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 Template:Math having a negative first derivative and with Template:Mvar (or Template:Math in continuous time) defined as consumption at time Template:Mvar, total utility from an infinite stream of consumption is given by:
<math display=block>
U\Bigl( \{c_t\}_{t=0}^\infty \Bigr) = \sum_{t=0}^\infty {f(t)u(c_t)}
</math>
Total utility in the continuous-time case is given by:
<math display=block>
U \Bigl( \{c(t)\}_{t=0}^\infty \Bigr) = \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 alsoEdit
ReferencesEdit
- 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.