1. Oligopoly-I

2. Topics to be Discussed Oligopoly Cournot & Stackelberg models
Reaction curves
A non-trivial example & a much simpler textbook example 2

3. Characteristics of Oligopoly
Small number of firms
Product differentiation may or may not exist
Barriers to entry
Natural
Scale economies
Patents
Technology
Name recognition
Strategic action
Flooding the market
Controlling an essential input 24

4. Equilibrium in a Oligopolistic Market
In oligopoly the producers must consider the response of competitors when choosing output and price.
Defining Cournot-Nash Equilibrium
Equilibrium: Firms do the best they can and have no incentive to change their output or price
Cournot-Nash Equilibrium: Each firm is doing the best it can, given what its competitors are doing 29

5. A non-trivial example Demand curve: P = 500 – 0.5X, where X = X1 + X2
AC1 = MC1 =100; AC2 = MC2 = 150
Can the second fellow survive if there is price competition?
Can he survive if there is quantity competition as in Cournot-Nash model?
TR1 = (500 – 0.5X).X1 = 500X1 – 0.5(X1 + X2)X1 = X12 – 0.5X1.X2 => MR1 = dTR1/dX1 = 500 – 2.(1/2).X1 – 0.5X2 – 0.5X1.(dX2/dX1) = 500 – X1 -0.5X2, assuming conjectural variation =dX2/dX1 =0

6. Π-maximization by firms I & II
MR1 = MC1 => 500 – X1 – 0.5X2 = 100 => X1 = X2 ----(a) giving the reaction function of firm 1, i.e., profit-maximizing value of X1 as function of X2.
(a) => If X1 = 0, then X2 = 800; If X2 =0, then X1 = 400
Similarly, MR2 = MC2 gives 500 –X2 -0.5X1 = 150 => X2 = X1 ---(b), giving the reaction function of firm 2
(b) => If X1 =0, then X2 = 350; If X2 =0, then X1 = 700

7. Situation 1: Cournot-Nash Equilibrium
Both firms are dormant (followers):
(a) & (b) => X1=300; X2=200; X=500; P=250; Π1=45,000; Π2=20,000; Π=65,000; Thus firm-2 in profit, though relatively inefficient. X2
Collusive solution: Max Π=( x)x – 100x =400x – 0.5x2
=> dΠ/dx = 400 –x =0 =>x=400. Why is this solution lying on
Firm 1’s reaction curve (a) where X1=400 and X2=0?
800
(a)
Attempting a competitive solution with MC1=AC1=100 & MC2=AC2=150: Firm-2 thrown out in equilibrium and firm-1 will charge price P=150-ε, which is marginally less than 150 to prevent firm-2 from surfacing. Thus, P=500 – 0.5x1 =>150 = 500 – 0.5x1 => x1 =700. Why is it lying on firm-2’s reaction curve (b)? Is it more meaningful to call it a monopoly solution or a contestable market solution?
350
(c)
200
(b)
125
450
300 X1
400
533
700

8. Situation 2 (Stackelberg): Firm I active (leader), Firm II dormant (follower)
Now firm 1 sets dX2/dx1=-1/2, as picked up from firm II’s reaction function (b)
Then MR1=MC1 => 500 –X1 -0.5(X2 – 0.5X1) = 100 => /4X1 -1/2X2 =100 => 400 = 3/4X1 + 1/2X2 => 3X1 +2X2 =400.4 => X1 = 400.4/3 – 2/3X (c), new reaction function of firm I
Solving (b) & (c) gives
X1=450; X2=125; X=575
P=212.5
Π1=50,625; Π2=7,812; Π=58,437
Thus, increase in intensity of competition increases output & reduces price; leader increases his market share.

9. Situation 3 (Stackelberg): Firm II active (leader), Firm I dormant (follower)
Now MR2 = 500 –X2 -0.5(X1 + (dX1/dX2).X2) = /4X2 – ½ X1
Hence MR2=MC2 => /4X2 – ½ X1 = 150 => X2 = 1400/3 – 2/3X (d), new reaction function of firm II
Solving (a) & (d) gives
X1=250; X2=300; X=550
P=225
Π1=31,250; Π2=22,500; Π=53,750
Thus, the relatively inefficient firm II increases market share & profit (though still less than that of firm I in absolute terms).
Lesson: Can we allow our generally inefficient PSUs to compete?

10. Situation 4 (Stackelberg): Both firms active (leaders)
Here we can check that
X1=400; X2=200; X=600
P=200
Π1=40,000; Π2=10,000; Π=50,000
Thus, even larger total output at even lower price

11. All 4 situations put together in game theory format
Player 1 Player 2
Dormant Active
Dormant ,000; 20, ,250; 22,500
Active ,625; 7,812 40,000; 10,000
To become active thus becomes the dominant strategy for both players

12. Text book example of Cournot Equilibrium
Market demand is P = 30 - Q where Q = Q1 + Q2
Assumption of MC1 = MC2 = 0 has a limitation not merely because it is trivially fixed at zero, but also because MCs are equal
Firm 1’s Reaction Curve: 4 45

13. Cournot Equilibrium 4 47

14. Textbook Duopoly ExampleQ1
The demand curve is P = 30 - Q and
both firms have 0 marginal cost.
Firm 2’s
Reaction Curve 30 15 a 10
Cournot Equilibrium
Firm 1’s
Reaction Curve 15 30
Is it a stable equilibrium? c d Q2 b
Doesn’t stability of Cournot equilibrium betray its own assumption? 54

15. First Mover Advantage-- The Stackelberg Model
Assumptions
One firm can set output first
MC = 0 as a simplifying assumption
Market demand is P = 30 - Q where Q = total output
Firm 1 sets output first and Firm 2 then makes an output decision 58

16. First Mover Advantage-- The Stackelberg Model
Firm 1
Must consider the reaction of Firm 2
Firm 2
Takes Firm 1’s output as fixed and therefore determines output with the Cournot reaction curve: Q2 = /2Q1 59

17. First Mover Advantage-- The Stackelberg Model
Firm 1
Choose Q1 so that: 60

18. First Mover Advantage-- The Stackelberg Model
Substituting Firm 2’s Reaction Curve for Q2:
Conclusion
Firm 1’s output is twice as large as firm 2’s
Firm 1’s profit is twice as large as firm 2’s 61

19. Why first-mover advantage?
First-mover’s output would be large.
If second-mover too produces a large output, then prices are driven down, causing loss to both.
If however, the second-mover produces a small output, then both firms make profits, but the first-mover makes larger profits corresponding to his larger output.
Since a rational second-mover values profits higher than revenge, he will set a small output, and both firms profit.

20. Implications of the Duopoly Example in the textQ1
Why this is not the competitive equilibrium? 30
Collusion
Curve
7.5
Collusive Equilibrium
For the firm, collusion is the best
outcome, followed by the Cournot
equilibrium and then the
competitive equilibrium
Firm 2’s
Reaction Curve 15
Competitive Equilibrium (P = MC; Profit = 0) 10
Cournot Equilibrium
Firm 1’s
Reaction Curve Q2 30 54