3. (35) Advantageous selection and efciency. Consider the product market model of Akerlof (1970]. The market is populated by a continuum of sellers with measure 5' = 1. Each seller has one unit of the good. Goods differ in quality 9. The distribution of quality across sellers is a uniform with support [0, 1]. The seller's valuation of the good is 1:09) = 1 :9. The market is also populated by a continuum of buyers with measure 3 > 1. Each buyer gets utility 9 p from purchasing a good of quality 9 at the price p. Information however is asymmetric. Sellers know the quality of their own good. Buyers only know the average quality of the goods that are put up for sale in equilibrium. :1. (10) Suppose that the market price is p E [0.1]. Plot 19(9) and p as functions of 9. In the graph, identify which sellers find it optimal to put their good on the market, and which find it optimal to keep it to themselves. [Hint: check the title of the question!] b. (5) Compute the reservation quality function RUG}. c. (5} Compute the average quality function 11(1)), i.e. the average quality of the goods that sellers choose to put on the market when the price is p. d. (5) Using your previous answers solve for the equilibrium price p\