As in the lemons model, suppose that there is one seller and one buyer who may exchange a good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it is uniformly distributed on [0, 1]). There is a fixed price of p = 1/2 at which trade may occur, which happens if and only if both the buyer and the seller agree to trade. Before deciding whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of v. The seller's payoff is p if trade occurs and v if trade does not occur. The buyer's payoff is 3v/2-p-c if trade occurs and he first learned the value of v; 3v/2 - p if trade occurs and he did not learn the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade does not occur and he did not learn the value of v. Find the probability that trade occurs for each c € (0, 1).
As in the lemons model, suppose that there is one seller and one buyer who may exchange a good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it is uniformly distributed on [0, 1]). There is a fixed price of p = 1/2 at which trade may occur, which happens if and only if both the buyer and the seller agree to trade. Before deciding whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of v. The seller's payoff is p if trade occurs and v if trade does not occur. The buyer's payoff is 3v/2-p-c if trade occurs and he first learned the value of v; 3v/2 - p if trade occurs and he did not learn the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade does not occur and he did not learn the value of v. Find the probability that trade occurs for each c € (0, 1).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![As in the lemons model, suppose that there is one seller and one buyer who may exchange a
good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of
v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it
is uniformly distributed on [0, 1]). There is a fixed price of p = 1/2 at which trade may occur,
which happens if and only if both the buyer and the seller agree to trade. Before deciding
whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of v. The seller's
payoff is p if trade occurs and v if trade does not occur. The buyer's payoff is 3v/2-p-c if
trade occurs and he first learned the value of v; 3v/2 - p if trade occurs and he did not learn
the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade
does not occur and he did not learn the value of v. Find the probability that trade occurs for
each c € (0, 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F59b5f329-35b9-417b-8e60-89d1f8e08f90%2Fapuycgo_processed.png&w=3840&q=75)
Transcribed Image Text:As in the lemons model, suppose that there is one seller and one buyer who may exchange a
good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of
v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it
is uniformly distributed on [0, 1]). There is a fixed price of p = 1/2 at which trade may occur,
which happens if and only if both the buyer and the seller agree to trade. Before deciding
whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of v. The seller's
payoff is p if trade occurs and v if trade does not occur. The buyer's payoff is 3v/2-p-c if
trade occurs and he first learned the value of v; 3v/2 - p if trade occurs and he did not learn
the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade
does not occur and he did not learn the value of v. Find the probability that trade occurs for
each c € (0, 1).
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