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Chapter 7 REVEALED PREFERENCE

Chapter 7 REVEALED PREFERENCE. 7.1 The Idea of Revealed Preference. ( x 1 , x 2 ) is chosen when ( y 1 , y 2 ) could have been chosen: p 1 x 1 + p 2 x 2 ≥ p 1 y 1 + p 2 y 2 ( x 1 , x 2 ) is directly revealed preferred to ( y 1 , y 2 ). 7.2 From Revealed Preference to Preference.

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Chapter 7 REVEALED PREFERENCE

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  1. Chapter 7 REVEALED PREFERENCE

  2. 7.1 The Idea of Revealed Preference • (x1, x2) is chosen when (y1, y2) could have been chosen: p1x1+p2x2≥p1y1+p2y2 • (x1, x2) is directly revealed preferred to (y1, y2).

  3. 7.2 From Revealed Preference to Preference • The Principle of Revealed Preference • Suppose there is a unique optimal bundle for each budget set; • Suppose the consumer always chooses the most preferred bundle she can afford; • Suppose the consumer has chosen (x1, x2) when faced by (p1, p2); • Suppose p1x1+p2x2≥p1y1+p2y2; • we must have

  4. 7.2 From Revealed Preference to Preference • Suppose the consumer has chosen (y1, y2) when faced by (q1, q2); • Suppose q1y1+q2y2≥q1z1+q2z2; • Then we know that • From transitivity we can conclude that: • (x1, x2) is indirectly revealed preferred to (z1, z2).

  5. 7.2 From Revealed Preference to Preference • (x1, x2) is indirectly revealed preferred to (z1, z2).

  6. 7.3 Recovering Preferences • Suppose the preference is convex and monotonic. • The weakly preferred set w/r to X contains the “smallest” monotonic convex set that includes X, Y, and Z.

  7. 7.4 The Weak Axiom of Revealed Preference • WARP: If • (x1, x2) is directly revealed preferred to (y1, y2); • and (x1, x2)≠(y1, y2); • then (y1, y2) cannot be directly revealed preferred to (x1, x2).

  8. 7.4 The Weak Axiom of Revealed Preference • Satisfying WARP

  9. 7.5 Checking WARP

  10. 7.6 The Strong Axiom of Revealed Preference • SARP: If • (x1, x2) is (directly or indirectly) revealed preferred to (y1, y2); • and (y1, y2)≠(x1, x2); • then (y1, y2) cannot be (directly or indirectly) revealed preferred to (x1, x2). • SARP is both necessary and sufficient for rational consumer behavior.

  11. 7.7 How to Check SARP • Transform the table: • Need to look for chains of arbitrary length to see if one observation is indirectly revealed preferred to another.

  12. 7.8 Index Numbers • Quantity index: • Paasche quantity index: • Laspeyres quantity index:

  13. 7.8 Index Numbers • The consumer is better off at t than at b. • No inference on consumer well-being.

  14. 7.8 Index Numbers • No inference on consumer well-being. • The consumer is better off at b than at t.

  15. 7.9 Price Indices • Price index: • Paasche price index: • Laspeyres price index:

  16. 7.9 Price Indices • The consumer is better off at b than at t. • The consumer is better off at t than at b.

  17. Indexing Social Security Payments • Indexing: Social security payments get adjusted with price indices so that the consumption bundle in year b is still affordable in year t. • Consumers are strictly better off with indexing.

  18. Indexing Social Security Payments

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