Answer to Question #67416 in Calculus for Jafrul

Question

A price-taking profit-maximising business, which operates at its optimal plant
size, has a TC curve give by TC = q³ − 2q² + 2q + 0.576 where TC
is measured in 1000s of £ per week and q is the rate of output measured in
1000s of units per week.
a) If the market price of output is £1.00 show that the firm will produce 1000
units per week and make a loss. Explain why the business is, at this price,
indifferent between producing and closing down. Draw a diagram to show
this.
b) If the market price of output is £3.28 what will each firm produce and what
profit is made?
c) Assuming that all firms in the industry have identical cost structures and that
there is freedom of entry, show that the long-run weekly rate of output will fall
to 1200 units.
d) What is the price of output when the industry is in equilibrium?