Econ 384 Intermediate Microeconomics II

Econ 384

Intermediate Microeconomics II

Lorne Priemaza, M.A.

[email protected]

Various material courtesy ofWiley & Sons INC.

mailto:[email protected]

Chapter 13

13.1 Market Structure

13.2 Homogeneous Oligopoly

13.3 Dominant Firm Markets

13.4 Oligopoly with Horizontally Differentiated Products

13.5 Monopolistic Competition

Appendix

13.1 Market StructureMarket structure depends upon two spectrums:

1)Number of firms in market

2)Product Differentiation

Definition: Product Differentiation between two or more products exists when the products possess attributes that, in the minds of consumers, set the products apart from one another and make them less than perfect substitutes.

Examples: Pepsi is sweeter than Coke, Brand Name batteries last longer than "generic" batteries.

13.1 Market Structure

13.1 Market StructureA) Perfect Competition

1) Many Firms

2) Homogeneous Products

examples: Lemonade stands, fries

B) Monopolistic Competition

1) Many Firms

2) Differentiated Products

Examples: dry cleaning, socks, burgers

13.1 Market StructureC) Homogeneous Products Oligopoly

1) Few Firms


Examples: Convenience Store, Apples

D) Differentiated Products Oligopoly

1) Few Firms

2) Differentiated Products

Examples: Cola, Breakfast Cereals

13.1 Market StructureE) Dominant Firm

1) One Large Firm, many small firms


Examples: Ketchup, MP3 Players

F) Monopoly

1) One Firm

2) One Product

Examples: Canadian Uranium, Canadian Health Insurance (government monopoly)

13.1 Measuring Market Structure1) Four-firm Concentration Ratio (4CR)

-Sum of the top 4 sales revenue (in percentage terms) in an industry

ie1) Internet: Shaw (50%) and Telus (50%)

4CR = 50%+50%=100%

ie2) French Fries: New York (10%), McDonalds (7%), Wendy’s (4%), Red Robin (3%)

4CR = 10%+7%+4%+3%=24%*Note: Values are assumptions

13.1 Measuring Market Structure2) Herfindahl-Hirschman Index (HHI)

-∑(Market Share)2

ie1) Monopoly: HHI=1002=10,000

ie2) 100 Identical Firms: HHI=100(1)2=100

-HHI ranges from 0 (infinite firms) to 10,000 (one firm)

*Note that the textbook calculations are inconsistent for HHI

13.1 Measuring Market Structure-TYPICALLY:

-Industries closer to perfect competition or monopolistic competition have low 4CR’s and HHI’s

-Oligopolies have intermediate 4CR’s and HHI’s

-Industries closer to monopolies and dominant firms have high 4CR’s and HHI’s

-This is a GENERALIZATION (there are deviations)

13.1 Measuring Market Structure

13.2 Homogeneous OligopolyIn perfect competition, each firm can ignore all

other firms.

Oligopoly markets feature COMPETITIVE INDERDEPENDENCE – firm A’s decisions affect the profits of other firms.

ex) if Firm A overproduces, price falls and Firm B’s profits decrease

How does this close interdependence affect firm behavior?

13Chapter Thirteen

Cournot OligopolyAssumptions

• Firms set outputs (quantities)*• Homogeneous Products• Simultaneous• Non-cooperative

*Definition: In a Cournot game, each firm sets its output (quantity) taking as given the output level of its competitor(s), so as to maximize profits.

Price adjusts according to demand.

14Chapter Thirteen

Simultaneously vs. Non-cooperatively

Definition: Firms act simultaneously if each firm makes its strategic decision at the same time, without prior observation of the other firm's decision.

Definition: Firms act non-cooperatively if they set strategy independently, without colluding with the other firm in any way

15Chapter Thirteen

Definition: The relationship between the price charged by firm i and the demand firm i faces is firm is residual demand

In other words, the residual demand of firm i is the market demand minus the amount of demand fulfilled by other firms in the market: Q1 = Q – Q2; firms are QUANTITY TAKERS (v. price takers in Perfect Competition)Note: We will initially assume only 2 firms, a DUOPOLY

Residual Demand

16

Price

Quantity0

Demand

Residual Demand when q2 = 10

10 units Residual Marginal Revenue when q2 = 10

MC

q1*

Residual Demand

Best response to q2 = 10

17Chapter Thirteen

Best Response/Reaction Function

Best Response- The point where (residual) marginal revenue equals marginal cost gives ONE best response of firm i to its rival's action.

Reaction Function-The graph of all possible best responses to rival actions

18q1

Reaction Function of Firm 1

0


q1*

q2* •

Chapter Thirteen

q2

Reaction Functions

19Chapter Thirteen

Cournot Equilibrium

Equilibrium: No firm has an incentive to deviate in equilibrium; each firm is maximizing profits given its rival's output

Each Firm’s output is a BEST RESPONSE to each other firm’s output.

20Chapter Thirteen

P = 100 - Q1 - Q2 MC = AC = 10

What is firm 1's profit-maximizing output when firm 2 produces 50?Residual demand: P = (100 - Q1) – 50 = 50 - Q1

TR=PQ= 50Q1 - Q12

MR50 = ∂TR/ ∂Q1 = 50 - 2Q1

Since profit is maximized when MR=MC,MR50 = MC 50 - 2Q1 = 1040 = 2Q20 = Q

Cournot Equilibrium Example

21


P = 100 - Q1 - Q2 MC = AC = 10

What is the equation of firm 1's reaction function?

Residual demand: P = (100 - Q2) - Q1

TR= PQ1 = 100Q1 - Q2 Q1 - Q12

MRr = ∂TR/ ∂Q1 =100 - Q2 - 2Q1

MRr = MC 100 - Q2 - 2Q1 = 10Q1r = 45 - Q2/2 firm 1's reaction function

•Similarly, Q2r = 45 - Q1/2

22Chapter Thirteen


P = 100 - Q1 - Q2 MC = AC = 10Q1r = 45 - Q2/2 Q2r = 45 - Q1/2

Calculate the Cournot equilibrium.

Q1 = 45 - Q2/2Q1 = 45 - (45 - Q1/2)/2Q1* = 30Q2* = 30P = 100 - Q1 - Q2 = 100 - 30 - 30 = 40 1* = 2* = TR – TC = (P-MC)Q*1* = 2* = (40-10)(30) = 900

23Chapter Thirteen

Cournot Solving Steps

1) Calculate Residual Demand2) Calculate (residual) MR3) MR=MC to find reaction functions4) Use reaction functions to solve for Q’s5) Use Q’s to solve for P

-Remember that Q1+Q2=QM

6) Solve for 7) Summarize

24q1

1) Each firm can calculate Reaction Functions

0

Z

q1*

q2* •

Chapter Thirteen

q2

How do firms achieve Cournot Equilibria?

2) Firm 2 will never produce over A

A

3) Knowing this, Firm 1 will never produce under B

4) Knowing this, Firm 2 will never produce over C

C

B

5) This reasoning continues until point Z


25

Cournot vs. Monopoly vs. PC

Since Pcournot > MC, Cournot prices are higher than perfect competition prices

Cournot firms have market powerBUT, a Cournot market produces more than a Monopoly, and at a lower price.Each firm’s pursuit of individual self-interest does not typically maximize the industry’s profits.

Each firm wishes the other would decrease quantityMonopoly profits are possible if firms collude (which is illegal)

26

PC vs. Cournot vs. Monopoly

Consider the following outcomes using our above example of P=100-Q:

The outcome changes greatly with number of firms.

27

P = a-bQ MC = c N identical firms

Find Cournot Equilibrium QuantityResidual demand P = a-b(Q1 + Qother)TR = PQ = aQ1-bQ1

2 – bQotherQ1

MR = ∂TR/ ∂Q = a-2bQ1 – bQother

Since profit is maximized when MR=MC,MR = MC a-2bQ1 – bQother = cQ1=(a-c)/2b – (1/2)Qother Since Qother = (N-1) Q1,

Q1=(a-c)/2b – (1/2)[(N-1)Q1] Since Q1=Q*

Cournot Equilibrium, Many Firms

)()1(

1*

b

ca

NQ

28

P = a-bQ MC = c N identical firms

Find Cournot Equilibrium Market PriceSince there are N firms,

Cournot Equilibrium, Many Firms

)()1( b

ca

N

NQM

cN

N

N

aP

b

ca

N

NbaP

bQaP M

)1()1(

)()1(

29Chapter Thirteen

Cournot Solving Steps Multi-Firm

1) Calculate Residual Demand2) Calculate (residual) MR3) MR=MC to find reaction functionsNew 3b) Remember that Qother = (N-1) Q1

4) Use reaction functions to solve for Q’s5) Use Q to solve for P

-Remember that ∑Qi=QM

6) Solve for 7) Summarize

30Chapter Thirteen

Outcome comparisons

Given the relationship P=a-bQ and MC=c,

13.2 Bertrand Oligopoly (Homogeneous Products)

Cournot Oligopoly –Firms compete on QUANTITY

Bertrand Oligopoly –Firms compete on PRICES

-Goods must be homogeneous/identical

-A firm’s residual demand depends on the other firm’s price:

Zero demand at prices higher than the other firm

Market demand at prices lower than the other firm

32

Bertrand Oligopoly (homogeneous)

Assumptions:

• Firms set price*• Homogeneous product• Simultaneous • Non-cooperative

*Definition: In a Bertrand oligopoly, each firm sets its price, taking as given the price(s) set by other firm(s), so as to maximize profits.

*Definition: In a Bertrand oligopoly, each firm sets its price, taking as given the price(s) set by other firm(s), so as to maximize profits.

33Quantity

Price

Market Demand

•Firm 1’s Residual Demand Curve

0Chapter Thirteen

Residual Demand Curve – Price Setting

P2

13.2 Bertrand Oligopoly (Homogeneous Products)

Firm A must undercut firm B’s price to sell anything

This will force firm B to undercut Firm A

... This will continue until neither firm can

decrease price further, P=MC The Perfect Competition Result!

35

Bertrand Equilibrium Example

P = 100 - QT MC = AC = 10

What is the Bertrand Equilibrium?

P = MC=10

P = 100 – QT

10 = 100 – QT

90 = QT

∏=TR-TC∏=(P-MC)Q∏=(10-10)90 = 0

Bertrand vs. Cournot

Cournot – Long-Run Competition (Firms choose output capacity)

Bertrand – Short-Run Competition (Firms have excess output)

------------------------------------------------------------------

Cournot – Firms can quickly adjust their price, so price competition is useless

Bertrand – Firms can only slowly adjust price, so firms believe a price cut can temporarily increase profits

37

Stackelberg model of oligopoly is a situation in which one firm acts as a quantity leader, choosing its quantity first, with all other firms acting as followers.

Call the first mover the “leader” and the second mover the “follower”.

The second firm is in the same situation as a Cournot firm: it takes the leader’s output as given and maximizes profits accordingly, using its residual demand.

The second firm’s behavior can, then, be summarized by a Cournot reaction function.

Stackelberg Oligopoly

38

Stackelberg Leader Choice

P = 100 - QL - QF MC = AC = 10

What is the equation of the follower’s reaction function?

Residual demand: P = (100 - QL) - QF

TR= PQF = 100QF - QF QL - QF2

MRFr = ∂TR/ ∂Q1 =100 - QL - 2QF

MRFr = MC 100 - QL - 2QF = 10QFr = 45 - QL/2 follower’s reaction function

The Stackelberg leader knows the follower’s reaction function, and can use that to choose its production:

39Chapter Thirteen


P = 100 - QL - QF MC = AC = 10QFr = 45 - QL/2

Calculate the Stackelberg equilibrium.

P = 100 - QL - QF = 100 - QL – (45 - QL/2 )P = 55 – QL/2

TR= PQL = 55QL – QL2/2

MRL = ∂TR/ ∂QL = 55 – QL

MRL = MC 55 – QL = 10QL = 45

40Chapter Thirteen


P = 100 - QL - QF MC = AC = 10QFr = 45 - QL/2 QL = 45

Continue Calculating the Stackelberg equilibrium.QFr = 45 - QL/2 = 45 - 45/2 QFr = 22.5

P = 100 - QL - QF = 100 - 45 – 22.5 = 32.5 L* = TR – TC = (P-MC)QL* = (32.5-10)45 = 1,012.5F* = TR – TC = (P-MC)QF* = (32.5-10)22.5 = 506.25

41


With a Stackelberg leader, price is $32.50, with the leader producing 45 units for a profit of $1,012.50 and the following producing 22.5 units for a profit of $506.25.

Notice that:

1) Price is lower than the Cournot equilibrium

2) Leader profits are higher than the cournot equilibrium

3) Follower profits are lower than the Cournot equilibrium

There is an advantage to moving first

42Chapter Thirteen

Stackelberg Solving Steps

1) Calculate Leader’s Residual Demand2) Calculate Leaders (residual) MR3) Leader’s MR=MC to find QL

4) Use QL to solve for QF

5) Use Q’s to solve for P -Remember that QL+QF=QM

1) Solve for ’s2) Summarize

13.3 Dominant Firm Model

The dominant firm model features:

1) A single company with an overwhelming market share (a dominant firm), D

2) many small producers (competitive fringe), each of whom has a small market share, F

The dominant firm faces market demand, and residual demand that takes into account the competitive fringe’s supply:

44

The dominant firm’s residual demand (DR) is market demand minus competitive fringe supply (in terms of Q)

Dominant Firm

45

Dominant Firm Example

P = 100 - QT SF: P =10+QF or QF =P - 10

MCD = AC = 10

What is the equation of the Dominant Firm’s Residual Demand?QR = QT – QF

QR = 100-P – (P-10)QR = 110-2PP = 55-QR/2

46


P = 100 - QT SF: P =10+QF or QF =P - 10MCD = AC = 10 QR = 90-2P (P = 55-QR/2)

Calculate Dominant Firm Quantities and PriceTRDR = PQD = 55QD-QD

2/2MRL = ∂TR/ ∂QL = 55 – QD

MRL = MC 55 – QD = 10QD = 45

P = 55-QR/2P = 55-45/2 = 32.5

47


P = 100 - QT SF: P =10+QF or QF =P - 10MCD = AC = 10 QR = 90-2P (P = 55-QR/2)

Calculate and check Competitive Fringe QuantitiesSF: P =10+QF

32.5 = 10+QF

QF = 22.5

QT = QD + QF

QT = 45 + 22.5 = 67.5

P = 100 – QT

32.5 = 100 – 67.5 = 32.5

48


P = 100 - QT SF: P =10+QF or QF =P - 10MCD = AC = 10 QR = 90-2P (P = 55-QR/2)QF = 22.5, QD = 45, P=32.5

Calculate market share and dominant firm profitD: Market Share = QD/ QT = 45/67.5*100 = 66.6%F: Market Share = QD/ QT = 22.5/67.5*100 = 33.3%

D* = TR – TC = (P-MC)QD* = (32.5-10)45 = 1,012.5At a price of $32.50, the dominant firm produces

45 units for a profit of $1,012.50, and fringe firms produce 22.5 total.

49Chapter Thirteen

Dominant Firm Solving Steps

1) Calculate Dominant Firm`s Residual Demand2) Calculate Dominant Firm`s (residual) MR3) Leader’s MR=MC to find QD

4) Use QD to solve for P5) Use P to solve for QF

-Remember that QD+QF=QM

1) Solve for and Market Share2) Summarize

50

Aside: Calculating SF

Fringe Firm: MC=5+20q, 40 firmsCalculate Fringe SupplyMC=5+20qq=(P-5)/20QF=40(P-5)/20QF=2P-10

Recall: A competitive firm’s supply comes from its MC

curve Identical firms supply can be summed (through q)

51

Growing Fringe:

As the size of the fringe grows, the price, and the production and profits of the dominant firm decreases (next slide):

There is therefore an incentive for the dominant firm to practice limit pricing (illegal in Canada):

Limit Pricing – a strategy whereby the dominant firm keeps its price below the level that maximizes its current profit in order to reduce the rate of expansion by the fringe

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Econ 384 Intermediate Microeconomics II