Evolution Variational Inequality Model of a Dynamic Adjustment Process in a Spatial Market Equilibrium Problem

In this paper, we consider a dynamic spatial market equilibrium problem with inequality market clearance conditions. Both supply and demand market prices are treated as equilibrium factors along with quantities shipped between the markets. The rates of change for each of the factors are functions of market conditions such as supply-demand relations and net gains from shipments between markets. After a brief review of the theory of evolution variational inequalities, an evolution variational inequality (EVI) model of the dynamic spatial market equilibrium problem is introduced. Under the maximal monotonicity conditions for the supply, demand, and transaction cost functions, an existence and uniqueness result for the solution path is established. Finally, we consider a finite- difference scheme - a discretized version of the EVI model. Within this single framework, both questions of the dynamics and convergence of an algorithm are addressed.