380 L10(2)-Lecture-WARP

380 L10(2)-Lecture-WARP - Revealed Preference R. Pope...

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Revealed Preference R. Pope Suppose one wants to construct a theory of demand without the notion of utility. As an economist, all you see are a price and quantity vectors, i.e., prices and choices. Yet there must be some notion of consistency if there is to be a theory and the theory of revealed preference is such a theory. It is based on sets and expenditures. Recall that at constant prices an budget line towards the axis represents a fall in expenditures and any budget line further out at those same prices means higher expenditures. Some Operational Ideas: Revealed Preferred: Bundle A is revealed preferred to bundle B if a person could have purchased B (expenditures are less than or equal to the expenditures at A) but chose A instead. Algebraically A A A A A B A B x y x y p x p y p x p y + + . That is an easy comparison. Now let’s look at a slightly more complicated case. A B y Figure 1-A Revealed Preferred to B slope equals - A x A y p p - x
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Thus when the budget line was 1, one could have purchased B in the sense that it doesn’t cost more to purchase B than A but chose A instead. Thus, A is revealed preferred to B. To see a case where A is not revealed to B or B to A, consider Figure 3 (see also Figure
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380 L10(2)-Lecture-WARP - Revealed Preference R. Pope...

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