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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 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 structure?

  • Your actions affect the profits of your rivals.

  • Your rivals’ actions affect your profits.


An example l.jpg
An Example structure?

  • 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

P structure?0

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

D structure?2 (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 structure?

  • 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 structure?

  • 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? structure?

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? structure?

  • 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 structure?

  • 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

Q structure?1 = 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 structure?

  • 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 structure?

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 structure?

  • 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 structure?

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 structure?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 example)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 q by setting its MR= MCA 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? by setting its MR= MC

  • 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 cartel and act as a monopoly?

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? cartel and act as a monopoly?

  • 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 cartel and act as a monopoly?

QB

rA

48

rB

QA

48

72


Conclusion l.jpg
Conclusion cartel and act as a monopoly?

  • 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 cartel and act as a monopoly?

  • 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 cartel and act as a monopoly?

  • 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 cartel and act as a monopoly?

  • 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? cartel and act as a monopoly?

  • 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 cartel and act as a monopoly?

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 cartel and act as a monopoly?

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s resultsQ = 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 for Cournot model to find the Stakelberg model’s resultsP = 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 for Cournot model to find the Stakelberg model’s results

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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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? for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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 for Cournot model to find the Stakelberg model’s results

  • 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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