Noncooperative Market Games in Normal Form Cournot model of quantity competition Stackelberg model of quantity competiti

1. Noncooperative Market Games in Normal Form • Cournot model of quantity competition • Stackelberg model of quantity competition • Bertrand model of price competition

2. Quantity Competition between Two Firms Competition using quantity named after Cournot Cournot equilibrium lies between monopoly and perfect competition

3. Monopoly Consider the following demand, inverse demand, and cost functions: Than we can write down the profit function as: Profit-maximizing output level can be found using FOC

4. Cournot Duopoly Modified demand, inverse demand, and cost functions: Than we can write down the profit function as: Profit-maximizing output level can be found using FOC Using symmetry:

5. Cournot Oligopoly Modified demand, inverse demand, and cost functions: Than we can write down the profit function as: Profit-maximizing output level can be found using FOC Using symmetry:

6. x2 (a-bc) 0.5(a-bc) (a-bc) 0.5(a-bc) x1 Graphic solution of the Cournot Duopoly game From the first order conditions of the Cournot Duopoly (slide 5): From which:

7. What if firms #1 has the ability to move first: 1. Will it do it or wait and a) moves simultaneously with #2 b) moves after #2 2. What are the corresponding outputs? (the same as in Cournot?) 3. Who fins and who looses (#1, #2, consumers) ?

8. Stackelberg Equilibrium Firm #1 chooses its output first, knowing that Firm #2 will choose its output using its best response function: Now we can modify profit function of Firm #1: FOC:

9. Why firm #1 cannot achieve the same equilibrium under Cournot as it can under Stackelberg? Who fins and who looses under Stackelberg compared to Cournot (#1, #2, consumers) ?

10. Duopoly with different costs From the FOC: Conclusions? Effect of the government subsidy?

11. Oligopolistic competition with free entry Recall: Number of firms with zero fixed costs? Fixed cost = F Number of firms? Aggregate output: Aggregate demand: Price: Firm’s profit:

12. Free Entry = Zero Profit

13. Bertrand model Assumptions: • Firms compete by choosing prices • Each firm has unlimited capacity • Consumers react even to tiny differences in prices Algebraically: The only Nash Equilibrium is: p1=p2=c

14. Rank: Cournot (2 firms), Bertrand , Stackelberg, perfect competition, and monopoly • For firm #1 • For firm #2 • For consumers