Bartech,Inc.is a firm operating in a competitive market.The manager of Bartech forecasts product price to be $28 in 2021.Bartech's average variable cost function is estimated to be $A V C = 10 - 0.003 Q + 0.0000005 Q ^ { 2 }$ Bartech expects to face fixed costs of $12,000 in 2021.At what level of output will Bartech's average variable cost reach its minimum value?

Question

Quizplus · Accepted Answer

To find the level of output at which Bartech's average variable cost (AVC) reaches its minimum value, we differentiate the AVC function with respect to Q and set the derivative equal to zero. The AVC function is $AVC = 10 - 0.003Q + 0.0000005Q^2$. Differentiating AVC with respect to Q gives us the first derivative: $\frac{d(AVC)}{dQ} = -0.003 + 0.000001Q$. Setting this equal to zero and solving for Q gives us $0.000001Q = 0.003$, or $Q = \frac{0.003}{0.000001} = 3000$ units.

Bartech,Inc AVC=10−0.003Q+0.0000005Q2A V C = 10 - 0.003 Q + 0.0000005 Q ^ { 2 }AVC=10−0.003Q+0.0000005Q2

Bartech,Inc $A V C = 10 - 0.003 Q + 0.0000005 Q ^ { 2 }$