An industry has two firms. The inverse demand function for this industry is p = 74 - 4q. Both firms produce at a constant unit cost of $26 per unit. What is the Cournot equilibrium price for this industry?

Question

Quizplus · Accepted Answer

In a Cournot equilibrium, the firms determine their output levels simultaneously, assuming that each firm expects the other firm's output to be fixed.

Let q1 and q2 be the quantities produced by the two firms. Then, the total quantity supplied by the industry is Q = q1 + q2.

Each firm maximizes its profit by choosing its output level q1 or q2, taking Q as given. The first-order condition for profit maximization is:

MR1 = MC1
(74 - 8q) = 26
q = 6

This means that each firm will produce 6 units, for a total industry output of 12 units.

We can then substitute this output level into the demand function to obtain the market price:

p = 74 - 4Q
p = 74 - 4(12)
p = 74 - 48
p = 26

Therefore, the Cournot equilibrium price for this industry is $42, which is choice (C).

An Industry Has Two Firms