Question

3. Given: TC = 2994 + 388Q -30Q² + 3Q³

a. Find equations for TFC, TVC, AFC, AVC, and MC.

b. the levels of output at which both AVC and MC are minimum.

c. Find the AVC and MC for the level of output at which the AVC curve is minimum. They should be the same $ amount

Note: the turning point of any curve is where it’s rate of change; i. e., it’s derivative equals zero.

* Please show work

Answer 1

Part A

The equations for TFC,TVC,AFC,AVC and MC can be derived from the equation for TC as given in the question.

TC is the sum of TFC and TVC. The constant part of TC is TFC (this is that part of TC which is independent of Q, the level of output) and the variable part of TC is TVC (this is that part of TC which varies with Q). AFC can be calculated from TFC. AVC can be calculated from TVC. MC can be calculated from TC.

Calculation details in the image below.

Part B

To find the levels of output at which AVC and MC are minimum, we will use the hint given in the question and calculate first derivative of AVC and MC and put these equal to zero and solve for the value of Q.

Since minimum point of MC occurs before the minimum point of AVC, value of Q is smaller corresponding to minimum level of MC as compared to that of AVC.

Calculation details in the image below.

Part C

To calculate the value of AVC and MC in $ terms corresponding to minimum point of AVC curve, we will use the value of Q calculated in part B corresponding to minimum AVC. It was 5.

We can check that value of both AVC and MC at Q=5 is $313.

Calculation details in the image below.