Optimal Investment, Heterogeneous Consumption, and Best Time for Retirement

Abstract

We study an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The optimal heterogeneous consumption strategies for a class of nonhomothetic utility maximizer are shown to consume only basic goods when the wealth is small, to consume basic goods and make savings when the wealth is intermediate, and to consume almost all in luxury goods when the wealth is large. The optimal retirement policy is shown to be both universal, in the sense that all individuals should retire at the same level of marginal utility that is determined only by income, labor cost, discount factor as well as market parameters, and not universal, in the sense that all individuals can achieve the same marginal utility with different utility and wealth. We also show that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income.