Multiperiod Consumption-Investment Decisions

Abstract

Publisher Summary The simplest version of the multiperiod consumption-investment problem considers a consumer with wealth w1, defined as the market value of his assets at the beginning of period 1, which must be allocated to consumption c1 and a portfolio investment w1–c1. The portfolio will yield an uncertain wealth level w2 at the beginning of period 2, which must be divided between consumption c2 and investment w2–c2. Consumption-investment decisions must be made at the beginning of each period, until the consumer dies and his wealth is distributed among his heirs. The consumer's objective is to maximize the expected utility of lifetime consumption. This chapter reviews uncertainty models of the multiperiod consumption-investment problem considered by Edmund Phelps, Nils Hakansson, and Jan Mossin and presents a more general multiperiod consumption-investment model but one that nevertheless leads to interesting hypotheses about observable aspects of consumer behavior. The main result is the proposition that if the consumer is risk averse, that is, the utility function for lifetime consumption is strictly concave and markets for consumption goods and portfolio assets are perfect, 3 then the consumer's observable behavior in the market in any period is indistinguishable from that of a risk averse expected utility maximizer who has a one-period horizon.