Product Differentiation, Competitive Toughness, and Intertemporal Substitution

• DOI: http://doi.org/10.1111/sjoe.12304
• Author: Vera Ivanova,Philip Ushchev
• Date: 01 July 2019
• Published date: 01 July 2019

Scand. J. of Economics 121(3), 1244–1269, 2019

DOI: 10.1111/sjoe.12304

Product Differentiation, Competitive

Toughness, and Intertemporal Substitution*

Vera Ivanova

National Research University Higher School of Economics, St Petersburg 190068, Russia

viivanova@hse.ru

Philip Ushchev†

National Research University Higher School of Economics, St Petersburg 190068, Russia

fuschev@hse.ru

Abstract

Standard measures of competitive toughness fail to capture the fact that, as consumers optimize

intertemporally,fir ms operating todaycompete with (as yet non-existent) businesses, which will

be started tomorrow. We develop a two-tier constant elasticity of substitution (CES) model of

dynamic monopolistic competition in which the impact of product differentiation on the market

outcome depends crucially on the elasticity of intertemporal substitution (EIS). The degree of

product differentiation per se fails to serve as a meaningful indicator of competitive toughness:

what matters is its cross-effect with EIS. We also extend the model to the case of non-CES

preferences in order to capture variable mark-ups.

Keywords: Elasticity of substitution; love for variety; mark-ups; monopolistic competition;

overlapping generations

JEL classification:D43; D90; D91; L13

I. Introduction

In many models of product differentiation used in industrial organization

(see chapters 4 and 5 of Belleflamme and Peitz, 2015), toughness of

competition is captured by a single parameter reflecting substitution

between varieties of a differentiated product. For example, in monopolistic

competition models based on Dixit and Stiglitz (1977), the role of such a

key parameter belongs to the elasticity of substitution.1Being essentially

static, these models do not take into account the fact that, as consumers

*The article was prepared within the frameworkof the HSE University Basic Research Program

and funded by the Russian Academic Excellence Project ‘5-100’. We thank Kristian Behrens,

Grigory Kosenok, Alexander Nesterov,YuliaParamonova, Sergey Slobodyan, Alexander Tarasov,

Pavel Tretyakov, and two anonymous referees, for helpful comments. Weowe special thanks to

the late Evgeniy Zhelobodko for encouraging us to start this project.

†P. Ushchev is now at Monash University, Australia.

1Another example is provided by spatial competition models of Hotelling (1929), wherethe key

parameter is the transport cost per unit of distance in the product space.

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The editors of The Scandinavian Journal of Economics 2018.

V. Ivanova and P. Ushchev 1245

optimize intertemporally, firms currently operating on the market compete

with firms – as yet non-existent – that will be launched in the future. In

this paper, we seek to show that taking this effect into account might revert

the standard intuition that greater product differentiation implies softer

competition.

To achieve this purpose, we develop a simple model of dynamic

monopolistic competition where the impact of product differentiation on

the market outcome depends crucially on the elasticity of intertemporal

substitution (EIS). The model shows how the degree of product

differentiation per se can fail to serve as a meaningful indicator of

competitive toughness because of the intertemporal nature of consumer

decisions.

Our model augments Dixit and Stiglitz (1977) in two ways. First, the

interplay between product differentiation and EIS is captured by using two-

tier constant elasticity of substitution (CES) preferences: the intratemporal

CES utility defined across the product range within a period is nested

into the upper-tier lifetime CES utility. Secondly, in allocating their labor

endowments, variety-loving individuals face a trade-off between wage labor,

which brings immediate income, and production of capital, which promises

an income flow in the future.2

Unlike numerous dynamic settings involving imperfect competition,

where a homogeneous final good is typically produced by means of

a differentiated intermediate good (Benassy, 1987, 1993; Grossman and

Helpman, 1990; Romer, 1990; Chou and Shy, 1991), our model describes

a one-sector economy with a differentiated final good.3This feature of

the model is not accidental: the fact that consumers are variety-lovers is

an essential part of the story, the reason being that we focus on how

preferences affect firm behavior and shape the market outcomes. The central

message of the paper is that the value of EIS is decisive for the impact of

product differentiation on the market outcome.

Our main findings can be summarized as follows. First and foremost,

we provide clear-cut comparative statics of the steady-state equilibrium

with respect to the demand-side characteristics. Namely, we show that

an increase in substitutability across varieties supplied at the same time

2Thus, we treat the concept of capital rather broadly, without focusing on specific features of

“physical” or “financial” capital. Improving labor qualification (i.e., investingin human capital)

can also be viewed as capital production.

3A recent example of using a similar approach is Bilbiie et al. (2012). This paper is very

different from ours, both in terms of economic issues addressed (they focus on pro- versus

counter-cyclical behavior of variable mark-ups) and in terms of technical implementation (they

work in continuous time and infinitely lived consumers). On top of that, these authors work

with a logarithmic intertemporal utility, while we work with CES with an arbitrary degree of

intertemporal substitution, which is more general.

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The editors of The Scandinavian Journal of Economics 2018.