Lec08-Revealed_Pref_Consumer_Welfare

Lec08-Revealed_Pref_Consumer_Welfare - Lecture Note 8:...

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Lecture Note 8: Revealed Preference and Consumer Welfare David Autor 14.03 Microeconomic Theory and Public Policy, Fall 2005 1
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1 Revealed Preference and Consumer Welfare We have to date been applying an axiomatic approach to characterizing consumer choice, basedonthe f ve axioms given in the 1st lectures. But there is an approach to assessing utility that requires even fewer assumptions and nevertheless gives strong results. This approach is called Revealed Preference . Consider Figure 8#1 where the consumer sequentially faces two budget sets, I 1 I 1 and I 2 I 2 . Point A on I 1 I 1 is initially chosen. This point is said to be “revealed preferred” to all other feasible points inside of the budget set. 8#1 I 1 I 2 A B C I 1 I 2 Now the consumer is faced with I 2 I 2 . If the consumer chooses point B , are they better or worse o f ? Worse o f ,because point A was revealed preferred to point B under the initial choice conditions. If they choose point C , are they better or worse o f ? The axiomatic approach would tend to suggest they are better o f because unless the indi f erence curve tangent to point A has an extremely shallow slope, point C would probably put them on a higher indi f erence curve. But under Revealed Preference, the answer is ambiguous. The reason is that we do not have any revealed preference information on whether A is preferred to C or vice versa—these choices were never available simultaneously. 2
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Take a second example (See Figure 8#2). I 1 I 2 A I 1 I 2 8#2 A’ A” No longer feasible under I 2 –I 2 Newly feasible under I 2 -I 2 x y Here the second budget set rotates through the originally chosen point A on the f rst budget set. We do not know the consumer’s new choice. Is the consumer better o f ,worse o f ,orcan ’twesay? We know that point A r.p. ( A, A 0 ] We do not know—but it is possible—that a point on ( A, A 00 ] is preferred to A. We say that the consumer is “weakly better o f .” De f nition 1 Weak Axiom of Revealed Preference: If A, B feasible and A chosen, then at any prices and income where A, B are feasible, the consumer will choose A over B. This axiom says two things: 1. People choose what they prefer. 2. Preferences are consistent . Therefore, a single observed choice reveals a stable preference. There is also a stronger form of this axiom.
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1.1 The power of WARP 1.1.1 Demonstration 1 The result that ∂X ∂P x | u = u 0 < 0 (i.e., the compensated demand curve is always downward sloping) depends on an untested assumption about diminishing MRS, giving rise to in- di f erence curves that are bowed inward towards the origin. Can we obtain the same result using only WARP? Suppose two points
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Lec08-Revealed_Pref_Consumer_Welfare - Lecture Note 8:...

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