Question

7. Given Demand fn. Q = 100 – 0.2P (Or P = 500 – 5Q), Cost fn. TC = 50 + 20Q + Q2

A. Find the profit maximizing price and output of a perfectly competitive market,
B. Assuming, a firm is monopoly
C. Compare the results

Answer 1

A. The condition for profit maximization for a competing firm is to choose such a volume of production that the price is equal to the marginal cost

$P=MC \\ 500-5Q = MC=TC’=20+2Q \\ 500-5Q=20+2Q \\ 480=6Q \\ Q= \frac{480}{6}=80 \\ P\; (price) = 500-5\times 80 = 100 \\ P \;(profit \; max) = TR-TC \\ TR=P \times Q \\ P(profit \; max) = 100 \times 80 - (50+20 \times 80 + 80^2) =8000 -8050 =-50$

B. The condition for maximizing profits in the monopoly market is the equality of marginal costs and marginal revenue:

$MC=MR \\ MC=TC’ = 20 +2Q \\ TR=Q(500-5Q) = 500Q -5Q^2 \\ MR = TR’ = 500 – 10Q \\ 20+2Q=500 -10Q \\ 12Q=480 \\ Q=\frac{480}{12}=40 \\ P(prise) = 500 -5 \times 40 = 300 \\ P(profit \; max) = TR-TC = P \times Q - (50 + 20Q + Q^2) \\ = 300 \times 40 50 20 \times 40-40^2 \\ = 12000 -50- 800 – 1600 \\ = 9550$

C. The firm will incur losses when releasing goods in a competitive market. Effective work is possible only in conditions of monopoly.