A firm with two plants,A and B,has the following estimated demand and marginal cost functions: In order to maximize profit,how many units of output should the firm produce?

Question

A firm with two plants,A and B,has the following estimated demand and marginal cost functions:  In order to maximize profit,how many units of output should the firm produce?

Quizplus · Accepted Answer

To maximize profit, the firm should produce where marginal revenue (MR) equals marginal cost (MC). From the given data, we can calculate the MR for each plant as follows:

MR(A) = 20 - 0.2Q(A) - 0.1Q(B)
MR(B) = 12 - 0.1Q(A) - 0.2Q(B)

To find the optimal quantity for each plant, we need to set its MR equal to its MC, and solve for Q. The MC for each plant is given as:

MC(A) = 6
MC(B) = 8

Setting MR(A) = MC(A), we get:

20 - 0.2Q(A) - 0.1Q(B) = 6
0.2Q(A) + 0.1Q(B) = 14

Setting MR(B) = MC(B), we get:

12 - 0.1Q(A) - 0.2Q(B) = 8
0.1Q(A) + 0.2Q(B) = 4

Solving these two equations simultaneously gives:

Q(A) = 10
Q(B) = 15

Therefore, the firm should produce 10 units at plant A and 15 units at plant B, for a total of 25 units. This is the quantity where MR = MC for the entire firm, so it maximizes profit.

A Firm with Two Plants,A and B,has the Following Estimated