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. At Straker Industries,average variable cost (AVC)reaches its minimum value at $________.
A)$24.50
B)$33.60
C)$72.80
D)$121.80

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.  At Straker Industries,average variable cost (AVC)reaches its minimum value at $________.
A)$24.50 
B)$33.60 
C)$72.80 
D)$121.80

Quizplus · Accepted Answer

To find the minimum value of AVC, we need to find the value of Q where the derivative of AVC with respect to Q equals zero.To do this, we first need to rewrite the AVC equation as: AVC = (a/Q) + b + cQ.Substituting TFC = 1000 and AQC = a + bQ + cQ^2, we know that a = 1000 and b = 0.Using the derivative, we get (dAVC/dQ) = -(a/Q^2) + c.If we set (dAVC/dQ) = 0, we get Q^2 = a/c.Substituting a = 1000 and c = 1, we get Q = 31.62.Plugging this value of Q back into the AVC equation, we get AVC = 33.60, which is the minimum value.

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 $A V C = a + b Q + c Q ^ { 2 }$