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Welcome to EC 209: Managerial Economics- Group A By: Dr. Jacqueline Khorassani. Week Ten. Managerial Economics- Group A. Week Ten- Class 1 Monday, November 5 11:10-12:00 Fottrell (AM) Aplia assignment is due tomorrow before 5 PM. Chapter 9 of Baye. Basic Oligopoly Models.

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Welcome to EC 209: Managerial Economics- Group A By: Dr. Jacqueline Khorassani

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Welcome to ec 209 managerial economics group a by dr jacqueline khorassani l.jpg

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

Week Ten


Managerial economics group a l.jpg

Managerial Economics- Group A

Week Ten- Class 1

Monday, November 5

11:10-12:00Fottrell (AM)

Aplia assignment is due tomorrow before 5 PM


Chapter 9 of baye l.jpg

Chapter 9 of Baye

Basic Oligopoly Models


What are the characteristics of oligopolistic market structure l.jpg

What are the characteristics of oligopolistic market structure?

  • Relatively few firms, usually less than 10.

    • Duopoly - two firms

    • Triopoly - three firms

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


Interdependence l.jpg

Interdependence

  • Your actions affect the profits of your rivals.

  • Your rivals’ actions affect your profits.


An example l.jpg

An Example

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

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


Slide7 l.jpg

P0

QH1

QH2

QL2

QL1

Q0

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

P

PH

PL

D1 (demand for your cars when

rival holds its price constant)

Q


Slide8 l.jpg

D2 (Rival matches your price change)

P

P0

D1

(Rival holds its

price constant)

Q

Q0

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

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

P2

P1

D

Q1

Q2


Cournot model l.jpg

Cournot Model

  • A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated).

  • Firms set output, as opposed to price.

  • The output of rivals is viewed as given or “fixed”.

  • Barriers to entry exist.


Cournot model general linear case l.jpg

Cournot Model: General Linear Case

  • Market demand in a homogeneous-product Cournot duopoly is

  • Total Revenue for firm 1 is

    PQ1 = aQ1 – bQ12 – bQ1Q2

  • Total Revenue for firm 2 is

    PQ2 = aQ2 – bQ22 – bQ1Q2


What are the marginal revenues l.jpg

What are the marginal revenues?

TR1= PQ1 = aQ1 – bQ12 – bQ1Q2

TR2 = PQ2 = aQ2 – bQ22 – bQ1Q2

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


Where do the quantities come from l.jpg

Where do the quantities come from?

  • Golden rule of profit maximization says get the output from the intersection of MC and MR

    MC=MR

    Firm 1’s MC = c1

    And its MR = a- bQ2 -2bQ1

    c1 =a- bQ2 -2bQ1

    2bQ1= -c1+a-bQ2

    • This is called Firm 1’s best response function

      • Q1 depends on Q2

        • Both firms produce identical products

          • So if Firm two produces more firm 1 must produce less


Best response function for a cournot duopoly l.jpg

Best-Response Function for a Cournot Duopoly

  • Firm 1’s best-response function is

  • Similarly, Firm 2’s best-response function is (c2 is firm 2’s MC)


Graph of firm 1 s best response function l.jpg

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

Graph of Firm 1’s Best-Response Function

Q2

(a-c1)/b

If Q1 = 0  Q2 = (a-c1)/b

Q2

r1

(Firm 1’s Reaction Function)

Q1

Q1

(a-c1)/2b


Cournot equilibrium l.jpg

Cournot Equilibrium

  • Exist when

    • No firm can gain by unilaterally changing its own output to improve its profit.

      • A point where the two firm’s best-response functions intersect.


Graph of cournot equilibrium l.jpg

Graph of Cournot Equilibrium

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

Q2

(a-c1)/b

Cournot Equilibrium

Q2M

Q2*

D

B

r2

r1

Q1*

A

(a-c2)/b

Q1

C

Equilibrium Quantities are at intersection of the response curves


Managerial economics group a17 l.jpg

Managerial Economics- Group A

  • Week Ten- Class 2

    • Tuesday, November 6

    • Cairnes

    • 15:10-16:00

  • Aplia assignment is due before 5PM today


Last class we looked at cournot equilibrium l.jpg

Last class we looked at Cournot Equilibrium

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

Q2

(a-c1)/b

Cournot Equilibrium

Q2M

Q2*

D

B

r2

r1

Q1*

A

(a-c2)/b

Q1

C

Equilibrium Quantities are at intersection of the response curves


What happens if firm 1 s mc goes up l.jpg

Cournot equilibrium after

firm 1’s marginal cost increase

r1**

Q2**

Cournot equilibrium prior to

firm 1’s marginal cost increase

Q2*

r2

Q1**

Q1*

What happens if Firm 1’s MC goes up?

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

Q2

r1*

(a-c1)/b

Q1

Firm 1’s production goes down


Example of cournot model see textbook page 324 for another example l.jpg

Example of Cournot Model (See textbook page 324 for another example)

  • Consider a case where there are two firms: A and B.

  • Market demand is given by Q = 339 – P

  • AC = MC = 147

  • The residual demand for firm A is

    qA = Q – qB

    qA = 339 – P - qB , or

    P = 339 - qA – qB


Firm a s demand is p 339 q a q b l.jpg

Firm A’s demand is P = 339 - qA – qB

  • Revenue for firm A

    = P qA = qA (339 - qA – qB)

    = 339 qA- qA2 - qAqB

  • Marginal Revenue for firm A

    = 339 - 2 qA – qB


Firm a s best response or reaction function is derived by setting its mr mc l.jpg

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

339 - 2 qA – qB = 147

or qA = 96 – 1/2 qB

Consider qB = 0; qA = 96

By the same reasoning qB = 96 – 1/2 qA


Slide23 l.jpg

Cournot Nash equilibrium is a combination of qA and qB so that both firms are on their reaction functions.

  • Firm A’s reaction function is

    qA = 96 – 1/2 qB

  • Firm B’s reaction function is

    qB = 96 – 1/2 qA

    qA = 96 – 1/2 (96 – 1/2 qA )

    Solve to find qA = 64

    Similarly qB = 64


What are the profits at equilibrium l.jpg

What are the profits at equilibrium?

  • What is the Price?

    P = 339 - qA - qB

    P = 339 - 64 - 64

    P = 211

    Remember that AC = 147

    Each firm’s profit = q (P-AC)

    Each firm’s profit = 64*(211-147) = 64 * 64 = 4096


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

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

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

  • Recall that market demand was Q = 339 – P

  • Or P = 339-Q

  • Revenue will be

  • PQ = 339Q – Q2

  • MR = 339 – 2Q

  • MC = 147

  • 339-2Q = 147

  • or Q = 96 & P = 243

  • Suppose the two firms divided the market between them so that each produced 48 units.

  • Each would earn profits of 48 * (243-147) = 4608

  • 4608> 4096


Collusion incentives in cournot oligopoly l.jpg

Collusion Incentives in Cournot Oligopoly

QB

rA

After Collusion

48

rB

QA

48


But will the cartel be a stable outcome l.jpg

But will the cartel be a stable outcome?

  • No

  • Given that firm B is producing 48 units what should firm A produce?

  • Look at Firm’s reaction function

    qA = 96 – 1/2 qB

    qA = 96 – 1/2 (48)

    qA = 72


Firm a has an incentive to cheat l.jpg

Firm A has an incentive to cheat

QB

rA

48

rB

QA

48

72


Conclusion l.jpg

Conclusion

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


Managerial economics group a30 l.jpg

Managerial Economics- Group A

  • Week Ten- Class 3

    • Thursday, November 8

    • 15:10-16:00

    • Tyndall

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


Stackelberg model characteristics l.jpg

Stackelberg Model: Characteristics

  • Firms produce differentiated or homogeneous products.

  • Barriers to entry.

  • Firm one is the leader.

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

  • Remaining firms are followers.

    • They choose their outputs so as to maximize profits, given the leader’s output.


Stackelberg model general linear case l.jpg

Stackelberg Model: General Linear Case

  • Two firms in the market

  • Market demand is P = a – b(Q1 + Q2)

  • Marginal cost for firm 1 and firm 2 is c1 and c2

  • Firm 1 is the leader

  • We showed earlier that Firm 2’s best response (reaction) function is given by

    Q2 = (a – c2)/2b – 1/2Q1


What does the leader do l.jpg

What does the leader do?

  • The leader “Firm 1” substitutes Firm 2’s reaction function into market demand function.

    • Where market demand function is P = a – b(Q1 + Q2)

    • And Firm2’s reaction function is Q2 = (a – c2)/2b – 1/2Q1

  • P = a – b(Q1 + (a – c2)/2b – 1/2Q1)

  • This is multiplied by Q1 to get the revenue function for Firm 1.

  • Differentiate the revenue function with respect to Q to get Firm 1’s marginal revenue function.

  • Set the MR = MC

  • Solve for Q1.

  • Q1 is equal to (a + c2 -2c1)/2b.

  • Use the reaction function for Q2 to find the expression for Q2.


Stackelberg equilibrium l.jpg

Cournot equilibrium

Stackelberg Equilibrium

Q2

r1

Stackelberg Equilibrium

Q2C

Q2S

r2

Q1M

Q1C

Q1S

Q1

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


Stackelberg summary l.jpg

Stackelberg Summary

  • Leader produces more than the Cournot equilibrium output.

    • Larger market share, higher profits.

    • First-mover advantage.

  • Follower produces less than the Cournot equilibrium output.

    • Smaller market share, lower profits.


Slide36 l.jpg

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

  • Only this time assume and Firm A is a leader

  • Find each firm’s output and profit


Example of stackelberg model l.jpg

Example of Stackelberg Model

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

  • Market demand is given by

    Q = 339 – P, and

    AC = MC = 147


Market demand is given by q 339 p l.jpg

Market demand is given by Q = 339 – P

  • The residual demand for firm A is

    qA = Q – qB

    qA= 339 – P - qB or

    P = 339 - qA – qB

  • Remember that firm B’s reaction function is

    qB = 96 – 1/2 qA

  • Plug in Firm B’s reaction function into Firm A’s demand

    P = 339 – qA - 96 + 1/2 qA

    P = 243- 1/2 qA


Firm a s demand is p 243 1 2 q a l.jpg

Firm A’s demand is P = 243- 1/2 qA

Firm A’s revenue is

PqA = 243 qA– 1/2 qA2

MR = 243 – qA

Set this equal to MC

147 = 243- qA

qA = 96

Use B’s reaction function

qB = 96 – 1/2 qA,

qB = 96 – 1/2 (96),

qB = 48


Profits l.jpg

Profits

Remember that

P = 339 - qA – qB

P = 339 – 96 – 48

P = 195, AC = 147

Firm A’s profit = 96 (195 - 147) = 4608

Firm B’s profit is 48 (195 – 147) = 2304


Bertrand model characteristics l.jpg

Bertrand Model: Characteristics

  • Few firms that sell to many consumers.

  • Firms produce identical products at constant marginal cost.

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

  • Barriers to entry.

  • Consumers enjoy

    • Perfect information.

    • Zero transaction costs.


Bertrand equilibrium l.jpg

Bertrand Equilibrium

  • Firms set P1 = P2 = MC! Why?

  • Suppose not

    AC= MC = 10 , P1=15 , P2= 18

  • How much is Firm 1’s profit per unit?

    P1 – AC= 5

  • How much is Firm 2’s profit per unit?

    • None, Firm Can’t sell any


What would firm 2 do l.jpg

What would Firm 2 do?

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

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

  • This undercutting continues... until

  • Equilibrium: Each firm charges P1 = P2 = MC = 10.


Contestable markets l.jpg

Contestable Markets

  • Key Assumptions

    • Producers have access to same technology.

    • Consumers respond quickly to price changes.

    • Existing firms cannot respond quickly to entry by lowering price.

    • Absence of sunk costs.


Key implications l.jpg

Key Implications

  • Strategic interaction between incumbents and potential entrants

  • Threat of entry disciplines firms already in the market.

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


Contestable markets46 l.jpg

Contestable Markets

  • Important condition for a contestable market is the absence of sunk costs.

    • Encourages new firms to enter

    • You enter the industry and if things don’t work out  exit


Another example l.jpg

Another example

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

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


Conclusion48 l.jpg

Conclusion

  • Different oligopoly scenarios give rise to different optimal strategies and different outcomes.

  • Your optimal price and output depends on

    • Beliefs about the reactions of rivals.

    • Your choice variable (P or Q) and the nature of the product market (differentiated or homogeneous products).

    • Your ability to credibly commit prior to your rivals.


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