Suppose that the inverse demand for bean sprouts is given by P(Y)= - 4Y and the total cost of producing Y units for any firm is TC(Y)= 10Y.If the industry consists of two Cournot duopolists, then in equilibrium each firm's production is
A)45 units.
B)22.50 units.
C)15 units.
D)30 units.
E)23.13 units.

Question

Quizplus · Accepted Answer

To find the equilibrium production levels of the two Cournot duopolists, we need to use the following steps:

1. First, we need to find the industry demand function by adding the individual demand functions of the two firms:
P(Y) = 370 - 4Y

2. We can then find the inverse supply function for each firm by using the first-order condition for profit maximization:
MR = MC
where MR is the marginal revenue (equal to the derivative of the industry demand function) and MC is the marginal cost (equal to the derivative of the cost function):
MR = 370 - 8Y
MC = 10

Setting MR = MC, we get:
370 - 8Y = 10
Y = 45

So each firm produces 45/2 = 22.5 units.

Therefore, the answer is D, each firm's production level is 30 units.

Suppose That the Inverse Demand for Bean Sprouts Is Given