Text Box: 150

MONOPOLY

 
 

 

 

 

 

 

 

 

 

 

 


SOLUTIONS TO TEXT PROBLEMS:

 

Quick Quizzes

 

1.   A market might have a monopoly because: (1) a key resource is owned by a single firm; (2) the government gives a single firm the exclusive right to produce some good; or (3) the costs of production make a single producer more efficient than a large number of producers.

 

      Examples of monopolies include:  (1) the water producer in a small town, who owns a key resource, the one well in town; (2) a pharmaceutical company that is given a patent on a new drug by the government; and (3) a bridge, which is a natural monopoly because (if the bridge is uncongested) having just one bridge is efficient.  Many other examples are possible.

 

2.   A monopolist chooses the amount of output to produce by finding the quantity at which marginal revenue equals marginal cost.  It finds the price to charge by finding the point on the demand curve that corresponds to that quantity.

 

3.   A monopolist produces a quantity of output that is less than the quantity of output that maximizes total surplus because it produces the quantity at which marginal cost equals marginal revenue rather than the quantity at which marginal cost equals price.  This lower production level leads to a deadweight loss.

 

4.   Examples of price discrimination include:  (1) movie tickets, for which children and senior citizens get lower prices; (2) airline prices, which are different for business and leisure travelers; (3) discount coupons, which lead to different prices for people who value their time in different ways; (4) financial aid, which offers college tuition at lower prices to poor students and higher prices to wealthy students; and (5) quantity discounts, which offer lower prices for higher quantities, capturing more of a buyer’s willingness to pay.  Many other examples are possible.

 

      Compared to a monopoly that charges a single price, perfect price discrimination reduces consumer surplus, increases producer surplus, and increases total surplus because there is no deadweight loss.

 

5.   Policymakers can respond to the inefficiencies caused by monopolies in one of four ways:  (1) by trying to make monopolized industries more competitive; (2) by regulating the behavior of the monopolies; (3) by turning some private monopolies into public enterprises; or (4) by doing nothing at all.  Antitrust laws prohibit mergers of large companies and prevent large companies from coordinating their activities in ways that make markets less competitive, but such laws may keep companies from merging and generating synergies that increase efficiency.  Some monopolies, especially natural monopolies, are regulated by the government, but it is hard to keep a monopoly in business, achieve marginal-cost pricing, and give the monopolist an incentive to reduce costs.  Private monopolies can be taken over by the government, but the companies are not likely to be well run.  Sometimes doing nothing at all may seem to be the best solution, but there are clearly deadweight losses from monopoly that society will have to bear.

 

 

 

Questions for Review

 

1.   Government-created monopoly comes from the existence of patent and copyright laws. Both allow firms or individuals to be monopolies for extended periods of time—20 years for patents, the life of the author plus 70 years for copyrights. But this monopoly power is good, because without it, no one would write a book or a song and no firm would invest in research and development to invent new products or pharmaceuticals.  

 

2.   An industry is a natural monopoly when a single firm can supply a good or service to an entire market at a smaller cost than could two or more firms. As a market grows, it may evolve from a natural monopoly to a competitive market.

 

3.   A monopolist's marginal revenue is less than the price of its product because its demand curve is the market demand curve. Thus, to increase the amount sold, the monopolist must lower the price of its good for every unit it sells. This cut in price reduces the revenue on the units it was already selling.

 

      A monopolist's marginal revenue can be negative because to get purchasers to buy an additional unit of the good, the firm must reduce its price on all units of the good. The fact that it sells a greater quantity increases the firm’s revenue, but the decline in price decreases the firm’s revenue. The overall effect depends on the price elasticity of demand. If demand is inelastic, marginal revenue will be negative.

 

4.   Figure 1 shows the demand, marginal-revenue, average-total-cost, and marginal-cost curves for a monopolist. The intersection of the marginal-revenue and marginal-cost curves determines the profit-maximizing level of output, Qm. The profit-maximizing price, Pm can be found using the demand curve. Profit is shown as the rectangular area with a height of (PMATCM) and a base of QM.

 

 

 

Figure 1

 

 

5.   The level of output that maximizes total surplus in Figure 1 is where the demand curve intersects the marginal-cost curve, Qc. The deadweight loss from monopoly is the triangular area between Qc and Qm that is above the marginal-cost curve and below the demand curve. It represents deadweight loss, because society loses total surplus because of the monopoly. The deadweight loss is equal to the value of the good (measured by the height of the demand curve) less the cost of production (given by the height of the marginal-cost curve), for the quantities between Qm and Qc.

 

6.   One example of price discrimination is in publishing books. Publishers charge a much higher price for hardback books than for paperback books—far higher than the difference in production costs. Publishers do this because die-hard fans will pay more for a hardback book when the book is first released. Those who don't value the book as highly will wait for the paperback version to come out. The publisher makes a greater profit this way than if it charged just one price.

 

      A second example is the pricing of movie tickets. Theaters give discounts to children and senior citizens because they have a lower willingness to pay for a ticket. Charging different prices helps the theater increase its profit above what it would be if it charged just one price.

 

      Many other examples are possible.

 

7.   The government has the power to regulate mergers between firms because of antitrust laws. Firms might want to merge to increase operating efficiency and reduce costs, something that is good for society, or to gain market power, which is bad for society.

 

8.   When regulators tell a natural monopoly that it must set price equal to marginal cost, two problems arise. The first is that, because a natural monopoly has a marginal cost that is always less than average total cost, setting price equal to marginal cost means that the price is less than average total cost, so the firm will incur a loss. The firm would then exit the industry unless the government subsidized it. However, getting revenue for such a subsidy would cause the government to raise other taxes, increasing the deadweight loss. The second problem of using costs to set price is that it gives the monopoly no incentive to reduce costs.

 

 

Problems and Applications

 

1.   The following table shows revenue, costs, and profits, where quantities are in thousands, and total revenue, total cost, and profit are in millions of dollars:

 

Price

Quantity

(1,000s)

Total Revenue

Marginal Revenue

Total Cost

Profit

$100

   0

$0

----

$2

 $-2

90

100

 9

$9

 3

 6

80

200

16

 7

 4

12

70

300

21

 5

 5

16

60

400

24

 3

 6

18

50

500

25

 1

 7

18

40

600

24

-1

 8

16

30

700

21

-3

 9

12

20

800

16

-5

10

6

10

900

9

-7

11

-2

0

1,000

0

-9

12

-12

 

a.   A profit-maximizing publisher would choose a quantity of 400,000 at a price of $60 or a quantity of 500,000 at a price of $50; both combinations would lead to profits of $18 million.

 

b.   Marginal revenue is always less than price. Price falls when quantity rises because the demand curve slopes downward, but marginal revenue falls even more than price because the firm loses revenue on all the units of the good sold when it lowers the price.

 

c.    Figure 2 shows the marginal-revenue, marginal-cost, and demand curves. The marginal-revenue and marginal-cost curves cross between quantities of 400,000 and 500,000. This signifies that the firm maximizes profits in that region.

 

 

Figure 2

 

d.   The area of deadweight loss is marked “DWL” in the figure. Deadweight loss means that the total surplus in the economy is less than it would be if the market were competitive, because the monopolist produces less than the socially efficient level of output.

 

e.   If the author were paid $3 million instead of $2 million, the publisher would not change the price, because there would be no change in marginal cost or marginal revenue. The only thing that would be affected would be the firm’s profit, which would fall.

 

f.    To maximize economic efficiency, the publisher would set the price at $10 per book, because that is the marginal cost of the book. At that price, the publisher would have negative profits equal to the amount paid to the author.

 

Figure 3

 

2.   Figure 3 illustrates a natural monopolist setting price, PATC, equal to average total cost. The quantity produced is QATC. Marginal cost pricing would yield the price PMC and quantity QMC. For quantities between QATC and QMC, the benefit to consumers (measured by the height of the demand curve) exceeds the cost of production (measured by the height of the marginal-cost curve). This means that the deadweight loss from setting price equal to average total cost is the triangular area shown in the figure.

 

3.   If the price of tap water rises, the demand for bottled water increases. This is shown in Figure 4 as a shift to the right in the demand curve from D1 to D2. The corresponding marginal-revenue curves are MR1 and MR2. The profit-maximizing level of output is where marginal cost equals marginal revenue. Prior to the increase in the price of tap water, the profit-maximizing level of output is Q1; after the price increase, it rises to Q2. The profit-maximizing price is shown on the demand curve: it is P1 before the price of tap water rises, but rises to P2. Average total cost is AC1 before the price of tap water rises and AC2 after. Profit increases from (P1AC1) x Q1 to (P2AC2) x Q2.

 

 

Figure 4

4.   a.   Figure 5 illustrates the market for groceries when there are many competing supermarkets with constant marginal cost. Output is QC, price is PC, consumer surplus is area A, producer surplus is zero, and total surplus is area A.

 

 

Figure 5

 

b.   If the supermarkets merge, Figure 6 illustrates the new situation. Quantity declines from QC to QM and price rises to PM.  Consumer surplus falls by areas D + E + F to areas B + C. Producer surplus becomes areas D + E, and total surplus is areas B + C + D + E. Consumers transfer the amount of areas D + E to producers and the deadweight loss is area F.

 

 

Figure 6

 

5.   a.   The following table shows total revenue and marginal revenue for each price and quantity sold:

 

Price

Quantity

Total Revenue

Marginal Revenue

Total Cost

Profit

24

10,000

$240,000

----

$50,000

$190,000

22

20,000

  440,000

    $20

 100,000

  340,000

20

30,000

  600,000

16

 150,000

  450,000

18

40,000

  720,000

12

 200,000

  520,000

16

50,000

  800,000

8

 250,000

  550,000

14

60,000

  840,000

4

 300,000

  540,000

 

b.   Profits are maximized at a price of $16 and quantity of 50,000. At that point, profit is $550,000.

 

c.    As Johnny's agent, you should recommend that he demand $550,000 from them, so he receives all of the profit (rather than the record company).

 

 6.  a.   The table below shows total revenue and marginal revenue for the bridge. The profit-maximizing price would be where revenue is maximized, which will occur where marginal revenue equals zero, because marginal cost equals zero. This occurs at a price of $4 and quantity of 400. The efficient level of output is 800, because that is where price is equal to marginal cost. The profit-maximizing quantity is lower than the efficient quantity because the firm is a monopolist.

 

Price

Quantity

Total Revenue

Marginal Revenue

 $8

0

$0

----

7

100

700

$7

6

200

1,200

5

5

300

1,500

3

4

400

1,600

1

3

500

1,500

-1

2

600

1,200

-3

1

700

700

-5

0

800

0

-7

 

b.   The company should not build the bridge because its profits are negative. The most revenue it can earn is $1,600,000 and the cost is $2,000,000, so it would lose $400,000.

 

c.    If the government were to build the bridge, it should set price equal to marginal cost to be efficient. Since marginal cost is zero, the government should not charge people to use the bridge.

 

 

Figure 7

 

d.   Yes, the government should build the bridge, because it would increase society's total surplus. As shown in Figure 7, total surplus has area ½x 8 x 800,000 = $3,200,000, which exceeds the cost of building the bridge.

 

7.   Larry wants to sell as many drinks as possible without losing money, so he wants to set quantity where price (demand) equals average total cost, which occurs at quantity QL and price PL in Figure 8. Curly wants to bring in as much revenue as possible, which occurs where marginal revenue equals zero, at quantity QC and price PC. Moe wants to maximize profits, which occurs where marginal cost equals marginal revenue, at quantity QM and price PM.

 

 

Figure 8

 

8.   a.   Long-distance phone service was originally a natural monopoly because the installation of phone lines across the country meant that one firm's costs were much lower than if two or more firms did the same thing.

 

b.   With communications satellites, the cost is no different if one firm supplies long-distance calls or if many firms do so. So the industry evolved from a natural monopoly to a competitive market.

 

c.    It is efficient to have competition in long-distance phone service and regulated monopolies in local phone service because local phone service remains a natural monopoly (being based on landlines) while long-distance service is a competitive market (being based on satellites).

 

9.   a.   A monopolist always produces a quantity at which demand is elastic. If the firm produced a quantity for which demand was inelastic, then if the firm raised its price, quantity would fall by a smaller percentage than the rise in price, so revenue would increase. Because costs would decrease at a lower quantity, the firm would have higher revenue and lower costs, so profit would be higher. Thus the firm should keep raising its price until profits are maximized, which must happen on an elastic portion of the demand curve.

 

b.   As Figure 9 shows, another way to see this is to note that on an inelastic portion of the demand curve, marginal revenue is negative. Increasing quantity requires a greater percentage reduction in price, so revenue declines. Because a firm maximizes profit where marginal cost equals marginal revenue, and marginal cost is never negative, the profit-maximizing quantity can never occur where marginal revenue is negative. Thus, it can never be on the inelastic portion of the demand curve.

 

 

Figure 9

 

c.    Total revenue is maximized where marginal revenue is equal to zero.

 

10.        Because the socially optimal output level is greater than the monopoly output level, the government should use a subsidy to encourage the monopoly to increase production.  The monopoly firm and many of its customers will likely favor such a move, but taxpayers who do not purchase the good will not be in favor of it.

 

11.  a.   The marginal revenue from selling to each type of consumer is shown in the following tables:

 

Price

Quantity of Adult Tickets

Total Revenue from Sale of Adult Tickets

Marginal Revenue from Sale of Adult Tickets

10

0

0

----

9

100

900

9

8

200

1,600

7

7

300

2,100

5

6

300

1,800

-3

5

300

1,500

-3

4

300

1,200

-3

3

300

900

-3

2

300

600

-3

1

300

300

-3

0

300

0

-3

 

 

Price

Quantity of Child Tickets

Total Revenue from Sale of Child Tickets

Marginal Revenue from Sale of Child Tickets

10

0

0

----

9

0

0

0

8

0

0

0

7

0

0

0

6

0

0

0

5

100

500

5

4

200

800

3

3

200

600

-2

2

200

400

-2

1

200

200

-2

0

200

0

-2

 

To maximize profit, you should charge adults $7 and sell 300 tickets. You should charge children $4 and sell 200 tickets. Total revenue will be $2,100 + $800 = $2,900. Because total cost is $2,000, profit will be $900.

 

b.   If price discrimination were not allowed, you would want to set a price of $7 for the tickets. You would sell 300 tickets and profit would be $100.

 

c.    The children who were willing to pay $4 but will not see the show now that the price is $7 will be worse off. The producer is worse off because profit is lower. Total surplus is lower. There is no one that is better off.

 

d.   In (a) total profit would be $400. In (b), there would be a $400 loss.

 

12.  a.   Figure 10 shows the firm’s demand, marginal revenue, and marginal cost curves.  The firm’s profit is maximized at the output where marginal revenue is equal to marginal cost.  Therefore, setting the two equations equal, we get:

 

                        1,000 – 20Q = 100 + 10Q

                        900 = 30Q

                        Q = 30

 

                        The monopoly price is P = 1,000 – 10Q = 700 cents or $7.

 

 

Figure 10

 

b.   Social welfare is maximized where price is equal to marginal cost:

 

                        1,000 – 10Q = 100 + 10Q

                        900 = 20Q

                        Q = 45

 

                        At an output level of 45, the price would be 550 cents or $5.50.

 

c.    The deadweight loss would be equal to (0.5)(15)(300 cents) = 2,250 cents = $22.50.

 

d.   i.          A flat fee of $20 would not alter the profit-maximizing price or quantity.  The deadweight loss would be unaffected.

 

            ii.          A fee of 50 percent of the profits would not alter the profit-maximizing price or quantity.  The deadweight loss would be unaffected.

 

            iii.         The marginal cost of production would rise by $1.50 if the artist was paid that amount for every unit sold.  The new marginal cost would be 100 + 160Q.  The new profit-maximizing output would be 5 and the price would rise to 900 cents.  The deadweight loss would be much larger.

 

            iv.         If the artist is paid 50 percent of the revenue, then total revenue is 500Q – 5Q2.  Marginal revenue becomes 500 – 10Q.  The profit-maximizing output level will be 20 and the price will be 600 cents.  The deadweight loss will be greater.

 

13.  a.   Figure 11 shows the cost, demand, and marginal-revenue curves for the monopolist. Without price discrimination, the monopolist would charge price PM and produce quantity QM.

 

 

Figure 11

 

b.   The monopolist's profit consists of the two areas labeled X, consumer surplus is the two areas labeled Y, and the deadweight loss is the area labeled Z.

 

c.    If the monopolist can perfectly price discriminate, it produces quantity QC, and has profit equal to X + Y + Z.

 

d.   The monopolist's profit increases from X to X + Y + Z, an increase in the amount Y + Z. The change in total surplus is area Z. The rise in the monopolist's profit is greater than the change in total surplus, because the monopolist's profit increases both by the amount of deadweight loss (Z) and by the transfer from consumers to the monopolist (Y).

 

e.   A monopolist would pay the fixed cost that allows it to discriminate as long as Y + Z (the increase in profits) exceeds C (the fixed cost).

 

f.    A benevolent social planner who cared about maximizing total surplus would want the monopolist to price discriminate only if Z (the deadweight loss from monopoly) exceeded C (the fixed cost) because total surplus rises by Z − C.

 

g.   The monopolist has a greater incentive to price discriminate (it will do so if Y + Z > C) than the social planner would allow (she would allow it only if Z > C). Thus if Z < C but Y + Z > C, the monopolist will price discriminate even though it is not in society's best interest.