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Assume that the market is perfectly competitive. If the cost function for John's Shoe Repair is �(�) = 100 + 10� − �) + 3 4 �4, what is the firm's marginal cost function? What is its profit-maximizing condition if the market price is p? What is its short-run supply curve?

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Answer:

Explanation:

C(q) = 100+10q-q^2+(1/3)q^3

To find the firm marginal cost function:

Take the derivative with respect to q

MC = 10 - 2q + q^2

Assuming that the market price is p , then the profit maximising condition is:

MR = MC

p = 10 - 2q + q^2

The short-run supply curve is the marginal cost curve that lies above the average variable cost.

The average variable cost is:

AVC =VC/Q

AVC = (10q-q^2+(1/3)q^3)/Q

AVC = 10 - q + (1/3)*q^2

So, the short-run supply curve is:

SRS = 10 - 2q + q^2 if p > 10 - q + (1/3)*q^2

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