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# Ch7 - Chapter Seven Revealed Preference Revealed Preference...

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Chapter Seven Revealed Preference

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Revealed Preference Analysis Suppose we observe the demands (consumption choices) that a consumer makes for different budgets. This reveals information about the consumer’s preferences. We can use this information to ...
Revealed Preference Analysis 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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Assumptions on Preferences Preferences do not change while the choice data are gathered. are strictly convex. are monotonic. Together, convexity and monotonicity imply that the most preferred affordable bundle is unique.
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).
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 e
Indirect Preference Revelation Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, by transitivity, x is revealed indirectly as preferred to z. Write this as x z so x y and y z x z. D e D e I e I e

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Indirect Preference Revelation x 2 x 1 x* z z is not affordable when x* is chosen.
Indirect Preference Revelation x 2 x 1 x* y* z x* is not affordable when y* is chosen.

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Indirect Preference Revelation x 2 x 1 x* y* z z is not affordable when x* is chosen. x* is not affordable when y* is chosen.
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

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But x* x* y* 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 D e
But x* x* y* and y* z 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 D e D e

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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 e D e I e
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.
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Ch7 - Chapter Seven Revealed Preference Revealed Preference...

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