Spatial Equilibrium in U.S. Agriculture: A Quadratic Programming Analysis

Abstract

A spatial competitive equilibrium for the crop and livestock sectors of the U.S. agricultural economy is approximated. Agricultural commodities are classified into three mutually exclusive classes : primary, intermediate and desired. Primary commodities represent available resources ; intermediate commodities are produced only as inputs for further production; desired commodities are wanted either for consumption or for other uses outside the system (export). The 48 contiguous states and the District of Columbia are partitioned into 10 markets, which are further partitioned into a total of 103 crop producing regions. In each market, demands for 10 desired commodities are represented by functions, linear in commodity prices. Production of crops and livestock and intermarket commodity shipments are represented by linear activities. The objective function maximizes aggregate producer profits. Since the demand functions are linear, total revenue is quadratic in the prices of desired commodities, hence the quadratic programming formulation. In the results, estimated prices for desired commodities are lower than observed prices and, with minor exceptions, estimated quantities exceed observed quantities.

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