Ex Post Uncertainty and the Consumer Problem

Abstract

Wealth uncertainty may be resolved before consumption in which case consumption is optimal. But if uncertainty remains at the consumption level, after allocative decisions are made, ex post relative consumption is suboptimal. Therefore, ex ante the consumer has to balance attitudes to risk with underlying preferences. We study this problem in the context of expected utility with preferences over two goods, one of which is subject to additive ex post uncertainty. State preferences determine the utility gambles, and attitudes to risk evaluate these gambles, in order to choose an optimal consumption gamble. We study how risk aversion interacts with preferences to determine the direction and size of comparative statics effects using lattice programming, monotone comparative statics, methods. Comparative statics depend on the evaluation of comparative utility loss along the distribution of uncertainty and lattice theoretic properties allow us to determine how these relate to preferences and consumption. With the global regularity imposed by LSE (quasi-supermodularity) properties in direct value lattices we study the comparative statics of comparative risk aversion, income and underlying risk. We give conditions for a more risk averse consumer to choose a less or more risky consumption bundle and show that the direct LSE property determines comparative statics under first order stochastic dominant changes in ex ante uncertainty. Extensive examples demonstrate.