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?
A)1,600
B)1,200
C)800
D)400
E)2,400

Question

Quizplus · Accepted Answer

We can start by finding the total quantity sold in the market by adding Grinch's output (QG) and Grubb's output (QG):

Q = QG + QG

Next, we can find the market price by plugging in the total quantity sold into the demand function:

p = $480 - 0.2Q

p = $480 - 0.2(QG + QG)

p = $480 - 0.4QG

Since Grinch and Grubb are playing a Cournot game, we can find Grinch's best response function by taking the derivative of Grinch's profit with respect to his output:

ΠG = (p - $30)QG

ΠG = ($480 - 0.4QG - $30)QG

ΠG = $450QG - 0.4QG^2

dΠG/dQG = $450 - 0.8QG

Setting this equal to zero and solving for QG, we get:

$450 - 0.8QG = 0

QG = 562.5

Rounding down to the nearest 100, Grinch's output in equilibrium is 800 units (choice C).

Suppose That Grinch and Grubb Go into the Wine Business