Answer to Question #189647 in Macroeconomics for hasan

Question

If the demand function faced by a firm is:

Q = 90 – 2P

TC = 2 + 57Q – 8Q² + Q³

Determine the level of output at which the firm maximizes the profit.

Determine the best level of output for the above question by the MR and MC approach.

Answer 1

$Q = 90 - 2P \\ P = 45 - 0.5Q \\ TC = 2 + 57Q - 8Q^2 + Q^3$

The firm’s profit-maximizing output level is:

$MR = MC \\ MR = TR'(Q) = 45 -Q \\ MC = TC'(Q) = 3Q^2 - 16Q + 57 \\ 3Q^2 - 16Q + 57 = 45 - Q \\ 3Q^2 - 15Q + 12 = 0 \\ Q^2 - 5Q + 4 = 0 \\ Q_1 = 4 \; units \\ Q_2 = 1\; unit$