6) A monopolist with marginal costs of 4 sells to two different groups of consumers. Each group has ten consumers. Individual demand of consumers in group A is given by QA(P)=20-P and for consumers in group B by QB(P)=16-P. (a) Suppose the monopolist cannot prevent arbitrage. Is price discrimination possible? Calculate the market output(s), price(s) and profits. (b) Suppose the monopolist can prevent arbitrage but does not know the type of consumers. Is price discrimination possible? Calculate the market output(s), price(s) and profits. (c) Suppose the monopolist can prevent arbitrage between groups but not within. Is price discrimination possible? Calculate the market output(s), price(s) and profits. (d) Suppose the monopolist can identify consumers and prevent arbitrage both between and within groups. Is price discrimination possible? Calculate the market output(s), price(s) and profits. 5) Let the demand of an industry be described by Q(P)=48-P. (a) Calculate the market output and priçe under monopoly assuming that the monopolist's cost function is C(Q)=Q²15+6Q+180. Find social welfare. (b) Consider a perfectly competitive industry with n firms in which each firm's cost function is C(q)=2q² +6q+18. Find the aggregate supply curve and compare to the monopolist's marginal cost in (a). (c) Calculate the market output and price in the long run under perfect competition assuming that each firm's cost function is in (b). Find social welfare and compare to the monopoly in (a). (d) Determine the Lerner index corresponding to the industries in (a) and (c).