Collusion under different pricing schemes

• DOI: http://doi.org/10.1111/jems.12392
• Author: Florian Gössl,Alexander Rasch
• Date: 01 October 2020
• Published date: 01 October 2020

J Econ Manage Strat. 2020;29:910–931.wileyonlinelibrary.com/journal/jems910

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© 2020 Wiley Periodicals LLC

Received: 6 February 2018

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Revised: 28 February 2020

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Accepted: 16 June 2020

DOI: 10.1111/jems.12392

ORIGINAL ARTICLE

Collusion under different pricing schemes

Florian Gössl

1

|Alexander Rasch

2,3

1

AXA Konzern AG, Cologne, Germany

2

Duesseldorf Institute for Competition

Economics (DICE), Duesseldorf, Germany

3

Leibniz Centre for European Economic

Research (ZEW), Mannheim, Germany

Correspondence

Alexander Rasch, Duesseldorf Institute for

Competition Economics (DICE),

University of Duesseldorf,

Universitaetsstrasse 1, 40225 Duesseldorf,

Germany.

Email: rasch@dice.hhu.de

Abstract

We analyze collusive outcomes under different pricing schemes in a differ-

entiated product market in which customers have elastic demand. Starting

with a situation in which firms can set two‐part tariffs to price discriminate, we

consider two policy interventions that ban price discrimination: Firms must set

(a) linear prices or (b) fixed fees. We find that collusion at maximum prices

becomes harder to sustain under linear prices. By contrast, the analysis shows

that the fixed fees policy facilitates collusion at maximum prices. The results

have important implications for competition policy.

1|INTRODUCTION

We analyze the impact of different pricing structures on firms' ability to maintain collusion. We examine the effects of

nonlinear pricing and the outcomes of related regulatory policies designed to address the practice, which is common in

many industries. Examples of businesses that employ nonlinear pricing include amusement parks, gas, media markets,

mobile telecommunications, and electricity. In these industries, the pricing structures typically consist of (at least) two

components: a fixed (entry) fee, which is independent of the quantity demanded, and a linear per‐unit price.

The question of whether price discrimination helps to fight collusion has received considerable attention from both

an academic and a practical point of view (see some motivating examples below). The literature has analyzed this issue

in terms of cases of first‐and third‐degree price discrimination (see below). Generally speaking, these types of price

discrimination are found to be good for competition and make collusion more difficult to sustain. However, the

question of the impact of second‐degree price discrimination on firms' ability to sustain collusion remains unanswered.

This article addresses this gap.

1

We investigate whether and how the possibility of coordinating on multiple price components instead of agreeing

upon one single (linear or fixed) collusive price influences firms' ability to sustain collusion. To derive policy re-

commendations, we also examine the effects on total welfare and customer surplus. To this end, building on the setup

by Yin (2004) who models two‐part tariff competition in duopoly, we analyze the incentives to collude under different

pricing schemes in a differentiated products setup (à la Hotelling, 1929) with variable demand. Total demand is elastic,

as local demand—the demand of a single customer—decreases in the price and in the distance to the respective firm

(i.e., considering transport costs). We start by analyzing collusive incentives in the case in which firms can price

discriminate and coordinate on two‐part tariffs. Turning to the situations in which price discrimination is prohibited,

we find that the comparison with regard to the sustainability of collusion at monopoly prices crucially depends on the

type of policy intervention—that is, whether authorities order the use of linear or fixed fees only. The scope for

collusion is largest when firms use fixed fees only, whereas collusion is most difficult to sustain when firms set linear

prices only.

What renders collusion particularly less attractive under linear pricing compared with nonlinear pricing is the

higher additional benefit from reducing the linear price: Not only does the reduction enlarge a deviating firm's market

share, but it increases inframarginal demand at the same time. Due to a lower linear collusive price, this effect is less

pronounced under two‐part tariffs. Moreover, this effect is even less pronounced under fixed fees, which explains why

collusion at monopoly prices is easiest to sustain in that scenario.

Our analysis has important implications for customer and total welfare—and, hence, for competition policy. In any

case, banning price discrimination turns out to be the right thing to do. Our model predicts that when authorities follow

a consumer standard, banning fixed fees is optimal. In this case, consumer surplus is always higher under linear pricing

than under two‐part tariffs—independent of whether firms collude or compete. By contrast, when authorities are

interested in maximizing social welfare, our analysis shows that linear prices should be banned. Again, independent of

whether the market is collusive or competitive, welfare is always highest under fixed fees.

1.1 |Motivating cases

Competition authorities have been debating whether to ban price discrimination and what the effects of such a ban on

collusion are. When firms use two‐part tariffs as a type of second‐degree price discrimination,

2

a ban can come in two

different forms: banning linear prices or banning fixed prices. Indeed, such regulatory interventions have been pro-

posed in markets in which price discrimination and collusion are important aspects. For example, in the United

Kingdom, the “big six”energy suppliers faced investigations over price‐fixing allegations.

3

At the same time, the Office

of Gas and Electricity Markets (Ofgem) introduced several restrictions on the retail residential energy market.

4

A

central proposal by Ofgem was that Ofgem itself would set a standardized (uniform) fixed (or “standing”) charge for all

standard tariffs, and that suppliers would then compete on a single unit rate for each standard tariff (Littlechild, 2014).

Such an intervention thus equates to banning of fixed fees.

Another prominent example is the market for (mobile) telecommunication services. Numerous investigations across

the world have documented price fixing in this market. Examples include the case of mobile phone service providers in

Hong Kong in 2000 (Chen & Lin, 2002) and a convicted mobile phone cartel in France (de Mesnard, 2009).

5

Moreover,

the different pricing components and subscription plans, which are important in this market, appear to play crucial

roles in these collusive cases. As Larsen (2010) points out in his extensive study of (allegedly) collusive behavior

regarding text messaging in the United States, firms set supracompetitive pay‐per‐use (PPU) prices for those customers

who did not opt for a monthly text plan, or exceed their monthly limit of text messages. Indeed, the author suggests that

“[a]s a first step, the FCC [Federal Communications Commission] should set a price cap on PPU rates closer to the

marginal cost of the service”(p. 242). In other words, competition in the linear price component would be restricted.

6

Furthermore, in an investigation in South Korea, the country's three largest wireless carriers were accused of

collusion and other unfair practices. In June 2017, the government announced measures to lower mobile expenses by

increasing the monthly discount rate for new mobile phone subscribers from 20% to 25%. Additionally, the government

ordered carriers to exempt the basic monthly subscription fee (11,000 won, approximately $9.90 USD) for elderly and

low‐income household members.

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Similar to the Ofgem example, such an intervention means that firms can no longer

compete in fixed fees.

1.2 |Related literature

Although price discrimination and nonlinear tariffs are important features of antitrust concerns, the literature on the

impact of different pricing schemes on collusion is sparse.

8

Concerning the relationship between third‐degree price

discrimination and collusion, Liu and Serfes (2007) investigate the impact of the availability of customer‐specific

information for market segmentation in a linear‐city model on the sustainability to collude. A higher degree of market

segmentation accompanied by a more diversified pricing structure is possible as the quality of customer information

increases. The authors show that collusion is harder to sustain as the firms' ability to segment customers improves.

A related study to Liu and Serfes (2007) is Colombo (2010). The author allows for different degrees of product

differentiation (i.e., firms are not located at the extremes of the linear city), and analyzes perfect (or first‐degree) price

discrimination. With perfect price discrimination, firms may set prices based on the exact location of a customer in so‐

called delivered pricing.

9

The author finds that collusion is easier to sustain the lower transport costs are,

10

and that

colluding on discriminatory prices is harder than on a uniform price.

11

For third‐degree price discrimination, Helfrich and Herweg (2016) find that price discrimination helps to fight

collusion not only under best‐response asymmetries (lower static Nash equilibrium profits under price discrimination)

GÖSSL AND Rasch

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