In this exercise, let's pretend there's only one make, model and age of used cars. A...

 

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In this exercise, let's pretend there's only one make, model and age of used cars. A used car can either be high quality or low quality. It is known that half of all existing used cars are high quality and the other half is low quality. If an owner of a used car wants to sell it, then the owner can make a take-it-or-leave-it offer to a potential buyer. He knows his car's quality, but the buyer does not, and there is no way to tell which it is before buying it (assume that a simple inspection wouldn't detect issues). Suppose the buyer values the high-quality used car at $20K and the low-quality used car at $10K. This means that the buyer's utility for getting the high-quality car at a price p is 20K - p, and his utility for getting the low-quality car at a price p is 10K - p. Getting a car which may be of high or low quality with equal probability at a price p gives him a utility of 15K - p (expected payoff). Not buying the car gives him a utility of 0. 1 The seller's reservation price is exactly $3K lower in each case, that is, the seller's utility from selling his car at a price p is p - 17K if it is of high quality, and p - 7K if it is of low quality. Not selling the car gives him a utility of 0. Suppose you are the buyer, and you receive a take-it-or-leave-it offer at a price p = $16K. Is it a best response to accept or not? Explain. In this exercise, let's pretend there's only one make, model and age of used cars. A used car can either be high quality or low quality. It is known that half of all existing used cars are high quality and the other half is low quality. If an owner of a used car wants to sell it, then the owner can make a take-it-or-leave-it offer to a potential buyer. He knows his car's quality, but the buyer does not, and there is no way to tell which it is before buying it (assume that a simple inspection wouldn't detect issues). Suppose the buyer values the high-quality used car at $20K and the low-quality used car at $10K. This means that the buyer's utility for getting the high-quality car at a price p is 20K - p, and his utility for getting the low-quality car at a price p is 10K - p. Getting a car which may be of high or low quality with equal probability at a price p gives him a utility of 15K - p (expected payoff). Not buying the car gives him a utility of 0. 1 The seller's reservation price is exactly $3K lower in each case, that is, the seller's utility from selling his car at a price p is p - 17K if it is of high quality, and p - 7K if it is of low quality. Not selling the car gives him a utility of 0. Suppose you are the buyer, and you receive a take-it-or-leave-it offer at a price p = $16K. Is it a best response to accept or not? Explain.

Answer rating: 100% (QA)

To determine whether accepting the takeitorleaveit offer at a price of 16K is the best res... View the full answer