Refer to the following.
A firm with two plants, A and B, has the following estimated demand and marginal cost functions:
$$\begin{array} { l }
Q _ { d } = 120 - 10 P \
M C _ { A } = 4 + ( 1 / 5 ) Q _ { A } \
M C _ { B } = 6 + ( 1 / 10 ) Q _ { B }
\end{array}$$
-In order to maximize profit, how many units of output should the firm produce?

Question

Refer to the following.
A firm with two plants, A and B, has the following estimated demand and marginal cost functions:
 $$\begin{array} { l } 
Q _ { d } = 120 - 10 P \
M C _ { A } = 4 + ( 1 / 5 ) Q _ { A } \
M C _ { B } = 6 + ( 1 / 10 ) Q _ { B }
\end{array}$$
-In order to maximize profit, how many units of output should the firm produce?

Quizplus · Accepted Answer

The profit-maximizing output is found where marginal cost equals marginal revenue. The marginal revenue curve is the derivative of the demand curve, which is MR = 120 - 20P. Setting this equal to the marginal cost of plant A, we get:120 - 20P = 4 + (1/5)Q_ASolving for Q_A, we get:Q_A = 58Similarly, setting MR equal to the marginal cost of plant B, we get:120 - 20P = 6 + (1/10)Q_BSolving for Q_B, we get:Q_B = 52Therefore, the firm should produce a total of Q_A + Q_B = 58 + 52 = 110 units of output.

Refer to the Following Qd=120−10PMCA=4+(1/5)QAMCB=6+(1/10)QB\begin{array} { l } Q _ { d } = 120 - 10 P \\M C _ { A } = 4 + ( 1 / 5 ) Q _ { A } \\M C _ { B } = 6 + ( 1 / 10 ) Q _ { B }\end{array}Qd​=120−10PMCA​=4+(1/5)QA​MCB​=6+(1/10)QB​​

Refer to the Following $\begin{array} { l } Q _ { d } = 120 - 10 P \\M C _ { A } = 4 + ( 1 / 5 ) Q _ { A } \\M C _ { B } = 6 + ( 1 / 10 ) Q _ { B }\end{array}$