Parametric method for computing network spatial equilibria

Abstract

Spatial equilibrium models determine regional production, consumption, and interregional commodity flows in a spatially separated market so as to achieve a price equilibrium. This thesis presents a parametric solution method for finding a single commodity spatial equilibria given nonlinear excess demands and linear transportation costs. The motivation of the parametric method stems from the pivoting type iteration concept as a model integration scheme in the model decomposition and integration approach for more general market equilibrium models which include the spatial equilibrium problems. To support the concept of model linkage and also provide motivation for the pivoting type iteration concept, an illustrative iterative model integration scheme which is based on the local approximation method is also presented. The suggested parametric algorithm for spatial equilibria alternates between a parametric quantity adjustment operation and a parametric price adjustment operation until an equilibrium solution is reached. It is shown that the algorithm converges in a finite number of iterations. Four major characteristics of the suggested parametric network algorithm are worth noted. First, it can explicitly handle the problems with nonlinear supply and demand functions. Second, each step of the algorithm is similar to pivoting steps of the mathematical programming theory. Third, the algorithm utilizes the intrinsic characteristics of the network structure resulting in the enhanced computational efficiency. Last one is the directness of the solution steps without resorting to an optimization framework.