TITLE:
Optimal Consumption under Uncertainties: Random Horizon Stochastic Dynamic Roy’s Identity and Slutsky Equation
AUTHORS:
David W. K. Yeung
KEYWORDS:
Optimal Consumption; Uncertain Inter-Temporal Budget; Stochastic Dynamic Programming; Slutsky Equation
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.2,
January
20,
2014
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 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 a set of random horizon stochastic dynamic Slutsky equations
are then derived. The extension incorporates realistic characteristics in
consumer theory and advances
the conventional microeconomic study on consumption to a more realistic optimal
control framework.