https://wiki.sarg.dev/index.php?action=history&feed=atom&title=Discount_functionDiscount function - Revision history2026-04-17T23:43:04ZRevision history for this page on the wikiMediaWiki 1.44.2https://wiki.sarg.dev/index.php?title=Discount_function&diff=707205&oldid=previmported>OlliverWithDoubleL: short description, links2024-10-26T06:56:30Z<p>short description, links</p>
<p><b>New page</b></p><div>{{short description|Economic model which weighs rewards based on when they are received}}<br />
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In [[economics]], a '''discount function''' is used in [[economic model]]s to describe the [[Weighting|weights]] placed on rewards received at different points in time. For example, [[discrete time| if time is discrete]] and [[utility]] is time-separable, with the discount function {{math|''f''(''t'')}} having a negative [[first derivative]] and with {{mvar|c{{sub|t}}}} (or {{math|''c''(''t'')}} in continuous time) defined as [[consumption (economics)|consumption]] at time {{mvar|t}}, total utility from an infinite stream of consumption is given by:<br />
<br />
<math display=block><br />
U\Bigl( \{c_t\}_{t=0}^\infty \Bigr) = \sum_{t=0}^\infty {f(t)u(c_t)}<br />
</math><br />
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Total utility in the [[continuous-time]] case is given by:<br />
<br />
<math display=block><br />
U \Bigl( \{c(t)\}_{t=0}^\infty \Bigr) = \int_{0}^\infty {f(t)u(c(t)) dt}<br />
</math><br />
<br />
provided that this integral exists. <br />
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[[Exponential discounting]] and [[hyperbolic discounting]] are the two most commonly used examples.<br />
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==See also==<br />
*[[Discounted utility]]<br />
*[[Intertemporal choice]]<br />
*[[Temporal discounting]]<br />
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==References==<br />
* 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.<br />
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[[Category:Intertemporal economics]]</div>imported>OlliverWithDoubleL