First‐best health policy in vaccine markets with health and network externalities

• Published date: 01 December 2023
• Author: Rabah Amir,Filomena Garcia,Iryna Topolyan
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jpet.12673

Received: 24 October 2023

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Accepted: 29 October 2023

DOI: 10.1111/jpet.12673

ORIGINAL ARTICLE

First‐best health policy in vaccine markets

with health and network externalities

Rabah Amir

1

|Filomena Garcia

2,3

|Iryna Topolyan

4

1

Department of Economics, The

University of Iowa, Iowa City, Iowa, USA

2

Economics Department, Poole College

of Management, NC State University,

Raleigh, North Carolina, USA

3

UECE, University of Lisbon, Lisbon,

Portugal

4

Department of Economics, University of

Cincinnati, Cincinnati, Ohio, USA

Correspondence

Rabah Amir, Department of Economics,

The University of Iowa, Iowa City,

IA, USA.

Email: rabah-amir@uiowa.edu

Abstract

This paper considers an oligopolistic market for a

vaccine, characterized by negative network effects,

which stem from the free‐riding behavior of indivi-

duals engaged in a vaccination game. Vaccine markets

often suffer from three imperfections: high concentra-

tion, network effects, and a health externality (conta-

gion). The first conclusion of the paper is that the

negative network externality is important as a market

distortion, as it may lead to significant welfare losses.

The second and main part of the paper develops a two‐

part per‐unit subsidy scheme that a social planner

could use to target both consumers and producers of

vaccines. The scope of such a subsidy scheme to induce

the firms to produce the first‐best output without

network effects (which is the most ambitious first‐best

target) is investigated. In many cases, while the first‐

best is attainable, it requires negative prices for

vaccines, which amounts to rewarding consumers to

induce them to vaccinate.

KEYWORDS

health externality, health policy, negative network effects,

pandemics

1|INTRODUCTION

Despite vaccines being widely considered by health professionals as the most effective tool for

the prevention and eradication of infectious diseases, vaccines have always remained a source

of controversy. In fact, the importance of this market for public health officials is often not

J Public Econ Theory. 2023;25:1229–1250. wileyonlinelibrary.com/journal/jpet © 2023 Wiley Periodicals LLC.

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matched by people's propensity to vaccinate, despite public awareness and promotion

campaigns for vaccines. For instance, global vaccination coverage is estimated at 80% for

Hepatitis B, 35% for the rotavirus vaccine (against diarrheal diseases, a leading cause of child

mortality), and 47% for yellow fever. For COVID‐19 in the United States, the rate is only 68.6%

in spite of the convenient and free availability of the vaccine. Vaccine hesitancy, as this

phenomenon is often termed, is a potent force that public health officials can simply not afford

to ignore. A historical account and analysis provided by Jana and Osborn (2013) goes as far as

referring to it as vaccinophobia.

1

In light of the direct (financial) and indirect perceived costs of vaccines, one reason behind

these significant gaps in coverage is the recognition that the larger the fraction of vaccinated

people, the less useful vaccines become to those not yet vaccinated, and therefore the lower

their willingness to incur the vaccination costs is. The underlying argument is clearly one of

free‐riding, a conclusion that is a direct implication of simple, agent‐based game‐theoretic

models of vaccination. Brito et al. (1991), Heal and Kunreuther (2005), Adida et al. (2013), and

Sorensen (2023) offer different versions of such games, the common key property of which is

that peoples' decisions to vaccinate are strategic substitutes.

2

A key prediction of these models

is that the fraction of people who opt not vaccinating is increasing the cost of the vaccine. The

notion that these simple models serve as a microfoundation for the fact that vaccine markets

are characterized by negative network effects on the demand side follows naturally and is

explicitly considered in Adida et al. (2013) and Amir et al. (2023).

The pioneering work of Veblen (1899) introduced the notion of bandwagon or positive

network effects in economics long ago. Negative network effects appeared initially as snob

effects in Leibenstein (1950), but were not investigated much in modern times. Nevertheless,

the influential studies by Rohlfs (1974,2001) and Katz and Shapiro (1985) are easily modified to

include the supply side for industries with negative network effects, following recent work by

Amir et al. (2023); also see Nuscheler and Roeder (2016).

The purpose of the present paper is to build on the recent study by Amir et al. (2023) and

provide new results on their model of vaccine markets with negative network effects. We adopt

a simple analog of the model by Katz and Shapiro (1985), with a linear inverse demand whose

intercept shrinks due to additive negative network effects. We adopt the well‐known solution

concept of rational‐expectations Cournot equilibrium (RECE), as in Rohlfs (1974), Katz and

Shapiro (1985), and Amir and Lazzati (2011). In such a setting, both firms and consumers

recognize the presence of negative network externalities and form rational and concordant

expectations as to how the latter affects the equilibrium outcome (also see Amir et al., 2021;

Garcia & Resende, 2011; Shapiro & Varian, 1998).

Exploiting the convenient specification of the model with linear demand and costs, the

unique RECE is easily fully characterized via closed‐form solutions for all variables of interest.

As argued in detail by Amir et al. (2023), the equilibrium properties of this model are consistent

with the main salient stylized facts that pertain to this industry, according to Arnould and

DeBrock (1996), Scherer (2007), and Danzon and Pereira (2011). These stylized facts may be

summarized as follows: (i) a natural monopoly or oligopoly with few firms as a stable market

1

Other relevant accounts may be found in Dasgupta et al. (2021) and Galiani (2022).

2

Just to mention some examples, Nganmeni et al. (2022) offer a cooperative games perspective. Hellmann and Thiele

(2022) consider voluntary testing and self‐isolation. Gallic et al. (2022) investigate the timing effects of vaccine arrival

on the optimal social‐distancing policy (see also Goenka et al., 2022; Makris, 2021). Finally, Federico et al. (2022)

consider optimal vaccination within a SIR model.

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