Multicommodity 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 paper is intended to study a solution method for the multicommodity spatial equilibrium problem by extending the parametric algorithm of Ahn and Seong. Since the parametric algorithm does not rely on optimization framework, it can be directly applied to multicommodity problems irrespective of whether the integrability condition is satisfied or not. Two methods, the serial and the parallel methods are suggested to solve multicommodity spatial problems. The serial method solves the problem by decomposing it into a sequence of single commodity subproblems and solving them in a sequential order. The parallel method iterates between the quantity adjustment step and the price adjustment step for all commodities, respectively. In the latter case, simultaneous equations should be solved. The two algorithms exploit the network structure of the problems and are expected to enhance computational efficiency. In particular, the serial method proves to converge to an equilibrium under some regularity conditions, and is readily dependent on the parametric algorithm of a single commodity. The principal characteristic of the suggested algorithms is the directness of the solution steps without resorting to an optimization framework. The principal characteristic of the suggested algorithms is the directness of the solution steps without resorting to an optimization framewark.