Suppose that two identical firms produce widgets in the market. And their costs are given by c1=60q1 and c= 60q2
Where q1 is the output of firm 1 and q2 is the output of firm 2.
Price is determined by the following demand curve
Qd=300-P, where q=q1+q2.
i) find cournot nash equilibrium
ii) calculate profit of each firm at this equilibrium
i) The Cournot-Nash equilibrium is found by setting the marginal revenue of each firm equal to its marginal cost.
For firm 1: MR1 = 300 - 2Q1 - P = 60
For firm 2: MR2 = 300 - 2Q2 - P = 60
Solving these equations simultaneously, we get:
Q1 = 120 and Q2 = 120
P = 60
ii) The profit of each firm at the Cournot-Nash equilibrium is given by:
Profit of firm 1 = (P - c1)Q1 = (60 - 60) * 120 = 0
Profit of firm 2 = (P - c2)Q2 = (60 - 60) * 120 = 0