3. (35) Advantageous selection and efficiency. Consider the product market model of Akerlof (1970). The market 1= populated by a contimmm of sellers with measure = 1. Each seller has one unit of the good. Goods differ in quality #. The distribution of quality across sellers iz a uniform with support [0,1]. The seller's valuation of the good is v(#) = 1 #. The market is also populated by a continuum of buyers with measure B = 1. Each buyer gets utility # p from purchasing a good of guality # 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. . (10) Suppose that the market price is p [0,1]. Plot v(#) and p as functions of #. 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 R(p). (5) Compute the average quality function wp(p), i.e. the average quality of the goods that sellers choose to put on the market when the price is p. P d. (5) Using your previous answers solve for the equilibrium price p*, the equilibrium reservation price R*, and the equilibrium average quality of goods sold p*. o . (10) Plot the buyer's valuation f and the seller's valuation v(#) as functions of #. Efficiency requires that all and only the goods such that 8 = (f) are traded. Is this efficiency condition satisfied in equilibrium? Explain