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1. Assume a perfectly competitive market. Let C = Q3 - 4Q2 + 4Q be the cost function of a hypothetical firm. Find its supply

(Use this for questions 3 and 4) Let Q denote the quantity of pizza. A pizza producer has variable cost (VC) and fixed cost (

4. Assume a monopoly. Along with the VC and FC given above, you find that the market demand function is P= -Q+40. How much wi

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Answer #1

1. The supply curve of a perfectly comeptitive firm is given by P = MC lying above minimum AVC.
C = TVC = Q3 - 4Q2 + 4Q
(This is TVC because there is no part independent of Q.)
AVC = TVC/Q = (Q3 - 4Q2 + 4Q)/Q = Q2 - 4Q + 4
d(AVC)/dQ = 2Q - 4 = 0
So, 2Q = 4
So, Q = 4/2 = 2
Minimum AVC = Q2 - 4Q + 4 = 22 - 4(2) + 4 = 4 - 8 + 4 = 0

MC = dC/dQ = 3Q2 - 2(4Q) + 4 = 3Q2 - 8Q + 4
Thus, supply curve is given by P = 3Q2 - 8Q + 4 for Q > 2.
At the lowest point, Q = 2, so, P = 3Q2 - 8Q + 4 = 3(2)2 - 8(2) + 4 = 12 - 16 + 4 = 0

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