Uncertainty and General Equilibrium

Abstract

This chapter consists of two parts; first, a standard introduction to choice under uncertainty, and second, how uncertainty is introduced into general equilibrium theory. It starts with lotteries and utility over lotteries, it defines Von Neumann–Morgenstern expected utility and the axioms that justify its form; then it introduces the Arrow–Pratt measure of absolute risk aversion, CARA and CRRA utility functions, stochastic dominance, Jensen’s inequality and discusses how risk aversion explains insurance, risk pooling and portfolio selection among risky assets, including Tobin’s preference for liquidity. Then the chapter mentions state-dependent utility and subjective expected utility. A discussion of Allais’ and Ellsberg’s paradoxes is followed by an introduction to prospect theory. The notion of informational cascades allows an enlightening use of Bayes’ Rule. Then the chapter moves to how uncertainty is introduced into general equilibrium theory; after a section on traditional marginalist authors, the chapter describes the intertemporal general equilibrium with contingent commodities and introduces the Radner equilibrium with uncertainty. There follows a short introduction to incomplete markets and sunspot equilibria. The chapter ends with a summing up of conclusions on general equilibrium theory, which is found difficult to defend. The online Appendix explains the Anscombe–Aumann approach to the existence of subjective expected utility; then it reports Wilson’s example of non-existence of equilibrium with incomplete markets, and finally it reports an interesting page on insurance by Alfred Marshall that gives a taste of how traditional authors dealt with uncertainty.