Differential Topology and General Equilibrium with Complete and Incomplete Markets

The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations, and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. This text combines two features. First, order conditions (of agents' maximization problems) and market clearing conditions, instead of aggregate excess demand functions. Then the application to that "extended system" of a homotopy argument, which is stated and proved in relatively elementary manner.