1 Market Structure And Competition Chapter 13. 2 Chapter Thirteen Overview 1.Introduction: Cola Wars...

1

Market Structure

And Competition

Chapter 13

2

Chapter Thirteen Overview

1. Introduction: Cola Wars

2. A Taxonomy of Market Structures

3. Monopolistic Competition

4. Oligopoly – Interdependence of Strategic Decisions• Bertrand with Homogeneous and Differentiated Products

5. The Effect of a Change in the Strategic Variable• Theory vs. Observation• Cournot Equilibrium (homogeneous)• Comparison to Bertrand, Monopoly• Reconciling Bertrand, and Cournot

6. The Effect of a Change in Timing: Stackelberg Equilibrium

Chapter Thirteen

3Chapter Thirteen

Market Structures

• The number of sellers

• The number of buyers

• Entry conditions

• The degree of product differentiation

4Chapter Thirteen

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.

5Chapter Thirteen

Product Differentiation

• "Superiority" (Vertical Product Differentiation) i.e. one product is viewed as unambiguously better than another so that, at the same price, all consumers would buy the better product

• "Substitutability" (Horizontal Product Differentiation) i.e. at the same price, some consumers would prefer the characteristics of product A while other consumers would prefer the characteristics of product B.

6Chapter Thirteen

Types of Market Structures

7Chapter Thirteen

Oligopoly

Assumptions:

• Many Buyers and Few Sellers

• Each firm faces downward-sloping demand because each is a large producer compared to the total market size • There is no one dominant model of oligopoly. We will review several.

8Chapter Thirteen

Cournot Oligopoly

Assumptions

• 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.

Residual Demand: Firm i's guess about its rival's output determines its residual demand.

9Chapter 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

10Chapter 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

Residual Demand

11

Price

Quantity0

Demand

Residual Demand when q2 = 10

10 unitsResidual Marginal Revenue when q2 = 10

MC

q1* Chapter Thirteen

Residual Demand

12Chapter Thirteen

Profit Maximization

Profit Maximization: Each firm acts as a monopolist on its residual demand curve, equating MRr to MC.

MRr = p + q1(p/q) = MC

Best Response Function:

The point where (residual) marginal revenue equals marginal cost gives the best response of firm i to its rival's (rivals') actions.

For every possible output of the rival(s), we can determine firm i's best response. The sum of all these points makes up the best response (reaction) function of firm i.

13q1

Reaction Function of Firm 1

0

Reaction Function of Firm 2

q1*

q2* •

Chapter Thirteen

q2

Profit Maximization

Example: Reaction Functions, Quantity Setting

14Chapter Thirteen

P = 100 - Q1 - Q2

MC = AC = 10

What is firm 1's profit-maximizing output when firm 2 produces 50?

Firm 1's residual demand:• P = (100 - 50) - Q1

• MR50 = 50 - 2Q1

• MR50 = MC 50 - 2Q1 = 10

EquilibriumEquilibrium: No firm has an incentive to deviate in equilibrium in the sense that each firm is maximizing profits given its rival's output

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

Firm 1's residual demand:• P = (100 - Q2) - Q1

• MRr = 100 - Q2 - 2Q1

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

•Similarly, one can compute that Q2r = 45 - Q1/2

15Chapter Thirteen

Profit Maximization

Now, calculate the Cournot equilibrium.

• Q1 = 45 - (45 - Q1/2)/2• Q1* = 30• Q2* = 30• P* = 40 • 1* = 2* = 30(30) = 900

16Chapter Thirteen

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.

17Chapter Thirteen

• Homogeneity implies that consumers will buy from the low-price seller.

• Further, each firm realizes that the demand that it faces depends both on its own price and on the price set by other firms

• Specifically, any firm charging a higher price than its rivals will sell no output.

• Any firm charging a lower price than its rivals will obtain the entire market demand.

Setting Price

18

Quantity

Price

Market Demand

•Residual Demand Curve (thickened line segments)

0Chapter Thirteen

Residual Demand Curve – Price Setting

19Chapter Thirteen

Residual Demand Curve – Price Setting

• Assume firm always meets its residual demand (no capacity constraints)

• Assume that marginal cost is constant at c per unit.

• Hence, any price at least equal to c ensures non-negative profits.

20Chapter Thirteen

Best Response Function

Each firm's profit maximizing response to the other firm's price is to undercut (as long as P > MC)

Definition: The firm's profit maximizing action as a function of the action by the rival firm is the firm's best response (or reaction) function

Example:

2 firmsBertrand competitors

Firm 1's best response function is P1=P2- eFirm 2's best response function is P2=P1- e

21Chapter Thirteen

Equilibrium

If we assume no capacity constraints and that all firms have the same constant average and marginal cost of c then:

For each firm's response to be a best response to the other's each firm must undercut the other as long as P> MC

Where does this stop? P = MC (!)

22Chapter Thirteen

Equilibrium

1. Firms price at marginal cost

2. Firms make zero profits

3. The number of firms is irrelevant to the price level as long as more than one firm is present: two firms is enough to replicate the perfectly competitive outcome.

Essentially, the assumption of no capacity constraints combined with a constant average and marginal cost takes the place of free entry.

23Chapter Thirteen

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

24

q1

q2

Follower’s Cournot Reaction Function

• Former Cournot Equilibrium

•

••

A

B(q1= 90)

C

Profit for firm 1 at A…0 at B…0 at C…1012.5at Cournot Eq…900

Chapter Thirteen

Stackelberg Equilibrium vs. Cournot

25Chapter Thirteen

A single company with an overwhelming market share (a dominant firm) competes against many small producers (competitive fringe), each of whom has a small market share.

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.

Dominant Firm Markets

26Chapter Thirteen

Bertrand Competition – Differentiated

Assumptions:

Firms set price*Differentiated productSimultaneous Non-cooperative

*Differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly

27Chapter Thirteen

Q1 = 100 - 2P1 + P2 "Coke's demand"Q2 = 100 - 2P2 + P1 "Pepsi's demand"

MC1 = MC2 = 5

What is firm 1's residual demand when Firm 2's price is $10? $0?

Q1(10) = 100 - 2P1 + 10 = 110 - 2P1

Q1(0) = 100 - 2P1 + 0 = 100 - 2P1

Bertrand Competition – Differentiated

28

Coke’s Price

MR0

Pepsi’s price = $0 for D0 and $10 for D10

0

100

Chapter Thirteen

Residual Demand, Price Setting, Differentiated Products

Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC

Key Concepts

Coke’s Quantity

290

110100

D0

D10

Chapter Thirteen

Key Concepts




Coke’s Price

Coke’s Quantity

30

Coke’s QuantityMR0

D0

0

MR10

110100

D10

Chapter Thirteen

Key Concepts




Coke’s Price

31

5

MR0

D0

0

D10

MR10

110100

Chapter Thirteen

Key Concepts




Coke’s Price

Coke’s Quantity

32

5

27.5

MR0

D0

0

D10

MR10

30

45 50

110100

Chapter Thirteen

Key ConceptsKey Concepts




Coke’s Price

Coke’s Quantity

33Chapter Thirteen

Key Concepts



Example:

MR1(10) = 55 - Q1(10) = 5

Q1(10) = 50P1(10) = 30

Therefore, firm 1's best response to a price of $10 by firm 2 is a price of $30

34Chapter Thirteen

Key Concepts



Example:

• Solving for firm 1's reaction function for any arbitrary price by firm 2

P1 = 50 - Q1/2 + P2/2

MR = 50 - Q1 + P2/2

MR = MC => Q1 = 45 + P2/2

35Chapter Thirteen

And, using the demand curve, we have:

• P1 = 50 + P2/2 - 45/2 - P2/4 or• P1 = 27.5 + P2/4 the reaction function

Key Concepts



36

Pepsi’sPrice (P2)

Coke’s Price (P1)

P2 = 27.5 + P1/4(Pepsi’s R.F.)

27.5

Chapter Thirteen

Equilibrium and Reaction FunctionsPrice Setting and Differentiated Products

37

P1 = 27.5 + P2/4 (Coke’s R.F.) P2 = 27.5 + P1/4

(Pepsi’s R.F.)

•

27.5

27.5

Chapter Thirteen

Pepsi’sPrice (P2)

Coke’s Price (P1)


P1 = 110/3

38

P2 = 110/3 •

BertrandEquilibrium

27.5

Chapter Thirteen

Pepsi’sPrice (P2)

Coke’s Price (P1)

P2 = 27.5 + P1/4(Pepsi’s R.F.)

P1 = 27.5 + P2/4 (Coke’s R.F.)


P1 = 110/327.5

39Chapter Thirteen

Equilibrium occurs when all firms simultaneously choose their best response to each others' actions.

Graphically, this amounts to the point where the best response functions cross.

Equilibrium

40Chapter Thirteen

Example: Firm 1 and Firm 2, continued

• P1 = 27.5 + P2/4• P2 = 27.5 + P1/4

Solving these two equations in two unknowns.

• P1* = P2* = 110/3

Plugging these prices into demand, we have:

• Q1* = Q2* = 190/3

• 1* = 2* = 2005.55• = 4011.10

Equilibrium

41Chapter Thirteen

Profits are positive in equilibrium since both prices are above marginal cost!

Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price.

This blunts price-cutting incentives and means that the firms' own behavior does not mimic free entry

Equilibrium

42Chapter Thirteen

Equilibrium

Only if I were to let the number of firms approach infinity would price approach marginal cost.

Prices need not be equal in equilibrium if firms not identical (e.g. Marginal costs differ implies that prices differ)

The reaction functions slope upward: "aggression => aggression"

43Chapter Thirteen

Cournot, Bertrand, and Monopoly Equilibriums

P > MC for Cournot competitors, but P < PM:

If the firms were to act as a monopolist (perfectly collude), they would set market MR equal to MC:

• P = 100 - Q• MC = AC = 10

• MR = MC => 100 - 2Q = 10 => QM = 45

• PM = 55• M= 45(45) = 2025• c = 1800

44Chapter Thirteen

A perfectly collusive industry takes into account that an increase in output by one firm depresses the profits of the other firm(s) in the industry. A Cournot competitor takes into account the effect of the increase in output on its own profits only.

Therefore, Cournot competitors "overproduce" relative to the collusive (monopoly) point. Further, this problem gets "worse" as the number of competitors grows because the market share of each individual firm falls, increasing the difference between the private gain from increasing production and the profit destruction effect on rivals.

Therefore, the more concentrated the industry in the Cournot case, the higher the price-cost margin.


45Chapter Thirteen

Homogeneous product Bertrand resulted in zero profits, whereas the Cournot case resulted in positive profits. Why?

The best response functions in the Cournot model slope downward. In other words, the more aggressive a rival (in terms of output), the more passive the Cournot firm's response.

The best response functions in the Bertrand model slope upward. In other words, the more aggressive a rival (in terms of price) the more aggressive the Bertrand firm's response.


46Chapter Thirteen

Cournot: Suppose firm j raises its output…the price at which firm i can sell output falls. This means that the incentive to increase output falls as the output of the competitor rises.

Bertrand: Suppose firm j raises price the price at which firm i can sell output rises. As long as firm's price is less than firm's, the incentive to increase price will depend on the (market) marginal revenue.


47Chapter Thirteen

Chamberlinian Monopolistic Competition

Market Structure

• Many Buyers• Many Sellers• Free entry and Exit• (Horizontal) Product Differentiation

When firms have horizontally differentiated products, they each face downward-sloping demand for their product because a small change in price will not cause ALL buyers to switch to another firm's product.

48Chapter Thirteen

1. Each firm is small each takes the observed "market price" as given in its production decisions.

2. Since market price may not stay given, the firm's perceived demand may differ from its actual demand.

3.If all firms' prices fall the same amount, no customers switch supplier but the total market consumption grows.

4. If only one firm's price falls, it steals customers from other firms as well as increases total market consumption

Monopolistic Competition – Short Run

49

Price

Quantity

d (PA=20)

Chapter Thirteen

Perceived vs. Actual Demand

50

d (PA=50)

d (PA=20)

Demand assuming no price matching

Chapter Thirteen

Price

Quantity


51

d (PA=50)

d (PA=20)

Demand (assuming price matching by all firms)

50 •

Chapter Thirteen

Price

Quantity



52Chapter Thirteen

Market Equilibrium

The market is in equilibrium if:

• Each firm maximizes profit taking the average market price as given

• Each firm can sell the quantity it desires at the actual average market price that prevails

53

Price

Quantity

d(PA=43)

Chapter Thirteen

Short Run Chamberlinian Equilibrium

54Quantity

d (PA=50)


d(PA=43)

Chapter Thirteen

Price


55Quantity

d (PA=50)

Demand (assuming price matching by all firms P=PA)


•

d(PA=43)

•

Chapter Thirteen

Price


56Quantity

d (PA=50)

Demand (assuming price matching by all firms P=PA)


50 •

d(PA=43)

•43

MR43

mc

57

15

Chapter Thirteen

Price


57Chapter Thirteen

Short Run Monopolistically Competitive Equilibrium

Computing Short Run Monopolistically Competitive Equilibrium

• MC = $15

• N = 100

• Q = 100 - 2P + PA

• Where: PA is the average market price N is the number of firms

58Chapter Thirteen


A. What is the equation of d40? What is the equation of D?

• d40: Qd = 100 - 2P + 40 = 140 - 2P

• D: Note that P = PA so that

• QD = 100 - P

B. Show that d40 and D intersect at P = 40

• P = 40 => Qd = 140 - 80 = 60 QD = 100 - 40 = 60

C. For any given average price, PA, find a typical firm's profit maximizing quantity

59Chapter Thirteen

Inverse Perceived Demand

P = 50 - (1/2)Q + (1/2)PA

MR = 50 - Q + (1/2)PA

MR = MC => 50 - Q + (1/2)PA = 15

Qe = 35 + (1/2)PA

Pe = 50 - (1/2)Qe + (1/2)PA

Pe = 32.5 + (1/4)PA

60Chapter Thirteen


D. What is the short run equilibrium price in this industry?

In equilibrium, Qe = QD at PA so that

100 - PA = 35 + (1/2)PA

PA = 43.33Qe = 56.66QD = 56.66

61Chapter Thirteen

Monopolistic Competition in the Long Run

At the short run equilibrium P > AC so that each firm may make positive profit.

Entry shifts d and D left until average industry price equals average cost.

This is long run equilibrium is represented graphically by:

MR = MC for each firmD = d at the average market priced and AC are tangent at average market price

62

Average Cost

Quantity

Price

Residual Demand shifts in as entry occurs

Marginal Cost

q*

P*

q**

P**

MRChapter Thirteen

Long Run Chamberlinian Equilibrium

63Chapter Thirteen

Summary

1. Market structures are characterized by the number of buyers, the number of sellers, the degree of product differentiation and the entry conditions.

2. Product differentiation alone or a small number of competitors alone is not enough to destroy the long run zero profit result of perfect competition. This was illustrated with the Chamberlinian and Bertrand models.

3. Chamberlinian) monopolistic competition assumes that there are many buyers, many sellers, differentiated products and free entry in the long run.

64Chapter Thirteen

Summary

4. Chamberlinian sellers face downward-sloping demand but are price takers (i.e. they do not perceive that their change in price will affect the average price level). Profits may be positive in the short run but free entry drives profits to zero in the long run.

5. Bertrand and Cournot competition assume that there are many buyers, few sellers, and homogeneous or differentiated products. Firms compete in price in Bertrand oligopoly and in quantity in Cournot oligopoly.

6. Bertrand and Cournot competitors take into account their strategic interdependence by means of constructing a best response schedule: each firm maximizes profits given the rival's strategy.

65Chapter Thirteen

Summary

7. Equilibrium in such a setting requires that all firms be on their best response functions.

8. If the products are homogeneous, the Bertrand equilibrium results in zero profits. By changing the strategic variable from price to quantity, we obtain much higher prices (and profits). Further, the results are sensitive to the assumption of simultaneous moves.

9. This result can be traced to the slope of the reaction functions: upwards in the case of Bertrand and downwards in the case of Cournot. These slopes imply that "aggressivity" results in a "passive" response in the Cournot case and an "aggressive" response in the Bertrand case.

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