Discount function

Short description: Economic model which weighs rewards based on when they are received

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({ct}t=0∞)=∑t=0∞f(t)u(ct)

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

U({c(t)}t=0∞)=∫0∞f(t)u(c(t))dt

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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