A natural monopolist faces the following demand curve: P = 334 - 4Q, its total cost is given by TC = 1500 + 14Q (marginal cost is the slope of total cost).
(a) If the government regulates the monopolist to charge a socially optimal price, what price will it charge and how many units will it sell? How much are the profit, consumer surplus, and producer surplus?
(b) If it is not a regulated monopolist, what is its profit-maximizing price and quantity (assuming single price monopolist)? How much are the profit, consumer surplus, producer surplus, and deadweight loss?
(c) If the regulated monopolist is allowed to charge a fair return price (which is $34), how much are the consumer surplus, producer surplus, and deadweight loss?
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63. Given a cost function C(Q) = 200 + 14Q + 8Q2, what is the marginal cost function? A. 14 + 16Qb. 14Q + 8Q2c. 200 + 8Q2d. 14 + 16Q2
Difficulty: Medium64. What is implied when the total cost of producing Q1 and Q2 together is less than the total cost of producing Q1 and Q2 separately?
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Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
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Chapter 05 - The Production Process and Costs65. For the cost function C(Q) = 1000 + 14Q + 9Q2 + 3Q3, what is the marginal cost of producing the fourth unit of output?
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107. Suppose the cost function is C(Q) = 50 + Q - 10Q2 + 2Q3. What is the total cost of producing 10 units?
108. Suppose the cost function is C(Q) = 50 + Q - 10Q2 + 2Q3. What is the variable cost of producing 10 units?
Chapter 05 - The Production Process and Costs