Disequilibrium and variational inequalities

Abstract

In this paper we introduce a new market disequilibrium model in a spatial economic setting, which generalizes a recent spatial disequilibrium model to the asymmetric case. We derive two alternative variational inequality formulations of the market conditions, in the case of price rigidities and/or controls, and discuss existence and uniqueness properties. We then propose a decomposition algorithm which resolves the variational inequality problem into three distinct and simpler variational inequality subproblems with special structure, which are then solved in sequential fashion. Any appropriate algorithm can then be used to solve the individual subproblems. The first variational inequality subproblem, however, is identical to the one governing the well-known spatial price equilibrium problem and, hence, a plethora of algorithms are available for its solution. We conclude with computational experience with the decomposition algorithm on large-scale market examples. This work bridges the study of disequilibrium and equilibrium problems via the theory of variational inequalities.