1. Lectures in Microeconomics-Charles W. Upton The Cournot Model

2. Assumptions Two firms A, and B produce widgets

3. The Cournot Model Assumptions Two firms A, and B produce widgets The industry demand function is D D P Q

4. The Cournot Model Assumptions Two firms A, and B produce widgets The industry demand function is D Firm A produces q A ; firm B produces q B D P Q

5. The Cournot Model Assumptions Two firms A, and B produce widgets The industry demand function is D Firm A produces q A ; firm B produces q B Firm A takes its demand function as D -q B D P Q qbqb DaDa

6. The Cournot Model Assumptions Two firms A, and B produce widgets The industry demand function is D Firm A produces q A ; firm B produces q B Firm A takes its demand function as D -q B D P Q qbqb DaDa An important assumption, the heart of the Cournot model.

7. The Cournot Model Solving A’s problem D DaDa

8. The Cournot Model Solving A’s problem D DaDa MC MR

9. The Cournot Model Solving A’s problem D DaDa MC MR qa*qa* p*

10. The Cournot Model Symmetry Just as Firm A is choosing q A to maximize profits, so too is Firm B choosing q B to maximize profits.

11. The Cournot Model Symmetry Just as Firm A is choosing q A to maximize profits, so too is Firm B choosing q B to maximize profits. If B changes its output, A will react by changing its output.

12. The Cournot Model A Reaction Function We do the mathematical approach first and then the graphical approach.

13. The Cournot Model A Reaction Function The industry demand function Q = 100 – 2p.

14. The Cournot Model A Reaction Function The industry demand function Q = 100 – 2p. The inverse demand function is P = 50 – (1/2)Q

15. The Cournot Model A Reaction Function The industry demand function Q = 100 – 2p. The inverse demand function is P = 50 – (1/2)Q A’s demand function is then P = 50 –(1/2)(q A +q B )

16. The Cournot Model A Reaction Function A’s demand function is then P = 50 –(1/2)(q A +q B ) The firm’s profits are  = Pq A – 5q A

17. The Cournot Model A Reaction Function A’s demand function is then P = 50 –(1/2)(q A +q B ) The firm’s profits are  = [50 –(1/2)(q A +q B )]q A – 5q A

18. The Cournot Model A Reaction Function  = [50 –(1/2)(q A + q B )]q A – 5q A

19. The Cournot Model A Reaction Function  = [50 –(1/2)(q A + q B )]q A – 5q A  = 50 q A –(1/2) q A 2 – (1/2)q B q A – 5q A

20. The Cournot Model A Reaction Function  = [50 –(1/2)(q A + q B )]q A – 5q A  = 50 q A –(1/2) q A 2 – (1/2)q B q A – 5q A  = 45q A –(1/2)q A 2 – (1/2)q B q A

21. The Cournot Model A Reaction Function

22. The Cournot Model A Reaction Function

23. The Cournot Model A Reaction Function

24. The Cournot Model Symmetry There is a similar reaction function for B q B = 45 – (1/2)q A q A = 45 – (1/2)q B

25. The Cournot Model Solving for A’s Output q A = 45 – (1/2)q B q B = 45 – (1/2)q A q A = 45 – (1/2)[45 – (1/2)q A ]

26. The Cournot Model Solving for A’s Output q A = 45 – (1/2)[45 – (1/2)q A ] q A = 22.5 + (1/4)q A

27. The Cournot Model Solving for A’s Output q A = 45 – (1/2)[45 – (1/2)q A ] q A = 22.5 + (1/4)q A (3/4)q A = 22.5

28. The Cournot Model Solving for A’s Output q A = 45 – (1/2)[45 – (1/2)q A ] q A = 22.5 + (1/4)q A (3/4)q A = 22.5 q A = (4/3)22.5

29. The Cournot Model Solving for A’s Output q A = 45 – (1/2)[45 – (1/2)q A ] q A = 22.5 + (1/4)q A (3/4)q A = 22.5 q A = (4/3)22.5 q A = 30 q B = 30

30. The Cournot Model A Graphical Approach q A = 45 – (1/2)q B We want to use the reaction function to come to a graphical solution,

31. The Cournot Model A Graphical Approach q A = 45 – (1/2)q B When B produces nothing A should react by producing the monopoly output (45).

32. The Cournot Model A Graphical Approach q A = 45 – (1/2)q B When B produces nothing A should react by producing the monopoly output (45). When B produces the output of the competitive industry (90), A should react by producing nothing.

33. The Cournot Model A Graphical Approach q A = 45 – (1/2)q B When B produces nothing A should react by producing the monopoly output (45). When B produces the output of the competitive industry (90), A should react by producing nothing. Similar rules apply for B’s reactions.

34. The Cournot Model Graphing the Reaction Function A’s Output B’s Output

35. The Cournot Model Graphing the Reaction Function A’s Output B’s Output If B produces the competitive output, A produces nothing. If B produces nothing, A acts like a monopoly 45 90 0

36. The Cournot Model Graphing the Reaction Function A’s Output B’s Output A’s Reaction Function 45 90

37. The Cournot Model Graphing the Reaction Function A’s Output B’s Output A’s Reaction Function If A produces the competitive output, B produces nothing. If A produces nothing, B acts like a monopoly. 45 90

38. The Cournot Model Graphing the Reaction Function A’s Output B’s Output A’s Reaction Function B’s Reaction Function 45 90

39. The Cournot Model Graphing the Reaction Function A’s Output B’s Output If A and B are off their reaction functions, they react and change output. Here B expands, A contracts. 90 45 90 45

40. The Cournot Model Graphing the Reaction Function A’s Output B’s Output

41. The Cournot Model Graphing the Reaction Function A’s Output B’s Output If A is here, B wants to be here

42. The Cournot Model Graphing the Reaction Function A’s Output B’s Output If B is here, A wants to be here

43. The Cournot Model Equilibrium A’s Output B’s Output A’s Reaction Function B’s Reaction Function

44. The Cournot Model The Basic Steps Plot the reaction functions –If B produces nothing, A behaves like a monopoly –If B produces competitive output, A produces nothing Solve for their intersection

45. The Cournot Model End ©2003 Charles W. Upton