Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow. The demand for wine is given by p = $480 - .2Q, where p is the price and Q is the total quantity sold. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Imports are prohibited. Grinch has constant marginal costs of $30 and Grubb has marginal costs of $60. How much is Grinch's output in equilibrium?

Question

Quizplus · Accepted Answer

In the Cournot duopoly, each firm chooses its quantity based on the assumption that the other firm's quantity remains constant. Grinch's profit-maximizing output level can be found by setting his marginal revenue equal to his marginal cost:

MR = p + (dQ/dx)Q = $480 - .4Q - .2Q = $480 - .6Q 
MC = $30

Setting MR = MC, we get:

$480 - .6Q = $30 
.6Q = $450 
Q = 750

Therefore, Grinch's equilibrium output level is 750.

Suppose That Grinch and Grubb Go into the Wine Business