2. Consider Problem 1 above. Assume that the firms form a cartel to act as a monopolist and maximize total industry prots (sum of Firm Aand Firm B profits). a. Determine the optimum output and selling price for each firm. b. Determine Firm A, Firm B, and total industry profits at the optimal solution found in part (a). c. Show that the marginal costs of the two rms are equal at the optimal solution found in part (a). 3. Compare the optimal solutions obtained in Problems 1 and 2 above. Specifically: a. How much higher (lower) is the optimal selling price when the two firms form a cartel to maximize industry profits compared with when they act independently? b. how much higher (lower) is total industry output? c. How much higher (lower) are total industry profits? 4. Alchem (L) is the price leader in the polygiue market. All 10 other manufacturers [follower (F) firms] sell polygiue at the same price as Alchem. Alchem allows the other rms to sell as much as they wish at the established price and supplies the remainder of the demand itself. Total demand for polygiue is given by the following function (QT = QL + OF): P = 20,000 4QT Alchem's marginal cost function for manufacturing and selling polygiue is MCL = 5,000 + 50L The aggregate marginal cost function for the other manufacturers of polygiue is