In this paper we introduce a dynamical system for the formulation and computation of spatial price equilibrium problems in quantity variables. The set of stationary points of the system corresponds to the set of solutions of the variational inequality problem governing the problem. We propose the Euler-type method for the computation of the equilibrium pattern and provide convergence results. We then demonstrate that the algorithm can be implemented on a massively parallel architecture and illustrate its performance on the Thinking Machine's CM-2 architecture. This research represents the first implementation of a massively parallel approach for the computation of either dynamical systems or variational inequality problems arising in economics.