Industrial Organisation (ES30044)
Seminar One: Monopoly
Industrial Organisation (ES30044)
Seminar One:
Monopoly
1. A law is passed fixing, below the level currently prevailing, the maximum price that can
be charged by a monopolist. The monopolist responds by increasing output. Is this
behaviour compatible with profit maximisation? Explain.
2. A profit-maximizing monopolist faces the demand curve q = 100 - 3p. It produces at a
constant marginal cost of £20 per unit. A quantity tax of £10 per unit is imposed on the
monopolist’s product. The price of the monopolist’s product
(a)
(b)
(c)
(d)
(e)
rises by £5
rises by £10
rises by £20
rises by £12
stays constant
3. A monopolist with constant marginal costs faces a demand curve with a constant
elasticity of demand and does not practice price discrimination. If the government
imposes a tax of £1 per unit of goods sold by the monopolist, the monopolist will
increase his price by more than £1 per unit. True / False? Explain.
4. Consider the market for iPhones. Apple holds the patent for iPhones. On the demand
side, there are n H high income consumers who are willing to pay a maximum price of
V H for an iPhone, and n L low-income consumers who are willing to pay a maximum
price of V L for an iPhone. Assume that V H > V L > 0 and that each consumer buys only
one iPhone. Suppose that Apple cannot price discriminate and is therefore constrained to
set a uniform market price:
(a) Draw the aggregate-demand curve facing Apple;
(b) Find the profit-maximising price set by Apple, considering all possible parameter
values of n H ,n L ,V H ,V L . Assume that production is costless.
(
)
5. A monopoly faces a demand function given by p = α − β q and has a unit production cost
of c > 0. Suppose the government imposes a specific tax of £t per unit on each unit of
output sold to consumers:
(a) Show that this tax imposition would raise the price paid by consumers by less than
t;
(b) How would your answer to (a) change if the market demand curve was given by
p = q −θ ?
6. Assume a continuum of consumers having different valuation for the annual services of a
car that are summarised by the familiar downward sloping demand curve. Suppose that
the consumers live for two periods denoted by t = 1, 2, and that the monopolist sells a
durable good that lasts for two periods. Thus if a consumer can purchase the good and
have it for his entire life, never having to replace it. Assume that the consumers’ different
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Industrial Organisation (ES30044)
Seminar One: Monopoly
valuations for the product are summarised by the aggregate period t = 1 inverse demand
curve for one period of service given by p ( q ) = α − β q . Compare the monopolist’s profits
from selling and renting.
7. Consolidated Incorporated operates a monopoly cartel of 12 members and faces an
aggregate demand function for its output of p ( Q ) = 200 − 40Q . How much profit does it
make if each constituent member faces a total cost function TCi ( qi ) = 50 + 10qi2 ?
8. We are going to model the market for electricity in Bath. A representative residence
derives utility from consuming electricity, e, and other goods, x. The consumer has quasilinear preferences such that his demand for electricity depends only on the relative price
of electricity, p, and not on the consumer’s income. His utility function is thus linear in x
and concave in e. For example:
U ( x, e) = x + a ln e
where a is some constant. The price of other goods, x, is normalised to one.
(a) Derive the consumer’s (uncompensated) demand for electricity;
(b) Let a residence’s demand for electricity be of the following form:
e = 1000 − 5 p
There are 3519 residences in Bath. Treat them as if they are identical. Find the market
demand function. Define market demand as E;
(c) There is one supplier of electricity in Bath. Call this electricity provider GSE. GSE
converts coal c, labour l, and capital k into electricity with the following production
function;
E = 900c.25 k 3.5l 1.75
GSE has built its power plants already, so its problem is to choose coal and labour.
Derive GSE’s cost function, taking k as fixed and assuming that q is the price of coal, w
is the price of labour, and r is the cost of capital?
(d) Given that GSE has already sunk its capital cost, what is the lowest price at which
GSE produces electricity?
(e) Since GSE is the only market supplier of electricity, it does not have to take this
price. Set up GSE’s profit maximization problem.
(f) Assume that GSE’s cost function is of the form
C ( E ) = 800 + 100 E +
24
E2
17595
How much electricity does GSE produce?
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Industrial Organisation (ES30044)
Seminar One: Monopoly
(g) What is the market price for electricity?
(h) What would the equilibrium price and quantity of electricity be if GSE is not the only
supplier of electricity (if the market is perfectly competitive)?
(i) Assume that there is a major technological improvement in the distribution of energy,
and this means that the consumer can more easily substitute between electricity and
other goods. How would you incorporate this into your model?
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