Two-Period Models of Consumption Decisions Under Uncertainty: a survey

One of the classical formulations of the theory of choice between saving and consumption is that of Irving Fisher, whose work culminated in his book The Theory of Interest [8]. In the two-period model introduced by him the individual consumer has a preference ordering over present and future consumption, and is able to lend and borrow in a perfect capital market at a given rate of interest. Especially after its reconsideration by Hirshleifer [10] the model has become very popular and has found many applications in theoretical work. In its simplest version, this model postulates a consumer with exogenously given amounts of income in the two periods and no opportunities for real investment; it is then used to analyse the dependence of consumption on the rate of interest and on (lifetime) income. In the absence of uncertainty, and with amounts consumed as the only arguments in the utility function, there is clearly no basis for portfolio choices; the consumer invests total savings in the highest-yielding asset available, and he is never a borrower in one asset and a lender in another. The general equilibrium implication of this model is evidently that the rate of return must be the same on all assets, which thereby become perfect substitutes for each other.