A firm can produce any quantity of good X with the following

A firm can produce any quantity of good X with the following cost structure: TC = 450,000 + 20Q, where Q measures units of output. What happens to the firm\'s average total cost of production as it expands output? What type of firm is this an example of? The industry demand for good X is Q = 100,000 - 500P. At the profit-maximizing output level, calculate the firm\'s ATC of production. 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

TC=4,50,000+20Q

a.) ATC=TC/Q

ATC=(450000+20Q)/Q

ATC=(450000/Q)+20; As firm expand output, that is as Q rises,ATC falls.

b.)It is a decreasing cost firm because as it expands output,average production costs decreases.

c.)Industry demand is Q=100000-500P

Profit maximization condition is MR=MC

TC=450000+20Q

MC=derivative of TC with respect to Q

MC=20

Demand is Q=100000-500P

Total revenue(TR)=PQ

P=(100000-Q)/500

PQ=TR=(100000Q-Q²)/500

MR=Derivative of total revenue with respect to Q

MR=(100000-2Q)/500

MR=MC

(100000-2Q)/500=20

100000-2Q=10000

90000=2Q

Q=45000;this is profit maxizing output level

ATC=(450000/Q)+20

ATC=(450000/45000)+20

ATC=30

d.)Two firm industry:

Q=45000 is split between them evenly.;each has 45000/2=22500 units of output

Each has TC=450000+20Q

Each has ATC=(450000/Q)+20

Each has ATC=(450000/22500)+20=40

since there are 2 firms, so total ATC=2(40)=80