1. Consider Akerlof's market for lemons, in which sellers get utility of Us = 7-1X/+M where M is dollars of other consumption and X, is the quality of the ith car that the seller owns. Buyers also get utility from car quality and other consumption. Suppose that all buyers' utility function is Ug = {1-12X{ + M. a. Consider a seller who own 2 cars. What does his utility function look like? b. Suppose the price of used cars in the market is P. According to the Akerloff model, which cars will be placed on the market? How do we represent the decision for a seller to sell in terms of a seller's utility? c. Do buyers or sellers value a car of a given quality more? Why is this important? d. Buyers cannot determine the quality of any individual car, but they do know the distribution of cars available for sale. Suppose that car quality is uniformly distributed between 0 and 200. At a market price of P=$100, what is the expected quality of a car offered for sale? What happens to the expected quality of cars if P=$80? e. Will any cars sell in this market if P=$80? f. Will any cars sell in this market if P=$120? 1. Consider Akerlof's market for lemons, in which sellers get utility of Us = 7-1X/+M where M is dollars of other consumption and X, is the quality of the ith car that the seller owns. Buyers also get utility from car quality and other consumption. Suppose that all buyers' utility function is Ug = {1-12X{ + M. a. Consider a seller who own 2 cars. What does his utility function look like? b. Suppose the price of used cars in the market is P. According to the Akerloff model, which cars will be placed on the market? How do we represent the decision for a seller to sell in terms of a seller's utility? c. Do buyers or sellers value a car of a given quality more? Why is this important? d. Buyers cannot determine the quality of any individual car, but they do know the distribution of cars available for sale. Suppose that car quality is uniformly distributed between 0 and 200. At a market price of P=$100, what is the expected quality of a car offered for sale? What happens to the expected quality of cars if P=$80? e. Will any cars sell in this market if P=$80? f. Will any cars sell in this market if P=$120