economics Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...

exponential discounting is a specific form of the

discount function 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 f(t) having a negative fi ...

, used in the analysis of choice over time (with or without

uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable ...

). Formally, exponential discounting occurs when total

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 given by :

U(\_^)=\sum_^\delta^(u(c_t)),

where ''c''_''t'' is

consumption Consumption may refer to: *Resource consumption *Tuberculosis, an infectious disease, historically * Consumption (ecology), receipt of energy by consuming other organisms * Consumption (economics), the purchasing of newly produced goods for curren ...

at time ''t'',

\delta

is the exponential

discount factor Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Efficient ...

, and ''u'' is the instantaneous utility function. In

continuous time In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "po ...

, exponential discounting is given by :

U(\_^)=\int_^ e^u(c(t))\,dt,

Exponential discounting implies that the

marginal rate of substitution In economics, the marginal rate of substitution (MRS) is the rate at which a consumer can give up some amount of one good in exchange for another good while maintaining the same level of utility. At equilibrium consumption levels (assuming no exte ...

between consumption at any pair of points in time depends only on how far apart those two points are. Exponential discounting is not dynamically inconsistent. A key aspect of the exponential discounting assumption is the property of dynamic consistency— preferences are constant over time. In other words, preferences do not change with the passage of time unless new information is presented. For example, consider an investment opportunity that has the following characteristics: pay a utility cost of C at date t=2 to earn a utility benefit of B at time t=3. At date t=1, this investment opportunity is considered favorable; hence, this function is: −δC + δ 2 B> 0. Now consider from the perspective of date t=2, this investment opportunity is still viewed as favorable given −C + δB> 0. To view this mathematically, observe that the new expression is the old expression multiplied by 1/δ. Therefore, the preferences at t=1 is preserved at t=2; thus, the exponential discount function demonstrates dynamically consistent preferences over time. For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, alternatives like

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 ...

have more empirical support.

References

*{{cite book , first1=Andreu , last1=Mas-Colell , author1-link=Andreu Mas-Colell, author2-link=Michael Whinston , first2=Michael D. , last2=Whinston, author3-link=Jerry Green (economist) , first3=Jerry R. , last3=Green , title=Microeconomic Theory , publisher=Oxford University Press , year=1995 , pages=733–736 , isbn=0-19-507340-1 , url=https://books.google.com/books?id=KGtegVXqD8wC&pg=PA733 Intertemporal economics

See also

References