Question

A firm's cost function is: C=20 - 3 Q^2 +2 Q^3 . Its demand is: P =200 - 0.25Q. Find the quantity supplied by the firm and the price charged. Is the firm making a profit?

Answer 1

TC = 20 - 3 Q^2 +2 Q^3, Pd =200 -0.25Q.
To find the quantity supplied by the firm and the price charged we should find the point, where MR = MC.
MC = TC' = 6Q + 6Q^2
MR = TR' = (P*Q)' = (200Q - 0.25Q^2)' = 200 - 0.5Q
6Q + 6Q^2 = 200- 0.5Q
12Q^2+ 13Q - 200 = 0
D = 169 + 4*12*200 = 9769
Q = (-13 + 98.8)/24 = 3.58, so Q = 4
P = 200 - 0.25*4 = $199


TP= P*Q - TC = 199*4 - 100 = $696, so firm is making profit.