Problem set 2: Monopoly and Monopsony
Taken from Besanko, David and Braeutigam, Ronald. Microeconomics 6th edition.
11.1 Suppose that the market demand curve is given by Q = 100 − 5P .
a What is the inverse market demand curve?
b What is the average revenue function for a monopolist in this market?
c What is the marginal revenue function that corresponds to this demand curve?
11.6 Suppose that United Airlines has a monopoly on the route between Chicago and Omaha,
Nebraska. During the winter (December–March), the monthly demand on this route is given by
P = a1 − bQ. During the summer (June–August), the monthly demand is given by P = a2 − bQ,
where a2 > a1 . Assuming that United’s marginal cost function is the same in both the summer
and the winter, and assuming that the marginal cost function is independent of the quantity Q of
passengers served, will United charge a higher price in the summer or in the winter?
11.10 Assume that a monopolist sells a product with the cost function C = F + 20Q, where C is
total cost, F is a fixed cost, and Q is the level of output. The inverse demand function is P = 60−Q,
where P is the price in the market. The firm will earn zero economic profit when it charges a price
of 30 (this is not the price that maximizes profit). How much profit does the firm earn when it
charges the price that maximizes profit?
11.11 Assume that a monopolist sells a product with a total cost function T C = 1, 200 + 0.5Q2
and a corresponding marginal cost function M C = Q. The market demand curve is given by the
equation P = 300 − Q.
a Find the profit-maximizing output and price for this monopolist. Is the monopolist profitable?
b Calculate the price elasticity of demand at the monopolist’s profit-maximizing price. Also
calculate the marginal cost at the monopolist’s profit-maximizing output. Verify that the
IEPR holds.
11.12 A monopolist faces a demand curve P = 210 − 4Q and initially faces a constant marginal
cost M C = 10.
a Calculate the profit-maximizing monopoly quantity and compute the monopolist’s total revenue at the optimal price.
b Suppose that the monopolist’s marginal cost increases to M C = 20. Verify that the monopolist’s total revenue goes down.
c Suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost
M C = 10. Find the long-run perfectly competitive industry price and quantity.
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d Suppose that all firms’ marginal costs increased to M C = 20. Verify that the increase in
marginal cost causes total industry revenue to go up.
11.15
Two monopolists in different markets have identical, constant marginal cost functions.
a Suppose each faces a linear demand curve and the two curves are parallel. Which monopolist
will have the higher markup (ratio of P to MC): the one whose demand curve is closer to the
origin or the one whose demand curve is farther from the origin?
b Suppose their linear demand curves have identical vertical intercepts but different slopes.
Which monopolist will have a higher markup: the one with the flatter demand curve or the
one with the steeper demand curve?
c Suppose their linear demand curves have identical horizontal intercepts but different slopes.
Which monopolist will have a higher markup: the one with the flatter demand curve or the
one with the steeper demand curve?
11.16 Suppose a monopolist faces the market demand function P = a − bQ. Its marginal cost is
given by M C = c + eQ. Assume that a > c and 2b + e > 0.
a Derive an expression for the monopolist’s optimal quantity and price in terms of a, b, c, and e.
b Show that an increase in c (which corresponds to an upward parallel shift in marginal cost) or
a decrease in a (which corresponds to a leftward parallel shift in demand) must decrease the
equilibrium quantity of output.
c Show that when e ≥ 0, an increase in a must increase the equilibrium price.
11.17 Suppose a monopolist has the demand function Q = 1, 000P −3 . What is the monopolist’s
optimal markup of price above marginal cost?
11.21 Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The market
demand curve for blades in Mexico is P = 968 − 20Q, where P is the price of blades in cents and Q
is annual demand for blades expressed in millions. Gillette has two plants in which it can produce
blades for the Mexican market: one in Los Angeles and one in Mexico City. In its L.A. plant, Gillette
can produce any quantity of blades it wants at a marginal cost of 8 cents per blade. Letting Q1 and
M C1 denote the output and marginal cost at the L.A. plant, we have M C1 (Q1 ) = 8. The Mexican
plant has a marginal cost function given by M C2 (Q2 ) = 1 + 0.5Q2 .
a Find Gillette’s profit-maximizing price and quantity of output for the Mexican market overall.
How will Gillette allocate production between its Mexican plant and its U.S. plant?
b Suppose Gillette’s L.A. plant had a marginal cost of 10 cents rather than 8 cents per blade.
How would your answer to part (a) change?
11.28 A coal mine operates with a production function Q = L/2, where L is the quantity of labor
it employs and Q is total output. The firm is a price taker in the output market, where the price
is currently 32. The firm is a monopsonist in the labor market, where the supply curve for labor is
w = 4L.
a What is the monopsonist’s marginal expenditure function, MEL?
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b Calculate the monopsonist’s optimal quantity of labor. What wage rate must the monopsonist
pay to attract this quantity of labor?
c What is the deadweight loss due to monopsony in this market?
11.31 National Hospital is the only employer of nurses in the country of Castoria, and it acts as a
profit maximizing monopsonist in the market for nursing labor. The marginal revenue product for
nurses is w = 50 − 2N , where w is the wage rate and N is the number of nurses employed (measured
in hundreds of nurses). Nursing services are provided according to the supply schedule w = 14 + 2N .
a How many nurses does National Hospital employ, and what wage will National pay its nurses?
b What is the deadweight loss arising from monopsony?
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