Multi‐part tariffs and differentiated commodity taxation

• Published date: 01 September 2020
• Author: Antonio Russo,Mohammed Mardan,Anna D'Annunzio
• Date: 01 September 2020
• DOI: http://doi.org/10.1111/1756-2171.12340

RAND Journal of Economics

Vol.51, No. 3, Fall 2020

pp. 786–804

Multi-part tariffs and differentiated

commodity taxation

Anna D’Annunzio∗

Mohammed Mardan∗∗,∗∗∗

and

Antonio Russo‡,§

We study commodity taxation in markets where firms, such as Internet Service Providers, en-

ergy suppliers, and payment card platforms, adopt multi-part tariffs. We show that ad valorem

taxes can correct underprovision and hence increase welfare, provided the government applies

differentiated tax rates to the usage and access parts of the tariff. We obtain this result in differ-

ent settings, including vertically interlinked markets, markets where firms adopt menus of tariffs

to screen consumers, and where they compete with multi-part tariffs. Our results suggest that

exempting these markets from taxation may be inefficient.

1. Introduction

Multi-part tariffs are common among telephone and Internet connection providers, energy

distributors (electricity and gas), payment card platforms, and parking operators. These firms

often charge consumers a fee for access in addition to a payment that depends on the amount

or duration of usage. These markets are generally characterized by market power on the sup-

ply side, which is likely to result in underprovision.1Governments often apply indirect taxation

(e.g., ad valorem and excise taxes) to the above industries, and given their importance in modern

∗TBS Business School; dannunzio.anna@gmail.com.

∗∗Norwegian School of Economics, CESifo; mohammed.mardan@nhh.no.

∗∗∗NoCeT.

‡Loughborough University; a.russo@lboro.ac.uk.

§CESifo.

We thank David Agrawal, Jan Brueckner, Youssef Benzarti, Jacques Crémer, Sebastian Kessing, Marko Runkel, and

Stephen Smith for comments on an early version of this article. Wealso thank audiences at ETH Zurich 2016, University

of Exeter 2016, ToulouseSchool of Economics 2017, LAGV conference 2016, IIPF conference 2016, CESifo PSE con-

ference 2017, OFS Workshopon Indirect Taxes 2017, CESifo Summer Institue 2019 (Taxation in the Digital Economy),

and CSEF-IGIER Symposium on Economics and Institutions 2019. We are grateful to the Editor, DavidMyatt, and to

three anonymous referees for insightful comments that substantiallyimproved the article. Part of this research was carried

out while Anna D’Annunzio was at CSEF (University FedericoII, Naples). All errors are our own.

1For example, the main U.S. cable operators hold de facto monopolies for high-speed services in several local

markets. The FederalCommunications Commission (FCC) repor ted that about 20% of households haveaccess to a single

786 © 2020, The RAND Corporation.

D’ANNUNZIO, MARDAN, AND RUSSO / 787

economies, the question arises of whether and how to design taxes without seriously distorting

provision and reducing growth. As we argue shortly below, this question is part of an ongoing

policy debate regarding the reform of indirect taxes applying to essentialser vices. However, quite

surprisingly, existing research has devoted little attention to the design of taxation in presence of

multi-part tariffs.

Motivated by the above considerations, we study taxation of goods and services when

providers charge multi-part tariffs. We explore a relevant dimension along which taxes can be

designed to reduce their distortionary impact: the parts of the tariff to which they apply. This

dimension has so far been ignored by the literature, although there are several examples of such

differentiation in reality.2We show that the government can correct underprovision, and hence

increase welfare, with a positive ad valorem tax on usage or access.

Our findings hinge on a simple observation. When a seller adopts linear pricing, it faces

a trade-off because, to gain revenue by selling marginal units, it must reduce its revenue from

inframarginal ones. As a result, suppliers operate on the elastic part of the demand curve in

equilibrium. Thus, if the government introduces a commodity tax (either unit or ad valorem),

the suppliers’ optimal response is to reduce provision. Consequently, if the good or service is

underprovided (as it is usually the case with imperfect competition), taxation aggravates the

distortion (Auerbach and Hines, 2002). However, when suppliers adopt multi-part tariffs, the

logic governing their choice of prices is different. Typically, suppliers design the usage fees to

induce the level of usage that maximizes the net surplus from consumption, which they can

capture via the access fees (Oi, 1971). As we show, this logic implies that taxation can have

counterintuitive effects, primarily because the supplier may not operate on the elastic part of

demand. Hence, ad valorem taxes can increase output, provided that different tax rates are set

on the “usage” and “access” part of the tariff. Thus, differentiated ad valorem taxes can produce

a double dividend, by correcting the distortions due to market power while raising revenue for

the government. In contrast, we do not find efficiency-enhancing effects for unit or uniform ad

valorem taxes.

In Section 3, we introduce an ad hoc model to convey the basic mechanism. We then pro-

vide foundations to this model, exploring several settings where underprovision takes place in

presence of multi-part tariffs. First, we consider a model with identical consumers and a mo-

nopolist providing access to a piece of infrastructure which is essential to consume some final

goods (Section 4). Examples include Internet service providers and payment-card systems. Al-

though the infrastructure supplier can recover consumer surplus via the access fee, consumers

are charged a usage fee higher than marginal cost in equilibrium. As shown by Economides and

Hermalin (2015), restricting consumption at the margin allows the infrastructure supplier to cap-

ture part of the surplus that would otherwise accrue to the sellers of final goods. The combination

of this fee with the mark-up set by final good suppliers implies that there is underprovision. We

show that the government can correct this distortion with a positive ad valorem tax on usage, as

long as marginal costs are not exceedingly large. If this condition holds, the equilibrium quantity

lies on the inelastic part of consumer demand, implying that the supplier’s optimal response to

the tax is to decrease the usage fee and increase provision. We extend this model in Section 6

where we consider a duopoly of infrastructure providers, showing that our main results continue

to hold.

Second, we consider taxation when the infrastructure provider offers a menu of tariffs to

screen different consumer types (Section 5). We assume perfect competition in the final goods

broadband provider for a service of up to 4 Mbits/s. This share rises to 30% and 55% for speeds up to 10 Mbit/s and 25

Mbits/s, respectively (see https://www.fcc.gov/document/chairman-remarks-facts- and-future-broadband-competition).

2For instance, excise taxes on either access or usage existin the telecom sector. In several U.S. states, subscribers

to wireless telecommunication services pay a separate per-line tax on top of ad valorem and other state-leveltaxes. Other

examples include taxes on SMS, calls, handsets, and SIM cards, applied by countries such as Argentina, Brazil, Mexico,

Greece, Turkey, Ukraine, and Pakistan (Katz, 2015; Matheson and Petit, 2017).

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