3. (25) Participation mandate in the market for lemons. Consider the product market model of Akerlof (1970) The market is populated by a continuum of sellers Each seller is endowed with a unit of the good. If the quality of his good is 9 E [1, 2], the seller gets utility 11(9) = 20 from consuming the good and utility p from selling the good at the price p. The fraction of sellers endowed with a good of quality 9 S 0 is F(8) = 6' 1' The market is also populated by a continuum of buyers. Each buyer gets utility 9 p from purchasing a good of quality 0 at the price 1). Information is asymmetric. Sellers know the quality of their own good. Buyers only know the average quality of the goods that are traded in equilibrium. a. Write down and solve the problem of the selleri b. Compute the reservation quality function RC0)7 i.e. the highest quality of the goods that sellers choose to trade when the price is p. c. Compute the average quality function My), ie the average quality of the goods that sellers choose to trade when the price is p