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