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1、Chapter SevenRevealed PreferenceRevealed Preference AnalysisuSuppose we observe the demands(consumption choices)that a consumer makes for different budgets.This reveals information about the consumers preferences.We can use this information to.Revealed Preference AnalysisTest the behavioral hypothes
2、is that a consumer chooses the most preferred bundle from those available.Discover the consumers preference relation.Assumptions on PreferencesuPreferencesdo not change while the choice data are gathered.are strictly convex.are monotonic.uTogether,convexity and monotonicity imply that the most prefe
3、rred affordable bundle is unique.Assumptions on Preferencesx2x1x1*x2*If preferences are convex andmonotonic(i.e.well-behaved)then the most preferredaffordable bundle is unique.Direct Preference RevelationuSuppose that the bundle x*is chosen when the bundle y is affordable.Then x*is revealed directly
4、 as preferred to y(otherwise y would have been chosen).ux*直接显示偏好于直接显示偏好于Direct Preference Revelationx2x1x*yThe chosen bundle x*isrevealed directly as preferredto the bundles y and z.zDirect Preference RevelationuThat x is revealed directly as preferred to y will be written as x y.Dp pIndirect Prefer
5、ence RevelationuSuppose 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 zso x y and y z x z.Dp pDp pIp pIp pIndirect Preference Revelationx2x1x*zz is not affordable when x*is chosen.Indire
6、ct Preference Revelationx2x1x*y*zx*is not affordable when y*is chosen.Indirect Preference Revelationx2x1x*y*zz 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.Indi
7、rect Preference Revelationx2x1x*y*zBut 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 Revelationx2x1x*y*zDp pBut x*x*y*and y*zz is not affordable when x*is chosen.x*is not affordable when y*is chosen.So x*and
8、 z cannot be compared directly.Indirect Preference Revelationx2x1x*y*zDp pDp pz 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 Revelationx2x1x*y*zBut x*x*y*and y*z so x*z.Dp pDp pIp pTwo Axioms of Revealed Preference
9、uTo apply revealed preference analysis,choices must satisfy two criteria-the Weak and the Strong Axioms of Revealed Preference.The Weak Axiom of Revealed Preference(WARP)uIf the bundle x is revealed directly as preferred to the bundle y then it is never the case that y is revealed directly as prefer
10、red to x;i.e.x y not(y x).u显示偏好的弱公理显示偏好的弱公理Dp pDp pThe Weak Axiom of Revealed Preference(WARP)uChoice data which violate the WARP are inconsistent with economic rationality.uThe WARP is a necessary condition for applying economic rationality to explain observed choices.The Weak Axiom of Revealed Pre
11、ference(WARP)uWhat choice data violate the WARP?The Weak Axiom of Revealed Preference(WARP)x2x1xyThe Weak Axiom of Revealed Preference(WARP)x2x1xyx is chosen when y is availableso x y.Dp pThe Weak Axiom of Revealed Preference(WARP)x2x1xyy is chosen when x is availableso y x.x is chosen when y is ava
12、ilableso x y.Dp pDp pThe Weak Axiom of Revealed Preference(WARP)x2x1xyThese statements are inconsistent with each other.x is chosen when y is availableso x y.y is chosen when x is availableso y x.Dp pDp pThe Strong Axiom of Revealed Preference(SARP)uIf the bundle x is revealed(directly or indirectly
13、)as preferred to the bundle y and x y,then it is never the case that the y is revealed(directly or indirectly)as preferred to x;i.e.x y or x ynot(y x or y x).Dp pDp pIp pIp pThe Strong Axiom of Revealed PreferenceuThat the observed choice data satisfy the SARP is a condition necessary and sufficient for there to be a well-behaved preference relation that“rationalizes”the data.uSuppose we have the choice data satisfy the SARP,then we can discover approximately where are the consumers indifference curves.