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5. Revealed Preference

Revealed preference:bundle (x1x2) consumer chooses is revealed preference to bundle (y1,2)

bundle he couldve chosen

Revealed Preference Analysis

Observe demands (consumption choices) that a consumer makes for dierent budgets

o eveals info about preferences

o !se info to"

Testbehavioral hypothesis

#onsumer chooses most preferred bundles from those available

Discover #onsumers preference relation

Assumptions on Preferences

$references

o %ont change &hile choice data are gathered

o 'trictly convex

o onotonic

#onvex monotonicitymost preferred aordable bundle * unique

Direct Preference Revelation

p1x1 + p2x2 p1y1 + p2y2 satis-ed that (x1,x2) directly revealed preferred to (y1y2)

.f" /undle x0 chosen &hen bundle y is aordable

o x0 * revealed directlyas preferred to y (other&ise y &ouldve been chosen)

o x revealed directly as preferred to y

Indirect Preference Revelation

x revealed directly preferred to y, and y revealed directly preferred to o by transitivity, x * revealed indirectlyas preferred to

Two Axioms of Revealed Preference

revealed preference analysis choices must satisfy criteria

o eak and the 'trong 3xioms of evealed $reference

Wea Axiom of Revealed Preference !WARP"

.f /undle x revealed directly as preferred to bundle y

o 4hen never the case that y is revealed directly to x

Ex.

3$ is a necessarycondition for apply economic rationality

to explain choices

5 .f (x)bought at (p), and (y) bought at (6)

o .f p1x2 + p2x2 p1y1 + p1y2

o 4hen cant be

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71y1 + 62y2 61x1 + 62x2 8

If y-bundle aordable when x-bundle is purchasedwhen y-bundle purchased, x-bundle not

aordable

#hoice data &hich violate 3$ are inconsistent &ith economic rationality" (violation)

'atisfying 3$"

#hecking is %ata 9iolate the 3$

#onsumer makes

follo&ing choices"o (p1,p2) * (:2,:2) (x1,x2) *

(1;,1)o (p1,p2) * (:2,:1) (x1,x2) * (