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In: Economics

Suppose there are only two types of cars in the used car market q=0 and q=1....

Suppose there are only two types of cars in the used car market q=0 and q=1. Half the cars are q=0 and the other half are q=1. Buyers still cannot tell the quality but they are aware of the quality distribution. Sellers are willing to accept any price p >0, but prefer to receive a higher price. If buyers do not know q, then they are willing to pay p=10000*Q+500 where Q is the average quality of the cars in the market. Suppose that sellers can get their car certified by having it tested by a third party. Denote y as the number of certifications. Let the cost of each certification be $750 for cars of quality q=1 and $ 4180 for cars of quality q=0. If buyers believe that the certification signals the quality, then they are willing to pay p=10, 500 for signal of high quality and p=500 for the signal of low quality. Find the range for the number of certifications (y) such that there isa separating equilibrium. In addition, what will be the pricein the pooling equilibrium?

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