Question

A firm estimated its short-run costs using an average variable cost function of the form AVC = a + bQ + cQ^2 and obtained the following results. Total fixed cost is $1,500. At what level of output is the average variable cost minimized, and what is the minimum average variable cost?

Answer 1

To find the level of output at which the average variable cost is minimized, differentiate the average variable cost function and set it equal to zero. Substitute the value of Q back into the average variable cost function to find the minimum average variable cost.

Step-by-step explanation:

To find the level of output at which the average variable cost is minimized, we need to differentiate the average variable cost function and set it equal to zero. The average variable cost function is AVC = a + bQ + cQ^2. Differentiating it with respect to Q, we get dAVC/dQ = b + 2cQ. Setting this equal to zero, we can solve for Q:

b + 2cQ = 0

Q = -b / (2c)

In this case, the minimum point is achieved at Q = -b / (2c), or the output level where Q = -b / (2c) will minimize the average variable cost. To find the minimum average variable cost, you can substitute this value of Q back into the average variable cost function.