Intertemporal choice with savoring of yesterday

The problem of intertemporal choice arises when outcomes are received in different moments of time. This paper presents an axiomatic model of intertemporal choice when consumption in the previous moment of time contributes to utility evaluation of consumption in the current moment. This model generalizes classic discounted utility theory (also known as constant or exponential discounting) in two ways. First, in every moment of time, a decision maker derives utility not only from current consumption but also from “residual” consumption in the previous moment of time. Second, these utilities are discounted with weights that are essentially a quasi-hyperbolic discounting function. The paper presents an application of the proposed model to the problem of optimal consumption and savings given a fixed income (wealth). When a decision maker derives satisfaction from both instantaneous consumption as well as a share of consumption in the previous moment of time, optimal consumption path is cyclic—periods of relatively high consumption are interchanged with periods of relatively low consumption. These cycles decay over time. Asymptotically, the consumption path exhibits conventional properties (constant, increasing or decreasing over time when a gross interest rate multiplied by discount factor is correspondingly equal to, greater than, or less than one).