Suppose the demand function in the industry is p = 100 - y and each firm has a constant marginal cost of $40 and no fixed costs. If the Cournot model of oligopoly accurately reflects firm behaviour in this industry, then the aggregate equilibrium output of n + 1 firms can be expressed as:
A)160(n + 1)/(n + 2).
B)20(n + 1).
C)60(n + 1)/(n + 2).
D)160n/(n + 1).

Question

Quizplus · Accepted Answer

In the Cournot model, each firm assumes the output of its competitors to be fixed and chooses its own output to maximize profit. The profit-maximizing output for each firm can be found by taking the derivative of its profit function with respect to its own output and setting it equal to zero:

π = (p - 40)q
π = (100 - y - 40)q
π = (60 - q)q
dπ/dq = 60 - 2q = 0
q* = 30

Therefore, the equilibrium output of each firm is 30, and the total industry output is (n + 1) * 30. The market clearing condition is:

y = (n + 1) * 30
100 - y = 70 - (n + 1) * 30
p = 70 - (n + 1) * 30

Substituting p into the demand function:

70 - (n + 1) * 30 = 100 - y
y = 60(n + 1)/(n + 2)

Thus, the aggregate equilibrium output of n + 1 firms can be expressed as 60(n + 1)/(n + 2). Therefore, the correct choice is C.

Suppose the Demand Function in the Industry Is P =