Question

4. Exercise 16.6 The industry demand function for bulk plastics is represented by the following equation:

P=800−20Q where Q represents millions of pounds of plastic.

The total cost function for the industry, exclusive of a required return on invested capital, is TC=300+500Q+10Q2

If this industry acts like a monopolist in the determination of price and output, the profit-maximizing level of price and output will be(------) $ and (------) million respectively.

The total profit at this price-output level is ($-------) million.

Assume that this industry is composed of many (500) small firms, such that the demand function facing any individual firm is P=$620 .

Under these conditions, the profit-maximizing level of price and (total industry) output will be($------------) and (-------)million respectively. (Hint: The industry’s total cost function remains unchanged.)

The total profit at this price-output level is ($----------) million.

Because of the risk of this industry, investors require a 15 percent rate of return on investment. Total industry investment amounts to $2 billion. If the monopoly solution prevails, the total industry profit is ($------------) million.

If the competitive solution most accurately describes the industry, which of the following is most likely to happen?

a) New firms will enter the market.

b) Number of firms remains unchanged.

c) Some firms will exit the market.

Suppose the Clean Water Coalition proposes pollution control standards for the industry that would change the industry cost curve to the following: TC=400+560Q+10Q2

What is the impact of this change on price, output, and total profits under the monopoly solution?

Price: Increase or Decrease or No change

Output: Increase or Decrease or No Change

Total Profits: Increase or Decrease or No change

Answer 1

Marginal cost (MC) = dTC/dQ = 500 + 20Q

(1) A monopolist maximizes Profit when MR = MC.

Total revenue (TR) = P x Q = 800Q - 20Q²

MR = dTR/dQ = 800 - 40Q

800 - 40Q = 500 + 20Q

60Q = 300

Quantity = 5

Price = 800 - (20 x 5) = 800 - 100 = 700

TR = 700 x 5 = 3,500

TC = 300 + (500 x 5) + (10 x 5 x 5) = 300 + 2,500 + 250 = 3,050

Profit = TR - TC = 3,500 - 3,050 = 450

(2) A competitive firm will maximize profit when P = MC.

620 = 500 + 20Q

20Q = 120

Q = 6 (Firm quantity)

Price = 620

Industry quantity = Firm quantity x Number of firms = 6 x 500 = 3,000

TR = 620 x 6 = 3,720

TC = 300 + (500 x 6) + (10 x 6 x 6) = 300 + 3,000 + 360 = 3,660

Firm Profit = 3,720 - 3,660 = 60

Industry profit = Firm profit x Number of firms = 60 x 500 = 30,000

(3) Industry return on investment ($ million) = Investment x Required rate of return = 2,000 x 15% = 300

Industry profit = 450 - 300 = 150

(4) Correct Option is (a)

Firms earning positive short run profit will attract new entry and new firms will enter.

(5) Price: Increase, Quantity: Decrease, Profit: Decrease

New MC = 560 + 20Q

When MC increases, with MR = MC, quantity will increase and price will decrease.

800 - 40Q = 560 + 20Q

60Q = 240

Q = 4

P = 800 - (20 x 4) = 800 - 80 = 720

TR = 720 x 4 = 2,880

TC = 400 + (560 x 4) + (20 x 4 x 4) = 400 + 2,240 + 320 = 2,960

Profit = 2,880 - 2,960 = - 80 (Loss)