Question

Consider a monopoly whose total cost function is TC=Q3-30Q2+302Q, whose marginal cost function is MC= 3Q2-60Q+302, whose demand is P=329-30Q, and whose marginal revenue function MR= 329-60Q, where Q is output and P is price.

Assume that the firm maximizes profit but cannot practice price discrimination 

How much does the firm produce?        

How much does the firm charge?

How large are the firms profit?

Answer 1

a) Since MR= MC, then $3Q^2-60Q + 302 = 329 -60Q$

$3Q^2 = 27$

$Q^2 = 27$$/3$

$Q^2 = 9$

$Q = 3$

b)

$P =329-30Q$

$P = 329 - 30(3)$

$P = 329 -90$

$P = 239$

C) Considering $Profit = PQ - TC$$Q = 3 and P = 239$

$TC=Q^3-30Q^2+302Q$

$= 3^3 -30 (3^2) + 302(3)$

$= 27 -270 + 906$

$TC = 663$

$PQ = 239 × 3 = 717$

$= 717 -663$

$= 54$