If $S T C = 200 + 2 q + 4 q ^ { 2 }$ and $S M C = 2 + 8 q$ where $q$ is output, what is the minimum level of average variable cost?
A)0
B)2
C)6
D)8

Question

Quizplus · Accepted Answer

Average Variable Cost (AVC) is calculated by dividing the variable cost by the quantity of output (q). The variable cost (VC) can be derived from the Total Cost (TC) equation by subtracting any fixed costs (FC). Since the given STC equation does not explicitly separate fixed and variable costs, we assume all terms involving q are variable costs. Thus, VC = $2q + 4q^2$. AVC is then $VC/q = 2 + 4q$. To find the minimum AVC, we take the derivative of AVC with respect to q and set it to zero: $d(AVC)/dq = 4$, which does not depend on q, indicating AVC is a linear function of q and does not have a minimum point in its domain. However, the lowest value given by the AVC formula directly is when q is at its lowest, which is 2 (since the AVC increases with q). Therefore, the minimum level of AVC given by the options is 2.

If STC=200+2q+4q2S T C = 200 + 2 q + 4 q ^ { 2 }STC=200+2q+4q2

If $S T C = 200 + 2 q + 4 q ^ { 2 }$