Answers to Chapter 5 Exercises
Review and practice exercises
5.1. Front yards. Front yards, if well tended, generate positive externalities for a house’s
neighbors. Do you think this is an important externality? Is the market solution inefficient?
Answer: The externality is likely to be important: one of the characteristics that make a
neighborhood attractive is precisely how well tended the front yards are. If each household
were to choose gardening e↵ort solely based on his or her benefits, it’s likely that the
equilibrium level of gardening e↵ort would be lower than optimal. However, its also likely
that neighborhood social pressure induces residents to put a little more e↵ort than they
would like: if they don’t, they risk being shunned by their neighbors. If the social norm
regarding acceptable gardening levels is at the socially optimal level, then it is possible that
the market solution be efficient.
5.2. AT&T. A recent estimated the long-run demand elasticity of AT&T in the period
1988–1991 was around -10.16 Assuming the estimate is correct, what does this imply in
terms of AT&T’s market power at the time?
Answer: A demand elasticity of 10 implies that AT&T’s demand is very elastic. In fact, the
author of the study that produced this estimate computes the welfare loss due to AT&T’s
market power to be less than 1% of sales volume.
5.3. Monopoly power.
demand.” Comment.
“The degree of monopoly power is limited by the elasticity of
Answer: Optimal monopoly pricing leads to the following relation between the price-cost
margin and demand elasticity: (p MC )/p = 1/✏, where p is price, MC marginal cost, and e
demand elasticity. It follows that the greater the value of ✏ the lower the value of (p MC )
and the lower monopoly profits. A monopolist facing a very elastic demand curve makes
profits at the level of a competitive firm.
5.4. Windows. Is the Windows operating system an essential facility? What about
the Intel Pentium microprocessor? To what extent does the discussion in Section 5.6 on
essential facilities (vertical integration, access pricing) apply to the above examples?
Answer: By means of preface: this is a very controversial question; not all economists agree
on a single answer. Having said that, both Microsoft (the producer of the Windows operating system) and Intel (the producer of the Intel Pentium microprocessor) provide computer
makers with essential components, without which the machines could not function. Nevertheless, strictly speaking, we cannot say that their output represents an essential facility.
The discussion in Section 5.6 applies to monopolists. The crucial di↵erence from the examples presented in the section is the fact that Microsoft and Intel are not monopolists:
computer makers always have the option of switching to another provider of components.
However, the widespread use of the Windows operating system, and the fact that Windows is only supplied by Microsoft, implies that the latter’s position is much closer to the
one of a monopolist than is Intel’s. Even though Intel’s chip design is very close to being
an industry standard, Intel is not the only company supplying microprocessors with that
design. Hence, the Windows operating system is closer to what is called an essential facility
than Intel’s Pentium processor.
Challenging exercises
5.5. Carbon tax.
Consider an industry with demand q = 1 p and supply q = p.
Suppose that each unit of output implies one unit of CO2 added to the atmosphere and a
marginal social cost of e, where e is the total level of emmissions.
(a) What is the level of CO2 emission at the market equilibrium?
Answer: Equating supply and demand, we get 1 p = p, or simply p = 12 . Substituting in
the supply curve (or the demand curve) we get q = 12 . Since one unit of output corresponds
to one unit of emissions, we conclude that the emissions level is 12 .
(b) What is the socially optimal level of CO2 emissions?
Answer: Since e = q, The total social marginal cost is given by q + q = 2 q, where the first
term corresponds to production cost and the second to cost from emissions. The inverse
demand is given by p = 1 q. Equating the two, we get
2q = 1
q
or simply q ⇤ = 13 .
(c) Determine the Pigou tax that achieves the social optimum.
Answer: Equilibrium output (supply = demand) is given by
q+t=1
Since the goal is q = 13 , it follows that t⇤ = 1
q
2 q ⇤ = 13 .
5.6. Common facility. Di↵erent divisions within a firm frequently compete for a common
resource. Suppose that divisions 1 and 2 of a given firm share a common facility F . Let
2
yi be the service level used by division i (i = 1, 2). Division i’s gross benefit in terms of
improved divisional earnings is given by yi 0.25 yi2 0.1 (y1 + y2 ).
(a) What are the equilibrium levels of yi if the various divisions act separately?
Answer: Each division maximizes
yi
0.25 yi2
0.1 (y1 + y2 )
Let us consider division 1. Since it cannot control the other division, the optimal solution
corresponds to maximizing
y1
0.25 y12
0.1 y1 = 0.9 y1
0.25 y12
The solution is y1 = 1.8. By symmetry, the same is true for the other division, so y2 = 1.8.
(b) What are the optimal levels of yi from an overall firm point of view?
Answer: The firm maximizes total benefit, that is
y1
0.25 y12
0.25 y22
0.1 (y1 + y2 ) + y2
= 0.8 (y1 + y2 )
0.25 (y12
+
0.1 (y1 + y2 ) =
y22 )
Maximizing with respect to y1 we get y1 = 1.6.
(c) Explain the di↵erence between the results in (a) and (b).
Answer: The equilibrium value is greater than the optimal value. The reason is that there
is a negative externality: when division 1 uses the facility more intensely, it does not take
into account that this costs division 2 lower divisional earnings. In other words, part of
division 1’s gain is not a gain for a firm as a whole.
(d) How can equilibrium and optimality be reconciled?
Answer: One possibility is to create a system of transfer pricing whereby each division pays
for the use of the common facility F . If the fee is set at .1 (the cost imposed on the other
facility), then the equilibrium solution will be optimal.
Applied exercises
5.7. Externality. Choose an market or an industry (or another situation from economic
life). Determine what externalities there might be in consumption or production. Propose
ways in which these externalities can be corrected (“internalized”). Compare your proposed
solution to reality and explain the di↵erences.
3