Question

Consider the following total cost function for Firm A: TC(Q)=4Q3-12Q2+2Q+1,000,000. Calculate TVC, AVC, TFC, AFC, AC. Does this cost function satisfy the law of diminishing returns? Hint: MC(Q)= 12Q2-24Q+2 Consider the following Long-run average cost function for Firm A: TC(Q)= 12Q+4 (Q represents the scale of operation). Does this firm benefit from scaling down? Explain your answer.

Answer 1

We are given that TC = 4Q^3 - 12Q^2 + 2Q + 1,000,000. We find that

TVC = Variable part of TC = 4Q^3 - 12Q^2 + 2Q

, AVC = TVC/Q = (4Q^3 - 12Q^2 + 2Q)/Q = 4Q^2 - 12Q + 2

TFC = fixed part of TC = 1,000,000

AFC = TFC/Q = 1,000,000/Q

AC = TC/Q = 4Q^2 - 12Q + 2 + 1,000,000/Q

Now we have MC = 12Q^2 - 24Q + 2. Find the derivative of MC and see that dMC/dQ = 24Q - 24. Since Q > or

= 0, dMC/dQ > 0 and this suggests that MC is an increasing function of Q which implies MP or marginal product

is a decreasing function. Hence there are diminishing returns.

Long run average cost function is LAC = 12Q + 4. As output rises, LAC rises as well. Hence there are

diseconomies of scale if the firm raises output. This firm, therefore, does not benefit from scaling down