Exercise 4: Collusion in prices Suppose there are three rms producing a homogeneous good, each with a cost function given by C ('15) = 4m, 1' = 1,2, 3. Firms are playing an infinitely,r repeated game, facing a market demand given by Q{p) = Hip2, where Q = q] + 12 + 33. Both rms discount prots with a common discount factor .5 E [I], 1}. Unlike the previous exercise, suppose now that competition is through prices. a} (1i) point} If rms were to collude, what would market price and total market output be? If rms were to split production and profits in equal parts, how many units would each rm be producing and what would each rm's prots he? (Hint: Set up the monopolist's problem) b} {if} point) For which value of cl will a firm be indifferent between honoring a collusive agreement or cheat- ing on it