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Exponential utility
 
 
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In economics
Economics

File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
 exponential discounting is a specific form of the discount function
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...
, used in the analysis of choice over time (with or without uncertainty
Uncertainty

Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, Uncertainty_principle , statistics, economics, finance, insurance, psychology, sociology, engineering, and information science....
). Formally, exponential discounting occurs when total utility
Utility

In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility....
 is given by

where ct is consumption
Consumption (economics)

Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally consumption is defined by opposition to Production theory basics....
 at time t, is the exponential discount factor, and u is the instantaneous utility function.

In continuous time, exponential discounting is given by

Exponential discounting implies that the marginal rate of substitution
Marginal rate of substitution

In economics, the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of satisfaction....
 between consumption at any pair of points in time depends only on how far apart those two points are.






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In economics
Economics

File:Ballard Farmers' Market - vegetables.jpgEconomics is the Social sciences that studies the Production theory basics, Distribution , and Consumption of Good and Service ....
 exponential discounting is a specific form of the discount function
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...
, used in the analysis of choice over time (with or without uncertainty
Uncertainty

Uncertainty is a term used in subtly different ways in a number of fields, including philosophy, Uncertainty_principle , statistics, economics, finance, insurance, psychology, sociology, engineering, and information science....
). Formally, exponential discounting occurs when total utility
Utility

In economics, utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one's utility....
 is given by

where ct is consumption
Consumption (economics)

Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally consumption is defined by opposition to Production theory basics....
 at time t, is the exponential discount factor, and u is the instantaneous utility function.

In continuous time, exponential discounting is given by

Exponential discounting implies that the marginal rate of substitution
Marginal rate of substitution

In economics, the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of satisfaction....
 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.

For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, some alternatives
Hyperbolic discounting

In behavioral economics, hyperbolic discounting refers to the empirical finding that people generally prefer smaller, sooner payoffs to larger, later payoffs when the smaller payoffs would be imminent....
 have more empirical support.