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
iii) suppose the two firms form a cartel to maximize joint profit, how many widgets will be produced? Calculate each firms profit.
i) The Cournot-Nash equilibrium is found by setting the marginal revenue of each firm equal to its marginal cost.
MR1 = 300 - 2Q1 - P
MC1 = 60
MR2 = 300 - 2Q2 - P
MC2 = 60
Solving for Q1 and Q2, we get:
Q1 = 120
Q2 = 120
P = 60
ii) The profit of each firm at the Cournot-Nash equilibrium is:
Profit1 = (300 - 2*120 - 60)*120 - 60*120 = 7200
Profit2 = (300 - 2*120 - 60)*120 - 60*120 = 7200
iii) The cartel will produce the quantity that maximizes joint profit, which is found by setting the marginal revenue of the cartel equal to its marginal cost.
MR = 300 - 2Q - P
MC = 120
Solving for Q, we get:
Q = 180
P = 0
The profit of each firm in the cartel is:
Profit1 = (300 - 2*180 - 0)*180 - 60*180 = 10800
Profit2 = (300 - 2*180 - 0)*180 - 60*180 = 10800