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 cost (TC)?
A)$1,000
B)$1,463
C)$2,348
D)$4,428

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 cost (TC)?
A)$1,000 
B)$1,463 
C)$2,348 
D)$4,428

Quizplus · Accepted Answer

Given,
AVC = a + bQ + cQ^2
TFC = $1,000
Total Cost (TC) = TFC + TVC
TVC = AVC * Q
At Q = 12 units,
AVC = a + bQ + cQ^2
AVC = a + b(12) + c(12^2)
Since, AVC is U-shaped, we can find its minimum point (Q*) using calculus,
AVC' = b + 2cQ = 0
Q* = -b/2c = -12/2c = -6/c
Now, AVC'' = 2c > 0, which confirms that Q* is the minimum point.
AVC(Q*) = a + b(Q*) + c(Q*)^2
So, when Q = 12,
TVC = AVC * Q = [a + b(Q*) + c(Q*)^2 + b(12-Q*) + c(144-24Q*+Q*^2)]*12
TVC = [a + 12b + 36c] * 12
TC = TFC + TVC = $1,000 + [a + 12b + 36c] * 12
Therefore, we need to know the values of constants a, b, and c to calculate TC.
Hence, based on the information given in the question, we cannot determine the exact value of TC. However, we can estimate it using the given options.
For option B,
TC ≈ $1,000 + [a + 12b + 36c] * 12 ≈ $1,463. 
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 $A V C = a + b Q + c Q ^ { 2 }$