Home > Duopoly and strategic behaviour, Micro concepts > Comparison of Cournot, Stackelberg and cartel duopoly

## Comparison of Cournot, Stackelberg and cartel duopoly

September 29, 2011

unfinished

In a duopoly, the residual demand curve faced by one firm is the market demand curve minus the supply of the rival firm: $D^r (P) = D (P) - S^o (P)$.

In the simple model I’m using for these examples, the market demand is Q = 500 – P and the firm (both firms in this duopoly case) have no fixed costs and a constant marginal cost of 150. So if the firms are firm A and firm B, then the residual demand curves for each firm are: $Q_A = 500 - P - Q_B$ and $Q_B = 500 - P - Q_A$.

This means the inverse residual demand curves for each firm are $P= 500 - Q_A - Q_B$.

In the duopoly series of posts on here, I’ve used the same model to illustrate three different forms of duopoly competition when the firms are identical. We can now compare the different effects on market price, market quantity, profitability of each firm, amount of market power on each firm and welfare for consumers.

In the monopoly model:
Market price: 325
Market output: 175
Firm’s profits: 30625
Lerner index: 0.538
Consumer surplus: 15312.5
Producer surplus: 30625
Welfare: 45937.5

In the Cournot model:
Market price: 266.667
Market output: 233.333
Firm’s profits: 13611.11 each (combined: 27222.22)
Lerner index: 0.438
Consumer surplus: 27222.222
Producer surplus: 27222.222
Welfare: 54444.444

In the Stackelberg model:
Market price: 237.5
Market output: 262.5
Firm’s profits: leader: 15312.5, follower: 7656.25(combined: 22968.75)
Lerner index: 0.368
Consumer surplus: 34453.125
Producer surplus: 22986.75
Welfare: 57439.88

In the cartel model (where neither cheats):
Market price: 325
Market output: 175
Firm’s profits: 15312.5 each (combined: 30625)
Lerner index: 0.538
Consumer surplus: 15312.5
Producer surplus: 30625
Welfare: 45937.5

Consumer surplus:

Producer surplus: