For the cubic total cost function TC = a + bQ + cQ^2 + dQ^3 , where a = 0, b = 25, c = -10, and d = 1, the firm's average variable cost is minimized at an output of: a

Accounting Dec 08, 2020

For the cubic total cost function TC = a + bQ + cQ^2 + dQ^3 , where a = 0, b = 25, c = -10, and d = 1, the firm's average variable cost is minimized at an output of:

a. ten.

b. five.

c. two.

d. one.

Expert Solution

The correct answer is: b. five.

Given the total cost curve:

TC=a+bQ+cQ2+dQ3TC=a+bQ+cQ2+dQ3

Where:

a = 0
b = 25
c = -10
d = 1

The firm's total variable cost will be:

VC=25Q−10Q2+Q3VC=25Q−10Q2+Q3

The average variable cost curve will be given by:

AVC=VCQ=25−10Q+Q2AVC=VCQ=25−10Q+Q2

The average variable cost curve is minimized when the first-order derivative of the average variable cost curve with respect to Q is equal to zero.

Minimizing the average total cost curve:

ΔAVCΔQ=−10+2Q=0ΔAVCΔQ=−10+2Q=0

−10+2Q=0−10+2Q=0

Solving for Q:

2Q=102Q=10

Q=102=5Q=102=5 units.

Thus, the firm's average variable cost curve is minimized at Q = 5 units.

Archived Solution

Unlocked Solution

You have full access to this solution. To save a copy with all formatting and attachments, use the button below.

Already a member? Sign In

Important Note: This solution is from our archive and has been purchased by others. Submitting it as-is may trigger plagiarism detection. Use it for reference only.

For ready-to-submit work, please order a fresh solution below.

Or get 100% fresh solution

Get Custom Quote