Please help me answer this question , thanks!

Suppose a local car dealership is offering an inspection service that can perfectly determine the quality of any car on the market. The dealership is trying to determine how much it will be able to charge for this procedure. Review the original assumptions about the Akerlof model. Specifically, we assume the buyer and seller utilities from equations:71 US = 2X, + M i=1 n 3 j=1 that car quality X is distributed uniformly from 0 to 100, and that the prevailing price P=50. a. b. Due to adverse selection, only some of the cars remain on the market (Q(P)). How are these cars distributed, and what is their average quality? Suppose a buyer picks a car i at random from the cars still available on the market, and thinks about whether to purchase it. What is her expected change in utility from this transaction? Even though her expected change in utility is negative, there is a possibility that she picked a relatively high-quality car and that her actual change in utility would be positive. What is the lowest value of X1 such that this will happen, and what is the probability that X,- is at least this high? Now suppose the local car dealership decides to offer this buyer its inspection service for free, before she decides whether to purchase the car. She resolves to purchase car i if it will increase her utility, and refrain from purchasing it if it will not increase her utility. Now, what is her expected change in utility from this transaction, considering that we do not yet know whether the car will be good enough to purchase? How does this differ from your answer in (b)? How much will the dealership be able to charge for the inspection service, assuming the price remains at $50 and that all other assumptions are constant? Justify your answer. Imagine that word about the inspection service gets out to everyone in the market, including sellers. How will sellers with high-quality cars react? How will sellers with lowquality cars react? Will there be any adverse selection in the market