Editing Discount function

{{short description|Economic model which weighs rewards based on when they are received}}

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:

<math display=block>
  U\Bigl( \{c_t\}_{t=0}^\infty \Bigr) = \sum_{t=0}^\infty {f(t)u(c_t)}
</math>

Total utility in the [[continuous-time]] case is given by:

<math display=block>
  U \Bigl( \{c(t)\}_{t=0}^\infty \Bigr) = \int_{0}^\infty {f(t)u(c(t)) dt}
</math>

provided that this integral exists.  

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

==See also==
*[[Discounted utility]]
*[[Intertemporal choice]]
*[[Temporal discounting]]

==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.

[[Category:Intertemporal economics]]