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

the maximizing level of of utput Q is when $MC = MR = P$

$MC = TC' = 57 - 16Q +3Q^2$

$P= 45 - 0.5Q$

$45 -0.5Q = 57 -16Q +3Q^2$

$3Q^2 - 15,5Q +12 =0$

$Q = 4.21$