04 Jun Question Eco 300. Intermediate Microeconomics
Question
Eco 300. Intermediate Microeconomics
Homework 4
1. A rm total cost curve is given by T C (q ) = q (q 4)2 + 2q .
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a) What is the formula for its AC curve?
b) Marginal costs are given by M C (q ) = 3q 2 16q + 18. Graph this
together with the AC curve.
2. Trapper Joe, the fur trader, has found that his production function in
p
acquiring pelts is given by q = 2 H where q =the number of pelts acquired
in a day, and H =the number of hours Joe employees spend hunting and
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trapping in one day. Joe pays his employees $8 an hour.
a) Calculate Joe total and average cost curves (as a function of q).
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b) What is Joe total cost for the day if he acquires four pelts? Six
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pelts? Eight pelts? What is Joe average cost per pelt for the day if he
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acquires four pelts? Six pelts? Eight pelts?
c) Graph the cost curves from part a and indicate the points from part
b.
3. Suppose that a rm faces a demand curve that has a constant elasticity
of 2. This demand curve is given by q = 256=P 2 . Suppose also that the
rm has a marginal cost curve of the form M C = 0:001q .
a) Graph these demand and marginal cost curves.
b) Calculate the marginal revenue curve associated with the demand
curve; graph the curve.
c) At what output level does marginal revenue equal marginal cost?
4. Assume that a rm acts as a price taker. Regardless of the demand,
it sells each unit of its product for $5.
a) Assume that the rm marginal cost is given by M C = 0:2q + 3.
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What is the level of output q that maximizes prot?
b) Assume the total cost is given by T C = 0:1q 2 + 3q + 10. Calculate
the rm prot.
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c) Graph these results and label rm supply curve.
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5. Suppose that a rm faces the demand curve of the form q = 60 2p.
a) Write down the total revenue curve as a function of q .
b) Assume M C = 0:2q and M R = 30 q . What output level should the
rm produce to maximize prots?
c) Graph the demand, M C , and M R curves and the point of prot
maximization.
1
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