The Exchange Model

The exchange model is the simplest of all general equilibrium models. Studying it will show us the directions to follow when studying more complex models like those that include production or take explicitly into account time and uncertainty. This chapter introduces the exchange model defined by the equilibrium manifold and the natural projection. It presents proof that the equilibrium manifold is indeed a smooth manifold. The smooth manifold structure implies that the natural projection is a smooth map. In terms of comparative statics, this tells us that equilibrium prices can be considered as depending linearly on the fundamentals defining an economy in sufficiently small neighborhoods of regular equilibria.