Question

Suppose firm A and B operate under conditions of constant marginal and average cost but that MCA = 10 and MCB = 8. The demand for the firm’s output is given by Q = 500 – 20P

a) If the firms practice Bertrand competition, what will the Nash Equilibrium market price be? What will be the profits for each firm?

b) If the firms practice Cournot competition, what will be the Nash equilibirum market price? What will be the profits for each firm?

c) If the firm A is the leader and firm B is the follower in this market, what will be the equilibrium price? What will be the profits for each firm?

Answer 1

a)

Bertrand game is a simultanieous move game. The two firms involved in such competition undercut their prices till the point where profits are vanished completely. If cost of Firm A increase, then the firm B respond by increasing the price to maintain their market share.

In this example, the nash equilibrium of the game is PA = PB = 10 since any other price would cause a retaliation from other firm.

Q = 500 - (20*10) = 300

QA = QB = 300

Profit of Firm A: (P - MC)*Q = (10 - 10)* 300 = 0

Profit of Firm B: (10 - 8)*300 = 600

b)