Question

You are provided with the following demand and cost information for a monopolist.

P=60-0.25 Q and TC=Q2+40Q+50 Where P is price, Q is quantity of the product and TC is total cost. Determine the profit maximizing level of output and prices. (10Marks)

Answer 1

$P = 60 -0.25Q$

$TR = P.Q$

$= (60-0.25Q)Q$

$TR = 60Q - 0.25Q^2$

$MR = \frac{dTR}{dQ}$

$= 60(1) - 0.5Q$

$MR = 60 - 0.5Q$

$TC = Q^2 + 40Q + 50$

$MC = \frac{dTC}{dQ}$

$= 2Q + 40$

Monopolistic profit-Maximizing condition

$MC = MR$

$60-0.5Q = 2Q + 40$

$60-40 = 2Q + 0.5Q$

$20 = 2.5Q$

$Q = \frac{20}{2.5 }$

$Q = 8$

a) Profit Maximizing price

Substituting into P equation

$P = 60-0.25Q$

$= 60 -0.25\times8$

= $60-2$

Profit Maximizing price $= 58$

b) Profit Maximizing level of output

$P = MC$

$60-0.25(Q) = 2Q + 40$

$60-40 = 2Q +0.25Q$

$20 = 2.25Q$

$= \frac{20}{2.25}$

Profit Maximizing level of output $= 8.89$