imperfect competition•under perfect competition or monopoly, short-run equilibrium refers to a...

Imperfect Competition

11

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

11Introduction

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)

𝑖=1

𝑛

(𝑠𝑖)2

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


• An empirical approach to market classification I – Monopolistic Competition


• 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.


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.


Figure 11.6 Demand and Cost Curves for a Monopoly

Marginal cost,Price

and cost

AverageMC($/meal)

total cost,ATC

P*ONE

Profit

ATC *

Demand, DONE

Marginal revenue, MRONE

QuantityQ*ONE of meals

How do we identify the level of output chosen by

the monopolist to produce?



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.


Figure 11.7 The Effect of Firm’s Entry on Demand for a Monopolistically Competitive Firm

PriceMCand cost

($/meal)ATC

P*TWOProfit

ATC*

DONE

MRTWO DTWO

MRONE

QuantityQ*TWO of meals

As a second firm enters, demand shifts downward and becomes more elastic.



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.


Figure 11.8 Long-Run Equilibrium for a Monopolistically Competitive Market

Price MCand cost ATC

($/meal)

P*N = ATC*

DNMRN

QuantityQ*N of meals

Because there is free entry, in the long run firms in monopolistic

competition cannot sustain economic profit.

However, since each firm faces a downward-sloping demand

curve, in the long run average total costs are not minimized in

monopolistic competition.

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.



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.

Assuming firms split production, each will produce 4 units, and each firm will earn $32 in profit.

84220220 QQMCQMR



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:

• And Firm B has reduced profit:

This incentive to defect makes it difficult to maintain collusive agreements.

AA QcPProfit 35$5)411(Profit A

BB QcPProfit 28$4)411(Profit B



Figure 11.1 Cartel Instability

Price($/unit)

$20

1211

4 MC

MR D

0 Quantity8 9

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.



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.


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


2. Firms compete by choosing the price at which they sell their products.

3. Firms set their prices simultaneously.



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

The only way to sell Playstations is to match or beat your competitor.

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TW

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PP

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if ,0

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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.


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


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.



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

Firm 1’s profit is

substituting in for P :

And Firm 2’s profit is:

21 ; qqQbQaP

cPq 11

cqqbaq 2111

cqqbaq 2122

Each firm’s profit depends on actions of the other firm.



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

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,

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ISA qqQP 32003200

ISA qqP 33200




The slope of the marginal revenue curve is twice the slope of the inverse demand curve.

For Saudi Arabia:

Solving for Saudi Arabia’s profit-maximizing output:

Similarly, Iran’s profit-maximizing output is

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MCMRSA

2036200 ISA qq

ISA qq 5.030

SAI qq 5.030




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

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.

SASAISA qqqqP 3170103320033200



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.



Figure 11.4 Reaction Curves and Cournot Equilibrium

Saudi Arabia’s quantity of oil,qS (millions of barrels/day)

70Iran’s reaction curve

160 I (qI = 30 − qs )2

50Nash

40 equilibrium

Saudi Arabia’s30reaction curve

120 SA (qS = 30 − qI )2

10

0 10

Iran’s quantity of oil,qI (millions of barrels/day)

20 30 40 50 60 70

Saudi Arabia’s best reaction to an increase in Iranian output is to

lower output.

The same holds true for Iran.

AB

C

D

E



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

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

SAIISA qqqq 5.030 ,5.030

200 3 3 200 3 20 3 20 $80 per barrelS IP q q

SASASA qqq 25.015305.0305.030

20 millionSAq



Cournot Equilibrium: A Mathematical Approach

Finally, we can compute the profit earned by Saudi Arabia:

and Iran:

Total output is 40 million barrels of oil per day, and total profit is $2.4 billion.

$20 20 million $80 $20 $1.2 billionSA SAq P

$20 20 million $80 $20 $1.2 billionI Iq P



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

• Total profit is

• Under collusion, production is less than that observed in the Cournot equilibrium (40 million BPD), and profits are higher by $300 million per day.

$20 $110 $20 30 million $2.7 billionSA I P Q

110$303200 P




With Bertrand competition, firms compete on price.

• Price will equal marginal cost; using the inverse demand curve

• 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.

MCP

20$3200 Q

60 millionQ




In summary

• Output under the three industry structures:

‒ Monopoly results in the lowest quantity produced, while Bertrand results in the most.

• Market price under the three industry structures:

‒ Bertrand yields the lowest price, while monopoly yields the highest.

• Profit under the three industry structures:

‒ Bertrand yields the lowest profit (0), while monopoly yields the highest.

bcm QQQ

mcb PPP

mcb 0



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.


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


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.



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.



Let’s return to Saudi Arabia and Iran in Cournot competition.

Inverse demand is given by (quantity measured in millions of barrels)

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 Iran

ISA qqQQP ;3200

2036200 ISASA qqMR

ISA qq 5.030

2036200 SAII qqMR

SAI qq 5.030



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.



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.

• Plug this in to Iran’s reaction function.

ISA qqP 33200

200 3 3(30 0.5 )SA SAP q q

SAqP 5.1110

203110 SASA qMR

30SAq

30 0.5(30)Iq

15Iq



Let’s compare Saudi Arabia’s decisions under a Stackelberg competition structure to the Cournot outcome.

Cournot Stackelberg

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.

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SASA

ISA

qqP

qqP

5.03033200

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ISA qq 5.030

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qP

15305.030

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I

SA

q

q20 ISA qq

.....



Market price is per barrel, and profit for each country is

Saudi Arabia Iran

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.

65$453200 P

20653020 PqSASA

daySA /000,000,350,1$ dayI /000,000,675$

20651520 PqII

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.



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 K2

As the price of Burton snowboards increases, Burton is in less demand but K2 is in greater demand, and vice versa.

KBB ppq 2900 BKK ppq 2900




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

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?

04900 KBB ppMR

KB pp 9004

KB pp 25.0225

04900 BKK ppMR

BK pp 9004

BK pp 25.0225




To find the equilibrium prices, plug one company’s reaction curve in to the other’s

Plugging this price in to K2’s reaction curve yields K2’s equilibrium price.

We can also find the equilibrium graphically.

300$30025.0225 Kp

KB pp 25.0 225

BB pp 25.022525.0225

25.2819375.0 Bp

300$Bp



Figure 11.5 Nash Equilibrium in a Bertrand Market

Burton’sprice, pB

K2’s reaction curve$500 (pK = 225 + 0.25 pB )

Nashequilibrium400

Burton’s reaction curve(pB = 225 + 0.25 pK )300

225200

100

0 K2’s price, pK2$100225

200 300 400 500

The same holds for K2.

As K2's chosen price rises, Burton's best response is

to raise its price.

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. Does Squeaky Clean have an incentive to cheat by producing an additional ton of chlorine? Explain.

c. Does Squeaky Clean’s decision to cheat affect Biobase’s profit? Explain.

d. 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:

and the profit for each firm (assuming they split output equally) is

QMR 432

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32 2 4 $24per tonP

416242

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1ProfitProfit QcPBBSC

4Q

16$ProfitProfit BBSC

In-text

figure it out

b. If Squeaky Clean produces one more ton, total quantity rises to 5. The new price is

and Squeaky Clean’s profit is

which is larger than the $16 under collusion. Yes, Squeaky Clean has an incentive to cheat and produce one more ton of chlorine.

c. If Squeaky Clean cheats, the price falls to $22. This reduces Biobase’sprofits to

22$5232 P

31622Profit SCSC QcP

18$Profit SC

12$21622Profit BBBB QcP

In-text

figure it out

d. If each firm produces one more ton of chlorine, the new price is

and profits for each firm are

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

And Squeaky Clean ’s profit is

which is lower than $12, so Squeaky Clean has no incentive to cheat.

616202

1

2

1ProfitProfit QcPBBSC

20$6232 P

18$7232 P

12$ProfitProfit BBSC

41618Profit SCSC QcP

8$Profit SC

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.


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

and the profit for each firm (assuming they split output equally) is

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40040600,1 QMCMR

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1

2

1ProfitProfit QcPBBAI

30Q

000,9$ProfitProfit BBAI

Additional

figure it out

b. If Asphalt, Inc. paves one more driveway, total quantity rises to 31. The new price is

and Asphalt, Inc.’s profit is

which is larger than the $9,000 under collusion. Yes, Asphalt, Inc. has an incentive to cheat and pave one more driveway.

980$3120600,1 P

16400980Profit AIAI QcP

280,9$Profit AI

Additional

figure it out

c. If both firms pave one more driveway each month, the new price is

and profits for each firm are

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

And Asphalt, Inc.’s profit is

which is higher than $8,960, so yes, Asphalt, Inc. has an incentive to cheat.

324009602

1

2

1ProfitProfit AIBBAI QcP

960$3220600,1 P

940$3320600,1 P

960,8$ProfitProfit BBAI

17400940Profit AIAI QcP

180,9$Profit AI

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

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.


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?

QP 2100

In-text

figure it out

a. Begin by substituting Q = qO + qG into the market inverse demand curve:

where qO and qG represent the quantity of oil changes done by OilPro and GreaseTech, respectively.

Now, derive each firm’s marginal revenue curve:

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.

OilPro GreaseTech

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GG qq 5.020

In-text

figure it out

b. To solve for the equilibrium, substitute one firm’s reaction curve into the other’s:

Using GreaseTech’s reaction curve:

c. The market price is found by substituting the market quantity into the market inverse demand curve.

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165.020 Gq

GO qqP 2100

OO qq 25.012

1275.0 Oq

16Oq

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44$P

In-text

figure it out

d. Finally, profit for each firm is

OilPro GreaseTech

The firm with the lower marginal cost provides more oil changes and makes more profit.

12 PqOO 20 PqGG

1244000,16 O

000,512$O

2044000,12 G

000,288$G

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

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.


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?

QP 20600,1

Additional

figure it out

a. Begin by substituting Q = qAI + qBB into the market inverse demand curve

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.

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.

BBAIBBAI qqqqP 2020600,120600,1

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1,600 20 40

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BB AI BB

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MR q q

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Additional

figure it out

b. To solve for the equilibrium, substitute one firm’s reaction curve into the other’s:

Using Blacktop Bros.’ reaction curve:

c. The market price is found by substituting the market quantity into the market inverse demand curve.

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67.165.035

AI

AI

q

q

1,600 20

1,600 20 16.67 26.67

$733.33

AI BBP q q

P

P

Additional

figure it out

d. Finally, profit for each firm is

Asphalt, Inc. Blacktop Bros.

The firm with the lower marginal cost paves more driveways and makes more profit.

61.556,5$

40033.73367.16

400

AI

AI

AIAI Pq

91.223,14$

20033.73367.26

200

AI

AI

BBBB Pq

In-text

figure it out

Return to the case of the two oil change producers OilPro and GreaseTechfrom the previous figure it out. Recall the inverse market demand for oil changes:

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.


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?

QP 2100

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.

Substitute GreaseTech’s reaction curve into the market demand curve:

which is OilPro’s inverse demand curve as a first mover. Setting marginal revenue equal to marginal cost yields

MCMR

100 2 100 2( 20 0.5 )O G O OP q q q q

2042100 GO qq

20 0.5G Oq q

OO qqP 402100

OqP 60

MCMR

12260 Oq

24Oq

In-text

figure it out

Substituting OilPro’s output choice into GreaseTech’s reaction function yields the latter’s output choice

To find the market price, return to the inverse demand curve

And the profit for each firm is given by

OG qq 5.020

)24(5.020 Gq

8Gq

GO qqP 2100

8242100 P

36$P

OO qP 12$

000,2412$36$ O

000,576$O

GG qP 20$

000,820$36$ G

000,128$G

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.

Substituting OilPro’s reaction curve into the market demand curve yields

which is GreaseTech’s inverse demand curve as first mover. Setting marginal revenue equal to marginal cost yields

MCMR

100 2 100 2( 22 0.5 )O G G GP q q q q

1224100 GO qq

GO qq 5.0225

GG qqP 442100

GqP 56

MCMR 20256 Gq

18Gq

In-text

figure it out

Substituting GreaseTech’s output choice into OilPro’s reaction function yields the latter’s output choice.

To find the market price, return to the inverse demand curve.

The profit for each firm is given by

)18(5.022 Oq

13Oq

GO qqP 2100

13182100 P

38$P

OO qP 20$

000,1320$38$ O

000,338$O

GG qP 12$

000,1812$38$ G

000,324$G

GO qq 5.022

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

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.


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?

P =120- 4Q

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

Substituting MI’s reaction curve into the market demand curve yields

which is JC’s inverse demand curve as a first mover. Setting marginal revenue equal to marginal cost yields

MCMR

)5.14(41204120 JCJCMIJC qqqqP

884120 MIJC qq

JCMI qq 5.14

JCJC qqP 2564120

JCqP 264

MCMR

6464 JCq

14JCq

Additional

figure it out

Substituting JC’s output choice into MI’s reaction function yields the latter’s output choice

To find the market price, return to the inverse demand curve

And the profit for each firm is given by,

JCMI qq 5.014

)14(5.014 MIq

7MIq

MIJC qqP 4120

7144120 P

36$P

JCJC qP 6$

000,146$36$ JC

000,420$JC

MIMI qP 8$

000,78$36$ MI

000,196$MI

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

Substituting JC’s reaction curve into the market demand curve yields

which is MI’s inverse demand curve as a first mover. Setting marginal revenue equal to marginal cost yields

MCMR

120 4 120 4( 14.25 0.5 )JC MI MI MIP q q q q

648120 MIJC qq

MIJC qq 5.025.14

MIMI qqP 2574120

JCqP 263

MCMR

6464 MIq

5.14MIq

Additional

figure it out

Substituting MI’s output choice into JC’s reaction function yields the latter’s output choice.

To find the market price, return to the inverse demand curve.

The profit for each firm is given by

)5.14(5.025.14 JCq

7JCq

MIJC qqP 4120

5.1474120 P

34$P

JCJC qP 6$

000,76$34$ JC

000,196$JC

MIMI qP 8$

500,148$34$ MI

000,377$MI

MIJC qq 5.025.14

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.


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:

Setting each firm’s marginal cost equal to marginal revenue provides the reaction curve for each firm:

KBB ppMR 5.131000

In-text

figure it out

BKK ppMR 5.04800

05.131000 KBB ppMR

KB pp 5.110003

KB pp 5.033.333

05.04800 BKK ppMR

BK pp 5.08004

BK pp 125.0200

b. Substituting K2’s reaction curve into Burton’s reaction curve yields the equilibrium price for Burton.

We can substitute Burton’s price into K2’s reaction curve to find the equilibrium price for K2

In-text

figure it out

KB pp 5.033.333

BB pp 125.02005.033.333

BB pp 625.033.433

22.462$Bp

BK pp 125.0200

22.462$125.0200 Kp

78.257$Kp

c. To find each firm’s output, substitute the prices from part b into the inverse demand curve for each firm.

d. The reaction curves:

In-text

figure it out

KBB ppq 5.15.11000

78.2575.122.4625.11000

34.693Bq

BKK ppq 5.02800

22.4625.078.2572800

55.515Kq

In-text

figure it out

Sticky Stuff produces taffy in a monopolistically competitive market. The inverse demand for its product is

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.


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

QP 50

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.

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. Long-run equilibrium occurs when industry profits are zero, or when Sticky’s daily fixed costs are exactly equal to its annual profit of $400,000.

10250 QMR

50 20 $30 per caseP

000,400$103020 MCPQ

Q240 20,000 cases per yearQ

Mangos produces smoothies in a monopolistically competitive market. The inverse demand for its product is

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.


a. To maximize profit, how many smoothies should Mangos produce each day?

b. What price will smoothies sell for?

c. What will be Mangos’ daily profit?

d. 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?

QP 05.08

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.

b. Plugging 60 in to the inverse demand curve gives the price.

c. Mangos’ profit is the quantity produced times the price, net of the constant marginal cost.

d. Long-run equilibrium occurs when industry profits are zero, or when Mangos’ daily fixed costs are \equal to its daily profit of $180.

60

61.0

21.08

Q

Q

QMR

5$6005.08 P

180$2560 MCPQ

Additional

figure it out

imperfect competition•under perfect competition or monopoly, short-run equilibrium refers to a...

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