Suppose in a Cournot duopoly that two firms, Firm 1 and Firm 2, face market demand $P = 50 -$ $Q$ and both have marginal cost, $M C = \$ 20$. The equilibrium industry profits in this market will be:
A) 150
B) 200
C) 250
D) 300

Question

Quizplus · Accepted Answer

In a Cournot duopoly with identical firms, the equilibrium quantity is found by setting the first order condition for each firm equal to zero: 
\begin{aligned} Q_{1}&= \frac{1}{3}(50-Q_{2}-20)\ Q_{2}&= \frac{1}{3}(50-Q_{1}-20) \end{aligned}
Solving for the equilibrium quantities by substitution yields: 
\begin{aligned} Q_{1}&= \frac{1}{3}(50-\frac{1}{3}(50-Q_{1}-20)-20)\ Q_{1}&= 12\ Q_{2}&= 12 \end{aligned}
Therefore, total output is 24 units, and the equilibrium price is:
\begin{aligned} P &= 50 - Q\ &= 50 - 24\ &= 26 \end{aligned}
Finally, total industry profit is:
\begin{aligned} \pi &= (P - MC) 	imes Q\ &= (26 - 20) 	imes 12\ &= 72 \end{aligned}
So, the correct answer is B.

Suppose in a Cournot Duopoly That Two Firms, Firm 1 P=50−P = 50 -P=50−

Suppose in a Cournot Duopoly That Two Firms, Firm 1 $P = 50 -$