In
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
:
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'',
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
:
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.
See also
*
Temporal discounting
In economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good or some cash at an earlier date compared with receiving it at a later ...
*
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 ...
*
Intertemporal choice Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the r ...
*
Keynes–Ramsey rule In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is express as a differential equation relating the rate of change of consumption with interest rates, time pre ...
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