The Computation of Economic Equilibria by Path Methods.

摘要

An introduction to the economic equilibrium model is given and it is demonstrated that a path method can be used to compute equilibria for pure exchange economies in a nonlinear setting. Next, a model is described for an economy in which the utility functions are piecewise linear and the consumption and production sets are polyhedral. It is shown that an equilibrium for this economy is the solution to a system of bilinear equations subject to certain linear inequality and complementarity constraints. Two approaches are discussed for computing equilibria for such economies. The first is the bilinear complementarity algorithm (BCA) and the second is the homotopy retraction algorithm (HRA). Convergence proofs are given for both methods using the general theory for path methods described above. No conclusion could be drawn as to which algorithm was superior, but both performed well enough that it appears that much larger equilibrium problems also can be solved efficiently by these methods.