Voting over selfishly optimal tax schedules: Can Pigouvian tax redistribute income?

• Author: Darong Dai
• DOI: http://doi.org/10.1111/jpet.12459
• Published date: 01 September 2020
• Date: 01 September 2020

J Public Econ Theory. 2020;22:1660–1686.wileyonlinelibrary.com/journal/jpet1660

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© 2020 Wiley Periodicals LLC

Received: 20 November 2019

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Accepted: 15 June 2020

DOI: 10.1111/jpet.12459

ORIGINAL ARTICLE

Voting over selfishly optimal tax schedules:

Can Pigouvian tax redistribute income?

Darong Dai

Institute for Advanced Research, Key

Laboratory of Mathematical Economics

(SUFE), Ministry of Education of China,

Shanghai University of Finance and

Economics, Shanghai, China

Correspondence

Darong Dai, Institute for Advanced

Research, Key Laboratory of Mathematical

Economics (SUFE), Ministry of Education

of China, Shanghai University

of Finance and Economics, 200433

Shanghai, China.

Email: dai.darong@sufe.edu.cn and

darongdai@hotmail.com

Abstract

This paper studies pairwise majority voting over

selfishly optimal nonlinear income tax schedules

proposed by a continuum of individuals who differ

in privately observable skills and make consump-

tion comparisons, which creates a negative posi-

tional externality. It shows that the tax schedule

preferred by the median skill type will win the

voting contest. Given a reference consumption de-

fined as the average consumption in the popula-

tion, all skills face the same Pigouvian tax rate in

the utilitarian optimum, whereas in selfish optima

high skills face a Pigouvian tax rate larger than that

facing low skills, generating a novel income redis-

tributive effect. Under a constant elasticity of labor

supply, two more results are obtained. First, for

Pareto, Champernowne, Weibull, and lognormal

skill distributions, the selfishly optimal tax sche-

dule facing high (low) skills tends to be more pro-

gressive when the bottom‐skill's (top‐skill's) status

concern intensifies. Second, it identifies the con-

ditions under which, in the voting equilibrium,

high skills face higher marginal tax rates while low

skills face lower ones than what they face in the

utilitarian optimum.

1|INTRODUCTION

There is growing empirical evidence

1

suggesting the interdependence among individuals in the

form of status effects, showing that an individual's utility depends on his or her absolute

consumption (or income) as well as on how it compares to the consumption (or income) of

others.

2

Given the efficiency justification of using public policy remedies to attack this sort of

positional externalities (e.g., Frank, 2008; Layard, 1980; Stiglitz, 2019), as well as the evidence

reported by Senik (2009) and Clark and Senik (2010) that social comparisons increase the

demand for income redistribution, some questions concerning the design of tax policies can

be raised as follows.

How does the status‐seeking motive shape the structure of nonlinear income taxation? Does

the between‐individual externality generated by the desire for status lead to a more progressive

or less progressive income tax system? How do the externality‐correcting and income‐

redistributing roles of a tax policy interact?

To address these issues with accounting for political feasibility, I focus on the nonlinear tax

schedules that emerge from political competition between schedules offered by the individuals

populating the economy. Individuals differ only in skill levels, and each individual is privately

informed about his skill type that determines his competitive wage rate and proposes a selfishly

optimal tax schedule in the sense of maximizing the utility of his own type. Also, I incorporate a

reference consumption level into individuals' utility to characterize relative consumption

concerns. Each individual is regarded as small and, hence, takes the reference consumption as

given when making consumption and labor supply decisions. As usual, I let the reference

consumption level be type‐independent, with a lower bound defined as the average con-

sumption in the population.

3

In effect, this reference consumption constraint must be binding

in the solution to optimal taxation programs. In consequence, a feasible tax schedule must meet

the added constraint imposed on the reference consumption, in addition to be incentive

compatible and respect the government budget constraint (or resource constraint under the

Walras' Law).

I establish first the socially optimal redistributive tax policy as a normative benchmark, and

then I derive and characterize the equilibrium taxation scheme under pairwise majority voting

over the feasible set of selfishly optimal nonlinear income tax schedules. Under the reference

consumption constraint described above, all skills face the same Pigouvian tax rate in the social

optimum. In contrast, there are two different Pigouvian tax rates in the selfish optimum pro-

posed by any skill type between the endpoints of skill distribution, with high skills uniformly

facing the larger one while low skills uniformly facing the smaller one. Since a selfish proposer

of any skill type prefers to redistribute resources from other skill types towards himself, the

objective function used by him to determine his optimal income schedule must employ the

1

See, for example, Solnick and Hemenway (1998), Alpizar, Carlsson, and Johansson‐Stenman (2005), Bowles and Park

(2005), Luttmer (2005), Clark, Frijters, and Shields (2008), Heffetz and Frank (2011), Oh, Park, and Bowles (2012),

Mujcic and Frijters (2015).

2

Throughout, “status seeking motive,”“status concern,”“relative consumption concern,”“consumption comparison,”

“envy,”“jealousy,”“negative positional externality”and “negative consumption externality”are interchangeable.

3

I follow the suggestion from an anonymous referee and examine other forms of reference consumption constraint in

Appendix C of the Online Appendix. Indeed, I provide the tax formulas for socially optimal and selfishly optimal

marginal tax rates under two alternative constraints, one is type‐dependent to capture the motive of pecuniary emu-

lation defined by Veblen (1899) and the other is simply imposing the median‐skill type's consumption as the lower

bound of a common reference consumption. Under these two constraints, I show that the Pigouvian tax in both the

social optimum and selfish optimum features income redistribution.

DAI

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