If the cost function for John\'s Shoe Repair is C(q) = 100+10q-q^2+(1/3)q^3, wha

Question

If the cost function for John's Shoe Repair is C(q) = 100+10q-q^2+(1/3)q^3, what is the firm's marginal cost function? What is its profit maximizing condition if the market price is p? What is its supply curve?

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Explanation / Answer

C(q) = 100+10q-q^2+(1/3)q^3 Take the derivative with respect to q MC = 10 - 2q + q^2 If the market price is a constant of p, then the profit maximizing 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 The long-run supply curve is the marginal cost curve that lies above the average total cost. ATC = C/Q ATC = (100+10q-q^2+(1/3)q^3)/Q ATC = 100/Q + 10 - q + (1/3)*q^2 So, the long-run supply curve is: LRS = 10 - 2q + q^2 if p > 100/Q + 10 - q + (1/3)*q^2

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