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11
Imperfect Competition
Introduction
11
Chapter Outline
11.1
What Does Equilibrium Mean in an Oligopoly?
11.2
Oligopoly with Identical Goods: Collusion and Cartels
11.3
Oligopoly with Identical Goods: Bertrand Competition
11.4
Oligopoly with Identical Goods: Cournot Competition
11.5
Oligopoly with Identical Goods but with a First-Mover: Stackelberg
Competition
11.6
Oligopoly with Differentiated Goods: Bertrand Competition
11.7
Monopolistic Competition
11.8
Conclusion
Introduction
11
Markets rarely fit all of the assumptions of perfect competition or monopoly.
In this chapter, we explore market structures that are collectively referred to as
imperfect competition.
•
Market structures with characteristics between those of perfect competition and
monopoly
We relax a number of assumptions to examine markets in a more realistic
manner:
•
•
•
Allow for varying degrees of competition
Allow for differentiated products
Allow for strategic behavior
Market Classification
•
How is the competitiveness of a market (or lack thereof)measured?
•
Herfindahl–Hirschman Index (HHI)
𝑛
෍(𝑠𝑖 )2
𝑖=1
Sum of squared market shares
•
Concentration Ratios
–
–
CR 4 – Total market share of top 4 firms
CR 8 – Total market share of top 8 firms
Market Classification
•
An empirical approach to market classification I – Monopolistic Competition
Market Classification
•
An empirical approach to market classification II – Oligopoly
Monopolistic Competition
11.7
• If there are no barriers to entry in a differentiated product market, we have
monopolistic competition.
‒ A market structure characterized by many firms selling a differentiated
product and with no barriers to entry
Model Assumptions: Monopolistic Competition
1. Industry firms sell differentiated products that consumers do not view as perfect
substitutes.
2. Other firms’ choices affect a firm’s residual demand curve.
3. Firms ignore any strategic interactions between their own quantity or price choice
and their competitors’ choices.
4. The market allows free entry and exit.
Monopolistic Competition
11.7
Equilibrium in Monopolistically Competitive Markets
To understand how equilibrium is reached in a monopolistically competitive
market, first examine how free entry affects noncompetitive market outcomes.
Consider a small town with a single fast-food burger restaurant.
• The restaurant is effectively a monopolist.
• The demand curve is Done, indicating a single firm.
• The firm will choose a level of production that equates marginal revenue with
marginal cost.
Monopolistic Competition
11.7
Figure 11.6 Demand and Cost Curves for a Monopoly
Price
and cost
($/meal)
Marginal cost,
MC
Average
total cost,
ATC
P*ONE
How do we identify the
level of output chosen by
the monopolist to produce?
Profit
ATC *
Demand, DONE
Marginal revenue, MRONE
Q*ONE
Quantity
of meals
Monopolistic Competition
11.7
Equilibrium in Monopolistically Competitive Markets
The result is a monopoly outcome.
Now suppose a second firm notices the profitability of operating a fast-food
restaurant in this town.
• With no barriers to entry, the second firm opens a restaurant.
Two things happen to the demand curve DONE when another firm enters.
1. First, because the second firm offers an (imperfect) substitute product, the demand
curve for the first firm’s food becomes flatter (more elastic).
2. Second, because demand is now split across two firms, DONE shifts in as well.
Unlike in previous oligopoly models, each firm takes the other’s actions as
given, and there is no strategic response to the behavior of rivals.
Monopolistic Competition
11.7
Figure 11.7 The Effect of Firm’s Entry on Demand for a
Monopolistically Competitive Firm
Price
and cost
($/meal)
P*TWO
ATC*
MC
ATC
As a second firm enters,
demand shifts downward
and becomes more elastic.
Profit
DONE
MRTWO
MRONE
Q*TWO
DTWO
Quantity
of meals
Monopolistic Competition
11.7
Equilibrium in Monopolistically Competitive Markets
Just as with perfect competition, entry will continue to occur until economic
profit is equal to zero.
However, unlike with perfect competition, this does not mean that price is
equal to marginal cost.
• The firms always face a downward-sloping demand curve.
• Entry will occur until demand is tangent with the average total cost curve.
• This is the point at which economic profits are exhausted.
Monopolistic Competition
11.7
Figure 11.8 Long-Run Equilibrium for a Monopolistically Competitive
Market
Price
and cost
($/meal)
MC
ATC
Because there is free entry, in the
long run firms in monopolistic
competition cannot sustain
economic profit.
P*N = ATC*
However, since each firm faces a
downward-sloping demand
curve, in the long run average
total costs are not minimized in
monopolistic competition.
MRN
Q*N
DN
Quantity
of meals
Oligopoly?
11.1
The second market structure we consider is oligopoly.
•
Competition between a small number of firms
It is important to examine what equilibrium means in an oligopoly.
• Under perfect competition or monopoly, short-run equilibrium refers to a price–
quantity combination that results in a market clearing.
‒ The market is stable at this point: there is no excess supply or demand, and consumers
and producers do not want to change their decisions.
• More complicated under oligopoly
‒ In an oligopolistic industry, each company’s actions influences what the other
companies want to do.
‒ To determine an outcome when no firm wants to change its decision, we must
determine more than just a price and quantity for the industry as a whole.
‒ Equilibrium starts with the same idea as perfect competition or monopoly: the market
clears but requires that no company want to change its behavior (price or quantity)
once it knows what other companies are doing.
Oligopoly with Identical Goods:
Collusion and Cartels
11.2
The situation described in the previous example means that there is an
incentive for firms to engage in collusion or to form a cartel.
• Oligopoly behavior occurs when firms coordinate and collectively act as a monopoly
to gain monopoly profits.
Model Assumptions: Collusion and Cartels
1. Firms make identical products.
2. Industry firms agree to coordinate their quantity and pricing decisions.
3. No firm deviates from the agreement, even if breaking it is in the firm’s best
interest.
Oligopoly with Identical Goods:
Collusion and Cartels
11.2
The Instability of Collusion and Cartels
The problem with maintaining collusion is that each firm has an incentive to
cheat.
Consider two firms, A and B, producing an identical product.
• Inverse demand is P = 20 −Q and marginal cost is MC = $4.
If the firms collude, they will produce the monopoly output.
•
Equate marginal revenue and marginal cost:
•
The monopoly price will be $12, and total profits will be $64.
MR  20  2Q  MC  20  2Q  4  Q  8
Assuming firms split production, each will produce 4 units, and each firm will
earn $32 in profit.
Oligopoly with Identical Goods:
Collusion and Cartels
11.2
The Instability of Collusion and Cartels
The problem is that each firm has an incentive to defect.
• What happens if Firm A decides to produce 5 units instead of 4?
‒ Total production is 9 units instead of 8, and total industry profit will fall.
• Given inverse demand P = 20 −Q, the new price will be $11, and total profits will be
$63.
• However, Firm A has increased individual profit:
Profit A  P  c  Q A 
• And Firm B has reduced profit:
Profit A  (11  4)5  $35
Profit B  P  c  QB 
Profit B  (11  4)4  $28
This incentive to defect makes it difficult to maintain collusive agreements.
Oligopoly with Identical Goods:
Collusion and Cartels
11.2
Figure 11.1 Cartel Instability
Price
($/unit)
Cartel members would maximize joint
profits by acting like a monopoly.
Firm A , however, has
an incentive to cheat on
the agreement and
produce another unit of
output.
$20
12
11
MC
4
MR
0
89
D
Quantity
Oligopoly with Identical Goods:
Collusion and Cartels
11.2
What Makes Collusion Easier?
A number of things can make it easier to sustain collusive agreements:
• Making it easy to detect and punish cheaters
• Little variation in marginal costs across producers; since the goal is to produce at
lowest cost, it is difficult to share profits if production costs vary greatly across cartel
members.
• Long time horizon makes defection more costly, as future monopoly profits are given
more weight.
Oligopoly with Identical Goods:
Bertrand Competition
11.3
With the collusion model, firms are focused on their output decision.
• In reality, firms often focus on their price decision instead.
• The Bertrand competition model describes an oligopoly in which each firm
chooses the price of its product.
• Strategic interaction ensues, with each firm responding to its rivals’ price
decision.
Model Assumptions: Bertrand Competition with Identical Goods
1. Firms make identical products.
2. Firms compete by choosing the price at which they sell their products.
3. Firms set their prices simultaneously.
Oligopoly with Identical Goods:
Bertrand Competition
11.3
Setting Up the Bertrand Model
Suppose two firms, Target and Walmart, are selling Sony Playstations.
• Products are identical; assume marginal cost is identical.
• Total quantity purchased is Q. Price at Walmart is PW; price at Target is PT.
Demand for Playstations at Walmart
Demand for Playstations at Target
Q, if PW  PT
Q, if PT  PW
Q
, if PW  PT
2
0, if PW  PT
Q
, if PT  PW
2
0, if PT  PW
The only way to sell Playstations is to match or beat your competitor.
Oligopoly with Identical Goods:
Bertrand Competition
11.3
Nash Equilibrium of a Bertrand Oligopoly
What should Target do if Walmart lowers the price of PlayStations to less than
Target’s?
• Target is left with two options if it still wants to sell PlayStations.
‒ It can match Walmart, so that the market is shared equally.
‒ it can undercut Walmart, so that all consumers purchase from Target.
What is the Nash equilibrium in this structure?
• Equilibrium occurs when each firm charges the marginal cost of production.
• With identical firms and products, if one firm is charging more than its marginal cost, the
other firm always has an incentive to undercut.
• Even though competition is imperfect, in Bertrand competition, market equilibrium is
identical to perfect competition and price equals marginal cost.
Oligopoly with Identical Goods:
Cournot Competition
11.4
If instead firms focus on the quantity decision
• Oligopolists in a local market may compete on price, but producers in larger markets
(e.g., commodities) may have to set production, because capacity constraints may
keep each firm from losing all of its customers.
This type of structure is called Cournot competition.
• Oligopoly model in which each firm chooses its production quantity rather than
price
Model Assumptions: Cournot Competition with Identical Goods
1. Firms make identical products.
2. Firms compete by choosing a quantity to produce.
3. All goods sell for the market price, which is determined by the sum of quantities
produced by all firms in the market.
4. Firms choose quantities simultaneously.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Setting Up the Cournot Model
Assume there are two firms in a Cournot oligopoly.
• Each firm has a constant marginal cost c.
• Firms 1 and 2 simultaneously choose production quantities q1 and q2.
Inverse demand is given by
P  a  bQ; Q  q1  q2
Firm 1’s profit is
1  q1 P  c
substituting in for P :
1  q1  a  bq1  q2   c
And Firm 2’s profit is:
 2  q2  a  bq1  q2   c
Each firm’s profit
depends on actions
of the other firm.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Equilibrium in a Cournot Oligopoly
Assume only two countries, Saudi Arabia and Iran, supply oil to the world.
• Each has a constant marginal cost of $20 per barrel.
Inverse demand is given by
P  200  3Q; Q  qSA  qI
Solving for the equilibrium in this model is similar to the monopoly case,
except Q is the sum of quantities. Rewriting the inverse demand curve,
P  200  3Q  200  3qSA  q I 
P  200  3qSA  3q I
Oligopoly with Identical Goods:
Cournot Competition
11.4
Equilibrium in a Cournot Oligopoly
The slope of the marginal revenue curve is twice the slope of the inverse
demand curve.
For Saudi Arabia:
MRSA  200  6qSA  3qI
Solving for Saudi Arabia’s profit-maximizing output:
MRSA  MC
200  6qSA  3q I  20
qSA  30  0.5q I
Similarly, Iran’s profit-maximizing output is
q I  30  0.5qSA
Oligopoly with Identical Goods:
Cournot Competition
11.4
Equilibrium in a Cournot Oligopoly
This differs from the monopoly outcome in that the profit-maximizing output
for each country depends on the choices of the other.
For instance, if the Saudis expect Iran to produce 10 million barrels per day,
they face the inverse demand curve
P  200  3qSA  3qI  200  3qSA  310  170  3qSA
This leftover demand is the residual demand curve.
•
In Cournot competition, the demand remaining for a firm’s output given competitor
firms’ production quantities
Similarly, a residual marginal revenue curve is a marginal revenue curve
corresponding to a residual demand curve.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Cournot Equilibrium: A Graphical Approach
The relationship between two firms’ output decisions in a Cournot oligopoly can be
seen graphically through the use of reaction curves.
• A function that relates a firm’s best response to its competitor’s possible actions
• In Cournot competition, this is the firm’s best production response to its
competitor’s possible quantity choices.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Figure 11.4 Reaction Curves and Cournot Equilibrium
Saudi Arabia’s quantity of oil,
qS (millions of barrels/day)
70
60
The same holds
true for Iran.
Iran’s reaction curve
I (qI = 30 − 12 qs )
50
40
30
20
10
0
Saudi Arabia’s best
reaction to an increase
in Iranian output is to
lower output.
Nash
equilibrium
A
B
E
C
Saudi Arabia’s
reaction curve
SA (qS = 30 − 12 qI )
D
10 20 30 40 50 60 70
Iran’s quantity of oil,
qI (millions of barrels/day)
Oligopoly with Identical Goods:
Cournot Competition
11.4
Cournot Equilibrium: A Mathematical Approach
We can also solve for a Cournot equilibrium mathematically.
•
•
Substitute one firm’s reaction curve into the other.
In the oil production example
qSA  30  0.5q I , q I  30  0.5qSA
qSA  30  0.530  0.5qSA   30  15  0.25qSA
qSA  20 million
Saudi Arabia’s equilibrium output is 20 million barrels per day.
Since Iran and Saudi Arabia have identical production costs, Iran will also produce 20
million barrels per day, and the market price will be
P  200  3qS  3qI  200  3  20   3  20   $80 per barrel
Oligopoly with Identical Goods:
Cournot Competition
11.4
Cournot Equilibrium: A Mathematical Approach
Finally, we can compute the profit earned by Saudi Arabia:
 SA  qSA   P  $20   20 million   $80  $20   $1.2 billion
and Iran:
 I  qI   P  $20   20 million   $80  $20   $1.2 billion
Total output is 40 million barrels of oil per day, and total profit is $2.4 billion.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Comparing Cournot to Collusion and to Bertrand Oligopoly
Under collusion, Saudi Arabia and Iran will act as a single monopolist, splitting
production evenly because production costs are the same.
•
•
Following the normal procedure, that marginal revenue equals marginal cost, total
output is 30 million barrels per day (BPD), with associated market price
P  200  330  $110
Total profit is
 SA   I   P  $20   Q   $110  $20   30 million  $2.7 billion
•
Under collusion, production is less than that observed in the Cournot equilibrium
(40 million BPD), and profits are higher by $300 million per day.
Oligopoly with Identical Goods:
Cournot Competition
11.4
Comparing Cournot to Collusion and to Bertrand Oligopoly
With Bertrand competition, firms compete on price.
•
Price will equal marginal cost; using the inverse demand curve
P  MC
200  3Q  $20
Q  60 million
•
The 2 countries would split this demand equally, selling 30 million barrels each.

How much profit do Saudi Arabia and Iran earn?
‒ Because both firms sell at a price equal to MC, each earns zero economic
profit.
At the Bertrand equilibrium, output quantity is higher than at the Cournot equilibrium,
price is lower, and there is no profit.
Oligopoly with Identical Goods:
Cournot Competition
Comparing Cournot to Collusion and to Bertrand Oligopoly
11.4
Oligopoly with Identical Goods:
Cournot Competition
11.4
Comparing Cournot to Collusion and to Bertrand Oligopoly
In summary
•
Output under the three industry structures:
Qm  Qc  Qb
‒ Monopoly results in the lowest quantity produced, while Bertrand results in
the most.
•
Market price under the three industry structures:
Pb  Pc  Pm
‒ Bertrand yields the lowest price, while monopoly yields the highest.
•
Profit under the three industry structures:
b  0  c  m
‒ Bertrand yields the lowest profit (0), while monopoly yields the highest.
Oligopoly with Identical Goods:
Cournot Competition
11.4
What Happens If There Are More than Two Firms in a Cournot Oligopoly?
The approach presented in previous slides extends to the case of multiple firms.
•
In general, as the number of firms increases, market outcomes still fall between the
monopoly and perfectly competitive cases, but
‒ outcomes will approach the perfectly competitive case.
‒ more competitors mean higher industry output, lower market price, and lower
industry profit.
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
So far, we have considered only the case in which competitors with market
power choose output or price simultaneously.
• In reality, firms may make decisions before or after observing a competitor’s choice.
This type of structure is called Stackelberg competition
• Oligopoly model in which firms make production decisions sequentially
Model Assumptions: Stackelberg Competition with Identical Goods
1. Firms make identical products.
2. Firms compete by choosing a quantity to produce.
3. All goods sell for the market price, which is determined by the sum of quantities
produced by all firms in the market.
4. Firms do not choose quantities simultaneously; they do it one after another, having
seen the other firms’ choices.
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Consider the outcomes of the Cournot competition model.
• Each firm chooses its optimal quantity based on what the firm believes its competitor(s)
might do.

What happens if one firm observes the other producing more than the Cournot
output?
‒ Could punish competitor by changing its own production.
Reaction curves are downward-sloping; the best response is to reduce output
from the Cournot equilibrium level.
The ability of a first mover to manipulate its competitor’s output in Stackelberg
competition means that there is a first-mover advantage.
• In Stackelberg competition, the advantage is gained by the initial firm in setting its
production quantity.
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Let’s return to Saudi Arabia and Iran in Cournot competition.
Inverse demand is given by (quantity measured in millions of barrels)
P  200  3Q; Q  qSA  qI
Each country has a constant marginal cost of production of $20 per barrel.
The two countries will produce where marginal revenue equals marginal cost, yielding the
following reaction functions:
Saudi Arabia
MRSA  200  6qSA  3q I  20
qSA  30  0.5q I
Iran
MRI  200  6q I  3qSA  20
q I  30  0.5qSA
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Stackelberg Competition and the First-Mover Advantage
Now suppose Saudi Arabia is a Stackelberg leader.This means it chooses its optimal
quantity of output before Iran does.
• Iran’s incentives remain the same; for any quantity Saudi Arabia chooses to produce,
Iran’s reaction function describes the optimal response.
• Importantly, Saudi Arabia realizes Iran will do this before it makes its first move.
‒ However, Saudi Arabia’s reaction curve is different; specifically, we must
substitute Iran’s reaction curve into the inverse demand curve.
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Stackelberg Competition and the First-Mover Advantage
• Substitute Iran’s reaction curve into the inverse demand curve and solve for the
optimal output for Saudi Arabia.
P  200  3qSA  3q I
P  200  3qSA  3(30  0.5qSA )
P  110  1.5qSA
MRSA  110  3qSA  20
qSA  30
• Plug this in to Iran’s reaction function.
qI  30  0.5(30)
q I  15
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Let’s compare Saudi Arabia’s decisions under a Stackelberg competition structure to the
Cournot outcome.
Cournot
Stackelberg
P  200  3qSA  3q I
MRSA  200  6qSA  3q I  20
qSA  30  0.5q I
.....
qSA  q I  20
P  200  3qSA  3q I
P  200  3qSA  330  0.5qSA 
P  110  1.5qSA
MRSA  110  3qSA  20
qSA  30
qI  30  0.530  15
In the Cournot equilibrium, each country produces 20 million barrels per day; now
Saudi Arabia produces 30 million barrels per day and Iran, 15 million.
Oligopoly with Identical Goods:
Stackelberg Competition
11.5
Market price is P  200  345 per
$65barrel, and profit for each country is
Saudi Arabia
 SA  qSA P  20  3065  20
 SA  $1,350,000,000 / day
Iran
 I  q I P  20  1565  20
 I  $675,000,000 / day
Saudi Arabia makes slightly more (by $150 million) than the Cournot equilibrium of $1.2
billion per day as a result of holding first-mover advantage, whereas Iran does much
worse.
Oligopoly with Differentiated
Goods: Bertrand Competition
11.6
Every model we have considered so far has shared a common assumption: that
all firms in a particular market sell an identical product.
• A more realistic situation—particularly with consumer goods—is that products in a
specific market are differentiated in important ways
• A differentiated product market is a market with multiple varieties of a common
product.
• We start by examining Bertrand competition with differentiated products.
Model Assumptions: Bertrand Competition with Differentiated Goods
1. Firms do not sell identical products. They sell differentiated products, meaning
consumers do not view them as perfect substitutes.
2. Each firm chooses the price at which it sells its product.
3. Firms set prices simultaneously.
Oligopoly with Differentiated
Goods: Bertrand Competition
11.6
Equilibrium in a Differentiated-Products Bertrand Market
Suppose there are two snowboard manufacturers, Burton and K2.
• Products are substitutes but not perfect substitutes.
• Differentiation means each firm faces a unique demand curve.
• Consider the following demand curves for the two companies’ snowboards, where
price is measured in dollars:
Burton
q B  900  2 p B  p K
K2
q K  900  2 p K  p B
As the price of Burton snowboards increases, Burton is in less demand but K2
is in greater demand, and vice versa.
Oligopoly with Differentiated
Goods: Bertrand Competition
11.6
Equilibrium in a Differentiated-Products Bertrand Market
Each company sets its price to maximize profits.
• For simplicity, assume the marginal cost of producing snowboards is zero.
• Burton and K2 set their price so that marginal revenue is equal to zero.
Burton
K2
MRB  900  4 p B  p K  0
4 p B  900  p K
MRK  900  4 p K  p B  0
4 p K  900  p B
p B  225  0.25 p K
p K  225  0.25 p B
These are the reaction curves for Burton and K2: as the competitor’s price
rises, own price rises.
‒ This is the opposite of quantity reaction in Cournot competition.

Why does this occur?
Oligopoly with Differentiated
Goods: Bertrand Competition
11.6
Equilibrium in a Differentiated-Products Bertrand Market
To find the equilibrium prices, plug one company’s reaction curve in to the
other’s
p B  225  0.25 p K
p B  225  0.25  225  0.25 p B 
0.9375 p B  281.25
p B  $300
Plugging this price in to K2’s reaction curve yields K2’s equilibrium price.
pK  225  0.25300  $300
We can also find the equilibrium graphically.
Oligopoly with Differentiated
Goods: Bertrand Competition
11.6
Figure 11.5 Nash Equilibrium in a Bertrand Market
Burton’s
price, pB
The same holds for K2.
$500
400
300
Nash
equilibrium
K2’s reaction curve
(pK = 225 + 0.25 pB )
As K2's chosen price rises,
Burton's best response is
to raise its price.
Burton’s reaction curve
(pB = 225 + 0.25 pK )
225
200
100
0
$100 200 300 400 500
225
K2’s price, pK2
Conclusion
11.8
In this chapter, we examined a number of models of imperfect competition:
• Bertrand, Cournot, and Stackelberg competition with identical goods
• Collusion
• Bertrand competition with differentiated goods
• Monopolistic competition
Choosing which model is a good fit for a particular market requires judgment
on the part of the economist.
In the next chapter, we look more closely at the concept of strategic
interaction, which underlies some of the models from this chapter.
In-text
figure it out
Suppose Squeaky Clean and Biobase are a small town’s only producers of chlorine for
swimming pools. The inverse demand curve for chlorine is
𝑃 = 32 − 2𝑄
where quantity is measured in tons and price is measured in dollars per ton. The two
firms have an identical marginal cost of $16 per ton.
Answer the following questions:
a. If the two firms collude, splitting the work and profits evenly, how much will each
firm produce at what price? How much profit will each firm earn?
b.
c.
d.
Does Squeaky Clean have an incentive to cheat by producing an additional ton of
chlorine? Explain.
Does Squeaky Clean’s decision to cheat affect Biobase’s profit? Explain.
Suppose both firms agree to each produce 1 ton more than they were producing
in part (a). How much profit will they earn? Does Biobase have an incentive to
cheat?
In-text
figure it out
a.
If the firms collude and act like a monopoly, they will set marginal
revenue equal to marginal cost:
MR  32  4Q
MR  MC  32  4Q  16 
Q4
P  32  2  4   $24 per ton
and the profit for each firm (assuming they split output equally) is
Profit SC  Profit BB 
1
P  c  Q  1 24  16 4
2
2
Profit SC  Profit BB  $16
In-text
figure it out
b.
If Squeaky Clean produces one more ton, total quantity rises to 5. The
new price is
P  32  25  $22
and Squeaky Clean’s profit is
Profit SC  P  c  QSC  22  16 3
Profit SC  $18
which is larger than the $16 under collusion. Yes, Squeaky Clean
an incentive to cheat and produce one more ton of chlorine.
c.
If Squeaky Clean cheats, the price falls to $22. This reduces Biobase’s
profits to
has
Profit BB  P  c  QBB  22  16 2  $12
In-text
figure it out
d.
If each firm produces one more ton of chlorine, the new price is
P  32  26   $20
and profits for each firm are
Profit SC  Profit BB 
1
P  c  Q  1 20  16 6
2
2
Profit SC  Profit BB  $12
Both firms are worse off.
Does Squeaky Clean have an incentive to cheat and produce one more ton?
When producing 4 tons of chlorine, the new price is
P  32  27   $18
And Squeaky Clean ’s profit is
Profit SC  P  c  QSC  18  16  4
Profit SC  $8
which is lower than $12, so Squeaky Clean has no incentive to cheat.
Additional
figure it out
Suppose there are only two driveway paving companies in a small town,
Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services
is
𝑃 = 1,600 − 20𝑄
where quantity is measured in pave jobs per month and price, in dollars per
job. The firms have an identical marginal cost of $400 per driveway.
Answer the following questions:
a. If the two firms collude, splitting the work and profits evenly, how many
driveways will each firm pave, and at what price? How much profit will
each firm make?
b.
Does Asphalt, Inc. have an incentive to cheat by paving one more
driveway each month?
c.
Suppose each firm decides to pave one more driveway each month. Does
Asphalt, Inc. have an incentive to cheat?
Additional
figure it out
a.
If the firms collude, they will set marginal revenue equal to marginal cost
MR  1,600  40Q
MR  MC  1,600  40Q  400 
Q  30
P  1,600  2030  $1,000
and the profit for each firm (assuming they split output equally) is
Profit AI  Profit BB 
1
P  c  Q  1 1,000  400 30
2
2
Profit AI  Profit BB  $9,000
Additional
figure it out
b.
If Asphalt, Inc. paves one more driveway, total quantity rises to 31. The
new price is
P  1,600  2031  $980
and Asphalt, Inc.’s profit is
Profit AI  P  c  Q AI  980  400 16
Profit AI  $9,280
which is larger than the $9,000 under collusion. Yes, Asphalt, Inc.
an incentive to cheat and pave one more driveway.
has
Additional
figure it out
c.
If both firms pave one more driveway each month, the new price is
P  1,600  2032   $960
and profits for each firm are
Profit AI  Profit BB 
1
P  c  Q AI  1 960  400 32
2
2
Profit AI  Profit BB  $8,960
Both firms are worse off.
Does Asphalt, Inc. have an incentive to cheat and pave one more driveway?
With 33 driveways per month, the new price is
P  1,600  2033  $940
And Asphalt, Inc.’s profit is
Profit AI  P  c  Q AI  940  400  17
Profit AI  $9,180
which is higher than $8,960, so yes, Asphalt, Inc. has an incentive to cheat.
In-text
figure it out
OilPro and GreaseTech are the only two firms that provide oil changes in a
local market in a Cournot duopoly (a two-firm oligopoly). The inverse demand
curve for oil changes is
P  100  2Q
where quantity is measured in oil changes per year in thousands and price is
measured in dollars per job. Assume OilPro has a marginal cost of $12 per job
and GreaseTech has a marginal cost of $20.
Answer the following questions:
a. Determine each firm’s reaction curve.
b.
How many oil changes will each firm produce in Cournot equilibrium?
c.
What will the market price of an oil change be?
d.
How much profit does each firm earn?
In-text
figure it out
a. Begin by substituting Q = qO + qG into the market inverse demand curve:


P the
100quantity
 2 qOofoil
qGchanges
 100done
 2qby
 2qGand
O OilPro
where qO and qG represent
GreaseTech, respectively.
Now, derive each firm’s marginal revenue curve:
MRO  100  4qO  2qG
G  100
O  4qcost
G to maximize profit;
Each firm will set marginalMR
revenue
equalto2q
marginal
since marginal revenue is a function of the other firm’s production choice, this
represents the reaction curve.
OilPro
MRO  MC  100  4qO  2qG  12
GreaseTech
MRG  MC  100  2qO  4qG  20
4qO  88  2qG
4qG  80  2qO
qO  22  0.5qG
qG  20  0.5qG
In-text
figure it out
b. To solve for the equilibrium, substitute one firm’s reaction curve into the
other’s:
qO  22  0.520  0.5qO 
qO  12  0.25qO
0.75qO  12
qO  16
Using GreaseTech’s reaction curve:
qG  20  0.516 
qG  12
c.
The market price is found by substituting the market quantity into the
market inverse demand curve.
P  100  2qO  qG 
P  100  216  12 
P  $44
In-text
figure it out
d. Finally, profit for each firm is
OilPro
 O  qO P  12
GreaseTech
 G  qG P  20 
 O  16,00044  12 
 G  12,00044  20 
 O  $512,000
 G  $288,000
The firm with the lower marginal cost provides more oil changes and makes
more profit.
Additional
figure it out
Let’s return to the example of the two small-town driveway paving companies,
Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services
is
P  1,600  20Q
where quantity is measured in pave jobs per month and price is measured in
dollars per job. Assume Asphalt, Inc. has a marginal cost of $400 per driveway
and Blacktop Bros. has a marginal cost of $200.
Answer the following questions:
a. Determine each firm’s reaction curve and graph it.
b.
How many oil changes will each firm produce in Cournot equilibrium?
c.
What will the market price of an oil change be?
d.
How much profit does each firm earn?
Additional
figure it out
a. Begin by substituting Q = qAI + qBB into the market inverse demand
curve
P  1,600  20q AI  q BB   1,600  20q AI  20q BB
where qAI and qBB represent the quantity of driveways paved by Asphalt, Inc.
and Blacktop Bros., respectively.
Now, derive each firm’s marginal revenue curve.
MRAI  1, 600  40q AI  20qBB
MRBB  1, 600  20q AI  40qBB
Each firm will set marginal revenue equal to marginal cost to maximize profit;
since marginal revenue is a function of the other firm’s production choice, this
represents the reaction curve.
Asphalt, Inc.
Blacktop Bros.
MRAI  1,600  40q AI  20q BB  400
40q AI  1,200  20q BB
q AI  30  0.5q BB
MRBB  1,600  20q AI  40q BB  200
40q BB  1,400  20q AI
q BB  35  0.5q AI
Additional
figure it out
b. To solve for the equilibrium, substitute one firm’s reaction curve into the
other’s:
q AI  30  0.535  0.5q AI 
q AI  12.5  0.25q AI
0.75q AI  12.5
q AI  16.67
Using Blacktop Bros.’ reaction curve:
q AI  35  0.516.67 
q AI  26.67
c.
The market price is found by substituting the market quantity into the
market inverse demand curve.
P  1, 600  20  q AI  qBB 
P  1, 600  20 16.67  26.67 
P  $733.33
Additional
figure it out
d. Finally, profit for each firm is
Asphalt, Inc.
 AI  q AI P  400
 AI  16.67733.33  400
 AI  $5,556.61
Blacktop Bros.
 BB  qBB P  200
 AI  26.67733.33  200
 AI  $14,223.91
The firm with the lower marginal cost paves more driveways and makes more
profit.
In-text
figure it out
Return to the case of the two oil change producers OilPro and GreaseTech
from the previous figure it out. Recall the inverse market demand for oil
changes:
P  100  2Q
where quantity is measured in thousands of oil changes per year, representing
the combined production of O and G; Q = qO + qG; and price is measured in
dollars per change. OilPro has a marginal cost of $12 per change, and
GreaseTech has a marginal cost of $20.
Answer the following questions:
a. Suppose the market is a Stackelberg oligopoly and OilPro is the first
mover. How much does each firm produce? What will the market price
be? How much profit does each firm earn?
b. Now suppose GreaseTech is the first mover. How much will each firm
produce, and what is the market price? How much profit does each firm
earn?
In-text
figure it out
a. Since OilPro moves first, calculate GreaseTech’s reaction curve and plug
that in to the market demand curve to determine OilPro’s output. To find
GreaseTech’s reaction curve, set marginal revenue equal to marginal cost.
MR  MC
100  2qO  4qG  20
qGcurve
 20into
 0.5
Substitute GreaseTech’s reaction
the q
market
demand curve:
O
P  100  2  qO  qG   100  2(qO  20  0.5qO )
P  100  2qO  40  qO
60 mover.
qO Setting marginal
which is OilPro’s inverse demand curve P
asa first
revenue equal to marginal cost yields
MR  MC
60  2qO  12
qO  24
In-text
figure it out
Substituting OilPro’s output choice into GreaseTech’s reaction function yields
the latter’s output choice
qG  20  0.5qO
qG  20  0.5(24)
qG  8
To find the market price, return to the inverse demand curve
P  100  2qO  qG 
P  100  224  8
P  $36
And the profit for each firm is given by
 O  P  $12 qO
 O  $36  $12 24,000
 G  P  $20 qG
 G  $36  $20 8,000
 O  $576,000
 G  $128,000
In-text
figure it out
b. We repeat the process for part b. Since GreaseTech moves first, calculate
OilPro’s reaction curve and plug that in to the market demand curve to
determine OilPro’s output. To find OilPro’s reaction curve, set marginal
revenue equal to marginal cost.
MR  MC
100  4qO  2qG  12
qO  225  0.5qG
Substituting OilPro’s reaction curve into the market demand curve yields
P  100  2  qO  qG   100  2(qG  22  0.5qG )
P  100  2qG  44  qG
P  56  qG
which is GreaseTech’s inverse demand curve as first mover. Setting marginal
revenue equal to marginal cost yields
MR  MC
56  2qG  20
qG  18
In-text
figure it out
Substituting GreaseTech’s output choice into OilPro’s reaction function yields
the latter’s output choice.
qO  22  0.5qG
qO  22  0.5(18)
qO  13
To find the market price, return to the inverse demand curve.
P  100  2qO  qG 
P  100  218  13
P  $38
The profit for each firm is given by
 G  P  $12 qG
 O  P  $20 qO
 O  $38  $20 13,000
 G  $38  $12 18,000
 O  $338,000
 G  $324,000
Additional
figure it out
Consider the case of two theaters, Jay’s Cinema (JC) and Mezzanine Inc. (MI).
The inverse demand for theater tickets is given as
P =120 - 4Q
where quantity is measured in thousands of theater tickets per year,
representing the combined production of JC and MI, Q = qJC + qMI , and price
is measured in dollars per ticket. JC has a marginal cost of $6 per ticket, and
MI has a marginal cost of $8.
Answer the following questions:
a. Suppose the market is a Stackelberg oligopoly and JC is the first mover.
How much does each firm produce? What will the market price of a
movie be? How much profit does each firm earn?
b.
Now suppose MI is the first mover. How much will each firm produce?
What is the market price? How much profit does each firm earn?
Additional
figure it out
a. Since JC moves first, we must calculate MI’s reaction curve and plug that
in to the market demand curve to determine what output level JC will
choose. To find MI’s reaction curve, set marginal revenue equal to
marginal cost
MR  MC
120  4q JC  8qMI  8
qMI  14  .5q JC
Substituting MI’s reaction curve into the market demand curve yields
P  120  4q JC  qMI   120  4(q JC  14  .5q JC )
P  120  4q JC  56  2q JC
P  64  2q JC
which is JC’s inverse demand curve as a first mover. Setting marginal revenue
equal to marginal cost yields
MR  MC
64  4q JC  6
q JC  14
Additional
figure it out
Substituting JC’s output choice into MI’s reaction function yields the latter’s
output choice
qMI  14  0.5q JC
qMI  14  0.5(14)
qMI  7
To find the market price, return to the inverse demand curve
P  120  4q JC  qMI 
P  120  414  7 
P  $36
And the profit for each firm is given by,
 JC  P  $6 q JC
 MI  P  $8 qMI
 JC  $36  $6  14,000
 MI  $36  $8 7,000
 JC  $420,000
 MI  $196,000
Additional
figure it out
b. We repeat the same process for part b. Since MI moves first, we must
calculate JC’s reaction curve, and plug that in to the market demand curve
to determine what output level MI will choose. To find JC’s reaction curve,
set marginal revenue equal to marginal cost
MR  MC
120  8q JC  4qMI  6
q JC  14.25  0.5qMI
Substituting JC’s reaction curve into the market demand curve yields
P  120  4  qJC  qMI   120  4(qMI  14.25  0.5qMI )
P  120  4qMI  57  2qMI
P  63  2q JC
which is MI’s inverse demand curve as a first mover. Setting marginal revenue
equal to marginal cost yields
MR  MC
64  4qMI  6
qMI  14.5
Additional
figure it out
Substituting MI’s output choice into JC’s reaction function yields the latter’s
output choice.
q
 14.25  0.5q
JC
MI
q JC  14.25  0.5(14.5)
q JC  7
To find the market price, return to the inverse demand curve.
P  120  4q JC  qMI 
P  120  47  14.5
P  $34
The profit for each firm is given by
 JC  P  $6 q JC
 MI  P  $8 qMI
 JC  $34  $6  7,000
 MI  $34  $8 14,500
 JC  $196,000
 MI  $377,000
In-text
figure it out
We just determined the Nash equilibrium for Burton and K2, with each firm
producing 600 snowboards (plug price back in to individual demand curves) at
a price of $300 per board. Now, suppose Burton launches an advertising
campaign so that the demand for Burton snowboards rises to qB = 800 –
1.5pB + 1.5pK and demand for K2 boards falls to qK = 1,000 – 2pK + 0.5pB .
Assume the marginal cost for each firm is still zero.
Answer the following questions:
a. Derive each firm’s reaction curve.
b.
What happens to each firm’s optimal price?
c.
What happens to each firm’s optimal output?
d.
Draw the reaction curves in a diagram and indicate the equilibrium.
In-text
figure it out
a.
To determine the firms’ reaction curves, first solve for each firm’s
marginal revenue curve:
MRB  1000  3 p B  1.5 p K
MRK  800  4 p K  0.5 p B
Setting each firm’s marginal cost equal to marginal revenue provides the
reaction curve for each firm:
MRB  1000  3 p B  1.5 p K  0
MRK  800  4 p K  0.5 p B  0
3 p B  1000  1.5 p K
4 p K  800  0.5 p B
p B  333.33  0.5 p K
p K  200  0.125 p B
In-text
figure it out
b.
Substituting K2’s reaction curve into Burton’s reaction curve yields the
equilibrium price for Burton.
p B  333.33  0.5 p K
p B  333.33  0.5200  0.125 p B 
p B  433.33  0.625 p B
p B  $462.22
We can substitute Burton’s price into K2’s reaction curve to find the
equilibrium price for K2
p K  200  0.125 p B
p K  200  0.125$462.22 
p K  $257.78
In-text
figure it out
c.
To find each firm’s output, substitute the prices from part b into the
inverse demand curve for each firm.
q B  1000  1.5 p B  1.5 p K
q K  800  2 p K  0.5 p B
 1000  1.5462.22   1.5257.78
 800  2257.78  0.5462.22 
q B  693.34
q K  515.55
d. The reaction curves:
In-text
figure it out
Sticky Stuff produces taffy in a monopolistically competitive market. The
inverse demand for its product is
P  50  Q
where quantity is measured in thousands of cases per year and price is
measured in dollars. Assume Sticky Stuff has a constant marginal cost of $10
per case and has no fixed cost. It’s total cost curve is TC = 10Q.
Answer the following questions:
a. To maximize profit, how many cases of taffy should Sticky Stuff produce
each year?
b.
What price will cases of taffy sell for?
c.
How much profit will Sticky Stuff earn each year?
d.
In reality, firms in monopolistic competition face fixed costs in the short
run. Given the answers to the previous questions, what would Sticky
Stuff’s fixed costs have to be in order for this industry to be in long-run
equilibrium? Explain
In-text
figure it out
a.
Sticky maximizes profit by setting marginal revenue equal to marginal
cost; since the inverse demand curve is linear, the marginal revenue
curve is also linear, with the same intercept and twice the slope.
MR  50  2Q  10
40  2Q
Q  20, 000 cases per year
b.
Plugging 20 in to the inverse demand curve gives the price.
c.
Sticky’s profit is the quantity produced times the price, net of the
constant marginal cost.
d.
P  50   20   $30 per case




  Qoccurs
 P when
MC industry
 20  profits
30  10
$400
000
Long-run equilibrium
are zero,
or ,when
Sticky’s daily fixed costs are exactly equal to its annual profit of $400,000.
Additional
figure it out
Mangos produces smoothies in a monopolistically competitive market. The
inverse demand for its product is
P  8  0.05Q
where quantity is measured in smoothies per day and price is measured in
dollars. Assume Mangos has a constant marginal cost of $2 per smoothie.
Answer the following questions:
a. To maximize profit, how many smoothies should Mangos produce each
day?
b.
What price will smoothies sell for?
c.
d.
What will be Mangos’ daily profit?
Firms in monopolistic competition face fixed costs in the short run. What
would Mangos’ fixed costs have to be for this industry to be in long-run
equilibrium?
Additional
figure it out
a.
Mangos maximizes profit by setting marginal revenue equal to marginal
cost; since the inverse demand curve is linear, the marginal revenue
curve is also linear, with the same intercept and twice the slope.
MR  8  0.1Q  2
0.1Q  6
Q  60
b.
Plugging 60 in to the inverse demand curve gives the price.
c.
 8  0produced
.05 60 times
 $5the price, net of the
Mangos’ profit is theP
quantity
constant marginal cost.
d.
 Q  Poccurs
 MC
 industry
60  5 
2 are
$180
Long-run 
equilibrium
when
profits
zero, or when
Mangos’ daily fixed costs are \equal to its daily profit of $180.
 



