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Monopolist Profit Maximization: Finding Output, Price, and Economic Profit, Assignments of Microeconomics

Shepherd UniversityMicroeconomics

Problems for chapter 9 of economics, focusing on a monopolist's profit maximization. Students are required to find the profit-maximizing level of output, the price the monopolist will charge, and the total economic profit. Several demand and cost functions for different scenarios.

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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PROBLEM SET 5
Problems for Chapter 9
1. Suppose that a pure monopolist has the following demand and cost functions:
Q P TR MR MC ATC
0 $105 -- -- --
1 100 45 105
2 83 40 72.5
3 71 35 60
4 63 30 52.5
5 55 35 49
6 48 40 47.5
7 42 45 47.14
8 37 55 48.13
9 33 65 50
10 29 75 52.5
a. Fill in the blank columns above. Graph the Demand Curve and the Marginal
Revenue Curve.
b. Find the profit-maximizing level of output, the price the monopolist will
charge, and the total economic profit the monopolist will earn. (NOTE:
There is no level of output where MR exactly equals MC. Choose the level of
output closest to MR = MC without letting MR become less than MC).
DEMAND
TOTAL FIXED COSTS = 60
pf3
pf4
pf5

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PROBLEM SET 5

Problems for Chapter 9

  1. Suppose that a pure monopolist has the following demand and cost functions: Q P TR MR MC ATC 0 $105 -- -- -- 1 100 45 105 2 83 40 72. 3 71 35 60 4 63 30 52. 5 55 35 49 6 48 40 47. 7 42 45 47. 8 37 55 48. 9 33 65 50 10 29 75 52. a. Fill in the blank columns above. Graph the Demand Curve and the Marginal Revenue Curve. b. Find the profit-maximizing level of output , the price the monopolist will charge, and the total economic profit the monopolist will earn. (NOTE: There is no level of output where MR exactly equals MC. Choose the level of output closest to MR = MC without letting MR become less than MC).

DEMAND TOTAL FIXED COSTS = 60

  1. Suppose that a pure monopolist has the following demand and cost functions: Q P TR MR TC MC 0 $105 -- $140 -- 1 100 220 2 95 280 3 90 320 4 85 340 5 80 370 6 75 410 7 70 460 8 65 520 9 60 590 10 55 670 11 50 760 12 45 860 a. Fill in the blank columns above. Graph the Demand Curve and the Marginal Revenue Curve. b. Find the profit-maximizing level of output , the price the monopolist will charge, and the total economic profit the monopolist will earn. (NOTE: There is no level of output where MR exactly equals MC).
  2. Suppose that a monopolist faces the following demand and cost functions: Q P TR MR TC MC ATC 0 $8.00 -- $6 -- -- 1 7.00 8 2 8. 2 6.00 9 1 4. 2.5 5.50 10 2 4. 3 5.00 12 4 4. 4 4.00 20 8 5. 5 3.00 35 15 7. a. Find the profit-maximizing level of output for the firm. Calculate the total profit for this level of output. b. Suppose the government imposes a lump-sum tax of $3.75 on this firm. (NOTE: The tax must be paid no matter how much the monopolist produces—thus add $3.75 to total costs at every level of output and recalculate MC and ATC). Show that this tax does not change the level of output the firm will produce, but will completely eliminate the monopoly profits. c. Is society better off because the monopoly profits have been eliminated? Explain. (HINT: Think about the conditions for resource efficiency).

DEMAND

DEMAND

  1. a. Q P TR MR TC MC ATC 0 8.00 0 6 1 7.00 7 7 8 2 8. 2 6.00 12 5 9 1 4. 2.5 5.50 **13.75 3.5**** 10 2 4. 3 5.00 **15 2.5**** 12 4 4. 4 4.00 16 1 20 8 5. 5 3.00 15 -1 35 15 7. **MR = TR/Q = TR/. The profit-maximizing output: Q = 2.5. Profit is $3.75. b. Q P TR MR TC MC ATC 0 8.00 0 9. 1 7.00 7 7 11.75 2 11. 2 6.00 12 5 12.75 1 6. 2.5 5.50 13.75 3.5 13.75 1 5. 3 5.00 15 2.5 15.75 2 5. 4 4.00 16 1 23.75 8 5. 5 3.00 15 -1 38.75 15 7. The tax is a fixed cost. Thus, it does not affect TVC, MC, or the profit-maximizing level of output. All that changes are the profits earned at the profit-maximizing level of output, which fall to zero. c. Static Efficiency: Since the tax changes neither prices nor the level of output, society is no better off. The monopolist still produces “too little and charges too high a price.” In other words, the monopolist does not produce at P = MC and therefore does not achieve allocative efficiency. The monopolist also does not produce at minimum ATC and thus does not achieve productive efficiency.

TEXT, p. P-18:

  1. a P Q TR MR TC MC ATC 20 0 0 8 18 1 18 18 14 6 14. 16 2 32 14 22 8 11. 14 3 42 10 32 10 10. 12 4 48 6 44 12 11. 10 5 50 2 58 14 11. 8 6 48 -2 74 16 12. 6 7 42 -6 92 18 13. 4 8 32 -10 112 20 14. 2 9 18 -14 147 35 16. b. c. At 5 units of output. d. MR = 2; MC = 14. e. At Q = 3. f. MR and MC both equal 10. g. Profits = TR – TC = 42 – 32 = 10. h. Q = 4; P = 12. (NOTE: In a competitive industry, this MC curve becomes the industry supply curve and this monopoly firm’s demand curve becomes the market demand curve. A competitive market would produce the amount of output where the market demand curve crosses the market supply curve (at Q = 4 where P = MC) and charge a price of $12. i. In the long-run , in a competitive industry, the price would be bid down to the minimum of the long-run ATC. If the ATC curve above (in part a) is a long-run ATC, the price will go down to $10.67.
      • 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 Q P, MR, MC D MR MC