Computation of Economic Equilibria for an Exchange Economy with Linear Production Technologies

The general economic equilibrium model has become an important mechanism for applications in such fields as development economics, international trade, macroeconomics, public finance, Internet economics and communication spectrum economy. In these applications, the computation of economic equilibria plays an important role and has attracted a lot of attention. Although several numerical procedures have been developed in the literature, how to efficiently compute economic equilibria still remains to be a challenging problem and appeals for more efficient alternatives. This project aims to develop a more efficient path-following method for computing economic equilibria of an exchange economy with linear production technologies. The emphasis will be on fully exploiting differentiability of the problem. As that in interior-point methods, a smooth path that leads to an economic equilibrium will be constructed by introducing an extra variable for deforming from a trivial exchange economy to the original one. Sard’s theorem and perturbations will be applied to derive the existence of the path. To follow the path numerically, an efficient predictor-corrector method will be proposed. Numerical comparisons with existing path-following methods will be carried out. The ultimately expected outcome of the project will be a more efficient path-following method for computing economic equilibria of an exchange economy with linear production technologies.