Optimal Investment, Heterogeneous Consumption and Best Time for Retirement

TL;DR

This paper develops a model for optimal investment, heterogeneous consumption, and retirement timing, revealing how wealth levels influence consumption choices and retirement policies, with implications for economic behavior and policy design.

Contribution

It introduces a non-homothetic utility maximization framework with non-concave luxury utility, analyzing optimal consumption and retirement strategies using PDE and stochastic control methods.

Findings

Individuals consume only basic goods at low wealth levels.

Optimal retirement occurs at a universal marginal utility level.

People tend to retire earlier if labor costs increase faster than income.

Abstract

This paper studies an optimal investment and consumption problem with heterogeneous consumption of basic and luxury goods, together with the choice of time for retirement. The utility for luxury goods is not necessarily a concave function. The optimal heterogeneous consumption strategies for a class of non-homothetic 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. It is also shown that individuals prefer to retire as time goes by if the marginal labor cost increases faster than that of income. The main tools used in analyzing the problem are from PDE and stochastic control theory including variational inequality and dual transformation. We finally conduct the simulation analysis for the featured model parameters to investigate practical and economic implications by providing their figures.