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
- and with defined as consumption at time t,
total utility is given by
Total utility in the continuous-time case is given by
provided that this integral exists.
For a comprehensive review, see: 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.