SOCIAL SCIENCE RESEARCH
Sebastian Kessing *
Robert Nuscheler **
Monopoly Pricing with Negative Network Effects:
the Case of Vaccines
* Freie Universität Berlin and European University Institute
** Wissenschaftszentrum Berlin für Sozialforschung
SP II 2003 – 06
ISSN Nr. 0722 – 6748
Markets and Political Economy
Markt und politische Ökonomie
Market Processes and Governance
Marktprozesse und Steuerung
Sebastian Kessing, Robert Nuscheler, Monopoly Pricing
with Negative Network Effects: the Case of Vaccines,
Discussion Paper SP II 2003 – 06, Wissenschaftszentrum
Wissenschaftszentrum Berlin für Sozialforschung gGmbH,
Reichpietschufer 50, 10785 Berlin, Germany, Tel. (030) 2 54 91 – 0
Monopoly Pricing with Negative Network Effects: the Case of Vaccines
by Sebastian Kessing and Robert Nuscheler *
We study the market for vaccinations considering income heterogeneity on the
demand side and monopoly power on the supply side. A monopolist has an
incentive to exploit the external effect of vaccinations and leave the poor
susceptible in order to increase the willingness to pay of the rich. Even the
possibility to perfectly price discriminate does not remove this incentive.
Pigouvian subsidies may even make things worse. Mandatory vaccination
programs covering only the poor succeed in eradicating the disease. This offers
an efficiency based rationale for distribution-oriented national or international
public health interventions.
Keywords: Vaccination, monopoly pricing, price discrimination, negative network
effects, Pigouvian subsidies, mandatory vaccination programs
JEL Classification: D42, D62, H23, I11, I18
Monopolpreisbildung mit negativen Netzwerkeffekten am Beispiel von
Wir untersuchen den Markt für Impfstoffe, wobei wir Einkommensungleichheit
auf der Nachfrageseite und Monopolmacht auf der Angebotsseite unterstellen.
Ein Monopolist hat den Anreiz, den externen Effekt von Impfungen aus-
zunutzen. So wird er die Armen strategisch ungeimpft lassen, um die Zahlungs-
bereitschaft der Reichen zu erhöhen. Selbst für den Fall der perfekten Preis-
diskriminierung bleibt dieser Anreiz bestehen. Pigou Subventionen können das
Marktergebnis noch verschlechtern. Staatliche Impfprogramme, die nur die
Armen abdecken, können die Krankheit auslöschen. Dies liefert eine effizienz-
basierte Begründung für verteilungsorientierte nationale wie internationale Inter-
ventionen in den Impfmarkt.
* We thank Kai A. Konrad, Helmut Bester, Johannes Münster, the participants of the
Microeconomic Colloquium at the Freie Universität Berlin, and the participants of the CEPR
workshop on “health economics and public policy” in Bergen for helpful comments. The usual
Traditionally, vaccinations were regarded as one of the prime examples of positive exter-
nalities. Consequently, government intervention in the form of mandatory vaccinations
and Pigouvian subsidies were considered to be appropriate policy responses to the distor-
tions caused by the externality. More recently, this traditional view has been challenged
by various contributions that produced a number of somewhat con?icting results about
the form and optimality of government intervention in the market for vaccines (see e.g.
Brito et al. (1991), Francis (1997), and Geo?ard and Philipson (1997)). These results typ-
ically depend on the speci?c assumptions made in the models about agent heterogeneity,
market structure and dynamics. This paper contributes to this literature by consider-
ing strategic incentives and optimal government responses in the context of two hitherto
neglected dimensions. First, individuals are assumed to di?er with respect to income.
Second, monopoly power on the supply side is considered.
In the existing theoretical literature agent heterogeneity is usually introduced, if at all,
through the assumption that the disutility of vaccinations, i.e. side e?ects, varies. Em-
pirically, disutility is di?cult to observe. As empirical studies of individual vaccination
decisions usually ?nd a clear positive relationship between income and the probability of
being vaccinated, introducing agent heterogeneity into the theoretical analysis through
income di?erences would seem to be a natural step. Philipson (1996, table 2, p. 624), for
example, ?nds a positive income e?ect on the probability of measles vaccination for chil-
dren in the U.S. England et al. (2001, p. 19) report that, if there is a fee, as with hepatitis
B in China, “poorer people are more likely to go without essential immunization”. More-
over, since government action usually a?ects people’s incomes, such an analysis promises
to be a better approximation of the consequences of di?erent policy measures.
The second key element in our treatment is its focus on monopoly power on the
supply side. This assumption is motivated by recent developments in the vaccine industry.
Important changes in U.S. legislation in 1986, which e?ectively shield manufacturers from
the liability risk of new vaccines, resulted in a substantial increase in R&D e?orts and
these have recently lead to a dramatic increase in the availability of a number of new
vaccines (BusinessWeek Online (2002)). Russell (2002) points out that two developments
have also increased monopoly power signi?cantly. First, there has been a shift from
commodity vaccines to vaccines which are heavily protected by intellectual property rights.
The new Hepatitis B vaccine introduced in the late 1980s has for example about thirty
associated patents. Similarly, Reiss and Strauss (1998) document that between 1980 and
1995 patent applications for vaccines at the European patent o?ce rose by a factor of
seven and that this development has been fuelled by the progress made in the ?eld of
genetically engineered vaccines in particular.1 Second, the ongoing concentration in the
industry at all levels, from research and development to marketing organizations, has
left only a few key players. Furthermore, as ?rms are increasingly specializing in speci?c
diseases and their core ?elds of expertise, competitive pressure is being further attenuated.
A vaccine monopolist has two main incentives: (i) to keep the disease alive and (ii)
to increase the prevalence of the disease in order to increase the willingness to pay for
vaccination.2 In their dynamic model Geo?ard and Philipson (1997) address the ?rst
incentive, but remain silent about the second incentive. We provide the missing part
of the analysis using a static model. On the demand side, we consider the case where
the population has to pay for the vaccinations, i.e. the costs are not covered by health
insurance companies or the state. Consequently, there is no bargaining either between
insurance companies or state agencies.3
We summarize both the income dependence of the individual willingness to pay and
the external e?ect of a reduced infection probability due to a higher number of vaccinated
individuals using a simple linear aggregate demand schedule faced by the monopolist.
1“The four industry leaders (Merck, GlaxoSmithKline, Aventis Pasteur, and Wyeth) are estimated to
spend more than US$750 million a year on vaccine R&D—as much as a ?vefold jump at some companies
since 1992.” (BusinessWeek Online (2002))
2Although not in a monopoly context, the case of measles o?ers some insights: more than 99 percent of
the disease burden of measles fall on low and middle income countries, with more than 750,000 deaths in
the year 2000. Full immunization could save roughly 28 million disability adjusted life years (see Kremer
(2002, pp. 70-71)).
3For an empirical analysis that tests whether price discrimination or bargaining is present in the U.S.
vaccine market see Kauf (1999).
The linearity assumption allows explicit results to be obtained, but none of the results
depend on it qualitatively. The decisive element in this setting is the monopolist’s second
strategic incentive mentioned above. This is most easily analyzed in a static environment.
But the results will also apply in a dynamic framework, since the importance of the
external e?ect increases.4 Although the emphasis of the analysis is on the case without
price discrimination we also consider perfect price discrimination. All qualitative results,
including the comparative statics, are robust. With price discrimination, vaccination
discrimination is in fact reduced. But, in contrast to the standard model without external
e?ects, the outcome may still be ine?cient. The ?ndings of the robustness of the strategic
incentives are relevant for policy recommendations since multi-tier pricing is pervasive in
real world vaccine markets (Russell (2002)).5
In the theory of public goods, the problemof under-provision can be eliminated by
Pigouvian subsidies. However, although vaccinations are an example of privately provided
public goods, subsidies do not work very well. At ?rst demand increases as the individual
price is reduced. However, this increase lowers the infection probability and thus reduces
the willingness to pay. This counteracting e?ect limits the e?ect of these subsidies (see
Geo?ard and Philipson (1997, p. 225)). We show that subsidies may make things even
worse. We assume that the price subsidy is ?nanced by lump-sum taxation creating
a negative income e?ect. If this e?ect is su?ciently large, the positive price e?ect is
overcompensated and a smaller proportion of people are vaccinated. This contrasts with
the classical regulation arguments for Pigouvian subsidies and strengthens Philipson’s
(2000) argument, that “Pigouvian subsidies traditionally seen as resolving the under-
provision problemof vaccines can be short-run, or out of steady state, arguments” (p.
1777), since these may even fail in static settings. Recently, Philipson and Mechoulan
(2003) have argued that subsidies are likely to distort R&D incentives.
4Francis (1997) showed that in his dynamic setting the externality disappears. The allocation is
e?cient. But with heterogenous individuals this result does not generally hold.
5The UN Accelerating Access Initiative supports di?erential pricing for AIDS drugs (see
http://www.unaids.org/acc access/). In this context Roche was more or less forced to increase the dis-
count on their AIDS drugs for developing countries to roughly 90 percent of the Swiss price (see M´
Another public policy usually suggested is mandatory vaccination. If mandatory vac-
cination programs do not cover the whole population, the people vaccinated lower the
probability that the susceptible will be infected. The willingness to pay is reduced, i.e.,
mandatory demand crowds out voluntary demand. This is a standard argument for why
it is di?cult to eradicate a disease by mandatory vaccination if not the entire population
is included in the program(see Philipson (2000, p. 1781)). However, such a program
is much more e?ective with income-dependant demand: as people’s incomes di?er, the
public programcan cover the poor and the monopolist the rich. Of course the willingness
to pay of the rich is reduced, but it remains relatively high due to the income e?ect. Full
vaccination can be achieved with a mandatory participation rate that is strictly smaller
than one. Thus, our analysis provides an e?ciency argument for public health vaccina-
tion programs that focus on the poor like those typically supported by the World Health
Organization (WHO) and the Worldbank.
The approach presented here is related to Brito et al. (1991). They consider a static
model with a continuum of individuals whose disutility from vaccination di?ers. Since
vaccines are provided free of charge, price discrimination cannot be studied in their setting.
The ?rst-best outcome can be implemented by subsidizing those who decide to vaccinate,
or by taxing those without immunization. But when the subsidy has to be ?nanced
through taxation, the ?rst-best can only be attained under the strong assumption of
identical marginal utility of income across individuals. In their dynamic model, Geo?ard
and Philipson (1997) address the question of disease eradication. Both price subsidies
and mandatory vaccination programs have limited impact, since the positive e?ects of
the respective policies are partly o?set by the negative e?ect of the externality.
The current paper is also related to the literature on network externalities, e.g. Bensaid
and Lesne (1996), Cabral et al. (1999), and Mason (2000). The main di?erence is the
sign of the network e?ect. This is positive in these models but negative in ours, leading
to completely di?erent results. With a positive network e?ect, introductory pricing may
occur to built up a certain critical network size. With vaccinations it is the other way
round: in order to prevent the market shrinking or disappearing a critical mass will never
The paper is organized as follows: in section 2 we present the main ingredients of our
model. The monopolist’s price setting problem and the comparative static properties of
this solution are studied in section 3. Perfect price discrimination is analyzed in section
4. In section 5 we discuss public policies that may be used to reduce discrimination and
thus increase social welfare. Section 6 concludes. The appendix provides a generalization
of the reduced formapplied throughout the paper.
Consider a population of mass one with individuals who di?er in income but are otherwise
homogenous. Income is denoted a and is continuously distributed on the interval [aL, aH],
where 0 < aL ? aH. An individual’s willingness to pay for vaccination depends on her
income a and the expected share of individuals who get vaccination, ?e ? [0, 1]:
p = p(?e, a).
The higher the expected rate of immunization ?e, the lower the expected share of sus-
ceptible individuals 1 ? ?e. A high ?e is associated with a low expected risk of infection
?e, ??e/??e < 0. Clearly, the willingness to pay for vaccination increases in the risk of
infection. We thus postulate ?p/??e < 0, which captures the external e?ect of vaccina-
tions. Furthermore, in line with the empirical evidence, it is assumed that the willingness
to pay increases in income ?p/?a > 0. While the external e?ect of vaccinations is a
general feature of the market, a positive income e?ect is not so obvious. In the appendix,
interpreting vaccination as an insurance decision, we derive a su?cient condition on pref-
erences for yielding a positive income e?ect. Finally, we assume p(1, a) > 0, implying the
existence of an exogeneous infection risk. While made for simplicity, this can be justi?ed
by infection threats fromother countries6, accidental laboratory outbreaks, or terrorist
6The way infectious diseases can spread around the world can be seen currently with the Severe Acute
Respiratory Syndrome (SARS) that originated in China.
7Although smallpox is said to be eradicated, there is a positive willingness to pay for vaccines.
To simplify the analysis, and in order to derive explicit closed form solutions, we
summarize the individual willingness to pay by the following simple linear scheme
p(?e, a) = z?(1 ? ?e) + zaa,
where za ? (0, 1) measures the income e?ect and z? > 0 the importance of the external
e?ect. The upper bound on za is justi?ed by normality, while the lower bound re?ects our
central assumption of a positive income e?ect. Furthermore we assume that the population
is uniformly distributed on the interval [aL, aH]. None of these assumptions is necessary
for the results we derive below. However, their use signi?cantly eases the presentation of
the main ideas. As will become clear, a downward sloping aggregate demand function is
su?cient for most results. We discuss the conditions under which demand is downward
sloping in the appendix.
There is a monopolist who provides a vaccine that yields perfect protection against
the disease and that has no side e?ects. His price setting problemis analyzed in a two
stage game. At stage 1 the monopolist sets the price pm. We analyze two versions of the
game, in section 3 we study standard monopoly pricing. Here pm is constant and denotes
the price at which the monopolist is willing to sell to all consumers actually demanding
vaccination. In section 4 the case of perfect price discrimination is addressed. The price
may depend on income so that pm = pm(a) is a price schedule. At stage 2 individuals
observe prices, formexpectations about the vaccination rate, and thus about the infection
probability, and decide whether to vaccinate or not, i.e. aggregate demand is realized.
Solving the game backwards leads to a subgame perfect Nash equilibrium. Deriving
aggregate demand requires ?rst analyzing the role of consumers’ expectations for vacci-
nation decisions. As the analyses di?er for the two cases studied they are relegated to
the respective sections of the paper (see lemma 1 and lemma 3 below). Once aggregate
demand is derived, determining the monopolist’s optimal policy is straightforward.
Let us ?rst consider the case of standard monopoly pricing where the monopolist only
quotes a single price. In order to derive the stage two vaccination equilibriumwe assume
symmetric expectations and require expectations to be consistent, i.e. expectations must
be ful?lled in equilibrium. The second useful property is the sorting of individuals by
income. In particular, for a given expected infection risk, an individual who decides to be
vaccinated knows that everybody richer than herself will also be vaccinated.
Before we solve for the equilibriumof the vaccination subgame, we de?ne the critical
consumer ?. Let pm > 0 be some ?xed price for the vaccine, then ? = ? (pm) solves
pm = p ?, a ?
= z? 1 ? ? + za aH ? ?? ,
where ? := aH ? aL. The income of the critical consumer is a := a ? = aH ? ??.
Since the willingness to pay p ?, a ?
strictly decreases in ?, the critical consumer is
well-de?ned, i.e. ? is unique.
In lemma 1 we show that there are unique expectations for every given price pm. How
consistency of expectations can be used to derive the aggregate demand is demonstrated
in lemma 2.
Lemma 1 Individuals facing a price pm will rationally expect ? (pm) to be the immuniza-
The proof is by contradiction.
So, suppose that individuals expect the
immunization rate ?e > ?. Then, the willingness to pay for vaccination of type ? is
p ?e, a ?
= z? (1 ? ?e) + za aH ? ?? < pm. Individual ? will not demand vaccination
and neither will all consumers with lower income than aH ? ??. Thus immunization
with expectations ?e > ? will actually be lower than ? so that expectations can never be
con?rmed. A similar reasoning applies to all ?e < ? proving inconsistency of all ?e = ?.
The lemma implies that we can concentrate on cases where the two arguments of the
willingness to pay function are identical. To ease notation we will thus write p (?) :=
p (?, a (?)). Notice that we also omit the bar.
Lemma 2 The aggregate demand function the monopolist is facing at the ?rst stage of
the game is given by
? + zaaH ? pm
z? + za?
- Monopoly Pricing with Negative Network Effects: the Case of Vaccines
- JEL Classification: D42, D62, H23, I11, I18
- Monopolpreisbildung mit negativen Netzwerkeffekten am Beispiel von Impfstoffen