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Discount function

Economic model which weighs rewards based on when they are received

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated July 31, 2026

In economics, a discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility is time-separable, with the discount function f(t) having a negative first derivative and with ct (or c(t) in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by:

U{\Bigl (}\{c_{t}\}_{t=0}^{\infty }{\Bigr )}=\sum _{t=0}^{\infty }{f(t)u(c_{t})}

Total utility in the continuous-time case is given by:

U{\Bigl (}\{c(t)\}_{t=0}^{\infty }{\Bigr )}=\int _{0}^{\infty }{f(t)u(c(t))dt}

provided that this integral exists.

Exponential discounting and hyperbolic discounting are the two most commonly used examples.

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Discounted utility

In economics, discounted utility is the utility of some future event, such as consuming a certain amount of a good, as perceived at the present time as opposed to at the time of its occurrence. It is calculated as the present discounted value of future utility, and for people with time preference for sooner rather than later gratification, it is less than the future utility.

Intertemporal choice

In economics, intertemporal choice is the study of the relative value people assign to two or more payoffs at different points in time. This relationship is usually simplified to today and some future date.

Time preference

In behavioral economics, time preference is the current relative valuation placed on receiving a good at an earlier date compared with receiving it at a later date. Applications for these preferences include finance, health, and climate change.