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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 c_t (or c(t) in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by:

$U\left(\right\{c_t{\}}_{t=0}^{\infty })=\sum _{t=0}^{\infty }f\left(t\right)u\left(c_t\right)$

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

$U\left(\right\{c\left(t\right){\}}_{t=0}^{\infty })={\int }_0^{\infty }f\left(t\right)u\left(c\right(t\left)\right)dt$

provided that this integral exists.

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

• Discounted utility
• Intertemporal choice
• Temporal discounting

• 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.