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Please show all work so I can better understand:
1. Suppose that the cost of producing x units is given by C(c) = 10,000 + 2X + 0.04X2
a) Find the average cost function, A(x).
b) How many units must be made to minimize the average cost per unit? Verify that this is a minimum using the 2nd derivative test.
c) What is the minimum average cost?
d) Find the marginal cost for the output determined in b).
e) Is the marginal cost increasing or decreasing at the quantity found in b).
f) If the product sells for $50 per unit, is it possible for the firm to earn a profit?
The cost of a unit of labour is $20 and the cost of a unit of capital is $80. The firm wants to produce 130 units of output. If capital is fixed in the short run at 5, then the firm should hire how many units of labour?
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