Discount function

Short description: Economics concept

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 [math]\displaystyle{ f(t) }[/math] having a negative first derivative and with [math]\displaystyle{ c_t }[/math] (or [math]\displaystyle{ c(t) }[/math] in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by

[math]\displaystyle{ U(\\{c_t\\}_{t=0}^\infty)=\sum_{t=0}^\infty {f(t)u(c_t)} }[/math].

Total utility in the continuous-time case is given by

[math]\displaystyle{ U(\\{c(t)\\}_{t=0}^\infty)=\int_{0}^\infty {f(t)u(c(t)) dt} }[/math]

provided that this integral exists.

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

## See also

* Discounted utility
* Intertemporal choice
* Temporal discounting

## References

* 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.

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