Lemons Market with Three Types: Consider the Akerlof lemons model with three types. Suppose the quality is g 6 {0,172} with Pr(q : 0) : Pr(q : 2) : o: E (071/2). Suppose that the valuation of a quality q car to the seller is q and to the buyer it is vq for some 1} > 1. Recall that in the lemons model all parameters (eg. 12) are commonly known but the seller is privately informed about the quality q. (a) Under which conditions on v and a does there exist a price p such the buyer and all seller types are willing to trade? (b) Under which conditions on v and a does there exist a price p such the buyer and seller types q E {0, 1} are willing to trade? (c) Under which conditions on v and a does there not exist a price p for which q > 0 is ever traded? (d) Explain the intuition for why a: matters for the fraction of cars sold in the market