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.The profit-maximizing (or loss-minimizing)output for Bartech is

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, set the price equal to marginal cost (MC). First, derive the MC from the AVC: $MC = \frac{d(AVC \cdot Q)}{dQ} = 10 - 0.006Q + 0.000001Q^2$. Set $MC = 28$ and solve for Q. The calculation shows that Q = 6,000 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 $A V C = 10 - 0.003 Q + 0.0000005 Q ^ { 2 }$