Discount function - Alchetron, The Free Social Encyclopedia

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 ∞ ) = ∑ t = 0 ∞ f ( t ) u ( c t ) .

Total utility in the continuous-time case is given by

U ( { c ( t ) } t = 0 ∞ ) = ∫ 0 ∞ f ( t ) u ( c ( t ) ) d t

provided that this integral exists.

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

References

Discount function Wikipedia

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