Cournot And Stackelberg Solver by Xavier Lehnhoff

1. Cournot
Demand: P = a - Q Cournot Equilibrium
Firm 1
a= 100 Quantity 32.667
Marginal Cost Firm 1 MC1 = 2 Price 34.667
Marginal Cost Firm 2 MC2= 2 Profits 1067.111
Total Quantity 65.333
Stackelberg
Demand: P = a - Q Stackelberg Equilibrium
Firm 1
a= 12 Quantity 3.500
Marginal Cost Firm 1 MC1 = 4 Price 5.750
Marginal Cost Firm 2 MC2= 3 Profits 6.125
Total Quantity 6.250
First mover advantage: occurs in the case of capacity decisions.
by Xavier Lehnhoff

2. Price must be the same for both
We need to make a decision about capacity
Firm 2 Product is homogeneous
Quantity 32.667 Decisions are simultaneous, static game
Price 34.667 Depending on what one player does and demand, we establish capacity
Profits 1067.111 In Cournot equilibrium, no players have incentive to cheat. In Collusion equilibrium, we
Firm 2
Quantity 2.750
Price 5.750
Profits 7.563

3. establish capacity
eat. In Collusion equilibrium, we have incentive to cheat