In the market for used cars there are good cars and bad cars. The...

  

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In the market for used cars there are good cars and bad cars. ● ● The good cars comprise a fraction G of all the cars that may be potentially up for sale, where 0<G<1. Buyers cannot distinguish a good car from a bad car, whereas each seller knows the type of car she has. The valuation of good and bad cars by buyers and sellers are given in the accompanying table. Buyers Sellers Expected price = Good 50 35 Bad 20 10 All buyers are risk neutral. (a) Assuming that all cars are put up for sale, calculate the expected price that a buyer would be willing to pay. (b) Suppose buyers pay this price. What is the minimum value of G for which both types of cars will be offered on the market? Show the reasoning. (c) Suppose that G=8/10. What is the maximum price buyers are willing to pay for a car? Will both types of cars be offered for sale in the market at this price? (d) Continue to assume that G-8/10 There is an agency that can assess each car and certify it as "good" or "bad". If certified as good, the seller can negotiate a price of 45 with the buyer. ● ● If uncertified cars are selling for the price you found in (c), what is the maximum that a seller of a good car will be willing to pay to get his car assessed? In the market for used cars there are good cars and bad cars. ● ● The good cars comprise a fraction G of all the cars that may be potentially up for sale, where 0<G<1. Buyers cannot distinguish a good car from a bad car, whereas each seller knows the type of car she has. The valuation of good and bad cars by buyers and sellers are given in the accompanying table. Buyers Sellers Expected price = Good 50 35 Bad 20 10 All buyers are risk neutral. (a) Assuming that all cars are put up for sale, calculate the expected price that a buyer would be willing to pay. (b) Suppose buyers pay this price. What is the minimum value of G for which both types of cars will be offered on the market? Show the reasoning. (c) Suppose that G=8/10. What is the maximum price buyers are willing to pay for a car? Will both types of cars be offered for sale in the market at this price? (d) Continue to assume that G-8/10 There is an agency that can assess each car and certify it as "good" or "bad". If certified as good, the seller can negotiate a price of 45 with the buyer. ● ● If uncertified cars are selling for the price you found in (c), what is the maximum that a seller of a good car will be willing to pay to get his car assessed?

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