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.

Answer 1

i) . The firm’s profit-maximizing output level is:

MR = MC,

MR = TR'(Q) = 45 - Q,

$MR=\frac {\Delta TR} {\Delta Q}$

$TR=Price ×Quantity (P×Q)$

$MC=TC ′ (Q)=3Q ^2 −16Q+57$

$3Q ^2 −16Q+57=45−Q$

$3Q ^2 −15Q+12=0$

$Q^2 - 5Q + 4 = 0$

$Q_1 = 4 units, Q_2 = 1 unit.$