Chapter 36 Equilibrium analysis with non-convex technologies

This chapter surveys the state of the art regarding the ArrowDebreu model of a Walrasian economy, consisting of a finite number of agents and commodities where one assumes perfect information, complete markets, no market imperfections, such as externalities, public goods, or non-convexities in consumption or production; firms are price-taking profit maximizers, and households are price-taking utility maximizers. In such a world, the basic properties of the classical ArrowDebreu model consist of the existence of competitive equilibria, the first and second welfare theorems, the computation of equilibria, and the local uniqueness and finiteness of equilibria. The chapter discusses that it is useful to adopt Walras' original conception of a competitive equilibrium as a solution to a (nonlinear) system of equations. Convexity plays an essential role in Scarf's analysis, both in the derivation of the market excess demand function from optimizing behavior on the part of agents and in the existence of a fixed-point that follows from Brouwer's theorem. Scarf's algorithm and its generalizations are the primary means of doing comparative statics in general equilibrium models. Computable general equilibrium models have replaced activity analysis and inputoutput analysis as the basic method of analyzing tax policy in national economies or trade policies among nations.