Chapter 09 - Basic Oligopoly Models

Chapter 9: Answers to Questions and Problems1.

a. D2.b. D1.c.

i. $20.ii. 0 units.

iii. $20 to $50.

2.

a. Q1=a−c12b

−12Q2=

200−262(3)

−12Q2=29−0.5Q2 and

Q2=a−c22b

−12Q1=

200−322(3)

−12Q1=28−0.5Q1

b. Q1 = 20; Q2 = 18.c. P = 200 – 3(38) = $86.d. Π1 = $1200; Π2 = $972.

3.a. 125 units.b. 100 units each.c. The leader produces 150 units and the follower produces 75 units.d. 150 units.e.

i. 75 units.ii. About 112.5 units.

4.

a. QF=a−cF2b

−12QL=

16,000−6,0002(4)

−12QL=1,250−0.5QL

b. QL = 1750; QF = 375.c. P = 16,000 – 4(2125) = $7,500.d. ΠL = $6.125 million; ΠF = $562,500.

5.a. Set P = MC to get 800 – 4Q = $260. Solving yields Q = 135 units.b. P = MC = $260.c. Each firm earns zero economic profits.

6.a. Oil production. Each firm produces output independently and the market price is

determined by the total amount produced.b. Diamond production. DeBeers is the leader that sets diamond production, and

smaller firms follow with their own levels of production.

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Chapter 09 - Basic Oligopoly Models

c. Competitive bidding by identical contractors. In this case, the contractor bidding the lowest fee will win the contract.

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Chapter 09 - Basic Oligopoly Models

7.

Model Output ProfitsCournot Q1 = Q2 = 33.33 π1 = π2 = $3,333.33Stackelberg QL = 50; QF = 25 πL = $3,750; πF = $1,875Bertrand Market output = 100 units ZeroCollusion Market output = 50 units Industry Profits = $7,500

8.a. Firm 1’s output and profit would increase. Firm 2’s output and profits would

decrease.b. For small changes in costs, there would be no change in output or profits.

9.a. Cournot duopoly.b. Bertrand duopoly.c. Stackelberg duopoly.d. Sweezy duopoly.

10. The equilibrium price will equal marginal cost, so P = 4. The profits will be P*Q – C(Q) = 4*Q – 4*Q = 0.

11. This would positively impact sales and the firm’s bottom line if Ford is the only company to offer such a program. However, one would expect rivals (such as GM) to respond with a similar plan. This would reduce the impact of Ford’s program on your sales and bottom line. Indeed, GM did quickly respond with its Drive America program.

12. This market is a homogeneous product Cournot oligopoly. Using the given information about demand and costs, each firm has a reaction function of

Qi=5900−8002(1)

−12Q j=2550−0.5Q j. Solving for equilibrium quantities results in

each firm producing 1700 units. This means the market price is P = 5900 – (3400) = $2,500. Since BlackSpot’s marginal cost is $800, it follows that its profit gross of fixed costs is (P – MC)Qi = ($2500 - $800)(1700) = $2,890,000. (Since profits net of fixed costs are only $890,000, it follows that BlackSpot’s fixed costs are $2 million). When marginal cost for BlackSpot falls to $500 (but Condensed Computers’ marginal cost remains at $800), BlackSpot’s new reaction function becomes

Qi=5900−5002(1)

−12Q j=2700−0.5Q j. Solving for equilibrium quantities using this

new reaction function for BlackSpot (but the old one for Condensed Computers) gives us 1900 units produced by BlackSpot and 1600 units produced by Condensed Computers. So, the market price is P = 5900 – (1900 + 1600) = $2,400. BlackSpot’s profit becomes ($2,400 – $500)(1900) – $2,000,000 = $1,610,000. So, profit increases by $720,000.

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Chapter 09 - Basic Oligopoly Models

13. In this homogeneous product Bertrand oligopoly, the equilibrium price equals marginal cost of $2.20. The total market quantity sold is Q = 80 – 6(2.20) = 66.8 units. If one station is self-serve while the other is full-service, the differentiated nature of the products may permit each firm to charge a price above $2.20. This will result in fewer units of gasoline being sold, but the firms will enjoy higher profits.

14. No. A quota may actually increase the profits of the follower.

15. OPEC must reduce its output when rivals (such as Russia, Omar, Mexico, Norway, and other non-OPEC countries) increase their output. This reduction in output lowers their profits, making it difficult to accomplish.

16. No. The industry is contestable.

17. You should support the legislation. Absent the legislation, this homogeneous product Bertrand oligopoly will result in marginal cost pricing and zero profits. Under the legislation, you will earn a profit of $75 – $60 = $15 on each unit sold. Your 20 percent of the contract amounts to 125 units, so your total profits under the congresswoman’s plan is $1,875 compared to the $0 you will earn under cutthroat Bertrand competition.

18. Yes, it would be profitable to merge. Your current Stackelberg output is

QC=1200+120−2(60)

2(6)=100. Your rival’s output is QF=

1200−1202(6)

−0.5 (100 )=40.

So, price is P = 1200 – 6(100 + 40) = 360. Your profits then are (360 – 60)(100) = $30,000, and your rival’s are (360 – 120)(40) = $9,600. If you merge, you would not face any competition. In addition, would be able to produce all output at your own facilities (which have lower costs). Your post-merger monopoly profits would be based on your monopoly output, which occurs where MR = MC: 1200 – 12Q = 60, or Q = 95 units. The monopoly price is $630. Your monopoly profits are ($630 – $60)(95) = $54,150, so you stand to gain $24,150 by merging. If you offer your rival $9,600.01 to merge, it is strictly better off and so are you.

19. Under the status-quo of Cournot oligopoly, your reaction function is Q1 = 39 – 0.5Q2. Your opponent’s reaction function is the same: Q2 = 39 – 0.5Q1. Solving for equilibrium, we have each firm producing 26 units. The price is P = 160 – 2(52) = 56. So, your profits are (56 – 4)(26) = $1,352. If costs were the same but you were the leader in a Stackelberg oligopoly, your equilibrium quantity would be

Qleader=160+4−2(4)

2(2)=39. Your opponent would be the follower, and produce

Qfollower=160−42(2)

−0.5 (39 )=19.5. The price would be P = 160 – 2(58.5) = 43, so your

profits would be (43 – 4)(39) = $1,521. Since this difference is only $169, it would not pay to spend $200 on the investment: The cost of establishing the first-mover advantage exceeds the benefits.

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Chapter 09 - Basic Oligopoly Models

20. When Ajinomoto was the sole supplier of lysine, it charged the monopoly price of $1.65 per pound and sold 76 million pounds; found by solving MR = MC. The dramatic price decline (to marginal cost) in the worldwide market for lysine after ADM entered the market can be explained by Bertrand competition: the two firms compete by setting price in the worldwide market driving price to marginal cost. At this price, 152 million pounds were sold in the worldwide market and each firm sold 76 million pounds (by assumption). The 1993 price increase can be explained by collusion: ADM and Ajinomoto set the monopoly price and produce an equal share of the monopoly output. Therefore, price rose to $1.65 per pound and 76 million pounds are sold on the worldwide market; with each firm supplying 38 million pounds of lysine.

21. The inverse demand function for this Sweezy oligopoly is P={900−0.5Qif Q≤2401,500−3Qif Q≥240.

The marginal revenue function is MR={ 900−Qi f Q<240[60,660 ] if Q=2401,500−6Q if Q>240

.

Therefore, changes in marginal cost in the range of $60 and $660 will not result in a change in the profit-maximizing level of output.

22. The 10 percent increase in rent is an increase in both firms’ fixed costs. No matter whether the Cournot, Stackelberg, Bertrand, or Sweezy model applies to these two firms’ mode of competition, a change in the firms’ fixed costs should not alter their strategic decisions regarding quantity or price. Therefore, Jones should not increase prices by 10 percent.

23. Since an excise tax is a per-unit tax it effectively increases each firms’ marginal cost. In a Cournot oligopoly, increases in marginal costs shift each firm’s reaction function closer to the origin. This results in each firm supplying a lower equilibrium output and charging a higher market price (including taxes). In a Bertrand oligopoly, where firms price at marginal cost in equilibrium, firms pass the entire amount of the excise tax to consumers. In equilibrium, prices rise by the amount of the excise tax and output declines. Finally, in a Sweezy oligopoly, small changes in marginal cost (through the excise tax in this case) have no effect on firms’ prices. In equilibrium, price and output do not change in response to small increases in the excise tax. For this reason, the Sweezy oligopoly is likely to generate the greatest increase in tax revenue.

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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.