1. A buyer is considering buying a used car from a seller. The car's quality q in uniformly distributed on [0,2] (this interval represents the large number of sellers on the market with cars of varying quality) and known to the seller, but not to the buyer. The buyer's value vB of the car equals its expected quality while the seller's value the car of quality q is given by vs(q) 99€ [0,1] 99€ [1,2] We are interested in studying Bayes Nash equilibria of the game in which the market price is set at some exogenously given fixed price p € [0, ∞0). The payoffs are the same as in class: if both agree to the sale, it's (v-p,p- vs(q)), otherwise it's (0,0), where vB is the expected quality of the car given the seller's strategy. (a) For each price p = [0, ∞), describe the subset QP of types of the seller willing to sell their car. (b) For each price pЄ [0,00), describe the expected quality q =E[q|q € QP] of the car for the set of seller types you identified above. (c) For which prices pЄ [0,00) is there a BNE with trade (i.e. buyer agrees to buy)?
1. A buyer is considering buying a used car from a seller. The car's quality q in uniformly distributed on [0,2] (this interval represents the large number of sellers on the market with cars of varying quality) and known to the seller, but not to the buyer. The buyer's value vB of the car equals its expected quality while the seller's value the car of quality q is given by vs(q) 99€ [0,1] 99€ [1,2] We are interested in studying Bayes Nash equilibria of the game in which the market price is set at some exogenously given fixed price p € [0, ∞0). The payoffs are the same as in class: if both agree to the sale, it's (v-p,p- vs(q)), otherwise it's (0,0), where vB is the expected quality of the car given the seller's strategy. (a) For each price p = [0, ∞), describe the subset QP of types of the seller willing to sell their car. (b) For each price pЄ [0,00), describe the expected quality q =E[q|q € QP] of the car for the set of seller types you identified above. (c) For which prices pЄ [0,00) is there a BNE with trade (i.e. buyer agrees to buy)?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1. A buyer is considering buying a used car from a seller. The car's quality q in uniformly distributed on [0,2] (this interval
represents the large number of sellers on the market with cars of varying quality) and known to the seller, but not to the
buyer. The buyer's value vB of the car equals its expected quality while the seller's value the car of quality q is given by
vs(q)
99€ [0,1]
99€ [1,2]
We are interested in studying Bayes Nash equilibria of the game in which the market price is set at some exogenously given
fixed price p € [0, ∞0). The payoffs are the same as in class: if both agree to the sale, it's (v-p,p- vs(q)), otherwise it's (0,0),
where vB is the expected quality of the car given the seller's strategy.
(a) For each price p = [0, ∞), describe the subset QP of types of the seller willing to sell their car.
(b) For each price pЄ [0,00), describe the expected quality q =E[q|q € QP] of the car for the set of seller types you
identified above.
(c) For which prices pЄ [0,00) is there a BNE with trade (i.e. buyer agrees to buy)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1858a710-c111-4513-9004-6c10bf7d1d6e%2F5f3a6d0a-b32f-49f2-8020-54212357d47b%2Fd31jqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A buyer is considering buying a used car from a seller. The car's quality q in uniformly distributed on [0,2] (this interval
represents the large number of sellers on the market with cars of varying quality) and known to the seller, but not to the
buyer. The buyer's value vB of the car equals its expected quality while the seller's value the car of quality q is given by
vs(q)
99€ [0,1]
99€ [1,2]
We are interested in studying Bayes Nash equilibria of the game in which the market price is set at some exogenously given
fixed price p € [0, ∞0). The payoffs are the same as in class: if both agree to the sale, it's (v-p,p- vs(q)), otherwise it's (0,0),
where vB is the expected quality of the car given the seller's strategy.
(a) For each price p = [0, ∞), describe the subset QP of types of the seller willing to sell their car.
(b) For each price pЄ [0,00), describe the expected quality q =E[q|q € QP] of the car for the set of seller types you
identified above.
(c) For which prices pЄ [0,00) is there a BNE with trade (i.e. buyer agrees to buy)?
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