Optimizing the Spatial Structure of the Agricultural Production Function

Abstract

Important characteristics of spatial agricultural production functions are derived by introducing a non-negative curvilinear spatial demand function for production input intensities. Given the usual neoclassical rationale assumptions of spatial demand for capital and labor inputs under competitive environment of farming in developing agricultural economies, the optimal production levels are determined by optimizing spatial demand for production inputs. Decreasing price-to-transport costs ratio (that is, decrease in the prices of capital goods or increase in freight rates) and increasing wage-to-travel costs ratio (that is, increase in labor wages or decrease in the travel rate) expand the limits of the (spatial) optimal boundary of the demand for agricultural capital goods and labor input respectively. These effects occur on account of the operation of (positive) spatial price gradient and (negative) wage-gradient in the market region. It may be noted that elasticities of demand for production factors are spatially variant and have significant effects on the alterations in the structure of agricultural production. However, the spatial optimal solution of production has a complicated relationship with them. The price elasticity has negative and wage elasticity has positive spatial gradients in the market region. Farmers located in the periphery of the market region are not much affected by the proportionate changes occurring in the prices of agricultural capital goods but are more sensitive to the proportional changes in labor wages. Because of a decreasing trend in capital input demand and increase in labor input with distance from the market, capital-product diminishes with a decreasing rate and labor-product increases with an increasing rate in the spatial structure of agricultural production. As a result, capital-labor ratio falls toward zero, which raises profit rate per unit of capital investment especially in the outer part of the market region. The equilibria of optimal production with price elasticity as well as of capital intensity with labor employment (that is, capital-labor ratio as unity) determine spatial limits of the optimal production zone which is shifted outward subject to the provision of cheap transportation, stabilizing market prices and/or increasing wage rate at the market center. It will help in extending outwardly the optimal spatial limits of capital investment and will mobilize capital resources of farmers in the periphery for efficient and competitive capital-dominated farming.