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 = $360 -.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 $45 and Grubb has marginal costs of $15.How much Grinch's output in equilibrium?
A)237.50
B)712.50
C)950
D)475
E)1,425

Question

Quizplus · Accepted Answer

To find the equilibrium output of Grinch, we need to use the cournot model:

Grinch's profit function:

π1(q1,q2) = (p - MC1)q1 = [360 - 0.4(q1+q2) - 45]q1

Grubb's profit function:

π2(q1,q2) = (p - MC2)q2 = [360 - 0.4(q1+q2) - 15]q2

Total demand:

Q = q1 + q2 = (F1S1 - F10)/0.4 = (3600 - 600)/0.4 = 75,000

Substituting π2 into π1:

π1(q1) = [360 - 0.4(q1 + (75,000 - q1)) - 45]q1
π1(q1) = [360 - 0.4(75,000) + 0.6q1 - 45]q1
π1(q1) = (0.2q1 - 6)q1

Taking the derivative w.r.t. q1:

dπ1(q1)/dq1 = 0.4q1 - 6 = 0

Solving for q1:

q1* = 15,000

Therefore, Grinch's output in equilibrium is q1* = 15,000 bottles of wine.

Suppose That Grinch and Grubb Go into the Wine Business