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

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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

Week Ten

Week Ten- Class 1

Monday, November 5

11:10-12:00Fottrell (AM)

Aplia assignment is due tomorrow before 5 PM

Chapter 9 of Baye

Basic Oligopoly Models

- Relatively few firms, usually less than 10.
- Duopoly - two firms
- Triopoly - three firms

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

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

- You and another firm sell differentiated products such as cars.
- How does the quantity demanded for your cars change when you change your price?

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

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

- 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.

- 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

TR1= PQ1 = aQ1 – bQ12 – bQ1Q2

TR2 = PQ2 = aQ2 – bQ22 – bQ1Q2

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

- 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

- Both firms produce identical products

- Q1 depends on Q2

- This is called Firm 1’s best response function

- 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

Q2

(a-c1)/b

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

Q2

r1

(Firm 1’s Reaction Function)

Q1

Q1

(a-c1)/2b

- 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.

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

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

- Week Ten- Class 2
- Tuesday, November 6
- Cairnes
- 15:10-16:00

- Aplia assignment is due before 5PM today

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

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*

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

- 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

- Revenue for firm A
= P qA = qA (339 - qA – qB)

= 339 qA- qA2 - qAqB

- Marginal Revenue for firm A
= 339 - 2 qA – qB

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

- 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 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

- 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

QB

rA

After Collusion

48

rB

QA

48

- 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

QB

rA

48

rB

QA

48

72

- 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.

- Week Ten- Class 3
- Thursday, November 8
- 15:10-16:00
- Tyndall

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

- 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.

- 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

- 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.

Cournot 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)

- 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.

- Only this time assume and Firm A is a leader
- Find each firm’s output and profit

- Note: Firm A knows Firm B’s reaction function.
- Market demand is given by
Q = 339 – P, and

AC = MC = 147

- 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 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

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

- 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.

- 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

- 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.

- 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.

- 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).

- 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

- 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.

- 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.