1. BUS 525: Managerial Economics Basic Oligopoly Models
Lecture 9
Basic Oligopoly Models

2. Overview I. Conditions for Oligopoly?
9-2
Overview
I. Conditions for Oligopoly?
II. Role of Strategic Interdependence
III. Profit Maximization in Four
Oligopoly Settings
Sweezy (Kinked-Demand) Model
Cournot Model
Stackelberg Model
Bertrand Model
IV. Contestable Markets
Perfect competition

3. Oligopoly Environment
9-3
A market structure there are only a few
Firms, each of which is large relative the total
industry
Relatively few firms, usually less than 10.
Duopoly - two firms
Triopoly - three firms
The products firms offer can be either differentiated or homogeneous.
Firms’ decisions impact one another.
Many different strategic variables are modeled:
No single oligopoly model.

4. Role of Strategic Interaction
9-4
Your actions affect the profits of your rivals.
Your rivals’ actions affect your profits.
How will rivals respond to your actions?

5. An Example You and another firm sell differentiated products.
9-5
You and another firm sell differentiated products.
How does the quantity demanded for your product change when you change your price?

6. D1 (Rival matches your price change) P
9-6
D1 (Rival matches your price change) P PH
QH1
QH2 P0 B Q0 PL
QL2
QL1
The firm initially is at point B, charging P0 selling Qo.
D1 based on the assumption that rivals will match any price change.
D2 based on the assumption that rivals will not match any price change.
Demand is more inelastic when rivals match a price change than when they do not.
For a given price reduction, a firm will sell more if rivals do not cut their prices(D2) than it will if they lower their prices (D1).
D2 (Rival holds its
price constant) Q

7. D2 (Rival matches your price change)
9-7 P Q D1 P0 Q0
D2 (Rival matches your price change)
(Rival holds its
price constant) A
Demand if Rivals Match Price Reductions but not Price Increases B
In Sweezy oligopoly, the manager believes that that other firms will match any price decrease but not match price increases.
Sweezy demand curve ABD1 D2
Note that demand is more inelastic when rivals match a price change than when they do not
Reason: For a given price reduction, a firm will sell more if rivals do not cut their prices D2 than it will if they lower their prices D1

8. Key Insight
9-8
The effect of a price reduction on the quantity demanded of your product depends upon whether your rivals respond by cutting their prices too!
The effect of a price increase on the quantity demanded of your product depends upon whether your rivals respond by raising their prices too!
Strategic interdependence: You aren’t in complete control of your own destiny!

9. Sweezy (Kinked-Demand) Model Environment
9-9
Few firms in the market serving many consumers.
Firms produce differentiated products.
Barriers to entry.
Each firm believes rivals will match (or follow) price reductions, but won’t match (or follow) price increases.
Key feature of Sweezy Model
Price-Rigidity.

10. Sweezy Demand and Marginal Revenue
9-10
Sweezy Demand and Marginal Revenue P
D2 (Rival matches your price change)
MR2
DS: Sweezy Demand D1
(Rival holds its
price constant)
MR1 P0 Q0
For prices above P0, the relevant demand curve is D1
For prices below P0, the relevant demand curve is D2 Q
MRS: Sweezy MR

11. Sweezy Profit-Maximizing Decision
9-11
Sweezy Profit-Maximizing Decision P
D2 (Rival matches your price change) A C
DS: Sweezy Demand
MRS
MC1 E
MC2 P0
MC3 Q0 C
D1 (Rival holds price
constant)
There will be a range CE , over which change in MC do not affect the profit maximizing level of output
In all other market conditions MC↓Q↑
Criticism where does P0 comes from
Explains price rigidities in many markets. e,.g. E Q

12. Sweezy Oligopoly Summary
9-12
Firms believe rivals match price cuts, but not price increases.
Firms operating in a Sweezy oligopoly maximize profit by producing where
MRS = MC.
The kinked-shaped marginal revenue curve implies that there exists a range over which changes in MC will not impact the profit-maximizing level of output.
Therefore, the firm may have no incentive to change price provided that marginal cost remains in a given range.

13. Cournot Model Environment
9-13
Cournot Model Environment
A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated).
Firms’ control variable is output in contrast to price.
Each firm believes their rivals will hold output constant if it changes its own output (The output of rivals is viewed as given or “fixed”).
Barriers to entry exist.

14. Inverse Demand in a Cournot Duopoly
9-14
Market demand in a homogeneous-product Cournot duopoly is
Thus, each firm’s marginal revenue depends on the output produced by the other firm. More formally,
TR1 =

15. Best-Response Function
9-15
Best-Response Function
Since a firm’s marginal revenue in a homogeneous Cournot oligopoly depends on both its output and its rivals, each firm needs a way to “respond” to rival’s output decisions.
Firm 1’s best-response (or reaction) function is a schedule summarizing the amount of Q1 firm 1 should produce in order to maximize its profits for each quantity of Q2 produced by firm 2.
Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.

16. Best-Response Function for a Cournot Duopoly
9-16
To find a firm’s best-response function, equate its marginal revenue to marginal cost and solve for its output as a function of its rival’s output.
Firm 1’s best-response function is (c1 is firm 1’s MC)
Firm 2’s best-response function is (c2 is firm 2’s MC)
C1(Q1) = c1Q1
MC = c1
Set MC =MR
c1 = a – bQ2-2bQ1 or Q1 = (a-c1)/2b-1/2Q2

17. Graph of Firm 1’s Best-Response Function
9-17
Graph of Firm 1’s Best-Response Function Q2
(a-c1)/b
Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2 Q2 r1
(Firm 1’s Reaction Function) Q1 Q1
Q1M

18. 9-18
Cournot Equilibrium
Situation where each firm produces the output that maximizes its profits, given the the output of rival firms.
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.

19. Graph of Cournot Equilibrium
9-19
Graph of Cournot Equilibrium Q2
(a-c1)/b r1
Cournot Equilibrium
Q2M E
Q2* C A B
Suppose firm 1 produces at Q1M units of output. Given this output, the profit maximizing output for firm 2 will correspond to point A on r2. Given this output, the profit maximizing output for firm 1 will no longer be Q1M but point B on r1. Given the reduced level of output for firm 1, point C on firm 2’s reaction curve that will maximize profit. This will continue until point E is reached. At Q1* and Q2* neither firm has any incentive to given that he believes that the other firm will not change its output level. r2
Q1*
Q1M
(a-c2)/b Q1

20. Summary of Cournot Equilibrium
9-20
Summary of Cournot Equilibrium
The output Q1* maximizes firm 1’s profits, given that firm 2 produces Q2*.
The output Q2* maximizes firm 2’s profits, given that firm 1 produces Q1*.
Neither firm has an incentive to change its output, given the output of the rival.
Beliefs are consistent:
In equilibrium, each firm “thinks” rivals will stick to their current output – and they do!

21. The Isoprofit Curve

22. Firm 1’s Isoprofit Curve
9-22
Firm 1’s Isoprofit Curve Q2
The combinations of outputs of the two firms that yield firm 1 the same level of profit r1 B C
Increasing Profits for Firm 1 A
0 = $100 D E
1 = $200
2 = $300
Q1M Q1

23. Another Look at Cournot Decisions
9-23
Another Look at Cournot Decisions Q2 r1
Firm 1’s best response to Q2* A
Q2* D B
 0 = $100 C
 1 = $200
 2 = $300 QA QB QD
Q1*
Q1M Q1

24. Another Look at Cournot Equilibrium
9-24
Another Look at Cournot Equilibrium Q2 r1
Firm 2’s Profits
Cournot Equilibrium
Q2M
Q2*
Firm 1’s Profits r2
Q1*
Q1M Q1

25. Collusion Incentives in Cournot Oligopoly
9-25
Collusion Incentives in Cournot Oligopoly Q2 r1
Q2M r2
Q1M Q1

26. Impact of Rising Costs on the Cournot Equilibrium
9-26
Impact of Rising Costs on the Cournot Equilibrium Q2
r1*
Cournot equilibrium after
firm 1’s marginal cost increase
r1** r2
Q2**
Q1**
Cournot equilibrium prior to
firm 1’s marginal cost increase
Q2*
Q1* Q1

27. Price Leadership Model
In a price leadership model, one dominant firm takes reactions of all other firms into account in its output and pricing decisions
Competitive fringe: A group of firm that act as a price taker in a market dominated by a price leader
A dominant firms demand curve is the residual demand curve that shows what it can sell after accounting for sales by other firms
Other firms accept whatever price is set by the dominant firm and produce an output where P=MC
Note that P>MC for dominant firm, total industry output is less than competitive output
Draw graph for price leadership model

28. Dominant Firm Model Fig : Equilibrium in the Dominant Firm Model
Industry Demand, DI, is the straight line ALJBC. The fringe firms’ supply curve is Sf. To obtain the dominant firm’s residual demand curve, subtract Sf from DI. For example, at price p1, the fringe supplies zero units and the dominant firm’s quantity demanded is the entire demand, q5. At price p2, the fringe supplies q1 and the dominant firm’s quantity demanded is q4 – q1 = q3. At price p3, the fringe supplies qf and the dominant firm’s quantity demanded is qT – qf = qD. And, at price p4, the fringe supplies the entire demand, q2, and the dominant firm’s quantity demanded is zero. In this manner, the dominant firm’s demand is derived as the line EGIBC. The dominant firm equates its marginal cost, MCD, to marginal revenue, MRD, and produces output qD and sets the price at p3. The fringe firms take price p3 as given and produce a combined output of qf units. Total output is qT= qD + qf
Fig : Equilibrium in the Dominant Firm Model

29. Stackelberg Model Environment
9-29
Stackelberg Model Environment
Few firms serving many consumers.
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. QD SF
MCD D
MRD QD QF QT

30. The Algebra of the Stackelberg Model
9-30
Since the follower reacts to the leader’s output, the follower’s output is determined by its reaction function
The Stackelberg leader uses this reaction function to determine its profit maximizing output level, which simplifies to

31. 9-31
Stackelberg Summary
Stackelberg model illustrates how commitment can enhance profits in strategic environments.
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.

32. Bertrand Model Environment
9-32
Bertrand Model Environment
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 (price is each firms’ control variable).
Barriers to entry exist.
Consumers enjoy
Perfect information.
Zero transaction costs.

33. Bertrand Equilibrium Firms set P1 = P2 = MC! Why?
9-33
Bertrand Equilibrium
Firms set P1 = P2 = MC! Why?
Suppose MC < P1 < P2.
Firm 1 earns (P1 - MC) on each unit sold, while firm 2 earns nothing.
Firm 2 has an incentive to slightly undercut firm 1’s price to capture the entire market.
Firm 1 then has an incentive to undercut firm 2’s price. This undercutting continues...
Equilibrium: Each firm charges P1 = P2 = MC.

34. Contestable Markets Key Assumptions Key Implications
9-34
Key Assumptions
Producers have access to same technology.
Consumers respond quickly to price changes.
Existing firms cannot respond quickly to deter entry by lowering price.
Absence of sunk costs.
Key Implications
Threat of entry disciplines firms already in the market.
Incumbents have no market power, even if there is only a single incumbent (a monopolist).

35. 9-35
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.

36. .
Basic model

38. Duopoly case

42. . . Zero cost monopoly Stackelberg solution Cournot solution P
120 .
Q = P 60 Q 60
120 P MR
Stackelberg solution
Cournot solution
Q = P
120 60 40 80
Price
Q per period
120
Monopoly 60
Equilibrium
Cournot 40
Stackelberg Q 60
120 40