Chapter Seven,Revealed Preference,Revealed Preference Analysis,Suppose 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 Analysis,Test the behavioral hypothesis that a consumer chooses the most preferred bundle from those available. Discover the consumers preference relation.,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,x2,x1,x1*,x2*,If preferences are convex and monotonic (i.e. well-behaved) then the most preferred affordable bundle is unique.,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). x*直接显示偏好于,Direct Preference Revelation,x2,x1,x*,y,The chosen bundle x* is revealed directly as preferred to the bundles y and z.,z,Direct Preference Revelation,That x is revealed directly as preferred to y will be written as x y.,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.,I,p,I,p,Indirect Preference Revelation,x2,x1,x*,z,z is not affordable when x* is chosen.,Indirect Preference Revelation,x2,x1,x*,y*,z,x* is not affordable when y* is chosen.,Indirect Preference Revelation,x2,x1,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,x2,x1,x*,y*,z,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,x2,x1,x*,y*,z,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,x2,x1,x*,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,x2,x1,x*,y*,z,But x*x* y* and y* z so x* z.,I,p,Two Axioms of Revealed Preference,To 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),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). 显示偏好的弱公理,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.,The Weak Axiom of Revealed Preference (WARP),What choice data violate the WARP?,The Weak Axiom of Revealed Preference (WARP),x2,x1,x,y,The Weak Axiom of Revealed Preference (WARP),x2,x1,x,y,x is chosen when y is available so x y.,The Weak Axiom of Revealed Preference (WARP),x2,x1,x,y,y is chosen when x is available so y x.,x is chosen when y is available so x y.,The Weak Axiom of Revealed Preference (WARP),x2,x1,x,y,These statements are inconsistent with each other.,x is chosen when y is available so x y.,y is chosen when x is available so y x.,The Strong Axiom of Revealed Preference (SARP),If the bundle x is revealed (directly or indirectly) 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 y,not ( y x or y x ).,I,p,The Strong Axiom of Revealed Preference,That 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. Suppose we have the choice data satisfy the SARP, then we can discover approximately where are the consumers indifference curves.,