EC 170 Industrial Organization Chapter 5 Business Strategy in Oligopoly Markets.

EC 170 Industrial Organization

Chapter 5

Business Strategy

in Oligopoly Markets


Introduction

• In the majority of markets firms interact with few competitors

• In determining strategy each firm has to consider rival’s reactions– strategic interaction in prices, outputs, advertising …

• This kind of interaction is analyzed using game theory– assumes that “players” are rational

• Distinguish cooperative and noncooperative games– focus on noncooperative games

• Also consider timing– simultaneous versus sequential games


Oligopoly Theory

• No single theory– employ game theoretic tools that are appropriate

– outcome depends upon information available

• Need a concept of equilibrium– players (firms?) choose strategies, one for each player

– combination of strategies determines outcome

– outcome determines pay-offs (profits?)

• Equilibrium first formalized by Nash: No firm wants to change its current strategy given that no other firm changes its current strategy


Nash Equilibrium

• Equilibrium need not be “nice”– firms might do better by coordinating but such coordination may

not be possible (or legal)

• Some strategies can be eliminated on occasions– they are never good strategies no matter what the rivals do

• These are dominated strategies– they are never employed and so can be eliminated

– elimination of a dominated strategy may result in another being dominated: it also can be eliminated

• One strategy might always be chosen no matter what the rivals do: dominant strategy


An Example

• Two airlines

• Prices set: compete in departure times

• 70% of consumers prefer evening departure, 30% prefer morning departure

• If the airlines choose the same departure times they share the market equally

• Pay-offs to the airlines are determined by market shares

• Represent the pay-offs in a pay-off matrix


The example (cont.)The Pay-Off Matrix

American

Delta

Morning

Morning

Evening

Evening

(15, 15)

The left-handnumber is the

pay-off toDelta

The right-handnumber is the

pay-off toAmerican

(30, 70)

(70, 30) (35, 35)

What is theequilibrium for this

game?



American

Delta

Morning

Morning

Evening

Evening

(15, 15)

If Americanchooses a morning

departure, Deltawill choose

evening

(30, 70)

(70, 30) (35, 35)

If Americanchooses an evening

departure, Deltawill still choose

evening

The morning departureis a dominated

strategy for Delta and so can be eliminated.

The Nash Equilibrium must therefore be one in which

both airlines choose an evening departure

(35, 35)

The morning departureis also a dominated

strategy for American and again can be eliminated


The example (cont.)

• Now suppose that Delta has a frequent flier program

• When both airline choose the same departure times Delta gets 60% of the travelers

• This changes the pay-off matrix



American

Delta

Morning

Morning

Evening

Evening

(18, 12) (30, 70)

(70, 30) (42, 28)

However, a morning departureis still a dominated strategy for Delta (Evening is still a dominant strategy.

If Deltachooses a morning

departure, Americanwill choose

eveningBut if Delta

chooses an eveningdeparture, American

will choosemorning

American has no dominated strategy

American knowsthis and so

chooses a morningdeparture

(70, 30)


Nash Equilibrium Again

• What if there are no dominated or dominant strategies?• The Nash equilibrium concept can still help us in

eliminating at least some outcomes• Change the airline game to a pricing game:

– 60 potential passengers with a reservation price of $500– 120 additional passengers with a reservation price of $220– price discrimination is not possible (perhaps for regulatory reasons

or because the airlines don’t know the passenger types)– costs are $200 per passenger no matter when the plane leaves– the airlines must choose between a price of $500 and a price of

$220– if equal prices are charged the passengers are evenly shared– Otherwise the low-price airline gets all the passengers

• The pay-off matrix is now:



American

Delta

PH = $500

($9000,$9000) ($0, $3600)

($3600, $0) ($1800, $1800)

PH = $500

PL = $220

PL = $220

If both price highthen both get 30

passengers. Profitper passenger is

$300

If Delta prices highand American lowthen American getsall 180 passengers.

Profit per passengeris $20

If Delta prices lowand American high

then Delta getsall 180 passengers.

Profit per passengeris $20

If both price lowthey each get 90

passengers.Profit per passenger

is $20


Nash Equilibrium (cont.)The Pay-Off Matrix

American

Delta

PH = $500

($9000,$9000) ($0, $3600)

($3600, $0) ($1800, $1800)

PH = $500

PL = $220

PL = $220

(PH, PL) cannot bea Nash equilibrium.If American prices

low then Delta shouldalso price low

($0, $3600)

(PL, PH) cannot bea Nash equilibrium.If American prices

high then Delta shouldalso price high

($3600, $0)

(PH, PH) is a Nashequilibrium.

If both are pricinghigh then neither wants

to change

($9000, $9000)

(PL, PL) is a Nashequilibrium.

If both are pricinglow then neither wants

to change

($1800, $1800)

There are two Nashequilibria to this version

of the game

There is no simple way to choose betweenthese equilibria. But even so, the Nash concept has eliminated half of the outcomes as equilibria

Custom and familiaritymight lead both to

price high

“Regret” mightcause both to

price low



American

Delta

PH = $500

($9000,$9000) ($0, $3600)

($3600, $0) ($1800, $1800)

PH = $500

PL = $220

PL = $220

(PH, PL) cannot bea Nash equilibrium.If American prices

low then Delta wouldwant to price low, too.

($0, $3600)

(PL, PH) cannot bea Nash equilibrium.If American prices

high then Delta shouldalso price high

($3600, $0)

(PH, PH) is a Nashequilibrium.

If both are pricinghigh then neither wants

to change

($9000, $9000)

(PL, PL) is a Nashequilibrium.

If both are pricinglow then neither wants

to change

($1800, $1800)

There are two Nashequilibria to this version

of the game

There is no simpleway to choose between

these equilibria, but at least we have eliminated half of the outcomes as

possible equilibria



American

Delta

PH = $500

($9000,$9000) ($0, $3600)

($3600, $0) ($1800, $1800)

PH = $500

PL = $220

PL = $220

($0, $3600)

($3600, $0)

($3,000, $3,000)

($1800, $1800)

Delta can see that if it sets a high price, then American

will do best by also pricing high. Delta

earns $9000

Suppose that Deltacan set its price first

Delta can also see that if it sets a low price, American

will do best by pricing low. Delta will then earn $1800

The only sensible choice for Delta is PH knowing that American will follow with PH and each will

earn $9000. So, the Nash equilibria now is (PH, PH)

($1800, $1800)

Sometimes, consideration of the timing of moves can help us find the equilibrium This means that

PH, PL cannot be an equilibrium

outcomeThis means that PL,PH

cannot be an equilibrium


Oligopoly Models

• There are three dominant oligopoly models– Cournot

– Bertrand

– Stackelberg

• They are distinguished by– the decision variable that firms choose

– the timing of the underlying game

• But each embodies the Nash equilibrium concept


The Cournot Model

• Start with a duopoly

• Two firms making an identical product (Cournot supposed this was spring water)

• Demand for this product is

P = A - BQ = A - B(q1 + q2)

where q1 is output of firm 1 and q2 is output of firm 2

• Marginal cost for each firm is constant at c per unit

• To get the demand curve for one of the firms we treat the output of the other firm as constant

• So for firm 2, demand is P = (A - Bq1) - Bq2


The Cournot model (cont.)

P = (A - Bq1) - Bq2$

Quantity

A - Bq1

If the output offirm 1 is increasedthe demand curvefor firm 2 moves

to the left

A - Bq’1

The profit-maximizing choice of output by firm 2 depends upon the output of firm 1

DemandMarginal revenue for firm 2 is

MR2 = (A - Bq1) - 2Bq2MR2

MR2 = MC

A - Bq1 - 2Bq2 = c

Solve thisfor output

q2

q*2 = (A - c)/2B - q1/2

c MC

q*2



q*2 = (A - c)/2B - q1/2

This is the best response function for firm 2

It gives firm 2’s profit-maximizing choice of output for any choice of output by firm 1

There is also a best response function for firm 1

By exactly the same argument it can be written:

q*1 = (A - c)/2B - q2/2

Cournot-Nash equilibrium requires that both firms be on their best response functions.


Cournot-Nash Equilibriumq2

q1

The best response function for firm 1 isq*1 = (A-c)/2B - q2/2


(A-c)/B

(A-c)/2B

Firm 1’s best response function



(A-c)/2B

(A-c)/B

If firm 2 producesnothing then firm1 will produce themonopoly output

(A-c)/2B

If firm 2 produces(A-c)/B then firm1 will choose to

produce no output


The Cournot-Nashequilibrium is at

Point C at the intersectionof the best response

functions

C

qC1

qC2


Cournot-Nash Equilibrium

q2

q1

(A-c)/B

(A-c)/2B


(A-c)/2B

(A-c)/B


C

q*1 = (A - c)/2B - q*2/2

q*2 = (A - c)/2B - q*1/2

q*2 = (A - c)/2B - (A - c)/4B + q*2/4

3q*2/4 = (A - c)/4B

q*2 = (A - c)/3B(A-c)/3B

q*1 = (A - c)/3B

(A-c)/3B


Cournot-Nash Equilibrium (cont.)

• In equilibrium each firm produces qC1 = qC

2 = (A - c)/3B• Total output is, therefore, Q* = 2(A - c)/3B• Recall that demand is P = A - BQ• So the equilibrium price is P* = A - 2(A - c)/3 = (A + 2c)/3• Profit of firm 1 is (P* - c)qC

1 = (A - c)2/9• Profit of firm 2 is the same• A monopolist would produce QM = (A - c)/2B• Competition between the firms causes their total output

to exceed the monopoly output. Price is therefore lower than the monopoly price

• But output is less than the competitive output (A - c)/B where price equals marginal cost and P exceeds MC


Numerical Example of Cournot Duopoly

• Demand: P = 100 - 2Q = 100 - 2(q1 + q2); A = 100; B = 2• Unit cost: c = 10• Equilibrium total output: Q = 2(A – c)/3B = 30;• Individual Firm output: q1 = q2 = 15• Equilibrium price is P* = (A + 2c)/3 = $40• Profit of firm 1 is (P* - c)qC

1 = (A - c)2/9B = $450• Competition: Q* = (A – c)/B = 45; P = c = $10• Monopoly: QM = (A - c)/2B = 22.5; P = $55• Total output exceeds the monopoly output, but is less

than the competitive output• Price exceeds marginal cost but is less than the

monopoly price



• What if there are more than two firms?

• Much the same approach.

• Say that there are N identical firms producing identical products

• Total output Q = q1 + q2 + … + qN

• Demand is P = A - BQ = A - B(q1 + q2 + … + qN)

• Consider firm 1. It’s demand curve can be written:P = A - B(q2 + … + qN) - Bq1

• Use a simplifying notation: Q-1 = q2 + q3 + … + qN

This denotes outputof every firm other

than firm 1

• So demand for firm 1 is P = (A - BQ-1) - Bq1



P = (A - BQ-1) - Bq1$

Quantity

A - BQ-1

If the output ofthe other firms

is increasedthe demand curvefor firm 1 moves

to the leftA - BQ’-1

The profit-maximizing choice of output by firm 1 depends upon the output of the other firms

DemandMarginal revenue for firm 1 is

MR1 = (A - BQ-1) - 2Bq1MR1

MR1 = MC

A - BQ-1 - 2Bq1 = c


q1

q*1 = (A - c)/2B - Q-1/2

c MC

q*1



q*1 = (A - c)/2B - Q-1/2

How do we solve thisfor q*1?The firms are identical.

So in equilibrium theywill have identical

outputs

Q*-1 = (N - 1)q*1

q*1 = (A - c)/2B - (N - 1)q*1/2

(1 + (N - 1)/2)q*1 = (A - c)/2B

q*1(N + 1)/2 = (A - c)/2B

q*1 = (A - c)/(N + 1)B

Q* = N(A - c)/(N + 1)B

P* = A - BQ* = (A + Nc)/(N + 1)

As the number offirms increases output

of each firm falls As the number of

firms increasesaggregate output

increases As the number offirms increases price

tends to marginal cost

Profit of firm 1 is P*1 = (P* - c)q*1 = (A - c)2/(N + 1)2B

As the number offirms increases profit

of each firm falls


Cournot-Nash equilibrium (cont.)

• What if the firms do not have identical costs?

• Once again, much the same analysis can be used

• Assume that marginal costs of firm 1 are c1 and of firm 2 are c2.

• Demand is P = A - BQ = A - B(q1 + q2)

• We have marginal revenue for firm 1 as before

• MR1 = (A - Bq2) - 2Bq1

• Equate to marginal cost: (A - Bq2) - 2Bq1 = c1


q1

q*1 = (A - c1)/2B - q2/2

A symmetric resultholds for output of

firm 2

q*2 = (A - c2)/2B - q1/2


Cournot-Nash Equilibrium

q2

q1

(A-c1)/B

(A-c1)/2B

R1

(A-c2)/2B

(A-c2)/B

R2C

q*1 = (A - c1)/2B - q*2/2

q*2 = (A - c2)/2B - q*1/2

q*2 = (A - c2)/2B - (A - c1)/4B + q*2/4

3q*2/4 = (A - 2c2 + c1)/4B

q*2 = (A - 2c2 + c1)/3B

q*1 = (A - 2c1 + c2)/3B

What happens to thisequilibrium when

costs change?

As the marginalcost of firm 2

falls its best responsecurve shifts to

the right

The equilibriumoutput of firm 2increases and of

firm 1 falls



• In equilibrium the firms produce qC1

= (A - 2c1 + c2)/3B; qC2 = (A - 2c2 + c1)/3B

• Total output is, therefore, Q* = (2A - c1 - c2)/3B

• Recall that demand is P = A - BQ

• So price is P* = A - (2A - c1 - c2)/3 = (A + c1 +c2)/3

• Profit of firm 1 is (P* - c1)qC1 = (A - 2c1 + c2)2/9B

• Profit of firm 2 is (P* - c2)qC2 = (A - 2c2 + c1)2/9B

• Equilibrium output is less than the competitive level

• Output is produced inefficiently: the low-cost firm should produce all the output


A Numerical Example with Different Costs

• Let demand be given by: P = 100 – 2Q; A = 100, B =2• Let c1 = 5 and c2 = 15• Total output is, Q* = (2A - c1 - c2)/3B = (200 – 5 – 15)/6 =

30• qC

1 = (A - 2c1 + c2)/3B = (100 – 10 + 15)/6 = 17.5• qC

2 = (A - 2c2 + c1)/3B = (100 – 30 + 5)/3B = 12.5• Price is P* = (A + c1 +c2)/3 = (100 + 5 + 15)/3 = 40• Profit of firm 1 is (A - 2c1 + c2)2/9B =(100 – 10 +5)2/18 =

$612.5• Profit of firm 2 is (A - 2c2 + c1)2/9B = $312.5• Producers would be better off and consumers no worse off if

firm 2’s 12.5 units were instead produced by firm 1


Concentration and Profitability

• Assume that we have N firms with different marginal costs

• We can use the N-firm analysis with a simple change

• Recall that demand for firm 1 is P = (A - BQ-1) - Bq1

• But then demand for firm i is P = (A - BQ-i) - Bqi

• Equate this to marginal cost ci

A - BQ-i - 2Bqi = ci

This can be reorganized to give the equilibrium condition:

A - B(Q*-i + q*i) - Bq*i - ci = 0

But Q*-i + q*i = Q*and A - BQ* = P*

P* - Bq*i - ci = 0 P* - ci = Bq*i


Concentration and profitability (cont.)

P* - ci = Bq*i

Divide by P* and multiply the right-hand side by Q*/Q*

P* - ci

P*=

BQ*

P*

q*i

Q*

But BQ*/P* = 1/ and q*i/Q* = si

so: P* - ci

P*=

si

The price-cost marginfor each firm is

determined by its ownmarket share and overallmarket demand elasticity

Extending this we have

P* - cP*

= H

The verage price-cost margin is determined by industry

concentration as measured by the Herfindahl-Hirschman Index


Price Competition: Bertrand

• In the Cournot model price is set by some market clearing mechanism

• Firms seem relatively passive

• An alternative approach is to assume that firms compete in prices: this is the approach taken by Bertrand

• Leads to dramatically different results

• Take a simple example– two firms producing an identical product (spring water?)

– firms choose the prices at which they sell their water

– each firm has constant marginal cost of $10

– market demand is Q = 100 - 2P

Check that withthis demand andthese costs the

monopoly price is$30 and quantity

is 40 units


Bertrand competition (cont.)

• We need the derived demand for each firm– demand conditional upon the price charged by the other firm

• Take firm 2. Assume that firm 1 has set a price of $25– if firm 2 sets a price greater than $25 she will sell nothing

– if firm 2 sets a price less than $25 she gets the whole market

– if firm 2 sets a price of exactly $25 consumers are indifferent between the two firms

– the market is shared, presumably 50:50

• So we have the derived demand for firm 2– q2 = 0 if p2 > p1 = $25

– q2 = 100 - 2p2 if p2 < p1 = $25

– q2 = 0.5(100 - 50) = 25 if p2 = p1 = $25



• More generally:– Suppose firm 1 sets price p1

• Demand to firm 2 is:

p2

q2

q2 = 0 if p2 > p1p1

q2 = 100 - 2p2 if p2 < p1

100100 - 2p1

q2 = 50 - p1 if p2 = p1

50 - p1

Demand is notcontinuous. Thereis a jump at p2 = p1

• The discontinuity in demand carries over to profit



Firm 2’s profit is:

2(p1,, p2) = 0 if p2 > p1

2(p1,, p2) = (p2 - 10)(100 - 2p2) if p2 < p1

2(p1,, p2) = (p2 - 10)(50 - p2) if p2 = p1

Clearly this depends on p1.

Suppose first that firm 1 sets a “very high” price: greater than the monopoly price of $30

For whateverreason!



With p1 > $30, Firm 2’s profit looks like this:

Firm 2’s Price

Firm 2’s Profit

$10 $30 p1

p2 < p1

p2 = p1

p2 > p1

What priceshould firm 2

set?

The monopolyprice of $30

What if firm 1prices at $30?

So, if p1 falls to $30, firm 2 should just

undercut p1 a bit and get almost all the monopoly profit

If p1 = $30, then firm 2 will only earn a

positive profit by cutting its price to $30 or less

At p2 = p1 = $30, firm 2 gets half of

the monopoly

profit


Bertrand competition (cont.)Now suppose that firm 1 sets a price less than $30

Firm 2’s Price

Firm 2’s Profit

$10 $30p1

p2 < p1

p2 = p1

p2 > p1

Firm 2’s profit looks like this:

What priceshould firm 2

set now?

As long as p1 > c = $10, Firm 2 should aim

just to undercutfirm 1

What if firm 1prices at $10?

Then firm 2 should also price at $10. Cutting price below costgains the whole market but loses

money on every customer

Of course, firm 1 will then

undercut firm 2 and so on



• We now have Firm 2’s best response to any price set by firm 1:– p*2 = $30 if p1 > $30

– p*2 = p1 - “something small” if $10 < p1 < $30

– p*2 = $10 if p1 < $10

• We have a symmetric best response for firm 1– p*1 = $30 if p2 > $30

– p*1 = p2 - “something small” if $10 < p2 < $30

– p*1 = $10 if p2 < $10


Bertrand competition (cont.)These best response functions look like this

p2

p1$10

$10

R1

R2

The best responsefunction for

firm 1The best response

function forfirm 2

The equilibriumis with both

firms pricing at$10

The Bertrandequilibrium has

both firms chargingmarginal cost

$30

$30


Bertrand Equilibrium: modifications• The Bertrand model makes clear that competition in prices is very

different from competition in quantities

• Since many firms seem to set prices (and not quantities) this is a challenge to the Cournot approach

• But the Bertrand model has problems too

– for the p = marginal-cost equilibrium to arise, both firms need enough capacity to fill all demand at price = MC

– but when both firms set p = c they each get only half the market

– So, at the p = mc equilibrium, there is huge excess capacity

• This calls attention to the choice of capacity

– Note: choosing capacity is a lot like choosing output which brings us back to the Cournot model

• The intensity of price competition when products are identical that the Bertrand model reveals also gives a motivation for Product differentiation


An Example of Product Differentiation

QC = 63.42 - 3.98PC + 2.25PP

QP = 49.52 - 5.48PP + 1.40PC

MCC = $4.96

MCP = $3.96

There are at least two methods for solving this for PC and PP

Coke and Pepsi are nearly identical but not quite. As a result, the lowest priced product does not win the entire market.


Bertrand and Product Differentiation

Method 1: CalculusProfit of Coke: C = (PC - 4.96)(63.42 - 3.98PC + 2.25PP)

Profit of Pepsi: P = (PP - 3.96)(49.52 - 5.48PP + 1.40PC)

Differentiate with respect to PC and PP respectively

Method 2: MR = MC

Reorganize the demand functions

PC = (15.93 + 0.57PP) - 0.25QC

PP = (9.04 + 0.26PC) - 0.18QP

Calculate marginal revenue, equate to marginal cost, solve for QC and QP and substitute in the demand functions


Bertrand competition and product differentiationBoth methods give the best response functions:PC = 10.44 + 0.2826PP

PP = 6.49 + 0.1277PC

PC

PP

RC

$10.44

RP

Note that theseare upward

sloping

The Bertrandequilibrium is

at theirintersection

B

$12.72

$8.11

$6.49

These can be solved for the equilibrium prices as indicated


Bertrand Competition and the Spatial Model

• An alternative approach is to use the spatial model from Chapter 4– a Main Street over which consumers are distributed

– supplied by two shops located at opposite ends of the street

– but now the shops are competitors

– each consumer buys exactly one unit of the good provided that its full price is less than V

– a consumer buys from the shop offering the lower full price

– consumers incur transport costs of t per unit distance in travelling to a shop

• What prices will the two shops charge?


Bertrand and the spatial model

Shop 1 Shop 2

Assume that shop 1 setsprice p1 and shop 2 sets

price p2

Price Price

p1

p2

xm

All consumers to theleft of xm buy from

shop 1And all consumers

to the right buy fromshop 2

What if shop 1 raisesits price?

p’1

x’m

xm moves to theleft: some consumers

switch to shop 2

Xm marks the location of the

marginal buyer—one who is

indifferent between buying either firm’s

good


Bertrand and the spatial model

Shop 1 Shop 2

Price Price

p1

p2

xm

How is xm

determined?

p1 + txm = p2 + t(1 - xm)

2txm = p2 - p1 + t

xm(p1, p2) = (p2 - p1 + t)/2t

This is the fractionof consumers whobuy from firm 1

So demand to firm 1 is D1 = N(p2 - p1 + t)/2t

There are n consumers in total


Bertrand equilibrium

Profit to firm 1 is 1 = (p1 - c)D1 = N(p1 - c)(p2 - p1 + t)/2t

1 = N(p2p1 - p12 + tp1 + cp1 - cp2 -ct)/2t

Differentiate with respect to p1

1/ p1 =N

2t(p2 - 2p1 + t + c) = 0

Solve thisfor p1

p*1 = (p2 + t + c)/2

What about firm 2? By symmetry, it has a similar best response function.

This is the bestresponse function

for firm 1

p*2 = (p1 + t + c)/2

This is the best response function for firm 2


Bertrand and Demand

p*1 = (p2 + t + c)/2 p2

p1

R1

p*2 = (p1 + t + c)/2

R2

(c + t)/2

(c + t)/2

2p*2 = p1 + t + c

= p2/2 + 3(t + c)/2

p*2 = t + c

c + t

p*1 = t + c

c + t


Stackelberg

• Interpret in terms of Cournot

• Firms choose outputs sequentially– leader sets output first, and visibly

– follower then sets output

• The firm moving first has a leadership advantage– can anticipate the follower’s actions

– can therefore manipulate the follower

• For this to work the leader must be able to commit to its choice of output

• Strategic commitment has value


Stackelberg Equilibrium: an example

• Assume that there are two firms with identical products

• As in our earlier Cournot example, let demand be:– P = 100 - 2Q = 100 - 2(q1 + q2)

• Total cost for for each firm is:– C(q1) = 10q1; C(q2) = 10q2

Both firms have constantmarginal costs of $10,

i.e., c = 10 for both firms

• Firm 1 is the market leader and chooses q1

• In doing so it can anticipate firm 2’s actions

• So consider firm 2. Demand is:– P = (100 - 2q1) - 2q2

• Marginal revenue therefore is:– MR2 = (100 - 2q1) - 4q2


Stackelberg equilibrium (cont.)

MR2 = (100 - 2q1) - 4q2

MR = (100 - 2q1) - 4q2 = 10 = c

Equate marginal revenuewith marginal costSolve this equation

for output q2

q*2 = 22.5 - q1/2

q2

q1

R2

22.5

45

This is firm 2’sbest response

function

Firm 1 knows thatthis is how firm 2

will react to firm 1’soutput choice

Firm 1 knows thatthis is how firm 2

will react to firm 1’soutput choice So firm 1 can

anticipate firm 2’sreaction

So firm 1 can anticipate firm 2’s

reaction

Demand for firm 1 is:

P = (100 - 2q2) - 2q1

But firm 1 knowswhat q2 is going

to be

P = (100 - 2q*2) - 2q1

P = (100 - (45 - q1)) - 2q1

P = 55 - q1

Marginal revenue for firm 1 is:

MR1 = 55 - 2q1

Equate marginal revenuewith marginal cost

55 - 2q1 = 10

Solve this equationfor output q1

q*1 = 22.522.5

q*2 = 11.25

11.25

From earlier example (slide 22) we know that 22.5 is the monopoly output. This is an

important result. The Stackelberg leader chooses the same output as a monopolist would.

But firm 2 is not excluded from the marketS


Firm 1’s best responsefunction is “like”

firm 2’s

Stackelberg equilibrium (cont.)

Aggregate output is 33.75

So the equilibrium price is $32.50 q2

q1

R2

22.5

45

Compare this withthe Cournotequilibrium

Compare this withthe Cournotequilibrium

22.5

11.25

Firm 1’s profit is (32.50 - 10)22.5

1 = $506.25

Firm 2’s profit is (32.50 - 10)11.25

2 = $253.125

45R1

SCWe know (see slide 22) that the

Cournot equilibrium is:

qC1 = qC

2 = 15

15

15

The Cournot price is $40

Profit to each firm is $450

Leadership benefitsthe leader firm 1 butharms the follower

firm 2

Leadership benefitsconsumers but

reduces aggregateprofits


Stackelberg and Commitment

• It is crucial that the leader can commit to its output choice– without such commitment firm 2 should ignore any stated intent

by firm 1 to produce 45 units

– the only equilibrium would be the Cournot equilibrium

• So how to commit?– prior reputation

– investment in additional capacity

– place the stated output on the market

• Finally, the timing of decisions matters

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EC 170 Industrial Organization Chapter 5 Business Strategy in Oligopoly Markets.

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