Revealed preference

Revealed preference theory, pioneered by economist Paul Anthony Samuelson in 1938, is a method of analyzing choices made by individuals, mostly used for comparing the influence of policies on consumer behavior. Revealed preference models assume that the preferences of consumers can be revealed by their purchasing habits. Revealed preference theory arose because existing theories of consumer demand were based on a diminishing marginal rate of substitution (MRS). This diminishing MRS relied on the assumption that consumers make consumption decisions to maximise their utility. While utility maximisation 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 defining utility functions by observing behaviour. Therefore, revealed preference is a way to infer the preferences of individuals given the observed choices. It contrasts with attempts to directly measure preferences or utility, for example through stated preferences. Taking economics to be an empirical subject, there is the issue that one cannot observe preferences. Let there be two bundles of goods, a and b, available in a budget set . If it is observed that a is chosen over b, then a is considered (directly) revealed preferred to b. If the budget set is defined for two goods; , and determined by prices and income , then let bundle a be and bundle b be . This situation would typically be represented arithmetically by the inequality and graphically by a budget line in the positive real numbers. Assuming strongly monotonic preferences, only bundles that are graphically located on the budget line, i.e. bundles where and are satisfied, need to be considered. If, in this situation, it is observed that is chosen over , it is concluded that is (directly) revealed preferred to , which can be summarized as the binary relation or equivalently as . WARP is one of the criteria which needs to be satisfied in order to make sure that the consumer is consistent with their preferences.