Problem 4: Lemons Beverly would like to sell her sports car and Jim would like to...

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Problem 4: Lemons Beverly would like to sell her sports car and Jim would like to buy a sports car. Both know the following: Half of all sports cars are lemons and half are good cars. 3 If the car is a lemon, it is worth $2,000 to the buyer and $1,000 to the seller; if the car is good, it is worth $6,000 to the buyer and $4,500 to the seller. The seller knows the condition of the car but the buyer does not. Beverly places an ad in the newspaper and offers a take-it-or-leave-it price of P. Assume throughout this question that if Jim is indifferent between buying and selling he will buy. 1. Show that there is a separating equilibrium in this game where only lemons are sold. 2. Show that the game does not have a pooling equilibrium where all cars are sold. 3. Now consider mixed strategies: If the car is good, Beverly offers to sell it for $5,000. If the car is a lemon, she offers to sell it for $5,000 with probability p and offers to sell it for $2,000 with probability 1-p, where 0 Problem 4: Lemons Beverly would like to sell her sports car and Jim would like to buy a sports car. Both know the following: Half of all sports cars are lemons and half are good cars. 3 If the car is a lemon, it is worth $2,000 to the buyer and $1,000 to the seller; if the car is good, it is worth $6,000 to the buyer and $4,500 to the seller. The seller knows the condition of the car but the buyer does not. Beverly places an ad in the newspaper and offers a take-it-or-leave-it price of P. Assume throughout this question that if Jim is indifferent between buying and selling he will buy. 1. Show that there is a separating equilibrium in this game where only lemons are sold. 2. Show that the game does not have a pooling equilibrium where all cars are sold. 3. Now consider mixed strategies: If the car is good, Beverly offers to sell it for $5,000. If the car is a lemon, she offers to sell it for $5,000 with probability p and offers to sell it for $2,000 with probability 1-p, where 0

Answer rating: 100% (QA)

1 Separating Equilibrium If P 2000 Jim will accept since the car must be a lemo... View the full answer