Discount function

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

$f(t)$ and with $c(t)$ defined as consumption at time t,

total utility is given by

$U(\{c_t\}_{t=0}^\infty)=\sum_{t=0}^\infty {f(t)u(c_t)}$.

Total utility in the continuous-time case is given by

$U(\{c(t)\}_{t=0}^\infty)=\int_{0}^\infty {f(t)u(c(t)) dt}$

provided that this integral exists.

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

See also

• Discounted utility
• Intertemporal choice
• Temporal discounting

References

For a comprehensive review, see: 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.