Computational Experience in Solving Equilibrium Models by a Sequence of Linear Complementarity Problems

This paper presents a modeling format and a solution algorithm for partial and general economic equilibrium problems. It reports on computational experience from a series of small to medium sized problems taken from the literature on computation of economic equilibria. The common characteristic of these models is the presence of weak inequalities and complementary slackness, e.g., a linear technology with alternative activities or various institutional constraints on prices. The algorithm computes the equilibrium by solving a sequence of linear complementarity problems. The iterative (outer) part of this algorithm is a Newton process. For the inner part, we use Lemke's almost complementary pivoting algorithm. Theoretical results for the performance of this algorithm are at present available only for the partial equilibrium cases. Our computational experience with both types of models, however, is encouraging. The algorithm solved all nine test problems when initiated at reasonable starting points. Five of these nine problems are solved for several different starting points, indicating a large region over which the algorithm converges. Our results demonstrate that the algorithm is economical in terms of the number of pivots, function evaluations and CPU time.