Download Intermediate Microeconomics

ECON 301
Intermediate Microeconomics
Spring 2007
Problem set #8: answers
1. Consider the following production function Q = 5KL0.5 − L, and assume that capital is fixed
at two units. At what point does M PL reach zero?
For the production function Q = 5L.5 K − L, when K = 2, Q = 10L.5 − L. M PL = 5L−.5 − 1.
Thus, M PL = 0 when L = 25.
2. Suppose inputs are only substitutable at two units of labor for every one unit of capital.
What would be the equation for the production function? What is the average and marginal
product of labor in this case?
The production function is Q = 2K + L. APL = 2K/L + 1. M PL = 1.
3. Perloff, fourth edition: question 5 page 260
a) Assuming that the average cost and marginal cost all have U-shape, a firm’s marginal and
average costs are likely to rise with extra business.
b) As shown in Figure 1, since the increased demand is only seasonal, it will not affect firms’
long run supply curve and the number of firms in the market if there is considerable entry cost.
During peaked demand period, firms will operate to the right of the minimum of the short run
average cost curve.
Figure 1
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4. Perloff, fourth edition: question 17 page 261
(a) See Figure 2, the firm’s supply curve shifts leftward due the storm. As a result, the market
supply curse shifts rightward as well.
(b) If TomatoFest suffered an economic loss in this case depends on the demand elasticity, which
determines how the price responds to a lower supply. In this situation, an ‘economic loss’ is defined
as negative profit.
Figure 2
5. Perloff, fourth edition: question 26 page 262
No. Although horizontal factor supply curves would generate a horizontal firm supply curve, it
could also be that one input increases in cost at the same rate and that another decrease in cost.
In either case, as firm and industry output expands, average cost will remain unchanged and the
industry longrun supply curve will be horizontal.
6. Perloff, fourth edition: problem 31 page 263
Marginal cost is computed by taking the derivative dC/dq. Profits are maximized by setting
M C = M R = p. For the function given, M C = 10 − 2q + q 2 . Thus profits are maximized when
p = 10 − 2q + q 2 .
7. Perloff, fourth edition: problem 33 page 263
In the long run price equals marginal cost, and profits are zero. Thus, given that industry
output Q = nq, the following will be true in long-run equilibrium, p = 24 − nq. Therefore,
24 − nq = 2q
(24 − nq)q = 16 + q 2 .
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Solving these equations for q, n, Q, and p yields
q = 4
n = 4
Q = 16
p = 8.
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