Applied mathematics

Optimal consumption under an uncertain inter-temporal budget: stochastic dynamic Slutsky equations

D. W. K. Yeung<sup>ab

a</sup> 199034, St. Petersburg State University, Russian Federation
^b SRS Consortium for Advanced Study in Cooperative Dynamic Games, Shue Yan University, Hong Kong, China

Abstract: This paper extends Slutsky's classic work on consumer theory to a stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertain future incomes. 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. A set of stochastic dynamic Slutsky equations is then derived. The extension incorporates realistic characteristics in consumer theory and advances the conventional static microeconomic study on consumption to a stochastic dynamic optimal control framework. Bibliogr. 17. Il. 2. Table 2.

Keywords: al consumption, uncertain inter-temporal budget, stochastic dynamic programming, slutsky equation.

UDC: 517.929

Received: March 21, 2013

Language: English