Everything about Revealed Preference totally explained
Pioneered by American economist
Paul Samuelson (
1915 – ),
revealed preference theory is a method by which it's possible to discern the best possible option on the basis of
consumer behavior. Essentially, this means that the
preferences 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. This diminishing MRS is based on the assumption that consumers make consumption decisions based on their intent to maximize their utility. While
utility maximization wasn't a controversial assumption, the
underlying utility functions couldn't 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
If a person chooses a certain bundle of goods (ex. 2 apples, 3 bananas) while another bundle of goods is affordable (ex. 3 apples, 2 bananas), then we say that the first bundle is revealed preferred to the second. It is then assumed that the first bundle of goods is always preferred to the second. This means that if the consumer ever purchases the second bundle of goods then it's assumed that the first bundle is unaffordable. This
implies that preferences are
transitive. In other words if we've bundles A, B, C, ...., Z, and A is revealed preferred to B which is revealed preferred to C and so on then it's concluded that A is revealed preferred to C through Z. With this theory economists can chart
indifference curves which adhere to already developed models of consumer theory.
The Weak Axiom of Revealed Preference
The
Weak Axiom of Revealed Preference (WARP) is a characteristic on the choice behavior of an economic agent. For example, if an individual chooses A and never B when faced with a choice of both alternatives, they should never choose B when faced with a choice of A,B and some additional options. More formally, if A is ever chosen when B is available, then there can be no budget set containing both alternatives for which B is chosen and A is not.
This characteristic can be stated as a characteristic of
Walrasian demand functions as seen in the following example. Let p
a be the price of apples and p
b be the price of bananas, and let the amount of money available be m=5. If p
a =1 and p
b=1, and if the bundle (2,3) is chosen, it's said that 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').
Further Information
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