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EconS 301, Spring 2015, Microeconomics with Calculus
Professor Rosenman
Homework 7
1. In response to leaky tanks polluting ground water, the Environmental Protection Agency
imposed new rules on gas stations. One of the rules required stations to monitor for leaks
periodically by measuring how much less gasoline there was in the tank at the end of the day,
compare it to how much was sold, and report any differential to authorities. This monitoring
took time and extra labor. Not surprisingly, some gas stations that did not suffer leaks went out
of business in the long run. A few even shut down immediately. Explain why. (3 points)
2. When Walmart opened its store in Pullman (which includes a super market section), the
demand facing the existing super markets like Safeway and Dismoores became more elastic –
with more competition the existing customers became more price sensitive. What should we
expect happened to the price mark-up over marginal cost at Safeway and Dismoores? Explain.
(3 points)
3. A firm has a total cost of TC=0.5q2+10q+200 where q is its output, and faces a demand for its
product given by q=100-2p where p is the price it charges.
a. Find the profit maximizing price and output for this firm. (3 points)
b. Is it making a profit? If not, why does the firm keep producing in the short run? (1 point)
c. If the state imposes a license fee of $100 on the firm, will it continue producing in the
short run? How about the long run? Explain. (2 points)
d. If the state taxes the firm at a rate of 0.2 per unit of output, so there is an additional
cost of 0,2q what will happen to the firm’s output and price in the short run? Explain. (2
points)
e. Going back to the cost curves before the new license fee, if demand is q=200-2p find the
profit maximizing output and price for this firm. Why has output gone up? (3 points)
4. Now suppose the firm in question 4 has the original demand and no license fee is a revenue
maximizing firm rather than a profit maximizing firm.
a. Find the output that maximizes its revenue and the price it will charge at that revenue?
Is it making a profit or a loss? (2 points)
b. If it must make at least a profit of 0, what output will it produce, and what price will it
charge? (1 point)
c. Ignoring the profit constraint, if the state taxes the firm at a rate of 0.2 per unit of
output, so there is an additional cost of 0,2q what will happen to the firm’s output and
price in the short run? Explain. (2 points)
d. Repeat parts a and b if demand goes up to q=200-2p. (3 points)
Extra credit 1: Explain why a profit maximizing firm should never have a price mark-up over marginal
cost that exceeds 100%. (3 xc points)
Extra credit 2: Let Q = (KL)1/2 and K=16 and PK=PL=1. If P=3-Q, find profit maximizing output and
price. Do the same if P=30-Q. Hint, use the XC problem from the last homework. (5 xc points)