The Competitive Nonlinear Spatial Equilibrium Analysis: An Empirical Study

Abstract

Regional differences in factor endowments, variations in the underlying conditions of regional demand and supply and concomitant inequalities in factor and product prices all contribute to the determination of spatial equilibrium. Attainment of an equilibrium is analogous to a solution which constitutes optimum level and pattern of regional production, and consumption and trade flow of the commodity in consideration. Literature abounds with linear spatial equilibrium studies, most of which are analyzed by iterative procedures for optimum allocation of discrete quantities. However, the recent development' and efficiency of nonlinear quadratic programming has made it feasible for a spatial equilibrium problem to be solved simultaneously for optimum level and pattern of regional production, and consumption and trade flow among regions. Obviously such efficiency has fostered attempts to develop empirical applications [3; 6]. In the application, however, two qualifications may be made regarding alternative use of regional resources and continuous regional demand and supply functions. First, in the nonlinear quadratic programming model, the continuous supply functions are meant to account for regional supply potentials in response to variations in prices. However, when they are linear, the supply functions may need to be restrained within some historically observed extreme because the use of estimated function outside the range of observation may result in an unrealistic solution. In other words, without some measure of restriction on regional resources to be allocated to the production of commodity under consideration, the spatial equilibrium analysis could result in an infeasible solution in that some regions may be expected to produce beyond their productive capacities. Under such circumstances, the problem of misallocation may be reduced to manageable size by imposing restrictions on regional resources. Secondly, there may not be the need to limit the spatial equilibrium model to two variable cases. If indi-