1. olig-1 ©2006 Chas. J. Goetz Oligopoly: Competition Among the Few Return u The Bertrand Oligopoly Model The Bertrand Oligopoly Model The Bertrand Oligopoly Model u Other Oligopoly Models Other Oligopoly Models Other Oligopoly Models u The Cournot Oligopoly Model The Cournot Oligopoly Model The Cournot Oligopoly Model u Assumptions for a “Hypothetical” Assumptions for a “Hypothetical” Assumptions for a “Hypothetical”

2. olig - 2 © 2006, Chas. J. Goetz Hypothetical Facts and Monopoly Result 0100200300400500600700800900 0 100 200 300 400 500 600 700 800 900 1000 P = 950 - Q MC = 50 Monopoly Price = 500 MR

3. olig - 3 © 2006, Chas. J. Goetz Monopolist’s Profit-maximizing Output 44550560224,72522,250 202,475 44650458224,78422,300 202,484 44750356224,84122,350 202,491 44850254224,89622,400 202,496 44950152224,94922,450 202,499 45050050225,00022,500 202,500 45149948225,04922,550 202,499 45249846225,09622,600 202,496 45349744225,14122,650 202,491 45449642225,18422,700 202,484 45549540225,22522,750 202,475 45649438225,26422,800 202,464 45749336225,30122,850 202,451 45849234225,33622,900 202,436 45949132225,36922,950 202,419 46049030225,40023,000 202,400 QPMRRevTcostProfit

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5. olig-5 ©2006 Chas. J. Goetz The Cournot Oligopoly Model uWho (or What) Is “Cournot”? Who (or What) Is “Cournot”?Who (or What) Is “Cournot”? uPremises of the Cournot Model Premises of the Cournot ModelPremises of the Cournot Model uMathematical Cournot Model Mathematical Cournot ModelMathematical Cournot Model uA Topographical Cournot Model A Topographical Cournot ModelA Topographical Cournot Model uDeriving the Reaction Curves Deriving the Reaction CurvesDeriving the Reaction Curves uThe “Solution” of the Model The “Solution” of the ModelThe “Solution” of the Model uEfficiency Properties: The Well Revisited Efficiency Properties: The Well RevisitedEfficiency Properties: The Well Revisited

6. olig - 6 © 2006, Chas. J. Goetz Hypothetical Facts and Monopoly Result Return 0100200300400500600700800900 0 100 200 300 400 500 600 700 800 900 1000 P = 950 - Q MC = 50 Monopoly Price = 500 MR

7. olig - 7 © 2006, Chas. J. Goetz

8. olig - 8 © 2006, Chas. J. Goetz Regardez le Croix d’Honneur Recherches sur les Principes Mathématiques de la Théorie des Richesses (1838) Antoine Augustin Cournot (1801-1877)

9. olig - 9 © 2006, Chas. J. Goetz Premises of Cournot Oligopoly Model l A few firms produce goods that are either perfect substitutes (homogeneous) or imperfect substitutes (differentiated). l Firms set output, as opposed to price. The market sets price where demand equals the amount supplied. l Each firm believes its rivals will hold output constant if it changes its own output.

10. olig - 10 © 2006, Chas. J. Goetz Mathematical Approach p = a-bQ c(q) = cq, constant marginal cost Firm i’s profit : (a-b(q -i +q i ))q i - cq i FOC: a-bq -i -2bq i - c = 0 q i = (a-bq -i - c)/2b = R(q -i ), i’s reaction Cournot Equilibrium: q i = R(q-i) for all i. n equations in n unknowns. But all firms are alike, use symmetry: q i =q Reaction: q = (a-b(n-1)q - c)/2b q = (a -c)/b(n+1) Q = (a-c)/b  n/(n+1)  (a-c)/b as n  . Competitive outcome!

11. olig - 11 © 2006, Chas. J. Goetz Mathematical Approach Preferrers

13. olig - 13 © 2006, Chas. J. Goetz Profits of Firm #1 – 3D View

14. olig - 14 © 2006, Chas. J. Goetz Profits of Firm #1 – 3D View, Filled Bird’s Eye View

15. olig - 15 © 2006, Chas. J. Goetz Profits of Firm #1 – Birds-eye View, Filled Unfilled Topographic

16. olig - 16 © 2006, Chas. J. Goetz Profits of Firm #1 – Birds-eye View, Unfilled Firm #2

17. olig - 17 © 2006, Chas. J. Goetz Profits of Firm #2 – 3D View Bird’s Eye View 3D Firm #1

18. olig - 18 © 2006, Chas. J. Goetz Profits of Firm #2 – Birds-eye View Unfilled Topographic

19. olig - 19 © 2006, Chas. J. Goetz Profits of Firm #2 – Birds-eye View, Unfilled

20. olig - 20 © 2006, Chas. J. Goetz Reaction Curves lEconomists often use “Reaction Curves.” Where did we see this before? lIn the Cournot case, the reaction curve for one firm plots its output decisions against various outputs for the other firm(s).

21. olig - 21 © 2006, Chas. J. Goetz Profits of Firm #2 – Birds-eye View, Unfilled

22. olig - 22 © 2006, Chas. J. Goetz Deriving Firm #2’s Reaction Curve

23. olig - 23 © 2006, Chas. J. Goetz Deriving Firm #1’s Reaction Curve

24. olig - 24 © 2006, Chas. J. Goetz Summary: Reaction Functions l Firm 1’s reaction (or best-response) function indicates the amount of Q 1 that firm 1 should produce in order to maximize its profits for each possible quantity of Q 2 produced by firm 2. l Since the products of the two firms are substitutes, an increase in firm 2’s output leads to a decrease in the profit-maximizing amount of firm 1’s product.

25. olig - 25 © 2006, Chas. J. Goetz 10 30 50 70 90 110 130 150 170 190 10 30 50 70 90 110 130 150 170 190 0100200300400500600700800900 Q2Q2 0 100 200 300 400 500 600 700 800 900 Q1Q1 Intersection of Reaction Curves

26. olig - 26 © 2006, Chas. J. Goetz

27. olig - 27 © 2006, Chas. J. Goetz 0100200300400500600700800900 Q2Q2 0 100 200 300 400 500 600 700 800 900 Q1Q1 Adjustments Toward Equilibrium When Firm Two Enters Firm #1’s Best-Reaction Curve Firm #2’s Best-Reaction Curve Redo

28. olig - 28 © 2006, Chas. J. Goetz 0100200300400500600700800900 Q2Q2 0 100 200 300 400 500 600 700 800 900 Q1Q1 Stable Equilibrium, Expectations Confirmed Summary

29. olig - 29 © 2006, Chas. J. Goetz Cournot Equilibrium l Situation where each firm produces the output that maximizes its profits, given the the output of rival firms l No firm can gain by unilaterally changing its own output

30. olig - 30 © 2006, Chas. J. GoetzQuestions lIs the Cournot Equilibrium also a Nash Equilibrium?Is the Cournot Equilibrium also a Nash Equilibrium? lIs the Cournot Equilibrium an efficient result for the firms? Nash Equilibrium

31. olig - 31 © 2006, Chas. J. Goetz Nash Equilibrium lthis result involves output combinations at which the profits of each firm are maximized, given its expectations about output from the other firm(s); land the outputs expected by all firms are indeed being produced by the other firm(s). That is, the expectations are validated by experience. The intersection of the reaction curves corresponds to a Nash equilibrium because

32. olig - 32 © 2006, Chas. J. Goetz But... A Nash Equilibrium is not always an “efficient” result for the players.

33. olig - 33 © 2006, Chas. J. Goetz 10 50 90 130 170 0100200300400500600700800900 0 100 200 300 400 500 600 700 800 900 10 40 70 100 130 160 190 Q2Q2 Q1Q1 Area to be “Zoomed”

34. olig - 34 © 2006, Chas. J. Goetz Zoomed Version Q2Q2 Q1Q1 Simplified

35. olig - 35 © 2006, Chas. J. Goetz 78.8 78.8 90.0 90.0 101.2 101.2 112.4 112.4 0100200300400500 0 100 200 300 400 500 78.8 90.0 101.2 112.4 Q2Q2 Q1Q1 Simplified Diagram Showing Cournot Equilibrium Analogue

36. olig - 36 © 2006, Chas. J. Goetz 78.8 78.8 90.0 90.0 101.2 101.2 112.4 112.4 0100200300400500 0 100 200 300 400 500 78.8 78.8 90.0 90.0 101.2 101.2 112.4 112.4 Q2Q2 Q1Q1 Well Problem Similar to the “Well Problem”

37. olig - 37 © 2006, Chas. J. Goetz 78.8 90.0 101.2 112.4 0100200300400500 0 100 200 300 400 500 90.0 90.0 101.2 101.2 112.4 112.4 Q 1 +Q 2 =450 Cournot vs. Collusive Result Q2Q2 Q1Q1 Equilibrium?

38. olig - 38 © 2006, Chas. J. Goetz 78.8 90.0 101.2 112.4 0100200300400500 0 100 200 300 400 500 90.0 90.0 101.2 101.2 112.4 112.4 Q 1 +Q 2 =450 Collusive Result Unstable? Q2Q2 Q1Q1 Monopoly Result

40. olig - 40 © 2006, Chas. J. Goetz Nash Equilibrium unilaterally A Nash equilibrium is a set of strategies, one for each player, such that no player has an incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. Return