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 $900 for cars of quality q=1 and $4100 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 is a separating equilibrium. In addition, what will be the price in the pooling equilibrium?