The consequences of a decision often do not all occur simultaneously. Thus a decision maker may have to consider his preferences for some consequence x at a time t1 and a consequence y at a time t2. This indicates the distinguishing characteristic of time preferences: the consequences accrue at two or more points in the future. A typical example is the stream of income and cash flow resulting from a long-term Investment. In this case it may be natural to divide time into discrete periods (e.g., months or quarters), and to use (x1, x2, …, xn) to indicate a time stream of consequences, where xi indicates the consequences in time period i. Alternatively, we may have a continuous stream of consequences, which we shall denote by x(·), where x(t) is the consequence at time t. For example, in consumption problems x(t) might represent a decision maker's rate of consumption at time t for each component of a commodity bundle. Because (1) many continuous-time problems can be reasonably formulated as discrete-time problems without oversimplifying the issues involved, and (2) the development of procedures for analyzing continuous-time problems are analogous to those for discrete ones, we emphasize the discrete-time problems in this chapter.

Two important features affecting time preferences are (1) the timing of the resolution of uncertainties and (2) the horizon to be used. Both of these considerations, discussed in Section 9.1, influence greatly the appropriateness of a given approach for specifying one's preferences.