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Problem 4: Natural Monopoly Regulation (25 points). A natural monopolist faces a demand curve P 100 2Q. The monopolist has a constant rnarginal cost MC 20 and an average cost AC = 20 + a) In an unregulated market, how many units will the monopolist sell? \'Vhat price will the monopolist charge? What is the I)VVL associated with this allocation? b) Suppose that a regulator imposes marginal cost price regulation by setting P 20. How many units will thc monopolist sell? What is thc DWL associated with this allocation? What arc the monopolist profits? c) Suppose that a regulator impos(ks average cost price regulation. What price will they set? How many units will the monopolist sell? What is the DWL associated with this allocation? What are the monopolist profits? d) Suppose that there are N = 20 consumers and the regulator wants to implement the optimal two-part tariff. What per unit price P should they choose? What fixed fee F should they choose? e) Suppose that each Of the N = 20 consumers has a fixed budget Of $60 to be spent On this good. Show that the optimal two-part tariff will not achieve the efficient Outcome in this scenario. What might the regulator do in this scenario?