Revealed Preferences Theory

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REVEALED PREFERENCE: AN ALTERNATIVE APPROACH
TO CONSUMER DEMAND
The model we have studied uses the preference-based approach to choice behaviour. It assumes that the consumer has preferences satisfying certain properties and that they choose what they prefer most. Preferences are,of course, something we cannot observe. So, we have begun by assuming something about things we cannot observe to ultimately make predictions about something we can observe –consumer demand behaviour. What would have happened if we started with something we can observe? (Choice-based approach.)

Consider two consumption bundles, x and y. Suppose that both of these bundles are affordable at some prices and income level. If the consumer buys one bundle instead of the other, then the bundle bought (chosen) is considered to be revealed preferred (RP) to the other. The presumption is that by actually choosing one bundle over another, the consumer conveys important information about their tastes. 1

The Weak Axiom of Revealed Preference
It is desirable that the behaviour of the consumer is consistent in the sense that they would not choose a bundle A over a bundle B one time and then choose B over A at some other time. This can be achieved by making the following assumption about the consumer’s behaviour. ASSUMPTION 1.1 Weak Axiom of Revealed Preference (WARP):

A consumer’s behaviour satisfies WARP if whenever x0 is revealed preferred to x1 , x1 is never revealed preferred to x0 .
Note that x0 is revealed preferred to x1 means that x0 is chosen when both x0 and x1 are affordable. And for x1 never to be revealed preferred to x0 we must have x0 not affordable whenever x1 is chosen; that is, the cost of x0 must be more than the cost of x1 at all prices x1 is chosen. Suppose that x0 is revealed preferred to x1 at prices p0 , and that x is chosen at some other prices p1 . Then WARP can formally be expressed as1 : p0 · x1 ≤ p0 · x0 =⇒ p1 · x0 > p1 · x1

The weak...
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