Discount function

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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[edit]


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.