Discount function explained

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(\{c _{t\}} ^{inf ty} ^{t =0} {f(t)u(c _{t)}} .

Total utility in the continuous-time case is given by

U(\{c(t)\} ^{inf ty} _{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.