Use the following data for a competitive industry and a price-taking firm that operates in this market.
Bartech, Inc. is a firm operating in a competitive market. The manager of Bartech forecasts product price to be $28 in 2015. 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 2015.
-What is the minimum average variable cost?

Question

Quizplus · Accepted Answer

AVC is minimized when the derivative of AVC with respect to Q is equal to zero. Taking the derivative of AVC and setting it equal to zero, we get:$$\frac{dAVC}{dQ} = -0.003 + 0.000001Q = 0$$Solving for Q, we get:$$Q = 3000$$Substituting Q = 3000 back into the AVC function, we get:$$AVC = 10 - 0.003(3000) + 0.0000005(3000)^2 = 5.50$$Therefore, the minimum average variable cost is $5.50.

Use the Following Data for a Competitive Industry and a Price-Taking