# Discount function

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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 having a negative first derivative and with (or in continuous time) defined as consumption at time *t*, total utility from an infinite stream of consumption is given by

- .

Total utility in the continuous-time case is given by

provided that this integral exists.

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

## See also[edit]

## References[edit]

- Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," ;;Journal of Economic Literature;;, vol. 40(2), pages 351-401, June.