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Consider a firm with the following cost function: C (q) = 4q^2 + 100 Find the...

Consider a firm with the following cost function:

C (q) = 4q^2 + 100


Find the long-run supply and the short-run supply of the firm, under the assumptions that the total cost function is the same in the long and in the short run, but the xed cost is sunk in the short run.

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Answer #1

Marginal cost curve is the supply curve when price is greater than min of AVC.

MC=dC/dq=8q

Thus P=MC=8Q

Thus Short run supply curve Qs=P/8

In long run, price=min of AC. AC=4Q+100/Q

AC is minimised when dAC/dQ=0

dAC/dQ=4-100/Q2=0

Thus Q=5 and AC=20+20=40

Thus P=40 is the long run supply curve

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