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14127_lec5_c_a_c

# 14127_lec5_c_a_c - 14.127 Lecture 5 Xavier Gabaix March 4...

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14.127 Lecture 5 Xavier Gabaix March 4, 2004

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0.1 Welfare and noise. A compliment Two firms produce roughly identical goods Demand of firm 1 is D 1 = P ( q p 1 + σε 1 >q p 2 + σε 2 ) where ε 1 2 are iid N (0 , 1) . Thus D 1 = P ( p 2 p 1 ( ε 1 ε 2 )) = P p 2 p 1 2 η ¯ p 2 p 1 σ 2 = Φ = P p 2 p 1 σ 2 where η is N (0 , 1) and ¯ Φ = 1 Φ , with Φ cdf of N (0 , 1)
Unlike in ε 0 case, here the demand is not dramatically elastic Slope of demand at the symmetric equilibrium p 1 = p 2 σ 2 p 2 p 1 1 ¯ p 2 p 1 = φ σ 2 σ 2 ∂p 1 D 1 = ∂p 1 Φ 1 = φ (0) σ 2 and “modified” elasticity 1 1 η = D 1 ∂p 1 D 1 = φ (0) σ 2 = π σ because D 1 = 1 2 . When σ 0 then η → ∞ . Even though the “true” elasticity is the measured elasticity is lower η < η true .

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Open question: how to correct that bias?
0.2 How to measure the quantity of noise σ ? Give people n mutual funds and ask them to pick their preferred and next preferred fund. Assume that all those funds have the same value q A = q B People do max q i p i + σε i = s i Call A -the best fund, B -the second best fund, s A s B all other funds. Increase p A by p . At some point the consumer is indifferent between A and B . q A p A + σε A p = q B p B + σε B

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If p A = p B then p = σ ( ε A ε B ) or p = σ ε (1: n ) ε (2: n ) Proposition. For large n p = B n σ where B n is the parameter of Gumbel attraction, B n = 1 1 �� nf F ¯ n
0.3 Could the fees be due to search costs? Ali Hortacsu and Chad Syverson, QJE 2004, forthcoming. Suppose you have x = \$200 , 000 and you keep it for 10 years. You pay 1 . 5% / year and thus lose 200 , 000 × 1 . 5% = 3 , 000 a year. Competing explanation people don’t know that two index mutual fund are the same thing.

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0.4 Open questions What are the regulatory implications of consumer confusion? Where does confusion σε i comes from? For instance, provide a cognitive model that gives a microfoundation for this “noise” Find a model that predicts the level of the confusion σ ? e.g., in the mutual fund market, give a model that
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14127_lec5_c_a_c - 14.127 Lecture 5 Xavier Gabaix March 4...

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