1 A firm can produce any quantity of good x with the followi

1. A firm can produce any quantity of good x with the following cost structure: TC 450,000 20Q, where Q measures units of output. a. What happens to the firm\'s average total cost of production as it expands output? b. What type of firm is this an example of? c. The industry demand for good X is Q 100,000 500P. At the profit- maximizing output level, calculate the firm\'s ATC of production. d. Suppose the profit-maximizing output level you calculated to answer part c Is split evenly between two firms, each with the cost structure given by TC 450,000 20Q. What is the ATC of production in this two-firm industry?

Solution

1.a. The firm\'s average total cost of production decreases as it expands output.

b. The firm is a monopoly firm.

P = (100000 - Q)/500

TR = 200Q - Q²/500

MR = 200 - Q/250

MC = 20

Profit will be maximised when MR = MC

200 - Q/250 = 20

Q = 45000

c. ATC = 450000/45000 + 20 = 30

d. Q₁ = 22500 & Q₂ = 22500

ATC₁ = 450000/22500 + 20 = 40 & ATC₂ = 40

ATC of industry = 80