Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated total variable cost (TVC)?
A)$171.40
B)$463.20
C)$1,348
D)$2,348

Question

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000.  If Straker Industries produces 12 units of output,what is estimated total variable cost (TVC)?
A)$171.40 
B)$463.20 
C)$1,348 
D)$2,348

Quizplus · Accepted Answer

The given average variable cost function is:

AVC = a + bQ + cQ^2

where AVC is average variable cost, Q is output, and a, b, and c are parameters to be estimated.

To find estimated TVC when Q=12, we need to plug in Q=12 in the given equation:

AVC = a + b(12) + c(12^2)

We also know that when Q=0 (i.e. no output), AVC=TFC/AFC.

AFC = TFC/Q = 1000/0 = undefined

Therefore, we cannot use AFC to estimate TVC at Q=12. Instead, we can use the following formula:

TVC = AVC * Q + TFC

TVC = (a + bQ + cQ^2) * Q + 1000

TVC = aQ + bQ^2 + cQ^3 + 1000

TVC = (a + 12b + 144c) + (b + 24c) + c

Now, we need to find the values of a, b, and c. To do so, we need additional information such as the cost data for two different output levels.

Therefore, we cannot find the exact value of TVC at Q=12 based on the given information. However, we can estimate the value using the given formula and comparing the options.

For Q=12,

TVC = a(12) + b(12^2) + c(12^3) + 1000

Option A: TVC = $171.40 
Option B: TVC = $463.20 
Option C: TVC = $1,348 
Option D: TVC = $2,348

We can see that option B has the lowest estimate for TVC at Q=12. Therefore, the best choice is B.

Straker Industries Estimated Its Short-Run Costs Using a U-Shaped Average AVC=a+bQ+cQ2A V C = a + b Q + c Q ^ { 2 }AVC=a+bQ+cQ2

Straker Industries Estimated Its Short-Run Costs Using a U-Shaped Average $A V C = a + b Q + c Q ^ { 2 }$