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11.2. A monopolist faces a market demand curve given by Q3D 70 — Р. The monopolisťs marginal revenue function is given by MR = 70 – 2Q. a. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what out put level will the monopolist choose in order to maxi- mize profits? What is the price at this output level? What are the monopolist's profits? b. Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25Q² – 5Q+300 and marginal cost is given by МС 3 0.5Q — 5. With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by 11 TC = 0.01Q³ – Q² + 45Q+ 100 and marginal costs given by MC = 0.03Q² – 2Q+45. Again, calculate the monopolisť's price-quantity combination that maximizes profits. What will profits be? (Hint: set MC = MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.)

11.2. A monopolist faces a market demand curve given by Q3D 70 — Р. The monopolisťs marginal revenue function is given by MR = 70 – 2Q. a. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what out put level will the monopolist choose in order to maxi- mize profits? What is the price at this output level? What are the monopolist's profits? b. Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25Q² – 5Q+300 and marginal cost is given by МС 3 0.5Q — 5. With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by 11 TC = 0.01Q³ – Q² + 45Q+ 100 and marginal costs given by MC = 0.03Q² – 2Q+45. Again, calculate the monopolisť's price-quantity combination that maximizes profits. What will profits be? (Hint: set MC = MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.)

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.1P
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11.2. A monopolist faces a market demand curve given by Q = 70 – P. The monopolist's marginal revenue function is given by MR = 70 – 2Q. a. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what out put level will the monopolist choose in order to maxi- mize profits? What is the price at this output level? What are the monopolisť's profits? b. Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25Q² – 5Q+300 %3D and marginal cost is given by МС — 0.5Q —5. With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by 11.4. TC = 0.01Q³ – Q² + 45Q+ 100 %3D and marginal costs given by МС — 0.03Q — 2Q+ 45. Again, calculate the monopolisť's price-quantity combination that maximizes profits. What will profits be? (Hint: set MC = MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.) d. Graph the market demand curve, the MR curve, and the three marginal cost curves from part a, part b, and part c. Notice that the monopolist's profit-making ability is constrained by (1) the mar- ket demand curve it faces (along with its associated MR curve), and (2) the cost structure underlying its production.
Transcribed Image Text:11.2. A monopolist faces a market demand curve given by Q = 70 – P. The monopolist's marginal revenue function is given by MR = 70 – 2Q. a. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what out put level will the monopolist choose in order to maxi- mize profits? What is the price at this output level? What are the monopolisť's profits? b. Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25Q² – 5Q+300 %3D and marginal cost is given by МС — 0.5Q —5. With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by 11.4. TC = 0.01Q³ – Q² + 45Q+ 100 %3D and marginal costs given by МС — 0.03Q — 2Q+ 45. Again, calculate the monopolisť's price-quantity combination that maximizes profits. What will profits be? (Hint: set MC = MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.) d. Graph the market demand curve, the MR curve, and the three marginal cost curves from part a, part b, and part c. Notice that the monopolist's profit-making ability is constrained by (1) the mar- ket demand curve it faces (along with its associated MR curve), and (2) the cost structure underlying its production.
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