A discount function is used in

economic model In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework desi ...

s to describe the weights placed on rewards received at different points in time. For example, if time is discrete and

utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...

is time-separable, with the discount function

f(t)

having a negative first derivative and with

c_t

(or

c(t)

in continuous time) defined as consumption at time ''t'', total utility from an infinite stream of consumption is given by :

U(\_^\infty)=\sum_^\infty

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

U(\_^\infty)=\int_^\infty {f(t)u(c(t)) dt}

provided that this integral exists. Exponential discounting and

hyperbolic discounting In economics, hyperbolic discounting is a time-''inconsistent'' model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers. According to the disc ...

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. Intertemporal economics

See also

References