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Discount function

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Economic model which weighs rewards based on when they are received

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 ct (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 } t = 0 ∞ ) = ∑ t = 0 ∞ f ( t ) u ( c t ) {\displaystyle U{\Bigl (}\{c_{t}\}_{t=0}^{\infty }{\Bigr )}=\sum _{t=0}^{\infty }{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 {\displaystyle U{\Bigl (}\{c(t)\}_{t=0}^{\infty }{\Bigr )}=\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

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.
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