Random horizon stochastic dynamic Slutsky equation under preference uncertainty

Abstract

This paper extends Slutsky's classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes, preferences and life-span. Utility maximization leading to a set of ordinary wealth-dependent demand functions is performed. A dual problem is set up to derive the wealth compensated demand functions. This represents the first time that wealth-dependent ordinary demand functions and wealth compensated demand functions are obtained under these uncertainties. The corresponding Roy's identity relationships and Slutsky equations in a random horizon stochastic dynamic framework with uncertain preferences are derived. The analysis incorporates realistic characteristics in consumer theory and advances the conventional microeconomic study on consumption to a more realistic optimal control framework.