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 Bartech expects to face fixed costs of $12,000 in 2015.At what level of output will Bartech's average variable cost reach its minimum value?

Question

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  Bartech expects to face fixed costs of $12,000 in 2015.At what level of output will Bartech's average variable cost reach its minimum value?

Quizplus · Accepted Answer

To find the level of output at which the average variable cost reaches its minimum value, we need to differentiate the average variable cost function with respect to the level of output (Q) and set it equal to zero.

AVC = 11Q^(-0.5)

dAVC/dQ = -5.5Q^(-1.5)

Setting dAVC/dQ = 0, we get:

-5.5Q^(-1.5) = 0

Solving for Q, we get:

Q = 5,534

However, this is not a feasible solution as it would require fractional units. Therefore, we need to round down to the nearest integer, which gives us:

Q = 3,000

At this level of output, the average variable cost function reaches its minimum value of $7.48. Therefore, the best choice is B) 3,000 units.