Suppose there are two groups of consumers: high demand (1) and low demand (2). Inverse demands are p=12q1,0SpS 12 p=3q2,0p8 a) Compute the inverse demand for the integrated market with two consumer groups. Plot it with p on the vertical and q = q1 +q2 on the horizontal. b) Suppose that the monopolist charges a uniform price on the integrated market and that his marginal cost is c = 0. Find price, quantity sold, consumer surplus and monopolist's prot. Compute the social welfare (sum of consumer surpluses and profits) (Hint: compute consumer surplus for high demand and low demand segments separately, then add them up. How much does the low demand group buy? How much does the high demand group buy?) c) Now assume that the monopolist can price discriminate between the market segments. Find the prices and quantities for the low demand and the high demand market. Find the monopolist's profit and total consumer surplus. Show that welfare goes down. d) Now assume that demands are the same but marginal cost is higher: c = 7. Show that under the uniform pricing the low demand group does not buy some markets are not served. Compute the social welfare. e) Allow the third degree price discrimination. Compute prices and quantities with c = 7. Show that now all markets are served and that welfare goes up relative to the uniform pricing case in part d)