Suppose that John wants to purchase a new car and meets a prospective seller who owns a vehicle, the quality of which John does not know how to assess. The seller does know the quality of the vehicle, it may be any number x from [O,1] - uniformly distributed. Thus x constitutes her reservation price: he/she will not sell the car for any less than x. John is an eager buyer, so he value quality x at ax; a> 1. Note that there is a one to one mapping of the sellers reservation price and quality.
Write down an expression for social surplus. Define this expression as W. Are there any gains from trade? Explain Now we consider the lemons problem. We know the seller will accept a sale if p > x. That is the price exceeds that of the reservation price. Thus for a given price p find the expected quality of the vehicle for John and his average valuation. Define this his average valuation as E[v].