LINEAR ECONOMIC MODELS

A parametric procedure for linear programming is shown to solve the bilinear complementarity problem, of which a special case is the problem of computing a competitive equilibrium of a piecewise linear economic model. THE PROBLEM OF COMPUTING an equilibrium of an economic model requires ordinarily the construction of a fixed point of a correspondence (H. Scarf [15]). R. Mantel [11] has shown, however, that for piecewise linear models the problem can be reduced to finding a "coordinate-wise value-preserving activity," which is an instance of the "bilinear complementarity problem" studied here. In this note, I present a constructive computational theory for the "regular" case in which certain nondegeneracy assumptions are satisfied. The algorithm can be implemented as a parametric linear programming procedure. An alternative algorithm for computing solutions has been proposed recently by G. Dantzig, B. C. Eaves, and D. Gale [3].