Revealed preference
Encyclopedia
Revealed preference theory, pioneered by American
economist
Paul Samuelson
, is a method by which it is possible to discern the best possible option on the basis of consumer behavior. Essentially, this means that the preference
s of consumers can be revealed by their purchasing habits. Revealed preference theory came about because the theories of consumer demand
were based on a diminishing marginal rate of substitution
(MRS). This diminishing MRS is based on the assumption that consumers make consumption decisions based on their intent to maximize their utility. While utility
maximization was not a controversial assumption, the underlying utility functions
could not be measured with great certainty. Revealed preference theory was a means to reconcile demand theory by creating a means to define utility functions by observing behavior.
. For instance, if the consumer buys the bundle of goods A over the bundle of goods B, where both the bundles of goods are affordable, it is said that A is directly revealed preferred over B. It is assumed that the consumer's preferences are stable over the observed time period, i.e. the consumer will not reverse his relative preferences regarding A and B.
As a concrete example, if a person chooses the bundle {2 apples, 3 bananas} over an affordable alternative {3 apples, 2 bananas}, then we say that the first bundle is revealed preferred to the second. It is assumed that the first bundle of goods is always preferred to the second, and that the consumer purchases the second bundle of goods only if the first bundle becomes unaffordable.
This assumption implies that preferences are transitive
. In other words, if we have bundles A, B, C, ..., Z, and A is revealed preferred to B, which is in turn revealed preferred to C and so on, then it follows that A is revealed preferred to C through Z. Under these hypotheses, economists are able to chart indifference curves which are employed in many models of consumer theory.
p1y1+p2y2 from the preceding equation we derive that the ,consumer prefers bundle of goods (x1,x2) over bundle of goods (y1,y2) or we can say that bundle of goods (x1,x2) is directly revealed preferred to (y1,y2).
as seen in the following example. Let pa be the price of apples and pb be the price of bananas, and let the amount of money available be m=5. If pa =1 and pb=1, and if the bundle (2,3) is chosen, it is said that the bundle (2,3) is revealed preferred to (3,2), as the latter bundle could have been chosen as well at the given prices. More formally, assume a consumer has a demand function x such that they choose bundles x(p,w) and x(p',w') when faced with price-wealth situations (p,w) and (p',w') respectively. If p·x(p',w') ≤ w then the consumer chooses x(p,w) even when x(p',w') was available under prices p at wealth w, so x(p,w) must be preferred to x(p',w').
If there exist only an apple and an orange, and an orange is picked, then one can definitely say that an orange is revealed preferred to an apple. In the real world, when it is observed that a consumer purchased an orange, it is impossible to say what good or set of goods or behavioral options were discarded in preference of purchasing an orange. In this sense, preference is not revealed at all in the sense of ordinal utility. One of the critics of the revealed preference theory states that "Instead of replacing 'metaphysical' terms such as 'desire' and 'purpose'" they "used it to legitimize them by giving them operational definitions." Thus in psychology, as in economics, the initial, quite radical operationalist ideas eventually came to serve as little more than a "reassurance fetish" for mainstream methodological practice."
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
economist
Economist
An economist is a professional in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy...
Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...
, is a method by which it is possible to discern the best possible option on the basis of consumer behavior. Essentially, this means that the preference
Preference
-Definitions in different disciplines:The term “preferences” is used in a variety of related, but not identical, ways in the scientific literature. This makes it necessary to make explicit the sense in which the term is used in different social sciences....
s of consumers can be revealed by their purchasing habits. Revealed preference theory came about because the theories of consumer demand
Demand
- Economics :*Demand , the desire to own something and the ability to pay for it*Demand curve, a graphic representation of a demand schedule*Demand deposit, the money in checking accounts...
were based on a diminishing 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 utility.-Marginal rate of substitution as the slope of indifference curve:...
(MRS). This diminishing MRS is based on the assumption that consumers make consumption decisions based on their intent to maximize their utility. While utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
maximization was not a controversial assumption, the underlying utility functions
Consumer theory
Consumer choice is a theory of microeconomics that relates preferences for consumption goods and services to consumption expenditures and ultimately to consumer demand curves. The link between personal preferences, consumption, and the demand curve is one of the most closely studied relations in...
could not be measured with great certainty. Revealed preference theory was a means to reconcile demand theory by creating a means to define utility functions by observing behavior.
Theory
The revealed preference theory is trying to understand the preferences of a consumer among bundles of goods available to him, given his budget constraintBudget constraint
A budget constraint represents the combinations of goods and services that a consumer can purchase given current prices with his or her income. Consumer theory uses the concepts of a budget constraint and a preference map to analyze consumer choices...
. For instance, if the consumer buys the bundle of goods A over the bundle of goods B, where both the bundles of goods are affordable, it is said that A is directly revealed preferred over B. It is assumed that the consumer's preferences are stable over the observed time period, i.e. the consumer will not reverse his relative preferences regarding A and B.
As a concrete example, if a person chooses the bundle {2 apples, 3 bananas} over an affordable alternative {3 apples, 2 bananas}, then we say that the first bundle is revealed preferred to the second. It is assumed that the first bundle of goods is always preferred to the second, and that the consumer purchases the second bundle of goods only if the first bundle becomes unaffordable.
This assumption implies that preferences are transitive
Transitive relation
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....
. In other words, if we have bundles A, B, C, ..., Z, and A is revealed preferred to B, which is in turn revealed preferred to C and so on, then it follows that A is revealed preferred to C through Z. Under these hypotheses, economists are able to chart indifference curves which are employed in many models of consumer theory.
Algebraic Analysis
Let there be 2 bundles of goods (x1,x2) and (y1,y2) available at price (p1,p2),assuming that the consumer has an income 'm'. It is observed that the consumer buys (x1,x2) bundle of goods.To translate this arithmetically following equation is formulated p1y1+p2y2The weak axiom of revealed preference
The weak axiom of revealed preference (WARP) is a characteristic on the choice behavior of an economic agent.The weak axiom of revealed preference states that if a consumer prefers bundle of good "A" over bundle of good "B" it will never happen so that in any situation where ,both "A" and "B" are present the consumer chooses bundle of good "B", we can also say that when good"A" is revealed preferred to good "B" good "B" will never be revealed preferred to good "A". For example, if an individual chooses orange out of a set of options including apple, they should never choose apple when faced with a choice of a different set of options which also includes orange and apple. More formally, if Apple is ever chosen when orange is available, then there can be no set containing both alternatives from which apple is chosen and orange is not. These two definitions however do not state the same necessary restrictions to satisfy WARP. The former prohibits ever choosing apple after orange was once chosen over apple. The latter (and weaker restriction) only requires to choose orange as well, if apple were to be chosen out of several choices.This characteristic can be stated as a characteristic of Walrasian demand functionsMarshallian demand function
In microeconomics, a consumer's Marshallian demand function specifies what the consumer would buy in each price and wealth situation, assuming it perfectly solves the utility maximization problem...
as seen in the following example. Let pa be the price of apples and pb be the price of bananas, and let the amount of money available be m=5. If pa =1 and pb=1, and if the bundle (2,3) is chosen, it is said that the bundle (2,3) is revealed preferred to (3,2), as the latter bundle could have been chosen as well at the given prices. More formally, assume a consumer has a demand function x such that they choose bundles x(p,w) and x(p',w') when faced with price-wealth situations (p,w) and (p',w') respectively. If p·x(p',w') ≤ w then the consumer chooses x(p,w) even when x(p',w') was available under prices p at wealth w, so x(p,w) must be preferred to x(p',w').
The strong axiom of revealed preference
The strong axiom of revealed preference (SARP) is an expansion of the concept of the weak axiom. A choice behavior that satisfies the weak axiom can form circles. That is if A is preferred to B and B to C then under the weak axiom it is possible that C is preferred to A. The strong axiom makes this behavior impossible, as it is the same as weak axiom plus the requirement that circles are not possible. (In two dimensions WARP=SARP).Criticism
Stanley Wong argues that revealed preference theory is a failed research program. According to Wong, Samuelson's 1938 presented revealed preference theory as an alternative theory to utility theory, while in 1950, Samuelson took the demonstrated equivalence of the two theories as a vindication for his position, rather than as a refutation.If there exist only an apple and an orange, and an orange is picked, then one can definitely say that an orange is revealed preferred to an apple. In the real world, when it is observed that a consumer purchased an orange, it is impossible to say what good or set of goods or behavioral options were discarded in preference of purchasing an orange. In this sense, preference is not revealed at all in the sense of ordinal utility. One of the critics of the revealed preference theory states that "Instead of replacing 'metaphysical' terms such as 'desire' and 'purpose'" they "used it to legitimize them by giving them operational definitions." Thus in psychology, as in economics, the initial, quite radical operationalist ideas eventually came to serve as little more than a "reassurance fetish" for mainstream methodological practice."
See also
- Conjoint analysisConjoint analysisConjoint analysis, also called multi-attribute compositional models or stated preference analysis, is a statistical technique that originated in mathematical psychology. Today it is used in many of the social sciences and applied sciences including marketing, product management, and operations...
- Hedonic regressionHedonic regressionIn economics, hedonic regression or hedonic demand theory is a revealed preference method of estimating demand or value. It decomposes the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic...
- Travel cost analysisTravel cost analysisThe travel cost method of economic valuation, travel cost analysis, or Clawson Method is a Revealed preference method of economic valuation used in cost benefit analysis to calculate the value of something that cannot be obtained through market prices...
- Contingent valuationContingent valuationContingent valuation is a survey-based economic technique for the valuation of non-market resources, such as environmental preservation or the impact of contamination...
or stated preference methods
External links
- Revealed Preference, review by Hal R. Varian, 2005, prepared for Samuelsonian Economics and the 21st Century.
- Lecture Notes in Microeconomic Theory, book by Ariel RubinsteinAriel RubinsteinAriel Rubinstein is an Israeli economist who works in game theory. He was educated at the Hebrew University of Jerusalem, 1972–1979, in both mathematics and economics...
, 2005.