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Welcome to Welcome to EC 209: Managerial EC 209: Managerial Economics- Group AEconomics- Group ABy:By: Dr. Jacqueline KhorassaniDr. Jacqueline Khorassani

Week TenWeek Ten

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Managerial Economics- Managerial Economics- Group AGroup A

Week Ten- Class 1Week Ten- Class 1Monday, November 5Monday, November 5

11:10-12:0011:10-12:00Fottrell (AM)Fottrell (AM)

Aplia assignment is due Aplia assignment is due tomorrow before 5 PMtomorrow before 5 PM

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Chapter 9 of BayeChapter 9 of Baye

Basic Oligopoly ModelsBasic Oligopoly Models

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What are the What are the characteristics of characteristics of oligopolistic market oligopolistic market structure?structure? Relatively few firms, usually less Relatively few firms, usually less

than 10.than 10.– Duopoly - two firmsDuopoly - two firms– Triopoly - three firmsTriopoly - three firms

The products firms offer can be The products firms offer can be either differentiated or either differentiated or homogeneous.homogeneous.

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Interdependence Interdependence

Your actions Your actions affect the profits affect the profits of your rivals.of your rivals.

Your rivals’ Your rivals’ actions affect actions affect your profits.your profits.

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An ExampleAn Example

You and another firm sell You and another firm sell differentiated products such as differentiated products such as cars.cars.

How does the quantity demanded How does the quantity demanded for your cars change when you for your cars change when you change your price?change your price?

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P

Q

D1 (demand for your cars when rival holds its price constant)

P0

PL

D2 (demand for your cars when rival matches your price change)

PH

Q0 QL2 QL1QH1 QH2

88

P

Q

D1

P0

Q0

D2 (Rival matches your price change)

(Rival holds itsprice constant)

D

Your demand if rivals match price reductions but not price increases “Kinked Demand Curve”

P1

Q1

P2

Q2

What if your rivals match your price reductions but not your price increases?

Cournot ModelCournot Model A few firms produce goods that are A few firms produce goods that are

either perfect substitutes either perfect substitutes (homogeneous) or imperfect (homogeneous) or imperfect substitutes (differentiated).substitutes (differentiated).

Firms set output, as opposed to price.Firms set output, as opposed to price. The output of rivals is viewed as The output of rivals is viewed as

given or “fixed”.given or “fixed”. Barriers to entry exist.Barriers to entry exist.

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Cournot Model: General Cournot Model: General Linear CaseLinear Case

Market demand in a homogeneous-product Market demand in a homogeneous-product Cournot duopoly isCournot duopoly is

Total Revenue for firm 1 is Total Revenue for firm 1 is PQPQ11 = aQ = aQ11 – bQ – bQ11

22 – bQ – bQ11QQ22

Total Revenue for firm 2 is Total Revenue for firm 2 is PQPQ22 = aQ = aQ22 – bQ – bQ22

22 – bQ – bQ11QQ22

21 QQbaP

1111

What are the marginal What are the marginal revenues?revenues?TRTR11= PQ= PQ11 = aQ = aQ11 – bQ – bQ11

22 – bQ – bQ11QQ22

TRTR22 = PQ = PQ22 = aQ = aQ22 – bQ – bQ2222 – bQ – bQ11QQ22

Each firm’s marginal revenue depends Each firm’s marginal revenue depends on the output produced by the other on the output produced by the other firm. firm.

212 2bQbQaMR

121 2bQbQaMR

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Where do the Where do the quantities come from?quantities come from?

Golden rule of profit maximization says get the Golden rule of profit maximization says get the output from the intersection of MC and MRoutput from the intersection of MC and MRMC=MRMC=MRFirm 1’s MC = cFirm 1’s MC = c11

And its MR = a- bQAnd its MR = a- bQ22 -2bQ -2bQ11

cc11 = = a- bQa- bQ22 -2bQ -2bQ11

2bQ2bQ11= -c= -c11+a-bQ+a-bQ22

– This is called Firm 1’s best response functionThis is called Firm 1’s best response function Q1 depends on Q2Q1 depends on Q2

– Both firms produce identical productsBoth firms produce identical products So if Firm two produces moreSo if Firm two produces more firm 1 must produce less firm 1 must produce less

21

211 2

1

2Q

b

caQrQ

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Best-Response Function Best-Response Function for a Cournot Duopolyfor a Cournot Duopoly

Firm 1’s best-response function isFirm 1’s best-response function is

Similarly, Firm 2’s best-response function Similarly, Firm 2’s best-response function is (is (cc22 is firm 2’s MC) is firm 2’s MC)

21

211 2

1

2Q

b

caQrQ

12

122 2

1

2Q

b

caQrQ

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Graph of Firm 1’s Best-Graph of Firm 1’s Best-Response FunctionResponse Function

Q2

Q1

(Firm 1’s Reaction Function)

Q2

Q1

r1

(a-c1)/b Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2

21

211 2

1

2Q

b

caQrQ

If Q1 = 0 Q2 = (a-c1)/b

(a-c1)/2b

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Cournot EquilibriumCournot Equilibrium

Exist whenExist when– No firm can gain by unilaterally changing No firm can gain by unilaterally changing

its own output to improve its profit.its own output to improve its profit. A point where the two firm’s best-A point where the two firm’s best-

response functions intersect.response functions intersect.

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Graph of Cournot Graph of Cournot EquilibriumEquilibrium

Q2*

Q1*

Q2

Q1

A

r2

Q2M

Cournot Equilibrium

(a-c1)/b

(a-c2)/b

r1

If Firm 1 produces A Firm 2 produces B

If Firm 2 produces B Firm 1 produces C

If Firm 1 produces C Firm 2 produces D

B

C

D

Equilibrium Quantities are at intersection of the response curves

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Managerial Economics- Managerial Economics- Group AGroup A Week Ten- Class 2Week Ten- Class 2

– Tuesday, November 6Tuesday, November 6– CairnesCairnes– 15:10-16:0015:10-16:00

Aplia assignment is due before Aplia assignment is due before 5PM today5PM today

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Last class we looked at Last class we looked at Cournot EquilibriumCournot Equilibrium

Q2*

Q1*

Q2

Q1

A

r2

Q2M

Cournot Equilibrium

(a-c1)/b

(a-c2)/b

r1

If Firm 1 produces A Firm 2 produces B

If Firm 2 produces B Firm 1 produces C

If Firm 1 produces C Firm 2 produces D

B

C

D

Equilibrium Quantities are at intersection of the response curves

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What happens if Firm 1’s What happens if Firm 1’s MC goes up? MC goes up?

Q2

Q1

r1**

r2

r1*

Q1*

Q2*

Q2**

Q1**

Cournot equilibrium prior to

firm 1’s marginal cost increase

Cournot equilibrium after

firm 1’s marginal cost increase

(a-c1)/b

When c1 goes up vertical intercept of firm 1’s reaction curves goes down

Firm 1’s production goes down

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Example of Cournot Model (See Example of Cournot Model (See textbook page 324 for another textbook page 324 for another example)example) Consider a case where there are two Consider a case where there are two

firms: A and B. firms: A and B. Market demand is given by Q = 339 – Market demand is given by Q = 339 –

P P AC = MC = 147AC = MC = 147 The residual demand for firm A is The residual demand for firm A is

qqAA = Q – q = Q – qB B

qqAA = 339 – P - q = 339 – P - qB B , or , or

P = 339 - qP = 339 - qAA – q – qB B

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Firm A’s demand is Firm A’s demand is P = 339 - qP = 339 - qAA – q – qBB

Revenue for firm A Revenue for firm A = P q= P qAA = q = qAA (339 - q (339 - qAA – q – qBB))

= 339 q= 339 qAA- q- qAA2 2 - q- qAAqqBB

Marginal Revenue for firm A Marginal Revenue for firm A = 339 - 2 q= 339 - 2 qAA – q – qBB

2222

Firm A’s best response (or Firm A’s best response (or reaction function) is derived by reaction function) is derived by setting its MR= MCsetting its MR= MC

339 - 2 q339 - 2 qAA – q – qB B = 147 = 147

or qor qAA = 96 – 1/2 q = 96 – 1/2 qBB

Consider qConsider qB B = 0; q= 0; qA A = 96= 96

By the same reasoning qBy the same reasoning qBB = 96 – = 96 – 1/2 q1/2 qAA

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Cournot Nash equilibrium is a Cournot Nash equilibrium is a combination of qcombination of qAA and q and qB B so that so that both firms are on their reaction both firms are on their reaction functions.functions.

Firm A’s reaction function isFirm A’s reaction function isqqAA = 96 – 1/2 q = 96 – 1/2 qBB

Firm B’s reaction function isFirm B’s reaction function isqqBB = 96 – 1/2 q = 96 – 1/2 qAA

qqAA = 96 – 1/2 (96 – 1/2 q = 96 – 1/2 (96 – 1/2 qAA ) )

Solve to find qSolve to find qA A = 64 = 64

Similarly qSimilarly qB B = 64= 64

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What are the profits at What are the profits at equilibrium? equilibrium?

What is the Price?What is the Price?P = 339 - qP = 339 - qAA - q - qBB

P = 339 - 64 - 64P = 339 - 64 - 64P = 211P = 211Remember that AC = 147Remember that AC = 147Each firm’s profit = q (P-AC) Each firm’s profit = q (P-AC) Each firm’s profit = 64*(211-147) = 64 * Each firm’s profit = 64*(211-147) = 64 *

64 = 409664 = 4096

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Could the two firms do better Could the two firms do better than this if they formed a cartel than this if they formed a cartel and act as a monopoly?and act as a monopoly?

The monopoly outcome is found by taking the The monopoly outcome is found by taking the marginal revenue curve for the industry and setting marginal revenue curve for the industry and setting it equal to MC. it equal to MC.

Recall that market demand was Q = 339 – PRecall that market demand was Q = 339 – P Or P = 339-QOr P = 339-Q Revenue will beRevenue will be PQ = 339Q – QPQ = 339Q – Q22 MR = 339 – 2Q MR = 339 – 2Q MC = 147 MC = 147 339-2Q = 147339-2Q = 147 or Q = 96 & P = 243or Q = 96 & P = 243 Suppose the two firms divided the market between Suppose the two firms divided the market between

them so that each produced 48 units. them so that each produced 48 units. Each would earn profits of 48 * (243-147) = 4608Each would earn profits of 48 * (243-147) = 4608 4608> 40964608> 4096

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Collusion Incentives in Collusion Incentives in Cournot OligopolyCournot Oligopoly

QB

QA

rA

rB

48

48

After Collusion

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But will the cartel be a But will the cartel be a stable outcome?stable outcome?

NoNo Given that firm B is producing 48 Given that firm B is producing 48

units what should firm A produce?units what should firm A produce? Look at Firm’s reaction functionLook at Firm’s reaction function

qqAA = 96 – 1/2 q = 96 – 1/2 qBB

qqAA = 96 – 1/2 (48) = 96 – 1/2 (48)

qqAA = 72 = 72

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Firm A has an incentive to Firm A has an incentive to cheatcheat

QB

QA

rA

rB

48

48

72

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ConclusionConclusion

The numerical example makes it The numerical example makes it clear that in a duopoly firms have clear that in a duopoly firms have an incentive to restrict output to an incentive to restrict output to the monopoly level. However they the monopoly level. However they also have an incentive to cheat also have an incentive to cheat on any agreement.on any agreement.

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Managerial Economics- Managerial Economics- Group AGroup A Week Ten- Class 3Week Ten- Class 3

– Thursday, November 8Thursday, November 8– 15:10-16:0015:10-16:00– TyndallTyndall

Next Aplia Assignment is due Next Aplia Assignment is due before 5 PM on Tuesday, before 5 PM on Tuesday, November 13November 13

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Stackelberg Model: Stackelberg Model: CharacteristicsCharacteristics Firms produce differentiated or Firms produce differentiated or

homogeneous products.homogeneous products. Barriers to entry.Barriers to entry. Firm one is the leader.Firm one is the leader.

– The leader commits to an output before The leader commits to an output before all other firms.all other firms.

Remaining firms are followers.Remaining firms are followers.– They choose their outputs so as to They choose their outputs so as to

maximize profits, given the leader’s maximize profits, given the leader’s output.output.

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Stackelberg Model: Stackelberg Model: General Linear CaseGeneral Linear Case Two firms in the marketTwo firms in the market Market demand is P = a – b(QMarket demand is P = a – b(Q11 + +

QQ22) ) Marginal cost for firm 1 and firm 2 Marginal cost for firm 1 and firm 2

is cis c11 and c and c22 Firm 1 is the leader Firm 1 is the leader We showed earlier that Firm 2’s We showed earlier that Firm 2’s

best response (reaction) function best response (reaction) function is given by is given by QQ22 = (a – c = (a – c22)/2b – 1/2Q)/2b – 1/2Q11

3333

What does the leader What does the leader do?do?

The leader “Firm 1” substitutes Firm 2’s The leader “Firm 1” substitutes Firm 2’s reaction function into market demand function.reaction function into market demand function.– Where market demand function is P = a – b(QWhere market demand function is P = a – b(Q11 + Q + Q22) ) – And Firm2’s reaction function is QAnd Firm2’s reaction function is Q22 = (a – c = (a – c22)/2b – )/2b –

1/2Q1/2Q11

P = a – b(QP = a – b(Q11 + (a – c + (a – c22)/2b – 1/2Q)/2b – 1/2Q11)) This is multiplied by QThis is multiplied by Q11 to get the revenue to get the revenue

function for Firm 1. function for Firm 1. Differentiate the revenue function with respect Differentiate the revenue function with respect

to Q to get Firm 1’s marginal revenue function. to Q to get Firm 1’s marginal revenue function. Set the MR = MC Set the MR = MC Solve for QSolve for Q11. . QQ11 is equal to (a + c is equal to (a + c22 -2c -2c11)/2b. )/2b. Use the reaction function for QUse the reaction function for Q22 to find the to find the

expression for Qexpression for Q22..

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Stackelberg Stackelberg EquilibriumEquilibrium

Q1

Q1M

r1

Q2C

Q1C

r2

Q2

Q1S

Q2S

Stackelberg Equilibrium

Note: Firm 1 is producing on Frim 2’s reaction function (maximizes its profits given the reaction of Firm 2)

Cournot equilibrium

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Stackelberg SummaryStackelberg Summary Leader produces Leader produces moremore than the than the

Cournot equilibrium output.Cournot equilibrium output.– Larger market share, higher profits.Larger market share, higher profits.– First-mover advantage.First-mover advantage.

Follower produces Follower produces lessless than the than the Cournot equilibrium output.Cournot equilibrium output.– Smaller market share, lower profits.Smaller market share, lower profits.

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Let’s use the same Let’s use the same numerical example we numerical example we used last class for Cournot used last class for Cournot model to find the model to find the Stakelberg model’s resultsStakelberg model’s results

Only this time assume Only this time assume and Firm A is a and Firm A is a leaderleader

Find each firm’s output and profitFind each firm’s output and profit

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Example of Example of Stackelberg ModelStackelberg Model

Note: Firm A knows Firm B’s Note: Firm A knows Firm B’s reaction function. reaction function.

Market demand is given by Market demand is given by Q = 339 – P, and Q = 339 – P, and

AC = MC = 147AC = MC = 147

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Market demand is given Market demand is given by by Q = 339 – PQ = 339 – P The residual demand for firm A is The residual demand for firm A is

qqAA = Q – q = Q – qB B

qqAA= 339 – P - q= 339 – P - qB B or or P = 339 - qP = 339 - qAA – q – qBB

Remember that firm B’s reaction function Remember that firm B’s reaction function isis

qqBB = 96 – 1/2 q = 96 – 1/2 qAA Plug in Firm B’s reaction function into Plug in Firm B’s reaction function into

Firm A’s demandFirm A’s demandP = 339 – qP = 339 – qAA - 96 + 1/2 q - 96 + 1/2 qAA

P = 243- 1/2 qP = 243- 1/2 qAA

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Firm A’s demand is Firm A’s demand is P = 243- 1/2 qP = 243- 1/2 qAA

Firm A’s revenue is Firm A’s revenue is

PqPqAA = 243 q = 243 qAA– 1/2 q– 1/2 qAA2 2

MR = 243 – qMR = 243 – qAA Set this equal to MC Set this equal to MC

147 = 243- q147 = 243- qAA

qqAA = 96 = 96Use B’s reaction functionUse B’s reaction function

qqBB = 96 – 1/2 q = 96 – 1/2 qA,A,

qqBB = 96 – 1/2 (96) = 96 – 1/2 (96),,

qqBB = 48 = 48

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ProfitsProfits

Remember that Remember that

P = 339 - qP = 339 - qAA – q – qBB

P = 339 – 96 – 48 P = 339 – 96 – 48

P = 195, AC = 147P = 195, AC = 147

Firm A’s profit = 96 (195 - 147) = Firm A’s profit = 96 (195 - 147) = 46084608

Firm B’s profit is 48 (195 – 147) = Firm B’s profit is 48 (195 – 147) = 23042304

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Bertrand Model: Bertrand Model: CharacteristicsCharacteristics

1.1. Few firms that sell to many Few firms that sell to many consumers.consumers.

2.2. Firms produce identical products at Firms produce identical products at constant marginal cost.constant marginal cost.

3.3. Each firm independently sets its price Each firm independently sets its price in order to maximize profits.in order to maximize profits.

4.4. Barriers to entry.Barriers to entry.5.5. Consumers enjoyConsumers enjoy

– Perfect information. Perfect information. – Zero transaction costs.Zero transaction costs.

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Bertrand EquilibriumBertrand Equilibrium Firms set PFirms set P1 1 = P= P22 = MC! Why? = MC! Why? Suppose notSuppose not

AC= MC = 10 , PAC= MC = 10 , P11=15 , P=15 , P22= 18= 18

How much is Firm 1’s profit per unit? How much is Firm 1’s profit per unit? PP11 – AC= 5 – AC= 5

How much is Firm 2’s profit per unit?How much is Firm 2’s profit per unit?– None, Firm Can’t sell anyNone, Firm Can’t sell any

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What would Firm 2 do?What would Firm 2 do?

Cut the price slightly below Firm Cut the price slightly below Firm 1’s (to 14)1’s (to 14)

Firm 1 then has an incentive to Firm 1 then has an incentive to undercut firm 2’s price. (to 13) undercut firm 2’s price. (to 13)

This undercutting continues... untilThis undercutting continues... until Equilibrium: Each firm charges PEquilibrium: Each firm charges P1 1

= P= P22 = MC = 10. = MC = 10.

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Contestable MarketsContestable Markets

Key AssumptionsKey Assumptions– Producers have access to same Producers have access to same

technology.technology.– Consumers respond quickly to price Consumers respond quickly to price

changes.changes.– Existing firms cannot respond quickly Existing firms cannot respond quickly

to entry by lowering price.to entry by lowering price.– Absence of sunk costs.Absence of sunk costs.

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Key ImplicationsKey Implications

Strategic interaction between Strategic interaction between incumbents and potential incumbents and potential entrantsentrants

Threat of entry disciplines firms Threat of entry disciplines firms already in the market.already in the market.

Incumbents have no market Incumbents have no market power, even if there is only a power, even if there is only a single incumbent (a monopolist).single incumbent (a monopolist).

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Contestable MarketsContestable Markets Important condition for a Important condition for a

contestable market is the absence contestable market is the absence of of sunk costssunk costs..– Encourages new firms to enterEncourages new firms to enter– You enter the industry and if things You enter the industry and if things

don’t work out don’t work out exit exit

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Another exampleAnother example

Consider a case where there are Consider a case where there are two firms – 1 and 2. Market two firms – 1 and 2. Market demand is given by Q = 1,000 – demand is given by Q = 1,000 – P; AC = MC = 4.P; AC = MC = 4.

Find the Cournot, Stackelberg, Find the Cournot, Stackelberg, Monopoly and Bertrand Monopoly and Bertrand outcomes.outcomes.

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ConclusionConclusion Different oligopoly scenarios give rise to Different oligopoly scenarios give rise to

different optimal strategies and different different optimal strategies and different outcomes.outcomes.

Your optimal price and output depends onYour optimal price and output depends on– Beliefs about the reactions of rivals.Beliefs about the reactions of rivals.– Your choice variable (P or Q) and the Your choice variable (P or Q) and the

nature of the product market nature of the product market (differentiated or homogeneous products).(differentiated or homogeneous products).

– Your ability to credibly commit prior to Your ability to credibly commit prior to your rivals.your rivals.