Discounted utility
Encyclopedia
Discounted utility is an economics
term in which economists, accountants, underwriters, and other financial analysts include the future discounted value
of a good in its present value
. This can be thought of as the idea of impatience, or the valuing of future enjoyment less than present enjoyment.
Such value calculations take the form:
where
is the value of some choice 
at time 
. 
, so that 
can be interpreted as a 'discounting factor'. In financial analysis, 
may represent lost opportunities, such as the risk-free
rate of return on a government, municipal, or corporate bond
.
In economics, however, where
represents so-called utility
, the interpretation of
is less straightforward. Sometimes it is explained as the degree of a person's patience. Given the interpretation of economic agents
as rational
, this exempts time-valuations from rationality judgments, so that someone who spends and borrows voraciously is just as rational as someone who spends and saves moderately, or as someone who hoards his wealth and never spends it.
Some formulations treat
not as a constant, but as a function 
that itself varies over time, for example in models which use the concept of hyperbolic discounting
. This view is consistent with empirical
observations that humans display inconsistent time preference
s. For example, experiments by Tversky
and Kahneman
showed that the same people who would choose 1 candy bar now over 2 candy bars tomorrow, would choose 2 candy bars 101 days from now over 1 candy bar 100 days from now. (This is inconsistent because if the same question were posed 100 days from now, the person would ostensibly again choose 1 candy bar immediately instead of 2 candy bars the next day.)
Despite arguments about how
should be interpreted, the basic idea is that all other things equal
, the agent prefers to have something now as opposed to later (hence
), and returns over time add up (hence 
).
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
term in which economists, accountants, underwriters, and other financial analysts include the future discounted value
Discounts and allowances
Discounts and allowances are reductions to a basic price of goods or services.They can occur anywhere in the distribution channel, modifying either the manufacturer's list price , the retail price , or the list price Discounts and allowances are reductions to a basic price of goods or services.They...
of a good in its present value
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
. This can be thought of as the idea of impatience, or the valuing of future enjoyment less than present enjoyment.
Such value calculations take the form:
where
is the value of some choice at time . , so that can be interpreted as a 'discounting factor'. In financial analysis, may represent lost opportunities, such as the risk-freeRisk-free interest rate
Risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss. The risk-free rate represents the interest that an investor would expect from an absolutely risk-free investment over a given period of time....
rate of return on a government, municipal, or corporate bond
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...
.
In economics, however, where
represents so-called utilityUtility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
, the interpretation of
is less straightforward. Sometimes it is explained as the degree of a person's patience. Given the interpretation of economic agentsHomo economicus
Homo economicus, or Economic human, is the concept in some economic theories of humans as rational and narrowly self-interested actors who have the ability to make judgments toward their subjectively defined ends...
as rational
Rationality
In philosophy, rationality is the exercise of reason. It is the manner in which people derive conclusions when considering things deliberately. It also refers to the conformity of one's beliefs with one's reasons for belief, or with one's actions with one's reasons for action...
, this exempts time-valuations from rationality judgments, so that someone who spends and borrows voraciously is just as rational as someone who spends and saves moderately, or as someone who hoards his wealth and never spends it.
Some formulations treat
not as a constant, but as a function that itself varies over time, for example in models which use the concept of hyperbolic discountingHyperbolic discounting
In behavioral economics, hyperbolic discounting is a time-inconsistent model of discounting.Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the...
. This view is consistent with empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
observations that humans display inconsistent time preference
Time preference
In economics, time preference pertains to how large a premium a consumer places on enjoyment nearer in time over more remote enjoyment....
s. For example, experiments by Tversky
Amos Tversky
Amos Nathan Tversky, was a cognitive and mathematical psychologist, a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his early work concerned the foundations of measurement...
and Kahneman
Daniel Kahneman
Daniel Kahneman is an Israeli-American psychologist and Nobel laureate. He is notable for his work on the psychology of judgment and decision-making, behavioral economics and hedonic psychology....
showed that the same people who would choose 1 candy bar now over 2 candy bars tomorrow, would choose 2 candy bars 101 days from now over 1 candy bar 100 days from now. (This is inconsistent because if the same question were posed 100 days from now, the person would ostensibly again choose 1 candy bar immediately instead of 2 candy bars the next day.)
Despite arguments about how
should be interpreted, the basic idea is that all other things equalCeteris paribus
or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...
, the agent prefers to have something now as opposed to later (hence
), and returns over time add up (hence ).