Tsinghua Micro Ch7 020927 - Chapter Seven Revealed...

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Chapter Seven Revealed Preference 显显显显显
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What Is the Question of the Chapter? Suppose we observe a collection of a consumer’s choices, can we discover his/her preference? Is this possible at all? If so, under what conditions is this possible? (This is the reverse question of finding the optimal choice)
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Digression: Science vs. Engineering ( 对对对对对对对对对对对对对对    显显显显显显显显显显 显显显显显显显 显显显显显显显显 显显显显显显显显显显显显 显显显显显显显显显显
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Maintained Assumptions on Preferences Preferences do not change while the choice data are gathered. are strictly convex. are monotonic.
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Assumptions on Preferences x 2 x 1 x 1 * x 2 * If preferences are convex and monotonic ( i.e . well-behaved) then the most preferred affordable bundle is unique.
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Direct Preference Revelation Suppose that the bundle x * is chosen when the bundle y is affordable. Then x* is revealed directly as preferred to y (otherwise y would have been chosen).
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Direct Preference Revelation x 2 x 1 x * y The chosen bundle x * is revealed directly as preferred to the bundles y and z. z
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Direct Preference Revelation That x is revealed directly as preferred to y will be written as x y. D
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Indirect Preference Revelation Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, we call x is revealed indirectly as preferred to z. Write this as x z so x y and y z x z. D D I I
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z is not affordable when x* is chosen. x* is not affordable when y* is chosen. So x* and z cannot be compared directly. Indirect Preference Revelation x 2 x 1 x* y* z But x* x* y* and y* z so x* z. D D I
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Two Axioms of Revealed Preference To apply revealed preference analysis, choices must satisfy two criteria -- the Weak and the Strong Axioms of Revealed Preference .
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The Weak Axiom of Revealed Preference (WARP) If the bundle x is revealed directly as preferred to the bundle y then it is never the case that y is revealed directly as preferred to x; i.e. x y not (y x). D D
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The Weak Axiom of Revealed Preference (WARP) Choice data which violate the WARP are inconsistent with economic rationality. The WARP is a necessary condition for applying economic rationality to explain observed choices.
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The Weak Axiom of Revealed Preference (WARP) What choice data violate the WARP?
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The Weak Axiom of Revealed Preference (WARP) x 2 x 1 x y y is chosen when x is available so y x. x is chosen when y is available so x y. D D
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Checking if Data Violate the WARP A consumer makes the following choices: At prices (p 1 ,p 2 )=($2,$2) the choice was (x 1 ,x 2 ) = (10,1).
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Tsinghua Micro Ch7 020927 - Chapter Seven Revealed...

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