On Convergence of the PIES Algorithm for Computing Equilibria

Abstract

Equilibria in market models with continuous market supply functions can be obtained by computing fixed points. With an activity analysis representation of production, fixed-point algorithms would converge slowly. Further, since the market model here is of a partial equilibrium nature, the market demand function may not exhibit the integratability condition, precluding the formulation of the market equilibrium problem as an economic surplus maximization problem. We examine an iterative algorithm, the PIES method, for locating equilibria in markets whose production is described by optimization over a finite set of activities and whose econometric demand function does not possess the integrability property. Convergence properties of the algorithm along with existence and uniqueness of market equilibrium are summarized.