Combining a path method and parametric linear programming for the computation of competitive equilibria

A path-following philosophy (continuation method, global Newton method) is used to compute equilibria for piecewise linear economies while taking advantage of the linear structure of the model. The existence of a path leading through certain faces of a polyhedral set to an equilibrium point is demonstrated. Computational experience is reported which indicates that this method is promising for models dealing with many commodities and relatively few consumers.Most of this paper has been extracted from the author's doctoral dissertation for the Department of Operations Research at Stanford University; the author would like to express indebtedness to his advisor, R. Wilson. Major revisions were made while the author was at Bell Laboratories in Whippany, New Jersey.