Answer to Question #211209 in Microeconomics for Ruchi

Question

The ABC Company produces chemicals in a perfectly competitive market. The current market price is $20. The firm’s total cost is given by C=50+2Q+Q2.

a. Determine the firm’s profit maximizing output and profit. Write down the equation for the firm’s supply curve in terms of price P. (6 marks)

b. Complying with more stringent environmental regulations increases the firm’s fixed cost from 50 to 100. Would this affect the firm’s output? Its supply curve? (4 marks

Answer 1

$C=50+2Q+Q^2\\P=20$

$MC=2+2Q\\P=MC......................profit\space max\\20=2+2Q\\20-2=2Q\\18=2Q\\Q=9..................profit\space max\space output$

Put P=MC to get supply

$P=2+2Q\\Q=\frac{P-2}{2}$

$Q_s=\frac{P-2}{2}$

Now fixed cost rises from 50 to 100

$C=100+2Q+Q^2\\MC=2+2Q$

Rise in fixed cost does not affect MC and thereby firm's output as well as supply.

LONG RUN

CASE 1

$When\space FC=50\\C=50+2Q+Q^2\\MC=2+2Q$

In long run equilibrium

$P=AC=MC\\AC=\frac{C}{Q}$

$\\=\frac{50+2Q+Q^2}{Q}$

$=\frac{50}{Q}+2+Q$

$MC=AC\\2+2Q=\frac{50}{Q}+2+Q\\2Q-Q=\frac{50}{Q}\\Q=\frac{50}{Q}\\Q^2=50\\Q=\sqrt{50}=7.071067812\\Q\approx7$

$Q\approx7$ is the output the individual firm will produce in the long run.

$P=MC=AC\\MC=2+2Q\\=2+2(7)\\=16$

P=16 is the profit that exists in the long run.

CASE 2

$when\space FC=100\\C=100+2Q+Q^2\\MC=2+2Q\\AC=\frac{100+2Q+Q^2}{Q}\\=\frac{100}{Q}+2+Q\\MC=AC\\2+2Q=\frac{100}{Q}+2+Q\\2Q-Q=\frac{100}{Q}\\Q=\frac{100}{Q}\\Q^2=100\\Q=10$

$P=MC\\P=2+2(10)\\=22.$

The effect of increase in FC has increased the efficient scale of a firm by i.e (10-7) and increases the long run equilibrium price by 6 i.e (22-16)

Since we are not given market demand, we are not aable to compute exact net of firms in the industry but it is sure that increase in fixed cost reduces the number of firms in the industries in the long run.