On the distributional effects of commodity taxation

• Published date: 01 August 2019
• Author: Oriol Carbonell‐Nicolau
• Date: 01 August 2019
• DOI: http://doi.org/10.1111/jpet.12370

Received: 2 July 2018

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Revised: 28 January 2019

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Accepted: 22 March 2019

DOI: 10.1111/jpet.12370

ORIGINAL ARTICLE

On the distributional effects of commodity

taxation

Oriol Carbonell‐Nicolau

Department of Economics, Rutgers

University, New Brunswick, New Jersey

Correspondence

Oriol Carbonell‐Nicolau, Department of

Economics, Rutgers University, 75

Hamilton St., New Brunswick, NJ 08901.

Email: carbonell-nicolau@rutgers.edu

Abstract

A commodity tax system is inequality reducing if the

after‐tax distribution of income Lorenz dominates the

before‐tax distribution of income, regardless of initial

conditions. This paper identifies necessary and sufficient

conditions under which an ad valorem commodity tax

system is inequality reducing, shedding light on the role

of taxing luxury—as opposed to necessary—commod-

ities in the equalization of after‐tax incomes.

KEYWORDS

D63, D71, commodity taxation, income inequality, Lorenz domination,

progressive taxation

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INTRODUCTION

The study of indirect taxation has traditionally revolved around the efficiency properties of

commodity tax systems. There is an extensive literature on optimal indirect taxation, which

dates back to the seminal work of Ramsey (1927).

1

The conditions under which a commodity

tax system minimizes its associated deadweight loss are well understood, but there is very little

work dealing with the distributional effects of commodity taxation as they pertain to income

inequality. Some authors have advocated consumption taxes as a means to encourage saving,

arguing that a progressive consumption tax—whereby each household is taxed on its

consumption, not income, at graduated rates—can mimic the distribution of the tax burden

in the current income tax (Seidman, 2003). Other authors have justified differential tax rates

across goods on grounds of equity, making a case for lower tax rates on goods consumed

disproportionately by low‐income households (Mirrlees et al., 2011, Chapter 6).

2

The

J Public Econ Theory. 2019;21:687–707. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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687

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See, for example, Salanié (2003) and references therein.

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The discussion in Mirrlees et al. (2011, Chapter 6) (see, in particular, their Section 6.2) propounds equity and efficiency arguments both for and against tax

uniformity. While equity principles favoring differentiated taxation—as a means of redistribution—are emphasized when indirect taxation is considered in

isolation, the takeaway from the general discussion in Mirrlees et al. (2011, Chapter 6) is that indirect taxationshould be uniform and that redistributive goals

should be left for direct tax and transfer policies.

discussion, however, is kept at an informal level, and can hardly be seen as a rigorous

foundation for the income inequality effects of commodity taxation.

This paper is an attempt to understand the conditions under which commodity taxation

reduces the inequality of the after‐tax income distribution. The analysis conducted here is akin

to that underlying the normative foundation for progressive income tax schedules based on the

relative Lorenz ordering, initiated by Jakobsson (1976) and Fellman (1976), and extended by

other authors in several directions (see, inter alia, Carbonell‐Nicolau & Llavador, 2018, 2019a,

2019b; Ebert & Moyes, 2000, 2007; Eichhorn, Funke, & Richter, 1984; Formby, James Smith, &

Sykes, 1986; Hemming & Keen, 1983; Ju & Moreno‐Ternero, 2008; Kakwani, 1977; Latham,

1988; LeBreton, Moyes, & Trannoy, 1996; Liu, 1985; Moyes, 1988, 1994; Preston, 2007; Thistle,

1988; Thon, 1987)

The paper confines attention to the linear case—the Ramsey setting—and leaves the case of

“mixed taxation,”covering the combined effects of commodity and (nonlinear) income

taxation, for future research. The received wisdom from the literature on optimal taxation is the

Atkinson–Stiglitz principle (Atkinson & Stiglitz, 1976), which asserts that, under separability of

utility between labor and consumption, indirect taxation is superfluous. Some remarks as to

why the Atkinson–Stiglitz principle is likely to fail in the present framework are furnished in

Section 4.

Section 2 presents a preliminary analysis of the case when pre‐tax incomes are unresponsive

to taxation. Given an initial distribution of incomes, a commodity tax system gives rise to an

after‐tax distribution of disposable incomes. Theorem 1 identifies necessary and sufficient

conditions on primitives under which a commodity tax system reduces income inequality—in

the sense of the relative Lorenz ordering—regardless of the initial income distribution it is

applied to. These conditions shed light on the distributional effects of taxing luxury goods—as

opposed to necessary goods. In particular, any progressive commodity tax system that taxes

luxuries and (weakly) subsidizes necessities leads to a decline in inequality (Corollary 1).

Section 3 extends the analysis to the case of endogenous income. Theorem 2 characterizes

inequality reducing commodity tax systems in the presence of potential effects of taxes on labor

supply. This result reveals that the condition defining luxuries (resp., necessities) is no longer

the sole determinant of the income inequality effects of commodity taxation: the wage elasticity

of (before‐tax) income also plays an important role. In particular, the effect of a luxury tax on

this elasticity might counter the induced bias of the tax burden towards the rich. Section 3

develops intuition for the main characterization in Theorem 2, while the formal proof is

relegated to the appendix. A number of applications illustrate Theorem 2.

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EXOGENOUS INCOME

Even though the full‐fledged model (developed in Section 3) encompasses the case of exogenous

income, it is useful to begin with the analysis of this case.

Consumer behavior is described by means of a social utility function





→u:

K

+, defined

over consumption bundles

x

, where

x

xx=( ,…,

)

K1

is a bundle of

≥

K1

traded goods. It is

assumed that xu()

is strictly increasing, continuous, and strictly quasi‐concave.

3

Let

s′

denote the collection of all utility functions satisfying the above conditions.

3

The results of the paper hold intact if one considers instead utility functions of the Cobb–Douglas type, or quasi‐linear utility functions, which fail strong

monotonicity and strict quasi‐concavity on (some of) the axes.

688

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CARBONELL‐NICOLAU