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

$TP_L = 10L + 5L^2 + L^3$

$MP_L=\frac {dTP_L} {dL} =10+10L+3L^2$

$AP_L=\frac {TP_L} {L} =10+5L+L^2$

When L=5;

$TP_L=10(5) + 5(5)^2 + (5)^3$

$TP_L=50+125+125$

$TP_L=300$

$MP_L=10+10(5)+3(5)^2$

$MP_L=10+50+75$

$MP_L=135$

$AP_L=10+5(5)+(5)^2$

$AP_L=60$