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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 ABy:Dr. Jacqueline Khorassani

### Chapter 9 of Baye

Week Ten

Managerial Economics- Group A

Week Ten- Class 1

Monday, November 5

11:10-12:00Fottrell (AM)

Aplia assignment is due tomorrow before 5 PM

Basic Oligopoly Models

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

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

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?

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

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

- 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

- 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?

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?

- 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

- Firm 1’s best-response function is
- Similarly, Firm 2’s best-response function is (c2 is firm 2’s MC)

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

Graph of Firm 1’s Best-Response FunctionQ2

(a-c1)/b

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

Q2

r1

(Firm 1’s Reaction Function)

Q1

Q1

(a-c1)/2b

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

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 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

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

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)

- 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 - 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

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

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?

- 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?

- 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

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

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 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

- 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

- 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?

- 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

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

- 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.

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

- 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

- 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 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

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

- 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

- 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?

- 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

- 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

- 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 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

- 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.

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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