Fall 2022 – EC11 – Problem Set 5
Question 1
Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $20,000
and a fixed cost of $10 billion. You are asked to advise the CEO as to what prices and quantities
BMW should set for sales in Europe and in the United States. The demand for BMWs in each
market is given by:
QE = 4, 000, 000 − 100PE
QU = 1, 000, 000 − 20PU
where the subscript E denotes Europe and the subscript U denotes the United States. Assume
that BMW can restrict U.S. sales to authorized BMW dealers only.
a.
What quantity of BMWs should the firm sell in each market, and what should the price be in each
market? What should the total profit be?
b.
If BMW were forced to charge the same price in each market, what would be the quantity sold in
each market, the equilibrium price, and the company’s profit?
Question 2
Suppose that two identical firms produce widgets and that they are the only firms in the market.
Their costs are given by C1(y1) = 60y1 and C2(y2) = 60y2, where y1 is the output of Firm 1 and
y2 the output of Firm 2. Price is determined by the following demand curve:
p = 300 − y
where y = y1 + y2.
a.
Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.
b.
Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced?
Calculate each firm’s profit.
c.
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Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1’s profit
differ from that found in part b above?
d.
Returning to the duopoly of part b, suppose Firm 1 abides by the agreement, but Firm 2 cheats by
increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits?
Question 3
A monopolist firm faces a demand with constant elasticity of −2.0. It has a constant marginal cost
of $20 per unit and sets a price to maximize profit. If marginal cost should increase by 25%, would
the price charged also rise by 25%?
Question 4
Consider a city that has a number of hot dog stands operating throughout the downtown area.
Suppose that each vendor has a marginal cost of $1.50 per hot dog sold and no fixed cost. Suppose
the maximum number of hot dogs that any one vendor can sell is 100 per day.
a.
If the price of a hot dog is $2, how may hot dogs does each vendor want to sell?
b.
If the industry is perfectly competitive, will the price remain at $2 for a hot dog? If not, what will
the price be?
c.
If each vendor sells exactly 100 hot dogs a day and the demand for hot dogs from vendors in the
city is Q = 4, 400 − 1, 200P, how many vendors are there?
d.
Suppose the city decides to regulate hot dog vendors by issuing permits. If the city issues only 20
permits and if each vendor continues to sell 100 hot dogs a day, what price will a hot dog sell for?
e.
Suppose the city decides to sell the permits. What is the highest price a vendor would pay for a
permit?
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Question 5
The employment of teaching assistants (TAs) by major universities can be characterized as a
monopsony. A monopsony is a case where there is a single buyer, rather than a single seller like in
the monopoly. That is, the university here is the single ”buyer” (employer) of TAs. Suppose the
demand for TAs is W = 30, 000 − 125n, where W is the wage (as an annual salary), and n is the
number of TAs hired. The supply of TAs is given by W = 1000 + 75n.
a) The expenditure on TA salaries is given by W ×n, where W is given by the supply curve (because
if the university pays W based on the supply curve, that is what is necessary to hire n TA’s, then
W ×n is the entire wage bill). Represent the marginal expenditure on TA’s hired in equation form.
How does it compare to the supply curve? (Hint: in the monopoly case we had total revenue and
calculated the MR and compared it to demand – here we look at the supply side.)
b)
Briefly explain the intuition behind the relationship between the marginal expenditure and the
wage W, assuming that all TA’s hired are paid the same wage.
c)
If the university takes advantage of its monopsonist position, how many TAs will it hire? What
wage will it pay? (The demand for TA’s represents the ”marginal value” to the university.)
d)
If, instead, the university faced an infinite supply of TAs at the annual wage level of $10,000, how
many TAs would it hire?
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