Monopoly and Monopolistic Competition

Monopoly and Monopolistic Competition 

Chapter 11 

Monopoly and 

Monopolistic Competition 

Page 1


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Numerical Example 

• You work for Nuxo Lighting Company. Nuxo 

produces d specialized i li dli lighting h i fi fixtures, generally ll 

acknowledged as the best in their class, and there are 

no close substitutes. substitutes A market-research market research firm has 

estimated the market demand to be Q = 2,000 - 5P 

• You estimate Nuxo's Nuxo s total cost for producing, producing 

storing, and marketing it's lighting line to be TC = 

100 + 4Q + 0.4Q2 Q Q 

• You are asked to estimate how many lights should 

be manufactured, and how should they be priced to 

maximize profits? 


Page 6

Numerical Example 

• Invert demand function: Q = 2000 - 5P so, 5P = 

2000 - QQ; hhence, P = 400 -.2Q 2Q 

• Find TR: PQ = 400Q -.2Q 2 

• derive MR; MR = 400 - .4Q 

• derive MC; MC = 4 + .8Q 

• Set MC = MR ⇒ 400 - .4Q = 4 + .8Q ⇒ 1.2Q = 

396; ⇒∴ Q = 330; P = 400 - .2(330) = $334, and 

400Q 2Q2 100 4Q 04Q2 396Q 6Q2 100 = $65,240. 

π = 400Q -.2Q 2 - 100 - 4Q - 0.4Q 2 = 396Q -.6Q 2 - 


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Page 8

Chapter Summary 

• Under monopoly, a firm maximizes profit if it 

sets its output rate at the point where marginal 

revenue equals marginal cost. 

• AAn iindustry d t that th t is i monopolized li d generally ll sets t 

a higher price and a lower output than if it 

were perfectly f tl competitive. titi 

• The perfectly competitive firm operates at a point 

at twhich hi hp price i equals l marginal i lcost, t whereas h th the 

monopolist operates at a point at which marginal 

revenue equals marginal cost (and price exceeds 

marginal cost). 


Page 9


• Cost-plus pricing only results in profit maximization if 

marginal g cost marked up pby ythe product's p price p 

elasticity of demand 

• Profit maximization for multi-product p firms 

• Fixed proportions: profit maximizing output occurs where 

the total marginal revenue curve intersects the marginal 

cost curve ffor the h bbundle dl of fproducts d ( (assuming i that h the h 

marginal revenue of each product is nonnegative) 

• Variable proportions: p p profit p maximizing goutput p occurs at 

the tangency point where profit is the highest; this also 

indicates the the optimal output combination. 


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• Monopolistically competitive firms 

• MMaximize i i profit fi bby setting i MR = MC MC. 

• Should set advertising so that the marginal 

revenue from an extra dollar of advertising 

equals the negative of its price elasticity of 

demand. 


Page 11

Chapter 11 Quiz 

1. If Harry Doubleday's price elasticity of demand is -2 and its profit maximizing price is $6, 

then 

A. average cost is $3.00. 

B. average cost is $.33. 

C. marginal cost is $3.00. 

D. marginal cost is $.33. 

E. average cost is $5.67. 

2. My Big Banana (MBB) has a monopoly in Middletown, United States, on large banana splits. 

The demand for this delicacy is given by Q = 80 - P. MBB's costs are given by TC = 40 + 

2Q + 2Q2. Its maximum monopoly profits are 

A. $267. 

B. $467. 

C. $627. 

D. $672. 

E. $674. 

Note: The profit maximizing price is 

P = MC /[1 + (1/ η )] (see equation (11.3). 

Therefore, 6 = MC /[1 −.5] ⇒MC = $3. 

2 2 

Note: π = (80 − Q ) Q−40 −2Q− 2 Q = 78 Q−40 − 3 Q . 

Therefore, dπ / dQ = 78 − 6Q = 0 ⇒ Q = 13 and P = 80 − Q = 67 ⇒ 

2 

π = 67(13) −40 −2(13) − 2(13 ) = 

$467. 

Monopoly and Monopolistic Competition Page 12


3. Harriet Quarterly wants a 25 percent return on the $100 of assets she has in her company. 

Her average variable costs are $50 per unit, and she has no fixed costs. If she sells 10 units, 

what price should she charge? 

A. $52.50 Note: π = .25 × $100 = $25 ⇒P − AVC = 2.5; since 

B. $62.50 

AVC = $50, this implies that P =$52.50. 

C. $75.00 

D. $87.50 

E. $125.00 

4. To maximize profit, the firm must 

A. mark up average variable costs. 

B. mark up marginal costs. 

C. mark up average fixed costs. 

D. set the markup equal to -1/(η + 1). 

E. b and d. 

Note: Since the profit maximizing price is 

P = MC /[1 + (1/ η )] (see equation (11.3), the firm must 

mark up marginal costs by the proportion -1/(η + 1). 



5. If price P, unit costs C, and quantity Q, are known, the markup of markup-cost pricing is 

A. (PQ - CQ)/Q. 

B. P - C/Q. 

C. (P - C)/Q. 

D. (P - C)/C. 

E. 1 - (P - C)/Q. 

6. Jack O. Trades produces joint products A and B with linear demands DA > DB. Jack's total 

marginal revenue curve changes slope at the quantity where (MRB is marginal revenue for B 

and MCB is marginal cost of B) 

A. MRB = MCB. 

B. DB = MCB. 

C. MRB = DB. 

D. MRB = 0. 

E. DB = 0. 

Note: On page 416 in the textbook, equation (11.6) defines the 

percentage markup as Markup = (price – cost)/cost; thus response 

D is the correct response here. 

Note: This is indicated in Figure 11.5 on page 425 of the 

textbook. When MRB = 0, the total marginal revenue curve 

for products A and B is equal to the marginal revenue curve 

for product A. 



7. If revenues from selling quantities x and y of jointly produced goods X and Y are TRX = 

100 - xy + 2x and TRY = 500 - xy + 3y, then marginal revenue with respect to X would be 

A. -2 - y. 

Note: According to equation (11.11a) on page 423 of the textbook, 

B. -y. 

product X’s marginal revenue is MR 

C. -x(2y + 5). 

X = ∂TRX / ∂ QX +∂TRY / ∂ QX. 

D. -(2y + 5). Therefore, MRX = − y + 2− y = 2(1 − 

y). 

E. 2(1 - y). 

8. For a producer of joint products X and Y with total revenue RX and RY, an isorevenue 

curve 

A. isolates RX and RY separately. 

B. shows points where RX = RY. 

C. shows points where revenue curves are tangent. 

D. shows points where RX/RY is constant. 

E. shows points where RX + RY is constant. 



9. So long as price exceeds average variable cost, in the model of monopolistic competition, a 

firm maximizes profits by producing where 

A. the difference between marginal revenue and marginal cost is maximized. 

B. marginal cost equals marginal revenue. 

C. marginal revenue equals price. 

D. the difference between price and marginal cost is maximized. 

E. price equals marginal cost. 

10. Consider Fred, who is employed by a national tire store and who earns a commission 

selling tires. He earns 25 percent of his gross sales revenue as a bonus. Fred's objective is to 

maximize 

A. total profits for the store. 

B. total revenues for the store. 

C. marginal revenue from sales. 

D. the difference between marginal revenues and marginal cost for the store. 

E. the number of customers he waits on per day. 


Chapter 11 Problems (1, 3, 5, 9, 11, 13) 

1. Harry Smith is the owner of a metals-producing firm that is an 

unregulated monopoly. After considerable experimentation and 

research, he finds that its marginal cost curve can be 

approximated by a straight line, MC = 60 + 2Q, where MC is 

marginal cost (in dollars), and Q is output. The demand curve 

for the product is P = 100 - Q, where P is the product price (in 

dollars) and Q is output. 

a. If he wants to maximize profit, what output should he 

choose? 



Harry should produce where marginal revenue equals 

marginal cost. Setting MR = dTR/dQ = d(100Q – Q 2 )/dQ = 

100 – 2Q equal to MC yields 100 – 2Q = 60 + 2Q Q = 

10. 

b. What price should he charge? 

Harry’s market clearing price at Q = 10 is P = 100 – 10 = 

90. 

3. The Coolidge Corporation is the only producer of a particular 

type of laser. The demand curve for its product is 

Q D = 8,300 - 2.1P 



and its total cost function is 

TC = 2,200 + 480Q + 20Q 2 

where P is price (in dollars), TC is total cost (in dollars), and Q 

is monthly output. 

a. Derive an expression for the firm's marginal revenue curve. 

Solving for P in the equation Q D = 8,300 - 2.1P, we find that 

P = (8,300 – Q)/2.1 = 3,952 – 0.476Q. Therefore, TR = 

PQ = (3,952 – 0.476Q)Q = 3,952Q – 0.476Q 2 , and MR = 

dTR/dQ = 3,952 – 0.952Q. 



b. To maximize profit, how many lasers should the firm 

produce and sell per month? 

The profit maximizing condition is MR = MC. We already 

know that MR = 3,952 – 0.952Q. Since TC = 2,200 + 480Q 

+ 20Q 2 , MC = dTC/dQ = 480 – 40Q. Therefore, 3,952 – 

0.952Q = 480 – 40Q ⇒ 40.952Q = 3,472 ⇒ Q = 84.8 

lasers per month. This quantity implies a price of P = 

(8,300 – 84.8)/2.1 = $3,912 per unit. 

c. If this number were produced and sold, what would be the 

firm's monthly profit? 



π = PQ − TC = 

= $145,012.80. 

− − + 

2 

3,912(84.8) 2,200 480(84.8) 20(84.8 ) 

5. The Wilcox Company has two plants with the marginal cost 

functions 

MC 1 = 20 + 2Q 1 

MC 2 = 10 + 5Q 2 

where MC, is marginal cost in the first plant, MC 1 is marginal 

cost in the second plant, Q 1 is output in the first plant, and Q 2 is 

output in the second plant. 



a. If the Wilcox Company minimizes its costs and produces 

five units of output in the first plant, how many units of 

output does it produce in the second plant? Explain. 

Wilcox is minimizing its costs if it is using both plants at 

outputs that equalize their marginal costs. If Wilcox is 

producing 5 units in the first plant, its marginal cost there is 

MC 1 = 30. For MC 2 to equal 30, Wilcox must produce 4 

units at plant 2. 

b. What is the marginal cost function for the firm as a 

whole? 



Setting MC 1 = MC 2 ⇒ Q 1 = 2.5Q 2 – 5. Therefore, Q = Q 1 

+ Q 2 = 3.5Q 2 – 5 ⇒ Q 2 = (Q + 5)/3.5. Consequently, MC 

= MC 1 = MC 2 = 10 + 5(Q + 5)/3.5 = (10/7)(Q + 12). 

c. Can you determine from these data the average cost 

function for each plant? Why or why not? 

We can determine average variable cost for each plant, but 

because we don’t have information on fixed costs, we 

cannot determine average total cost for each plant. 



9. The demand for diamonds is given by 

P Z = 980 - 2Q Z 

where Q Z is the number of diamonds demanded if the price is 

P Z per diamond. The total cost (TC Z) of the De Beers 

Company (a monopolist) is given by 

2 

TCZ = 100 + 50QZ + 0.5QZ Monopoly and Monopolistic Competition Page 24


where Q Z is the number of diamnds produced and put on the 

market by the De Beers Company. Suppose that the 

government could force De Beers to behave as if it were a 

perfect competitor; that is, via regulation, force the firm to 

price diamonds at marginal cost. 

a. What is social welfare when De Beers acts as a single price 

monopolist? 



The firm produces where marginal revenue = marginal 

cost. So, 980 – 4Q = 50 + Q, and the profit maximizing 

output and price for the firm is 186 diamonds at a price of 

$608. To find social welfare, sum consumer and producer 

surplus. At this point, consumer surplus is 0.5(186)(980 – 

608) = $34,596. Producer surplus is 0.5(186)(186) + 

(372)(186) = $86,490. Total surplus, or social welfare, is 

$121,086. 

b. What is social welfare when De Beers acts as a perfect 

competitor? 

When De Beers acts as a perfect competitor, the market 

will produce where demand = marginal cost. Now, 980 – 



2Q = 50 + Q, and the industry output is 310 diamonds at a 

price of $360. Consumer surplus is 0.5(310)(620) = 

$96,100. Producer surplus is 0.5(310)(310) = $48, 050. 

Total surplus is $144,150. 

c. How much does social welfare increase when De Beers 

moves from monopoly to competition? 

Eliminating De Beers’s monopoly power creates an 

additional $23,064 of surplus. 



11. The McDermott Company estimates its average total cost to 

be $10 per unit of output when it produces 10,000 units, which 

it regards as 80 percent of capacity. Its goal is to earn 20 

percent on its total investment, which is $250,000. 

a. If the company uses cost-plus pricing, what price should it 

set? 

$15 = [0.20($250,000) + $10(10,000)]/10,000. 

b. Can it be sure of selling 10,000 units if it sets this price? 

There is no assurance that 10,000 units can be sold at this 

price. 



c. What are the arguments for and against a pricing policy of 

this sort? 

Markup pricing is not sensible if the markup is not based 

on the elasticity of demand. If the decision maker knows 

the elasticity of demand and uses it, markup pricing is profit 

maximizing. If the decision maker doesn’t, then it can be 

silly. 

12. The Backus Corporation makes two products, X and Y. For 

every unit of good X that the firm produces, it produces two 

units of good Y. Backus's total cost function is 



TC = 500 + 3Q + 9Q 2 

where Q is the number of units of output (where each unit 

contains one unit of good X and two units of good Y) and TC 

is total cost (in dollars). The demand curves for the firm's two 

products are 

P = 400 − Q 

P = 300 − 3Q 

X X 

Y Y 

where P X and Q X are the price and output of product X and P Y 

and Q Y are the price and output of product Y. 



a. How much of each product should the Backus Corporation 

produce and sell per period of time? 

P X = 400 – Q X, P Y = 300 – 3Q Y, MC = 3 + 18Q. 

MR X = 400 – 2Q X = 400 – 2Q, MR Y = 300 – 6Q Y = 600 – 

24Q. 

Setting MR = MR X + MR Y = 1,000 – 26Q = 3 + 18Q = 

MC yields Q = 997/44 = 22.66, QX = 22.66, and QY = 

45.32. 

We also need to check that each product’s individual 

marginal revenue is positive at the proposed solution 

values, which in fact each is. 

b. What price should it charge for each product? 



P X = 400 – 22.66 = 377.33, P Y = 300 – 3(45.32) = 164.04. 


Oligopoly 

Chapter 13 

Oligopoly 

Page 1

Oligopoly 

Oligopoly 

• Industry has small number of firms 

• AAutomobiles bil 

• Airlines 

• Pharmaceuticals 

• Overnight mail 

• Behavior of firms often difficult to predict 

• Sometimes firms compete vigorously 

• Coke and Pepsi, airlines (sometimes) 

• Sometimes they explicitly or implicitly collude 

• Oil producers (e.g., OPEC cartel) 

Page 2

Oligopoly 

Oligopoly 

• Problem in forming strategy is this (consider 

two rivals, You and Me) 

• Your decisions materially affect my profit and vice versa 

• You know this, I know this, I know that you know this, 

etc etc. 

• Thus, how I should behave depends on how I think you 

are likely to behave. 

• Thi This iis lik like a game of f chess h where h we not only l hhave 

to 

anticipate the other’s decisions, but we may even be able 

to influence the other’s choices. 

• What transpires depends upon the information 

available and the mindsets of the parties and, we 

will see, see their skill in playing games. 

games 

Page 3

Oligopoly 

Four Possibilities 

• We will set the stage by considering four ways 

in which oligopoly firms might behave and 

implications for market outcomes. 

• None of these is necessarily the right or 

wrong g way; y they y are just j possibilities p and any, y 

or all, might occur in different settings at 

different points p in time. 

• We will show that what happens depends 

upon mindset and information. 

Page 4

Oligopoly 

Four Possibilities 

• Consider that BOTH firms fail to recognize that their output 

and price decisions affect their rival and each seeks to expand 

its market share. 

• Firms might collude (explicitly or implicitly) to maximize their 

joint profit (perhaps by means of quotas) 

• Firms might act separately (and simultaneously) in setting 

prices prices, each seeking to maximize profits. profits However, However they do 

acknowledge that their decisions affect each other. 

• Another situation might arise if one firm becomes the 

accepted leader in setting its output (or price) first. The leader 

anticipates that its decisions will provoke a reaction from the 

follower and the leader seeks to maximize profit p ggiven 

this 

anticipated reaction. 

Page 5

Oligopoly Case 1: Compete for Market Share 

Oligopoly 

• Two possible mindsets for managers 

• Firms view themselves as price takers. 

• Each firm wishes to maximize market 

share, subject to not losing money at 

margin margin. 

• Each firm increases output as long as 

P>MC. Firms stop increasing output 

when P=MC. 

Page 6

Oligopoly Case 1: Compete for Market Share 

MARKET DEMAND P=53-Q OR Q = 53 - P 

FIRM 1 

FIRM 2 

TC1 = 5Q1 TC =05Q2 FIRM 2 TC2 = 0.5Q 2 

2 

Prices driven down to marginal cost (each firm sets P=MC). 

Each firm lowers price to seek market share if P > MC. MC 

So price ultimately driven down to MC of both firms. 

FIRM 1 P = MC 1 

53 - Q 1 -Q 2 = 5 ⇒ Q 1 = 48 - Q 2 

FIRM 2 P = MC 2 

53 - Q 1 -Q 2 = Q 2 

53 - (48 - Q 2) - Q 2 = Q 2 ⇒ Q 2 = 5 

Oligopoly 

Q 1 = 48 - Q 2 = 43 

P = 53 - (43 + 5) = 5 

Π 1 = 43(5) - 43(5) = 0 

Π 2 = 5(5) - 0.5(5) 2 = 12.5 

Page 7

Oligopoly Model 2: Collusion (max joint π) 

Oligopoly 

• Suppose that firms get together and 

explicitly pli itl agree to t joint j i t output tp t and d 

quotas. 

• Joint profit maximized where total MC = 

MR. 

• Behave like monopoly with 2 plants 

• Each firm has quota such that marginal 

costs are equal q (this ( way yjoint j profit p is 

maximized). 

Page 8

Oligopoly 


FIRM 1 TC 1 = 5Q 1 

FIRM 2 TC 2 = 0.5Q 2 2 

Π = (53 - Q1 -Q2)(Q1 + Q2) - 5Q1 - 0.5Q 2 

2 

Q Q Q 2 Q Q Q 2 Q Q 2 

= 53Q1 + 53Q2 - Q 2 

1 -2Q1Q2 - Q 2 

2 -5Q1-0.5Q 2 

2 

= 48Q1 + 53Q2 –Q2 1 -2Q1Q2 - 1.5Q 2 

2 

dΠ/dQ 1 = 48 - 2Q 1 -2Q 2 = 0 ⇒ Q 1 = 24 - Q 2 

dΠ/dQ 2 = 53 - 2Q 1 -3Q 2 = 0 ⇒ Q 2 = 17⅔ - ⅔Q 1 

Q 1 = 24 - (17⅔ - ⅔ Q 1) ⇒ Q 1= 19 

Q 2 = 17⅔ - ⅔(19) ⇒ Q 2= 5 

P = 53 -19 -5 = 29 

Π = 24(29) -5(19) -0.5(5) 2 

( ) ( ) () 

= 588.5 

Page 9

Here are our results so far! 

Q 1 Q 2 P П 1 П 2 

Price war 43 5 5 0 12.5 

Collusion 19 5 29 456 132.5 

Cournot 

Stackelberg 

Oligopoly 

Page 10

Oligopoly 

Other outcomes are possible… 

• Remarks about Collusion 

• Ob Obviously i l collusion ll i iis potentially i ll quite i profitable. fi bl 

• Does this (ever) happen? Yes, but rare: 

• GE and Westinghouse (turbine market) 

• ADM, Ajinomoto, and Kyowa Hakko (lysine 

market) k ) 

• Why is collusion somewhat rare? 

11. Ill Illegal l (or ( potentially i ll illegal) ill l) in i many domiciles d i il 

2. Collusion is not sustainable unless some punishment 

mechanism ec a s exists e sts (because (beca se it t is s potentially pote t a y quite q te 

profitable to “cheat” on your rival). 

Page 11

Oligopoly Case 3: Cournot Equilibrium 

•Two firms: each wishes to maximize profit. 

•However, oweve , they ey make e concurrent co c e decisions dec s o s 

•Each sets MC = MR 

•Each recognizes that its MR depends on 

market demand and therefore on the decision 

of its rival. 

•Optimal Optimal output for each firm depends on 

output of rival – reaction functions 

•An equilibrium involves: 

Oligopoly 

•Firm A making its profit maximizing 

output choice given the choice of firm B 

•Firm Firm B making its profit maximizing 

output choice given the choice of firm A 

Q(1)* 

Q(1) 

Cournot EQUILIBRIUM 

Q(1)=fQ(2) 

1's reaction function 

Q(2)* 

Q(2)=fQ(1) 

2's reaction function 

Page 12 

Q(2)


FIRM 1 TC 1 = 5Q 1 

FIRM 2 TC 2 = 0.5Q 2 2 

PROFIT FIRM 1 Π1 = (53-Q1-Q2)Q1 -5Q1 = 48Q1 -Q 2 

1 -Q1Q2 derivative = 48 - 2Q 1 - Q 2 = 0 

Oligopoly 

Q 1 = 24 - ½Q 2 

PROFIT FIRM 2 Π (53 Q Q )Q 05Q2 PROFIT FIRM 2 Π2 = (53-Q2-Q1)Q2 – 0.5Q 2 

2 

= 53Q2 - 1.5Q 2 

2 -Q2Q1 derivative = 53- 3Q2 -Q1 = 0 

(1'S REACTION FUNCTION) 

Q 2 = 17⅔ - ⅓ Q 1 (2'S REACTION FUNCTION) 

SUBSTITUTE 2'S REACTION FUNCTION INTO 1'S..... 

Q Q1 =24 = 24 - ½(17⅔ - ⅓ Q Q1 ) 

Q2 = 17⅔ - ⅓ (18.2) 

P = 53 - (18.2+11.6) 

⇒ 

⇒ 

⇒ 

Q Q1 =182 = 18.2 

Q2 = 11.6 

P = 23.2 

Π1 = 18.2(23.2) – 5(18.2) 

Π2 = 11.6(23.2) – 0.5(11.6) 

⇒ Π1 = 331.2 

2 ⇒ Π2 = 201.8 

Page 13

Here are our results so far! 

Q 1 Q 2 P П 1 П 2 

Price war 43 5 5 0 12.5 

Collusion 19 5 29 456 132.5 

Cournot 18.2 11.6 23.2 331.2 201.8 

Stackelberg 

Oligopoly 

Page 14

Oligopoly Case 4: Stackelberg Equilibrium 

Oligopoly 

• Two firms: each wishes to maximize profit; each will set MC 

=MR = MR. 

• However, they make sequential rather than concurrent decisions; 

one firm (the leader) will make its output decision first, first 

whereas the other firm (the follower) will choose output after 

its observes the choice of the leader firm. 

• Each firm knows and acknowledges its role; leader or 

follower 

• The leader anticipates that the follower will use its reaction function 

and simply incorporates this in its profit maximizing calculation; 

• The follower selects its profit p maximizing g output p having g seen the 

leader’s output; i.e. follower will simply use its reaction function. 

Page 15


FIRM 1 TC 1 = 5Q 1 

FIRM 2 TC 2 = 0.5Q 2 2 

FIRM 1 (Leader) Π: Π1 = (53-Q1-Q2)Q1 -5Q1 Q 2 = 17⅔ - ⅓ Q 1 (reaction ( function calculated before) ) 

Π1 = (53- Q1-(17⅔ - ⅓ Q1))Q1 -5Q1 = 53Q1 -Q 2 

1 -17⅔Q1 + ⅓ Q 2 

1 -5Q1 

=30⅓Q ⅔ Q 2 

= 30⅓ Q1 - ⅔ Q 2 

1 

derivative 30⅓ -1⅓Q 1 = 0 ⇒ Q 1 = 22.75 

FIRM 2 (Follower) quantity decision is determined by its reaction function: 

Q2 = 17⅔ - ⅓ Q1 Q2 = 17⅔ - ⅓ 22.75 ⇒ Q2 = 10.09 

Oligopoly 

P = 53-(22.75+10.09) ⇒ P = 20.16 

Π 1 = 22.75(20.16) - 5(22.75) ⇒ Π 1 = 344.9 

Π 2 = 10.09(20.16) – 0.5(10.09) 2 ⇒ Π 2 = 152.5 

Page 16

Here are our “final” results! 

Q 1 Q 2 P П 1 П 2 

Price war 43 5 5 0 12.5 

Collusion 19 5 29 456 132.5 

Cournot 18.2 11.6 23.2 331.2 201.8 

Stackleberg 22 22.75 75 10 10.09 09 20 20.16 16 344 344.99 152 152.55 

Oligopoly 

Page 17

Oligopoly 

Applications and Reality Check 

• Do oligopoly markets really “compete by capacity choice” 

(rather than on price)? 

• Some do, and quite profitably: 

• Aluminum (4 major firms worldwide); market sets 

price. 

• Bulk chemicals (DuPont often a leader); 

• Enterprise-scale computing (historically, IBM was the 

leader). 

• Others mostly try try to get to Cournot solution: Boeing & 

Airbus. 

•The Boeing-Airbus article in Financial Times: What is 

Mulally trying to do? 

Page 18

Oligopoly 

Boeing – Airbus Article 

From the Financial Times, 2002: 

What h was Mulally l ll 

trying to do here? 

Page 19

Oligopoly 

Quiz problem 7 (Collusion) 

• Two ready-to-eat breakfast cereal manufacturers, Lots of 

Sugar and Buckets of Goo, Goo face combined demand for their 

products given by Q = 75 - P. Their total costs are given by 

TCLots of Sugar = 0.1Q2 Lots of Sugar and TCBuckets of Goo = 5QBuckets of 

Goo. If they successfully collude, their total profits will be 

_____. 

Note that MCLots of Sugar = 0.2Q and MCBuckets of Goo = 5; note 

also that that MC is smaller than 5 for Q < 10, but equal to 5 

ffor Q ≥ 10. 10 Th Then MR = 75 – 2Q = 5 = MC ⇒ Q = 35 and d P 

= 75 – 35 = 40. Thus Lots of Sugar produces 25 units, 

Buckets of Goo produces 10 units, and total profit is 40(35) - 

.1(252 ) – 5(10) = $1,287.50. 

Page 20

Oligopoly 

Quiz problem 9 (Stackelberg) 

Glyde Air Fresheners is the dominant firm in the 

solid room aromatizer industry which has a total 

market demand given by Q = 80 - 2P. Glyde has 

competition from a fringe of four small firms that 

produce where their individual marginal costs equal 

th the market k t price. i The Th fringe f i firms fi each h have h ttotal t l 

2 

costs given by TC i = 10 Qi + 2 Qi 

. If Glyde’s total 

costs are given i bby TC G = 100 + 6 Q QG, 

what h price i 

should Glyde establish for air fresheners? 

Page 21

Quiz problem 9 (Stackelberg) 

Begin by analyzing one of the followers (“fringe” firms). Since P = MC, this 

implies that P=10+4q, or q=0.25(P-10). If we let QF be the total production 

from all four followers, then QF = 4q = P-10. Since Q = 80 - 2P, this implies 

that P = 40 – 0.5Q = 40 – 0.5QG – 0.5QF ⇒ P = 40 – 0.5QG – 0.5(P – 10) ⇒ 

QF = 20 - QG/3. / This is the reaction function for the followers. 

Next, we maximize Glyde’s profit, which is π G = PQG - 100 - 6QG . 

Substituting P = 40 – 0.5QG – 0.5QF into the profit equation yields π G 

= 40QG 2 

−0.5QG −0.5QFQG −100 − 6QG= 

2 

ddπ 

π G 

34 −0.5QG −0.5QFQG − 100. Therefore, = 34 − QG dQ 

− 0.5QF = 0 ⇒ QG 

= 36, QF = 20−12=8, Q = QF + QG = 36+8=44, P = 40 – 0.5Q = 40 – 22 = 

$18 $18. 

Oligopoly 

G 

Page 22

Chapter 13 Problems (1, 3, 5, 7, 11) 

1. The Bergen Company and the Gutenberg Company are the 

only two firms that produce and sell a particular kind of 

machinery. The demand curve for their product is 

P=580-3Q 

where P is the price (in dollars) of the product, and Q is the 

total amount demanded. The total cost function of the Bergen 

Company is 

TC B = 410Q B 

where TC B is its total cost (in dollars) and Q B is its output. The 

total cost function of the Gutenberg Company is 

Monopoly and Oligopoly Lecture Page 24


TC G = 460Q G 

where TC G is its total cost (in dollars) and Q G is its output. 

a. If these two firms collude and they want to maximize their 

combined profits, how much will the Bergen Company 

produce? 

Bergen’s marginal cost is always less than Gutenberg’s 

marginal cost. Therefore Bergen would produce all the 

combination’s output. Setting Bergen’s marginal cost equal 

to the marginal revenue derived from the demand function, 

we get 410 = 580 – 6Q ⇒ Q B = 170/6 and Q G = 0. 



b. How much will the Gutenberg Company produce? 

As discussed in part a, Gutenberg’s marginal cost is always 

greater than Bergen’s. If Gutenberg were to produce 1 unit 

and Bergen 1 unit less, it would reduce their combined 

profits by the difference in their marginal costs. If 

Gutenberg were to produce 1 unit without any reduction in 

Bergen’s output, it would reduce their combined profits by 

the same amount. 

c. Will the Gutenberg Company agree to such an 

arrangement? Why or why not? 



If direct payments for output restrictions between the 

firms were legal, Gutenberg would accept the zero output 

quota. But if competition were to break out, Gutenberg 

would make zero profits and Bergen would earn $2.00. 

Thus the most Bergen would pay for Gutenberg’s 

cooperation is $408.33 and the least Gutenberg would 

accept to not produce is $.01. 

3. An oligopolistic industry selling a particular type of machine 

tool is composed of two firms. The two firms set the same 

price and share the total market equally. The demand curve 

confronting each firm (assuming that the other firm sets the 

same price as this firm) follows, as well as each firm’s total cost 

function. 



a. Assuming that each firm is correct in believing that the 

other firm will charge the same price as it does, what is the 

price that each should charge? 

Each should charge a price of $9,000. 



b. Under the assumptions in part a, what daily output rate 

should each firm set? 6 

5. The International Air Transport Association (IATA) has been 

composed of 108 U.S. and European airlines that fly 

transatlantic routes. For many years, IATA acted as a cartel: It 

fixed and enforced uniform prices. 

a. If IATA wanted to maximize the total profit of all member 

airlines, what uniform price would it charge? 



The IATA would charge the price that clears the market at 

the level of output where the marginal revenue equals the 

horizontally summed marginal cost curves of each operator 

in the market. 

b. How would the total amount of traffic be allocated among 

the member airlines? 

The traffic should be allocated so that the marginal costs of 

all the members operating in the market would be equal 

and that no member not currently in the market would 

have a lower marginal cost. 



c. Would IATA set price equal to marginal cost? Why or why 

not? 

No, the IATA would set a price equal to the marginal cost 

multiplied by 1/(1 + 1/e), where e is the elasticity of 

demand in the market in question. 

7. Two firms, the Alliance Company and the Bangor Corporation, 

produce vision systems. The demand curve for vision systems 

is 

P = 200,000 - 6(Q l + Q 2) 



where P is the price (in dollars) of a vision system, Q l is the 

number of vision systems produced and sold per month by 

Alliance, and Q 2 is the number of vision systems produced and 

sold per month by Bangor. Alliance’s total cost (in dollars) is 

TC l = 8,000Q l 

Bangor’s total cost (in dollars) is 

TC 2 = 12,000Q 2 

a. If each of these two firms sets its own output level to 

maximize its profits, assuming that the other firm holds 

constant its output level, what is the equilibrium price? 



P = $73,888.34 (derived in part b). 

b. What is the output of each firm? 

Alliance and Bangor’s profits can be written as 

π1 = [200,000 – 6(Q1 + Q2)]Q1 – 8,000Q1 = 192,000Q1 – 

2 

6 Q 1 – 6Q1Q2, π2 = [200,000 – 6(Q1 + Q2)]Q2 – 8,000Q2 = 188,000Q2 – 

6 Q – 6Q1Q2. 2 

2 

Profit maximizing levels of output are determined by setting 

the first derivative of each firm’s profit function equal to 

zero and solving for Q 1 and Q 2. 



dπ 1/dQ 1 = 192,000 – 12Q 1 – 6Q 2 = 0. 

dπ 2/dQ 2 = 188,000 – 6Q 1 – 12Q 2 = 0. 

Solving these two equations, we get Q 1 = 10,888.89 and Q 2 

= 10,222.22. P = 200,000 – 6(10,888.89 + 10,222.22) = 

$73,333.34. 

c. What is the profit of each firm? 

2 

π1 = 192,000Q1 – 6 Q 1 – 6Q1Q2 = $711,407,550, 

2 

π2 = 188,000Q2 – 6 Q 2 – 6Q1Q2 = $626,962,890. 



11. The West Chester Corporation believes that the demand 

curve for its product is 

P = 28 - 0.14Q 

where P is price (in dollars) and Q is output (in thousands of 

units). The firm’s board of directors, after a lengthy meeting, 

concludes that the firm should attempt, at least for a while, to 

increase its total revenue, even if this means lower profit. 

a. Why might a firm adopt such a policy? 



Higher market shares established by sacrificing current 

profits might allow the firm to charge higher prices and earn 

higher profits in the future because of having established a 

brand name. Also there might be a learning curve effect; 

this means that future cost savings from increased current 

output should be added to current marginal revenues when 

determining the profit maximizing level of current output 

and price. 

b. What price should the firm set if it wants to maximize its 

total revenue? 

To maximize sales, the firm should produce where marginal 

revenue equals zero. MR = 28 – 0.28Q = 0 ⇒ Q = 100. 



c. If the firm’s marginal cost equals $14, does the firm produce 

a larger or smaller output than it would if it maximized 

profit? How much larger or smaller? 

If the firm’s marginal cost equals 14, it should produce 

50,000 units, which is 50,000 units less than if it maximizes 

sales.

Monopoly and Monopolistic Competition

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