Problem 1

• A monopolist has a demand function and a cost function given by the following table. How many should he produce? And what price should he sell it? And what will be his profits?

Q P C 0 6 1 15 11 2 13 16 3 11 21 4 8 26 5 7 31 6 6 36 7 5 41

Problem 1

• A monopolist has a demand function and a cost function given by the following table. How many should he produce? And what price should he sell it? And what will be his profits?

Q P C TR MR MC 0 6 1 15 11 15 15 5 2 13 16 26 11 5 3 11 21 33 7 5 4 8 26 32 -1 5 5 7 31 35 3 5 6 6 36 36 1 5 7 5 41 35 -1 5

I completed the attached table, which should

answer all. Note =12

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

b. Assuming that the industry is competitive, what will be the price of widgets?

c. How many will be sold?

d. How many plants/firms will produce widgets?

e. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

Q =3. Simply divide output by cost for each entry in the table

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

b. Assuming that the industry is competitive, what will be the price of widgets?

c. How many will be sold?

d. How many plants/firms will produce widgets?

e. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

P=12, for that defines LRMC

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

b. Assuming that the industry is competitive, what will be the price of widgets?

c. How many will be sold?

d. How many plants/firms will produce widgets?

e. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

Q = 420-10P

If P=12, Q = 300

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

b. Assuming that the industry is competitive, what will be the price of widgets?

c. How many will be sold?

d. How many plants/firms will produce widgets?

e. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

Total output =300,

each plant produces 3,

N = 100

Problem 2

• Q = 420 - 10 P• There is one and

only one way of producing widgets. The cost varies with the number produced at each plant.

Q C 0 0 1 22 2 28 3 36 4 52 5 70

Assume initially that, by law, a firm is limited to operating one and only one plant.

a. What level of output minimizes average cost? Explain your answer.

b. Assuming that the industry is competitive, what will be the price of widgets?

c. How many will be sold?

d. How many plants/firms will produce widgets?

e. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

LRMC = 12, find where MR =12,

and that occurs at Q = 150

Pashigian, Chapter 9, Exercise 5

Pashigian, Chapter 9, Exercise 5

(P-MC)/P = -1/. If the price elasticity is -2, and the firm is

engaging in profit maximization, then P= 2 MC. If P = 1.3 AC, then 2MC = 1.3 AC, so that MC = 0.65

AC. And, if MC is less than average cost, average cost is falling. That

means economies of scale.

Pashigian, Chapter 9, Exercise 6

Pashigian, Chapter 9, Exercise 6

The monopolist is not maximizing profits. The new plants have minimum average cost of (say) ACnew, which is less than ACold, the minimum of the former plants. Since the monopolist uses the rule MR - MC, the lower marginal cost (ACnew) leads it to expand production and lower price. Thus the increase in output to Q1.

Pashigian, Chapter 9, Exercise 6

The problem is with the amount of output it continues to produce in the old plants. The problem makes it clear that the monopolist does not reduce output in his old plants, though he clearly should. The right operating rule for the monopolist is to have MC equal for all plants and that requires that he reduce output in the existing plants from say qo to q1

Pashigian, Chapter 9, Exercise 9

Pashigian, Chapter 9, Exercise 9

Find the point where the Marginal cost curve hits the demand curve. Set that price as the regulated price. Firms will follow the rule MR = MC and go to the point where the marginal cost curve hits the demand curve. The situation is illustrated in the following graph. Here P* is the regulated price that maximizes output and Q* is the maximum output.

If people are offered the chance to bid for the monopoly, then they will bid up to the difference between average cost and price (marginal cost) times quantity. That is shown as the shaded area in the graph. Note that this is a positive area only if MC > AC, and that implies that AC must be increasing.

Pashigian, Chapter 9, Exercise 11

Pashigian, Chapter 9, Exercise 11

I disagree. If the monopolist were to keep output constant and eat the tax, the statement would be correct. But the monopolist will see his marginal cost rising by $10. Following the rule MR = MC, the monopolist will see that now MR < MC which is up by $10. Thus the monopolist will cut output to raise marginal revenue. Suppose for instance he cuts output to 900,000 units to reach the point where MR = MC (given that marginal cost is up by $10.). On the way from 1,000,000 to 900,000 units, each cut in output is costing him less revenue than it is saving him in cost, thus reducing his losses. In the end, profits go down, but by less than $10 million.