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Chapter Seven

Chapter Seven. Revealed Preference. Direct Preference Revelation. Suppose that the bundle x * is chosen when the bundle y is affordable. Then the bundle x* is revealed directly as preferred to the bundle y (otherwise y would have been chosen). Direct Preference Revelation. x 2.

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Chapter Seven

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  1. Chapter Seven Revealed Preference

  2. Direct Preference Revelation • Suppose that the bundle x* is chosen when the bundle y is affordable. Then the bundle x* is revealed directly as preferred to the bundle y (otherwise y would have been chosen).

  3. Direct Preference Revelation x2 The chosen bundle x* isrevealed directly as preferredto the bundles y and z. x* z y x1

  4. p D Direct Preference Revelation • That a bundle x is revealed directly as preferred to another bundle y will be written as x y.

  5. p p D D Indirect Preference Revelation • Suppose that x is revealed directly preferred to y, and that y is revealed directly preferred to z. Then, by transitivity, x is revealed indirectly as preferred to z. That x is revealed indirectly as preferred to z will be written as x zso x y and y z x z. p I p I

  6. Indirect Preference Revelation x2 z is not affordable when x* is chosen. x* z x1

  7. p p D D The Weak Axiom of Revealed Preference (WARP) • The WARP is: If the bundle x is revealed directly as preferred to the bundle y then it is never the case that the bundle y is revealed directly as preferred to the bundle x; i.e. x y not (y x).

  8. The Weak Axiom of Revealed Preference (WARP) • What sort of choice data would violate the WARP?

  9. p p D D The Weak Axiom of Revealed Preference (WARP) x2 x is chosen when y is availableso x y. y is chosen when x is availableso y x. These statements are inconsistent with each other. y x x1

  10. Recovering Indifference Curves • Suppose we have a set of choice data which satisfy the SARP. • Then we can discover approximately where are the consumer’s indifference curves. • How?

  11. Index Numbers • Over time, many prices change. Are consumers better or worse off “overall” as a consequence? • Index numbers give approximate answers to such questions.

  12. Index Numbers • There are two basic types of indices • price indices, and • quantity indices • Each type of index compares expenditures in a base period and in a current period by taking the ratio of these expenditures.

  13. Quantity Index Numbers • A quantity index is a price-weighted average of quantities demanded; i.e. • (p1,p2) can be base period prices (p1b,p2b) or current period prices (p1t,p2t).

  14. Quantity Index Numbers • If (p1,p2) = (p1b,p2b) then we have the Laspeyres quantity index;

  15. Quantity Index Numbers • If (p1,p2) = (p1t,p2t) then we have the Paasche quantity index;

  16. Quantity Index Numbers • How can quantity indices be used to make statements about changes in welfare?

  17. Quantity Index Numbers • If thenso consumers overall were better off in the base period than they are now in the current period.

  18. Quantity Index Numbers • If thenso consumers overall are better off in the current period than in the base period.

  19. Price Index Numbers • A price index is a quantity-weighted average of prices; i.e. • (x1,x2) can be the base period bundle (x1b,x2b) or else the current period bundle (x1t,x2t).

  20. Price Index Numbers • If (x1,x2) = (x1b,x2b) then we have the Laspeyres price index;

  21. Price Index Numbers • If (x1,x2) = (x1t,x2t) then we have the Paasche price index;

  22. Price Index Numbers • How can price indices be used to make statements about changes in welfare? • Define the expenditure ratio

  23. Price Index Numbers • Ifthenso consumers overall are better off in the current period.

  24. Price Index Numbers • But, ifthenso consumers overall were better off in the base period.

  25. Full Indexation? • Changes in price indices are sometimes used to adjust wage rates or transfer payments. This is called “indexation”. • “Full indexation” occurs when the wages or payments are increased at the same rate as the price index being used to measure the aggregate inflation rate.

  26. Full Indexation? • Since prices do not all increase at the same rate, relative prices change along with the “general price level”. • A common proposal is to index fully Social Security payments, with the intention of preserving the “purchasing power” of these payments.

  27. Full Indexation? • The usual price index proposed for indexation is the Paasche quantity index (the Consumers’ Price Index). • What will be the consequence?

  28. Full Indexation? x2 Base period budget constraint Base period choice x2b Current period budgetconstraint before indexation x1 x1b

  29. Full Indexation? x2 Base period budget constraint Base period choice Current period budgetconstraint after full indexation x2b x1 x1b

  30. Full Indexation? x2 Base period budget constraint Base period choice Current period budgetconstraint after indexation x2b Current period choiceafter indexation x2t x1 x1b x1t

  31. Full Indexation? x2 (x1t,x2t) is revealed preferred to(x1b,x2b) so full indexation makesthe recipient strictly better off if relative prices change betweenthe base and current periods. x2b x2t x1 x1b x1t

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