Question

A firm in a competitive industry has the following total and marginal cost functions: ? = ?? + ?? + ?? ?? = ? + ?? Suppose that the current market price is $20 and the firm is producing 8 units of output.

a. Is the firm maximizing profit? If not, at what quantity should the firm produce in order to maximize profits?

b. Write down the following cost functions for this firm: i. Variable Cost ii. Fixed Cost iii. Average Cost iv. Average Variable Cost v. Average Fixed Cost

c. Graph AC, MC and AVC on a single graph for values of ? between ? ?? ??. You can use Excel.

d. At what output level is AC minimized (this can be a non-integer)?

e. At what range of prices will the profit-maximizing firm produce a positive level of output ? > ??

f. At what range of prices will the profit-maximizing firm earn positive profits?

g. At what range of prices will the profit-maximizing firm earn negative profits?

Answer 1

As per the Chegg Policy, answering the first four parts

a.

Firm maximizes profit when P = MC

at 8 units of output, MC = 2 + 2*8 = 18

Market Price = 20

Since, Market Price is not equal to MC, firm is not maximizing its profit.

In order to maximize profit, firm should set, P = MC

20 =  ? + ??

q = 9

b.

i. Variable Cost VC = 2q + q^2

ii. Fixed Cost = 60

iii. Average Cost, AC = C/q = (60+2q+q^2) / q

AC = (60/q) + 2 + q

iv. AVC = (2q + q^2)/q = 2 + q

v. AFC = TFC/q = (60/q)

c.

d.

AC = (60/q) + 2 + q

First order condition,

dAC/dq = 0

(-60/q^2) + 1 = 0

q^2 = 60

q* = 7.75