ch07 - Chapter 7: Revealed Preference Econ 306 by Rust,...

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Chapter 7: Revealed Preference Econ 306 by Rust, Cho, and Diaz
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Revealed Preference Analysis •S u p p o s e w e o b s e r v e t h e d e m ands (consumption choices) that a consumer makes for different budget. This reveals information about the consumer’s preferences. •W e c a n u s e t h i s i n f o r m a t i o n t o Test the behavioral hypothesis that a consumer chooses the most preferred bundle from those available. Discover the consumer’s preference relation.
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Revealed Preference Analysis (continued) •P r e f e r e n c e s Do not change while the choice data are gathered. Are strictly convex. Are monotonic. •T o g e t h e r , c o n v e x i t y a n d m o n o t o n i c i t y i m p l y t h a t t h e m o s t preferred affordable bundle is unique.
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Direct Preference Revelation •S u p p o s e t h a t t h e b u n d l e i s c h o s e n w h e n t h e bundle is affordable. Then is revealed directly as preferred to (otherwise y would have been chosen). •I n F i g u r e 7 . 1 , t h e b u n d l e i s c e r t a i n l y a n a f f o r d a b l e purchase at the given budget- the consumer could have bought it if he or she wanted to, and would even have had money left over. Since is the optimal bundle, it must be better than anything else that the consumer could afford. •T h a t i s r e v e a l e d d i r e c t ly as preferred to will be written as ) , ( 2 1 x x ) , ( 2 1 y y ) , ( 2 1 y y ) , ( 2 1 x x ) , ( 2 1 x x ) , ( 2 1 x x ) , ( 2 1 y y ) , ( 2 1 y y ) , ( ) , ( 2 1 2 1 y y x x D
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07.01
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Direct Preference Revelation (continued) •T h e P r i n c i p l e o f R e v e a l e d P r e f e r e n c e s Let be the chosen bundle when prices are , and let be some other bundle such that . Then if the consumer is choosing the most preferred bundle she can afford, we must have • If X is revealed preferred to Y, it doesn’t automatically mean that X is preferred to Y. • Why? ) , ( ) , ( 2 1 2 1 y y x x D ) , ( 2 1 x x ) , ( 2 1 p p ) , ( 2 1 y y 2 2 1 1 2 2 1 1 y p y p x p x p ± t ±
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Direct Preference Revelation (continued) •“ R e v e a l e d p r e f e r r e d j u s t m e a n s t h a t X w a s c h o s e n w h e n was affordable; “preference” means that the consumer ranks X ahead of Y. • If the consumer chooses the best bundle she can afford, then “ revealed preferred” implies “preference,” but that is a consequence of the model of behavior, not the definitions of the terms.
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ch07 - Chapter 7: Revealed Preference Econ 306 by Rust,...

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