Economic modeling approaches: optimization versus equilibrium

The paper discusses three general classes of nonlinear programming models. Our objective is to show how to represent optimization problem, such as nonlinear programs, in a compact format using extended mathematical programming. This is a useful tool, especially in cases when complementarity representation, such as mixed complementarity problems, could be difficult to apply. We reflect on the special features of the abstract neoclassical growth model with infinite horizon and illustrate four distinct approaches to computing equilibrium transition paths. The relationship between optimization and equilibrium modeling is explored. We conclude with a test of a new model representation (extended mathematical programming) using two common general equilibrium studies in the literature: Ramsey and Negishi. The new framework allows to define complementarity problems for a model formulated as an optimization problem, thus the resulting model becomes in fact a complementarity problem.