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.
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
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