Consider a natural monopoly with a market demand curve of QD=50P. The monopolist's costs are described...

 

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Consider a natural monopoly with a market demand curve of QD=50P. The monopolist's costs are described by TC = 4Q and MC = 4. Marginal revenue is given by MR = 100 - 4Q. (a) Find the quantity that the monopolist will produce and the price that it will set to maximize profit. How much profit, M, do they make? (b) Suppose the monopolist could distinguish between two market segments in this market, those with a high valuation of the good, and those with a lower valuation of the good. Explain why price discrimination could increase profits for the monopolist. (c) Calculate consumer surplus at the monopolist price and quantity. How would we expect consumer surplus to change if this market became perfectly competitive? Should the government intervene? (d) Suppose that, through innovation, a new firm is able to enter the market to compete with the monopoly, creating a duopoly. The two firms (A and B) decide to cooperate or compete with the price they each set. They choose between mimicking a monopoly and setting a monopoly price, PM, or competing and setting a lower price to try and capture more of the market. The payoff matrix below describes the corresponding profits to each of their decisions. (A,B) PM Lower P PM M (¹/2,¹/2) (700, 200) What is A's best response to B setting the monopoly price? What is B's best response to A setting the lower price? Lower P (200,700) (450,450) What is the Nash equilibrium? Are they maximizing joint profits? Explain why neither have any incentive to individually change their strategy at this outcome. Consider a natural monopoly with a market demand curve of QD=50P. The monopolist's costs are described by TC = 4Q and MC = 4. Marginal revenue is given by MR = 100 - 4Q. (a) Find the quantity that the monopolist will produce and the price that it will set to maximize profit. How much profit, M, do they make? (b) Suppose the monopolist could distinguish between two market segments in this market, those with a high valuation of the good, and those with a lower valuation of the good. Explain why price discrimination could increase profits for the monopolist. (c) Calculate consumer surplus at the monopolist price and quantity. How would we expect consumer surplus to change if this market became perfectly competitive? Should the government intervene? (d) Suppose that, through innovation, a new firm is able to enter the market to compete with the monopoly, creating a duopoly. The two firms (A and B) decide to cooperate or compete with the price they each set. They choose between mimicking a monopoly and setting a monopoly price, PM, or competing and setting a lower price to try and capture more of the market. The payoff matrix below describes the corresponding profits to each of their decisions. (A,B) PM Lower P PM M (¹/2,¹/2) (700, 200) What is A's best response to B setting the monopoly price? What is B's best response to A setting the lower price? Lower P (200,700) (450,450) What is the Nash equilibrium? Are they maximizing joint profits? Explain why neither have any incentive to individually change their strategy at this outcome.