Discount function

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:

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

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

$$U(\{c(t){\}}_{t=0}^{\mathrm{\infty }})=\underset{0}{\overset{\mathrm{\infty }}{\int }}f(t)u(c(t))dt$$

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.