Download Department of Economics

Shanghai University for International Business and Economics
Jonathan Haughton, May 2015
Intermediate Microeconomics
HOMEWORK ASSIGNMENT II.1
Answers to this assignment are due back on Tuesday, May 26, 2015. You may work on this assignment in groups
of up to three, if you wish. Explain all of your answers neatly in clear, concise English. Present your work nicely.
I will correct and grade your answers.
1.
Short questions
a.
A firm has increasing returns to scale and is making profits. The government is concerned that the firm
has grown too big, and splits it into two smaller firms of equal size. What effect would this have on
overall profits? Explain.
Is this statement true? “A profit-maximizing firm in a perfectly competitive industry can make positive
profits in long-run equilibrium if it has a technology with constant returns to scale.” Explain.
The government wants to raise more revenue, so it introduces a tax of 50% on economic profit. What
effect will this have on the supply curve of a price-taking firm? Explain.
b.
c.
2.
Mechanics of cost curves
A firm has the following cost curve: c(y) = 500 + 100 y – 12 y2 + y3.
a.
Write down equations for MC and AVC.
a. Does MC = AVC when output is zero?
b. Find the shutdown point (i.e. the output and price below which the firm would shut down
even in the short-run).
c. Graph AC, MC, and AVC. [You might want to use Excel. Be accurate. Make the graph
beautiful!]
b.
For each of the following market prices, calculate the firm’s profit maximizing output and its
(economic) profit:
a. P = 180
b. P = 120
c. P = 60.
c.
What would the market price have to be for the market to be in equilibrium – i.e. for there to be no
entry or exit?
d.
Calculate the firm’s producer surplus if it faces a market price of 180.
3.
Metro fares
An urban rapid-transit line runs crowded trains (with 200 passengers per car) at rush hours, but nearly empty
trains (20 passengers per car) at off-peak hours. A management consultant argues the following:
“The cost of running a car for one trip on this line is about 500 yuan, regardless of the number of
passengers. So the per-passenger cost is about 2.5 yuan at rush hour but rises to 25 yuan per passenger
in off-peak hours. Consequently, we had better discourage off-hour business.”
a.
Is the consultant’s argument correct? Explain.
b.
Many metro systems sell monthly “commuter” tickets that allow for multiple rides at a reduced price
per ride; these are mostly used by rush-hour riders. Are such tickets a good idea? Explain.
4.
Tax Incidence
Consider a perfectly competitive constant-cost industry in long-run equilibrium, which produces
toothbrushes. The government introduces a tax of ¥3 per toothbrush; the proceeds are to be used for “dental
education.” Explain, with the aid of appropriate diagrams (for both a typical firm, and the industry) why, in
the short-run, the price paid by consumers for toothbrushes will rise by less than ¥3, but in the long-run the
prices will rise by ¥3.
SUIBE – microeconomics
Assignment II.1
Page 1 of 2
5.
Monopoly output, price, and profit
A monopolist has a long-run cost function given by c(y) = 600 + 30 y. [Technically, the 600 here represents
“quasi-fixed” costs, that the firm has to incur if it produces anything, rather than ordinary fixed costs.] The
demand curve is given by y = 500 – 10 p.
a. Calculate the profit-maximizing output and price.
b. For the output and price in a., compute the firm’s profits, and the deadweight loss.
c. At the output in a., what is the value of the price-elasticity of demand for this good?
d. For the output in a., compute the Lerner Index.
e. The government puts a price ceiling in place at a price of 35. Compute the new quantity, profit,
and deadweight loss.
f. Someone suggests that the price ceiling should be set at a price of 32. Compute the resulting
quantity, profit, and deadweight loss.
SUIBE – microeconomics
Assignment II.1
Page 2 of 2