Discount function
Economic model which weighs rewards based on when they are received
title: "Discount function" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["intertemporal-economics"] description: "Economic model which weighs rewards based on when they are received" topic_path: "economics" source: "https://en.wikipedia.org/wiki/Discount_function" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary 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 c (or c(t) in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by:
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 \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.
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.
::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::