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Revealed Preference: Understanding Consumer Choices

In this chapter, we explore the concept of revealed preference and what it tells us about consumer preferences. We discuss the weak axiom of revealed preference (WARP) and the strong axiom of revealed preference (SARP), along with some maintained assumptions. We also look at how index numbers can be used to compare consumption bundles and price changes over time.

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Revealed Preference: Understanding Consumer Choices

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  1. Chapter 7 Revealed Preference • Economists infer from choices a lot! free money on the floor my new office • Before, from w to choice • now from choice to w • this has policy content: household, university

  2. Choices

  3. Chapter 7 Revealed Preference • Key Concept: what does choice reveal about preferences? • The weak axiom of revealed preference (WARP) • The strong axiom of revealed preference (SARP)

  4. Some maintained assumptions • A1: The consumer’s preferences are stable over the time period for which we observe his/her choice behaviors. • A2: There exists a unique demanded bundle for each budget set (easy to relax). • A3: The consumer is always choosing the best s\he can afford (model of behavior).

  5. If (x1, x2) is chosen at (p1, p2, m), (y1, y2)≠ (x1, x2) and p1y1+p2 y2≤m, then (x1, x2) is directly revealed preferred to (y1, y2). • Denote this by (x1, x2) d (y1, y2). • d is solely about choices though choices are related to preferences.

  6. Fig. 7.1

  7. (x1, x2) d (y1, y2). • d is solely about choices though choices are related to preferences.

  8. From revealed preference (d) to preference (w) • Suppose (x1, x2) d (y1, y2) and the consumer is choosing the best s\he can afford, then (x1, x2) s (y1, y2).

  9. The weak axiom of revealed preference (WARP) • If (x1, x2) d (y1, y2), then it cannot happen that (y1, y2) d (x1, x2).

  10. Fig. 7.4

  11. WARP is a weak and logical implication of consumers’ maximizing behaviors. • An example

  12. If (x1, x2) d (y1, y2) and (y1, y2) d (z1, z2), then we say that (x1, x2) is indirectly revealed preferred to (z1, z2). • Denote this by (x1, x2) id (z1, z2). • Allow indirect revealed preference for “chains” of observed choices longer than 3.

  13. Fig. 7.2

  14. If either (x1, x2) d (y1, y2) or (x1, x2) id (y1, y2), we say (x1, x2) is revealed preferred to (y1, y2). • Denote this by (x1, x2) r (y1, y2).

  15. Give an example to recover preferences. • How do we know whether the consumer is maximizing if we only observe choices? • We are questioning A3 (the idea is A1 and A2 are OK).

  16. Fig. 7.3

  17. The strong axiom of revealed preference (SARP) • If (x1, x2) r (y1, y2), then it cannot happen that (y1, y2) r (x1, x2).

  18. SARP is a necessary and sufficient condition for optimizing behavior, but the proof is beyond the scope of this course. • Sufficiency: If choices satisfy SARP, then we can construct preferences for which the observed behavior is optimizing.

  19. Index numbers • Compare the consumption bundles of a consumer at two different times. • Let b stand for the base period. • Let t stand for some other period. • At t: prices (p1t, p2t), consumption (x1t, x2t) • At b: prices (p1b, p2b), consumption (x1b, x2b)

  20. Quantity index: compare the average consumption of these two periods, naturally could use the prices to be the weights • Laspeyres quantity index (use base price): Lq=(p1b x1t + p2b x2t)/(p1b x1b + p2b x2b), if Lq<1, at base price, base is chosen over t, so better off at base than at t (Lq>1?) • Paasche quantity index (use t price): Pq=(p1t x1t + p2t x2t)/(p1t x1b + p2t x2b), if Pq>1, at t price, t is chosen over base, so better off at t than at base (Pq<1?)

  21. Price index: compare the average price of these two periods, naturally could use the quantities to be the weights • Laspeyres price index (use base q): Lp=(p1t x1b + p2t x2b)/(p1b x1b + p2b x2b) (wage adjustment) if Lp<1 (says nothing since prices different) • Paasche price index (use t q): Pp=(p1t x1t + p2t x2t)/(p1b x1t + p2b x2t) (GDP deflator)

  22. Define a new index of the change in total expenditure M=(p1t x1t + p2t x2t)/(p1b x1b + p2b x2b). • Lp<M: p1t x1b + p2t x2b <p1t x1t + p2t x2t, t period is better than base (intuitively, when income grows faster than prices, better off after this change) • Pp>M: p1b x1b + p2b x2b> p1b x1t + p2b x2t, base is better than t (intuitively, when prices grow faster than income, worse off)

  23. Social security: indexing so that base consumption is still affordable, then t cannot be worse than base

  24. Fig. 7.6

  25. Chapter 7 Revealed Preference • Key Concept: what does choice reveal about preferences? • The weak axiom of revealed preference (WARP) • The strong axiom of revealed preference (SARP)

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