Two identical firms compete as a Cournot duopoly.The demand they face is P = 100 − 2Q.The cost function for each firm is C(Q)= 4Q.The equilibrium output of each firm is:
A) 8.
B) 16.
C) 32.
D) 36.

Question

Quizplus · Accepted Answer

To find the equilibrium output of each firm, we first need to find the overall market output at equilibrium. We can do this by setting the total quantity Q produced by both firms equal to the quantity demanded at equilibrium:

Q = (100 - P)/2

Q = (100 - (q1 + q2))/2

Q = 100/2 - (q1 + q2)/2

Q = 50 - Q/2

(Q/2) + Q = 50

(3/2)Q = 50

Q = 33.33

So at equilibrium, each firm would produce Q/2 = 16.67 units. However, since output is measured in whole units, the closest choice is B, 16.

Two Identical Firms Compete as a Cournot Duopoly