Question

TC = 1000 + 174Q -4Q2 + Q3

Derive the AVC function?

Derive the MC function?

How much is AVC at an output of 10 units?

At what output level does AVC reach a minimum?

At what output level does MC reach a minimum?

Illustrate with AVC-MC diagram

Answer 1

a. The given total cost function is:

The variable cost function is the part of the total cost function that depends on the quantity produced:

Average variable cost function is derived by dividing the variable cost function by quantity:

b. The marginal cost function is derived by differentiating the total cost function with respect to quantity:

c. Average variable cost at 10 units of output is:

d. In order to minimize AVC, the following problem is solved:

Solving the problem:

Hence, AVC is minimized at quantity level of 2 units.

e. In order to minimize MC, the following problem is solved:

Solving the problem:

Hence, MC is minimized at quantity level of 4/3 units.

e. Plotting the MC and AVC functions:

The red curve is the MC curve and the blue curve is the AVC curve.