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Suppose That There Are Two Types of Cars,good and Bad

question 46

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Suppose that there are two types of cars,good and bad.The qualities of cars are not observable but are known to the sellers.Risk-neutral buyers and sellers have their own valuation of these two types of cars as follows:
 Types of Cars  Buyer’s Valuation  Beller’s Valuation  Good  (50% probability)  5,0004,500 Bad  (50% probability)  3,0002,500\begin{array} { | l | l | l | } \hline \text { Types of Cars } & \text { Buyer's Valuation } & \text { Beller's Valuation } \\\hline \text { Good } & & \\\text { (50\% probability) } & 5,000 & 4,500 \\\hline \text { Bad } & & \\\text { (50\% probability) } & 3,000 & 2,500 \\\hline\end{array} Now suppose that sellers value a good car at $4,500 and a bad car at $2,500,and quality is not observed by the buyers.What is the highest price that risk-neutral buyers will offer for a used car if they recognize adverse selection?


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