates,” Journal of Farm Economics, Vol. 48, pp. 477–480, May 1966

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  5. Hartley, H. O. “Total Supply Functions Estimated From Farm Samples.” Unpublished paper. Department of Statistics, Iowa State University, 1962; Day, Richard, “On Aggregating Linear Programming Models of Production.” Journal of Farm Economics, Vol. 45, pp. 797–813, Nov. 1963

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  7. The basic demand functions come from the following: Brandow, G. E: Interrelations Among Demands for Farm Products and Implications for Control of Market Supply. Penn Agr. Exp. Sta. Bul. 680, 1961. Slope coefficients of demand functions were derived from Brandow’s estimates and 1965 exports for wheat, feed grains and oilmeals were added.

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  8. Takayama, T. and Judge, G. G. “Spatial Equilibrium and Quadratic Programming.” Journal of Farm Economics, Vol. 46, pp. 67–93, February 1964.

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  9. cf. Schrader, L. F. and King, G. A. “Regional Location of Beef Cattle Feeding.” Journal of Farm Economics, Vol. 44, pp. 64–81, February 1962; and Judge, G. G. “Interregional Price and Allocation Models of the Agricultural Sector.” Paper presented before the Interregional Competition Research Methods Workshop, North Carolina State University, 1963.

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  10. Takayama, T. and Judge, G. G. “An Interregional Activity Analysis Model for the Agricultural Sector.” Journal of Farm Economics, Vol. 44, pp. 349–365, May 1964.

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  12. Samuelson, P. A. “Spatial Price Equilibrium and Linear Programming,” American Economic Review, Vol. 42, pp. 283–303, June 1952.

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Heady, E.O., Hall, H.H. (1969). Application of Linear and Nonlinear Programming Models in Specifying Land Use, Spatial Equilibrium and Prices for Agriculture. In: Fox, K.A., Sengupta, J.K., Narasimham, G.V.L. (eds) Economic Models, Estimation and Risk Programming: Essays in Honor of Gerhard Tintner. Lecture Notes in Operations Research and Mathematical Economics, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46198-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-46198-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04638-7

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