NI_11th Edtion (1) (1)-69

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(presumably those who would not buy the good at the P1 price) are offered a lower price,
P2. This lower price generates additional demand of Q2 " Q1. Consequently, a total out-
put of Q2 is produced at an average cost of A. With this pricing system, the profits on the
sales to high-price demanders (given by the rectangle P1DBA) balance the losses incurred
on the low-priced sales (BFEC). Furthermore, for the ‘‘marginal user,’’ the marginal cost
pricing rule is being followed: It is the ‘‘intramarginal’’ user who subsidizes the firm so it
does not operate at a loss. Although in practice it may not be so simple to establish pric-
ing schemes that maintain marginal cost pricing and cover operating costs, many regula-
tory commissions do use price schedules that intentionally discriminate against some
users (e.g., businesses) to the advantage of others (consumers).
Rate of return regulation
Another approach followed in many regulatory situations is to permit the monopoly to
charge a price above marginal cost that is sufficient to earn a ‘‘fair’’ rate of return on
investment. Much analytical effort is then devoted to defining the ‘‘fair’’ rate concept and
to developing ways in which it might be measured. From an economic point of view,
some of the most interesting questions about this procedure concern how the regulatory
activity affects the firm’s input choices. If, for example, the rate of return allowed to firms
exceeds what owners might obtain on investment under competitive circumstances, there
will be an incentive to use relatively more capital input than would truly minimize costs.
And if regulators delay in making rate decisions, this may give firms cost-minimizing
By charging a high price (P1) to some users and a low price (P2) to others, it may be possible for a
regulatory commission to (1) enforce marginal cost pricing and (2) create a situation where the profits
from one class of user (P1DBA) subsidize the losses of the other class (BFEC).
Price
Quantity
per period
F
E
B
D
C
AC
MC
D
P1
P2
Q1 Q2
A
FIGURE 14.7
Two-Tier Pricing
Schedule
Chapter 14: Monopoly 521
incentives that would not otherwise exist. We will now briefly examine a formal model of
such possibilities.16
A formal model
Suppose a regulated utility has a production function of the form
q ¼ f ðk, lÞ: (14:43)
This firm’s actual rate of return on capital is then defined as
s ¼ pf ðk, lÞ " wl
k
, (14:44)
where p is the price of the firm’s output (which depends on q) and w is the wage rate for
labor input. If s is constrained by regulation to be equal to (say) s, then the firm’s problem
is to maximize profits
p ¼ pf ðk, lÞ " wl " vk (14:45)
subject to this regulatory constraint. The Lagrangian for this problem is
+ ¼ pf ðk, lÞ " wl " vkþ k½wl þ sk" pf ðk, lÞ): (14:46)
Notice that if l ¼ 0, regulation is ineffective and the monopoly behaves like any profit-
maximizing firm. If l ¼ 1, Equation 14.46 reduces to
+ ¼ ðs" vÞk, (14:47)
which, assuming s > v (which it must be if the firm is not to earn less than the prevailing
rate of return on capital elsewhere), means this monopoly will hire infinite amounts
of capital—an implausible result. Hence 0 < l < 1. The first-order conditions for a
maximum are
@+
@l
¼ pfl " wþ kðw" pf1Þ ¼ 0,
@+
@k
¼ pfk " v þ kðs" pfkÞ ¼ 0,
@+
@k
¼ wl "þsk" pf ðk, lÞ ¼ 0:
(14:48)
The first of these conditions implies that the regulated monopoly will hire additional labor
input up to the point at which pfl ¼ w—a result that holds for any profit-maximizing firm.
For capital input, however, the second condition implies that
ð1" kÞpfk ¼ v " ks (14:49)
or
pfk ¼
v " ks
1" k
¼ v " kðs" vÞ
1" k
: (14:50)
Because s > v and l < 1, Equation 14.50 implies
pfk < v: (14:51)
16This model is based on H. Averch and L. L. Johnson, ‘‘Behavior of the Firm under Regulatory Constraint,’’ American
Economic Review (December 1962): 1052–69.
522 Part 6: Market Power
The firm will hire more capital (and achieve a lower marginal productivity of capital)
than it would under unregulated conditions. Therefore, ‘‘overcapitalization’’ may be a
regulatory-induced misallocation of resources for some utilities. Although we shall not do
so here, it is possible to examine other regulatory questions using this general analytical
framework.
Dynamic Views Of Monopoly
The static view that monopolistic practices distort the allocation of resources provides the
principal economic rationale for favoring antimonopoly policies. Not all economists
believe that the static analysis should be definitive, however. Some authors, most notably
J. A. Schumpeter, have stressed the beneficial role that monopoly profits can play in the
process of economic development.17 These authors place considerable emphasis on inno-
vation and the ability of particular types of firms to achieve technical advances. In this
context the profits that monopolistic firms earn provide funds that can be invested in
research and development. Whereas perfectly competitive firms must be content with a
normal return on invested capital, monopolies have ‘‘surplus’’ funds with which to under-
take the risky process of research. More important, perhaps, the possibility of attaining a
monopolistic position—or the desire to maintain such a position—provides an important
incentive to keep one step ahead of potential competitors. Innovations in new products
and cost-saving production techniques may be integrally related to the possibility of
monopolization. Without such a monopolistic position, the full benefits of innovation
could not be obtained by the innovating firm.
Schumpeter stresses the point that the monopolization of a market may make it less
costly for a firm to plan its activities. Being the only source of supply for a product elimi-
nates many of the contingencies that a firm in a competitive market must face. For exam-
ple, a monopoly may not have to spend as much on selling expenses (e.g., advertising,
brand identification, and visiting retailers) as would be the case in a more competitive
industry. Similarly, a monopoly may know more about the specific demand curve for its
product and may more readily adapt to changing demand conditions. Of course, whether
any of these purported benefits of monopolies outweigh their allocational and distribu-
tional disadvantages is an empirical question. Issues of innovation and cost savings can-
not be answered by recourse to a priori arguments; detailed investigation of real-world
markets is a necessity.
SUMMARY
In this chapter we have examined models of markets in
which there is only a single monopoly supplier. Unlike the
competitive case investigated in Part 4, monopoly firms do
not exhibit price-taking behavior. Instead, the monopolist
can choose the price–quantity combination on the market
demand curve that is most profitable. A number of conse-
quences then follow from this market power.
• The most profitable level of output for the monopolist
is the one for which marginal revenue is equal to
marginal cost. At this output level, price will exceed
marginal cost. The profitability of the monopolist will
depend on the relationship between price and average
cost.
• Relative to perfect competition, monopoly involves a
loss of consumer surplus for demanders. Some of this
is transferred into monopoly profits, whereas some
of the loss in consumer supply represents a deadweight
loss of overall economic welfare.
17See, for example, J. A. Schumpeter, Capitalism, Socialism and Democracy, 3rd ed. (New York: Harper & Row, 1950), especially
chap. 8.
Chapter 14: Monopoly 523
• Monopolists may opt for different levels of quality than
would perfectly competitive firms. Durable goods
monopolists may be constrained by markets for used
goods.
• A monopoly may be able to increase its profits further
through price discrimination—that is, charging differ-
ent prices to different categories of buyers. The ability
of the monopoly to practice price discrimination
depends on its ability to prevent arbitrage amongbuyers.
• Governments often choose to regulate natural monop-
olies (firms with diminishing average costs over a
broad range of output levels). The type of regulatory
mechanisms adopted can affect the behavior of the
regulated firm.
PROBLEMS
14.1
A monopolist can produce at constant average and marginal costs of AC ¼ MC ¼ 5. The firm faces a market demand curve
given by Q ¼ 53 " P.
a. Calculate the profit-maximizing price–quantity combination for the monopolist. Also calculate the monopolist’s profits.
b. What output level would be produced by this industry under perfect competition (where price ¼ marginal cost)?
c. Calculate the consumer surplus obtained by consumers in case (b). Show that this exceeds the sum of the monopolist’s
profits and the consumer surplus received in case (a). What is the value of the ‘‘deadweight loss’’ from monopolization?
14.2
A monopolist faces a market demand curve given by
Q ¼ 70" p:
a. If the monopolist can produce at constant average and marginal costs of AC ¼ MC ¼ 6, what output level will the monop-
olist choose to maximize profits? What is the price at this output level? What are the monopolist’s profits?
b. Assume instead that the monopolist has a cost structure where total costs are described by
CðQÞ ¼ 0:25Q2 " 5Qþ 300:
With the monopolist facing the same market demand and marginal revenue, what price–quantity combination will be cho-
sen now to maximize profits? What will profits be?
c. Assume now that a third cost structure explains the monopolist’s position, with total costs given by
CðQÞ ¼ 0:0133Q3 " 5Qþ 250:
Again, calculate the monopolist’s price–quantity combination that maximizes profits. What will profit be? Hint: Set MC ¼
MR as usual and use the quadratic formula to solve the second-order equation for Q.
d. Graph the market demand curve, the MR curve, and the three marginal cost curves from parts (a), (b), and (c). Notice that
the monopolist’s profit-making ability is constrained by (1) the market demand curve (along with its associated MR curve)
and (2) the cost structure underlying production.
14.3
A single firm monopolizes the entire market for widgets and can produce at constant average and marginal costs of
AC ¼ MC ¼ 10:
Originally, the firm faces a market demand curve given by
Q ¼ 60" P:
a. Calculate the profit-maximizing price–quantity combination for the firm. What are the firm’s profits?
b. Now assume that the market demand curve shifts outward (becoming steeper) and is given by
Q ¼ 45" 0:5P:
524 Part 6: Market Power
What is the firm’s profit-maximizing price–quantity combination now? What are the firm’s profits?
c. Instead of the assumptions of part (b), assume that the market demand curve shifts outward (becoming flatter) and is
given by
Q ¼ 100" 2P:
What is the firm’s profit-maximizing price–quantity combination now? What are the firm’s profits?
d. Graph the three different situations of parts (a), (b), and (c). Using your results, explain why there is no real supply curve
for a monopoly.
14.4
Suppose the market for Hula Hoops is monopolized by a single firm.
a. Draw the initial equilibrium for such a market.
b. Now suppose the demand for Hula Hoops shifts outward slightly. Show that, in general (contrary to the competitive case),
it will not be possible to predict the effect of this shift in demand on the market price of Hula Hoops.
c. Consider three possible ways in which the price elasticity of demand might change as the demand curve shifts: It might
increase, it might decrease, or it might stay the same. Consider also that marginal costs for the monopolist might be
increasing, decreasing, or constant in the range where MR ¼ MC. Consequently, there are nine different combinations of
types of demand shifts and marginal cost slope configurations. Analyze each of these to determine for which it is possible
to make a definite prediction about the effect of the shift in demand on the price of Hula Hoops.
14.5
Suppose a monopoly market has a demand function in which quantity demanded depends not only on market price (P) but
also on the amount of advertising the firm does (A, measured in dollars). The specific form of this function is
Q ¼ ð20" PÞð1þ 0:1A" 0:01A2Þ:
The monopolistic firm’s cost function is given by
C ¼ 10Qþ 15þ A:
a. Suppose there is no advertising (A ¼ 0). What output will the profit-maximizing firm choose? What market price will this
yield? What will be the monopoly’s profits?
b. Now let the firm also choose its optimal level of advertising expenditure. In this situation, what output level will be chosen?
What price will this yield? What will the level of advertising be? What are the firm’s profits in this case? Hint: This can be
worked out most easily by assuming the monopoly chooses the profit-maximizing price rather than quantity.
14.6
Suppose a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per unit. Assume
the monopoly sells its goods in two different markets separated by some distance. The demand curve in the first market is
given by
Q1 ¼ 55" P1,
and the demand curve in the second market is given by
Q2 ¼ 70" 2P2:
a. If the monopolist can maintain the separation between the two markets, what level of output should be produced in each
market, and what price will prevail in each market? What are total profits in this situation?
b. How would your answer change if it costs demanders only $5 to transport goods between the two markets? What would be
the monopolist’s new profit level in this situation?
c. How would your answer change if transportation costs were zero and then the firm was forced to follow a single-price
policy?
d. Now assume the two different markets 1 and 2 are just two individual consumers. Suppose the firm could adopt a linear
two-part tariff under which marginal prices charged to the two consumers must be equal but their lump-sum entry fees
might vary. What pricing policy should the firm follow?
Chapter 14: Monopoly 525
14.7
Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of $10 per unit. Monopolized
marginal costs increase to $12 per unit because $2 per unit must be paid to lobbyists to retain the widget producers’ favored
position. Suppose the market demand for widgets is given by
QD ¼ 1,000" 50P:
a. Calculate the perfectly competitive and monopoly outputs and prices.
b. Calculate the total loss of consumer surplus from monopolization of widget production.
c. Graph your results and explain how they differ from the usual analysis.
14.8
Suppose the government wishes to combat the undesirable allocational effects of a monopoly through the use of a subsidy.
a. Why would a lump-sum subsidy not achieve the government’s goal?
b. Use a graphical proof to show how a per-unit-of-output subsidy might achieve the government’s goal.
c. Suppose the government wants its subsidy to maximize the difference between the total value of the good to consumers
and the good’s total cost. Show that, to achieve this goal, the government should set
t
P
¼ " 1
eQ,P
,
where t is the per-unit subsidy and P is the competitive price. Explain your result intuitively.
14.9
Suppose a monopolist produces alkaline batteries that may have various useful lifetimes (X). Suppose also that consumers’
(inverse) demand depends on batteries’ lifetimes and quantity (Q) purchased according to the function
PðQ,XÞ ¼ gðX ' QÞ,
where g 0 < 0. That is, consumers care only about the product of quantity times lifetime: They are willing to pay equally for
many short-lived batteries or few long-lived ones. Assume also that battery costs are given by
CðQ,XÞ ¼ CðXÞQ,
where C 0(X) > 0. Show that, in this case, the monopoly will opt for the same level of X as does a competitive industry even
though levels of output and prices may differ. Explain your result. Hint: Treat XQ as a composite commodity.
Analytical Problems
14.10 Taxation of a monopoly good
The taxation of monopoly can sometimes produce results differentfrom those that arise in the competitive case. This problem
looks at some of those cases. Most of these can be analyzed by using the inverse elasticity rule (Equation 14.1).
a. Consider first an ad valorem tax on the price of a monopoly’s good. This tax reduces the net price received by the
monopoly from P to P(1 " t)—where t is the proportional tax rate. Show that, with a linear demand curve and constant
marginal cost, the imposition of such a tax causes price to increase by less than the full extent of the tax.
b. Suppose that the demand curve in part (a) were a constant elasticity curve. Show that the price would now increase by pre-
cisely the full extent of the tax. Explain the difference between these two cases.
c. Describe a case where the imposition of an ad valorem tax on amonopoly would cause the price to increase bymore than the tax.
d. A specific tax is a fixed amount per unit of output. If the tax rate is t per unit, total tax collections are tQ. Show that the
imposition of a specific tax on a monopoly will reduce output more (and increase price more) than will the imposition of
an ad valorem tax that collects the same tax revenue.
14.11 More on the welfare analysis of quality choice
An alternative way to study the welfare properties of a monopolist’s choices is to assume the existence of a utility function for
the customers of the monopoly of the form utility ¼ U(Q, X), where Q is quantity consumed and X is the quality associated
with that quantity. A social planner’s problem then would be to choose Q and X to maximize social welfare as represented by
SW ¼ U(Q, X) " C(Q, X).
526 Part 6: Market Power
a. What are the first-order conditions for a welfare maximum?
b. The monopolist’s goal is to choose the Q and X that maximize p ¼ P(Q, X) Æ Q " C(Q, X). What are the first-order condi-
tions for this maximization?
c. Use your results from parts (a) and (b) to show that, at the monopolist’s preferred choices, @SW/@Q > 0. That is, as we
have already shown, prove that social welfare would be improved if more were produced. Hint: Assume that @U/@Q ¼ P.
d. Show that, at the monopolist’s preferred choices, the sign of @SW/@X is ambiguous—that is, it cannot be determined (on
the sole basis of the general theory of monopoly) whether the monopolist produces either too much or too little quality.
14.12 The welfare effects of third-degree price discrimination
In an important 1985 article,18 Hal Varian shows how to assess third-degree price discrimination using only properties of the
indirect utility function (see Chapter 3). This problem provides a simplified version of his approach. Suppose that a single good
is sold in two separated markets. Quantities in the two markets are designated by q1, q2 with prices p1, p2. Consumers of the
good are assumed to be characterized by an indirect utility function that takes a quasi-linear form: V(p1, p2, I) ¼ v(p1, p2) þ I.
Income is assumed to have an exogenous component (!I), and the monopoly earns profits of p ¼ p1q1 þ p2q2 " c(q1 þ q2),
where c is marginal and average cost (which is assumed to be constant).
a. Given this setup, let’s first show some facts about this kind of indirect utility function.
(1) Use Roy’s identity (see the Extensions to Chapter 5) to show that the Marshallian demand functions for the two goods
in this problem are given by qi (p1, p2, I) ¼ "@v/@pi.
(2) Show that the function v (p1, p2) is convex in the prices.
(3) Because social welfare (SW) can be measured by the indirect utility function of the consumers, show that the welfare
impact of any change in prices is given by DSW ¼ Dv þ Dp. How does this expression compare with the notion (intro-
duced in Chapter 12) that any change in welfare is the sum of changes in consumer and producer surplus?
b. Suppose now that we wish to compare the welfare associated with a single-price policy for these two markets, p1 ¼ p2 ¼ p,
with the welfare associated with different prices in the two markets, p1 ¼ p!1 and p2 ¼ p!2. Show that an upper bound to the
change in social welfare from adopting a two-price policy is given by DSW * ð p" cÞðq!1 þ q!2 " q1 " q2Þ. Hint: Use a first-
order Taylor expansion for the function v around p!1, p
!
2 together with Roy’s identity and the fact that v is convex.
c. Show why the results of part (b) imply that, for social welfare to increase from the adoption of the two-price policy, total
quantity demanded must increase.
d. Use an approach similar to that taken in part (b) to show that a lower bound to the change in social welfare from adopting a
two-price policy is given by DSW + ð p!1 " cÞðq!1 " q1Þ þ ð p!2 " cÞðq!2 " q2Þ. Can you interpret this lower bound condition?
e. Notice that the approach taken here never uses the fact that the price–quantity combinations studied are profit maximizing
for the monopolist. Can you think of situations (other than third-degree price discrimination) where the analysis here
might apply? Note: Varian shows that the bounds for welfare changes can be tightened a bit in the price discrimination case
by using profit maximization.
SUGGESTIONS FOR FURTHER READING
Posner, R. A. ‘‘The Social Costs of Monopoly and
Regulation.’’ Journal of Political Economy 83 (1975):
807–27.
An analysis of the probability that monopolies will spend
resources on the creation of barriers to entry and thus have
higher costs than perfectly competitive firms.
Schumpeter, J. A. Capitalism, Socialism and Democracy,
3rd ed. New York: Harper & Row, 1950.
Classic defense of the role of the entrepreneur and economic
profits in the economic growth process.
Spence, M. ‘‘Monopoly, Quality, and Regulation.’’ Bell Jour-
nal of Economics (April 1975): 417–29.
Develops the approach to product quality used in this text and
provides a detailed analysis of the effects of monopoly.
Stigler, G. J. ‘‘The Theory of Economic Regulation.’’ Bell Jour-
nal of Economics and Management Science 2 (Spring 1971): 3.
Early development of the ‘‘capture’’ hypothesis of regulatory
behavior—that the industry captures the agency supposed to regu-
late it and uses that agency to enforce entry barriers and further
enhance profits.
Tirole, J. The Theory of Industrial Organization. Cambridge,
MA: MIT Press, 1989, chaps. 1–3.
A complete analysis of the theory of monopoly pricing and
product choice.
Varian, H. R. Microeconomic Analysis, 3rd ed. New York:
W. W. Norton, 1992, chap. 14.
Provides a succinct analysis of the role of incentive compatibil-
ity constraints in second-degree price discrimination.
18H. R. Varian, ‘‘Price Discrimination and Social Welfare,’’ American Economic Review (September 1985): 870–75.
Chapter 14: Monopoly 527
EXTENSIONS OPTIMAL LINEAR TWO-PART TARIFFS
In Chapter 14 we examined a simple illustration of ways in
which a monopoly may increase profits by practicing second-
degree price discrimination—that is, by establishing price (or
‘‘outlay’’) schedules that prompt buyers to separate themselves
into distinct market segments. Here we pursue the topic of
linear tariff schedules a bit further. Nonlinear pricing sched-
ules are discussed in Chapter 18.
E14.1 Structure of the problem
To examine issues related to price schedules in a simple con-
text for each demander, we define the ‘‘valuation function’’ as
viðqÞ ¼ piðqÞ ' qþ si, (i)
where pi(q) is the inverse demand function for individual i and si
is consumer surplus. Hence vi represents the total value to indi-
vidual i of undertaking transactions of amount q, which includes
total spending on the good plus the value of consumer surplus
obtained. Here we will assume (a) there are only two demanders1
(or homogeneous groups of demanders) and (b) person 1 has
stronger preferences for this good than person 2 in the sense that
v1ðqÞ > v2ðqÞ (ii)
for all values of q. The monopolist is assumed to have
constant marginal costs (denoted by c) and chooses a tariff
(revenue) schedule, T(q), that maximizes profits given by
p ¼ Tðq1Þ þ Tðq2Þ " cðq1 þ q2Þ, (iii)
where qi represents the quantitychosen by person i. In select-
ing a price schedule that successfully distinguishes among
consumers, the monopolist faces two constraints. To ensure
that the low-demand person (2) is served, it is necessary that
v2ðq2Þ " Tðq2Þ + 0: (iv)
That is, person 2 must derive a net benefit from her optimal
choice, q2. Person 1, the high-demand individual, must also obtain
a net gain from his chosen consumption level (q1) and must pre-
fer this choice to the output choice made by person 2:
v1ðq1Þ " Tðq1Þ + v1ðq2Þ " Tðq2Þ: (v)
If the monopolist does not recognize this ‘‘incentive com-
patibility’’ constraint, it may find that person 1 opts for the
portion of the price schedule intended for person 2, thereby
destroying the goal of obtaining self-selected market separa-
tion. Given this general structure, we can proceed to illus-
trate a number of interesting features of the monopolist’s
problem.
E14.2 Pareto superiority
Permitting the monopolist to depart from a simple single-
price scheme offers the possibility of adopting ‘‘Pareto supe-
rior’’ tariff schedules under which all parties to the transaction
are made better off. For example, suppose the monopolist’s
profit-maximizing price is pM. At this price, person 2 con-
sumes qM2 and receives a net value from this consumption of
v2ðqM2 Þ " pMqM2 : (vi)
A tariff schedule for which
TðqÞ ¼ pMq for q * qM2 ,
aþ pq for q > qM2 ,
%
(vii)
where a > 0 and c < p < pM , may yield increased profits for
the monopolist as well as increased welfare for person 1. Spe-
cifically, consider values of a and p such that
aþ pqM1 ¼ pMqM1
or
a ¼ ðpM " pÞqM1 , (viii)
where qM1 represents consumption of person 1 under a single-
price policy. In this case, a and p are set so that person 1 can still
afford to buy qM1 under the new price schedule. Because p < pM ,
however, he will opt for q!1 > qM1 . Because person 1 could have
bought qM1 but chose q!1 instead, he must be better off under the
new schedule. The monopoly’s profits are now given by
p ¼ aþ pq1 þ pMqM2 " cðq1 þ qM2 Þ (ix)
and
p" pM ¼ aþ pq1 þ pMqM1 " cðq1 " qM1 Þ, (x)
where pM is the monopoly’s single-price profits ½¼ ðpM " cÞ3
ðqM1 þ qM2 Þ). Substitution for a from Equation viii shows
p" pM ¼ ðp" cÞðq1 " qM1 Þ > 0: (xi)
1Generalizations to many demanders are nontrivial. For a discussion, see
Wilson (1993, chaps. 2–5).
	PART SIX: Market Power
	CHAPTER 14 Monopoly
	Dynamic Views of Monopoly��������������������������������
	Summary��������������
	Problems���������������
	Suggestions for Further Reading��������������������������������������
	Extensions: Optimal Linear Two-Part Tariffs��������������������������������������������������