A Cournot oligopoly has 19 firms, and inverse market demand $P = 60 - Q$. All firms have marginal cost, $M C = \$ 20$. The equilibrium output for each firm will be:
A) 1 unit
B) 2 units
C) 3 units
D) 4 units

Question

Quizplus · Accepted Answer

The market demand function can be rewritten as:
Q = 60 - P
Q = 60 - (∑q_i)
where q_i is the output of firm i.

The best response function for each firm is:
q_i = (1/(2*(n-1))) * (60 - ∑j≠i q_j)
where n is the number of firms (in this case, n = 19).

Substituting the marginal cost and simplifying, we get:
q_i = (20/(2*(19-1))) * (60 - ∑j≠i q_j)
q_i = 20/18 * (60 - ∑j≠i q_j)
q_i = (20/18) * (60 - (19-1)*q_i)
q_i = (20/18) * (41 - q_i)
q_i = 40/18 - (1/18)*q_i
q_i = (40/17) * (1/2)
q_i ≈ 1.18

Rounding down, we get an equilibrium output of 1 unit for each firm. Therefore, the best choice is B.

A Cournot Oligopoly Has 19 Firms, and Inverse Market Demand P=60−QP = 60 - QP=60−Q

A Cournot Oligopoly Has 19 Firms, and Inverse Market Demand $P = 60 - Q$