Multiple‐quality Cournot oligopoly and the role of market size

• DOI: http://doi.org/10.1111/jems.12387
• Published date: 01 October 2020
• Date: 01 October 2020

J Econ Manage Strat. 2020;29:932–952.wileyonlinelibrary.com/journal/jems932

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© 2020 Wiley Periodicals LLC

Received: 27 November 2018

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Revised: 2 May 2020

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Accepted: 5 June 2020

DOI: 10.1111/jems.12387

ORIGINAL ARTICLE

Multiple‐quality Cournot oligopoly and the role of

market size

Ngo Van Long

1,2

|Zhuang Miao

3

1

Department of Economics, McGill

University, Montreal, Quebec, Canada

2

Hitotsubashi Institute of Advanced Study,

Hitotsubashi University, Tokyo, Japan

3

School of International Trade and

Economics, Central University of Finance

and Economics, Haidian District, Beijing,

China

Correspondence

Zhuang Miao, School of International

Trade and Economics, Central University

of Finance and Economics, 39 South

College Road, Haidian District, 100081

Beijing, China.

Email: cufemiao@163.com

Abstract

We model an oligopoly where firms are allowed to freely enter and exit the

market and choose the quality level of their products by incurring different

setup costs. Using this framework, we study the mix of firms in the long‐run

Cournot–Nash equilibrium under different cost structures and the effects of

market size on market outcomes. Specifically, we consider two alternative

specifications of cost structure. In the first specification, quality upgrading

requires a large increment in the setup cost or R&D investment. Under this

cost structure, we show that in the Nash equilibrium, each firm specializes in a

single quality level, and an increase in the market size leads to (a) an increase

in the fraction of firms that specialize in the high‐quality product, (b) an

increase in the market share of the high‐quality product, and (c) a reduction in

firms’markups and in markup dispersion. Under the second type of cost

structure where quality upgrading only requires higher marginal cost, we find

that all firms will produce both types of product, and the value share of the

high‐quality product increases as the market expands, but in quantity terms,

the market share of the high‐quality product does not change. Finally, we find

that trade liberalization has broadly similar effects to that of a market ex-

pansion, but the supply of the high‐quality product from the smaller economy

may decrease.

1|INTRODUCTION

Do increased competitive pressure and/or market expansion induce firms to upgrade the quality of their products,

leading to an increase of the average quality of products in the market place? Can market expansion lead to the demise

of firms that produce the low‐quality products? Does trade liberalization have similar effects on product quality to those

of a pure market expansion? The answers to these questions may well depend on the nature of the industry under

consideration, in particular its cost structure and possibly on its mode of competition. While there is an existing

theoretical and empirical literature that has shed light on these questions (see, e.g., Berry & Waldfogel, 2010;

Fajgelbaum, Grossman, & Helpman, 2011; Vives, 2008), there remain some gaps in the analysis of the role of the

trade‐off between fixed cost and marginal cost in the quality upgrading process and of firms’decision on whether they

should offer a wide range of qualities, or, instead, specialize in one end or the other of the quality spectrum. Moreover,

the existing studies on the relation between market size and products’quality are incomplete. We apply our theoretical

framework to the study of this issue and expand the relevant literature by adding the analysis under the Cournot

oligopoly competition mode and allowing variable markups.

1

In this paper, we develop the model of Cournot oligopoly with vertically differentiated products and show how the

effect of market expansion on the average quality depends crucially on the industry's cost structure. We demonstrate

that the equilibrium features of the model depend on whether the additional investments required to produce the high‐

quality product involve sinking large costs (i.e., quality upgrading is intensive in overhead factors, such as R&D) or

incurring higher variable costs per unit of quality (i.e., quality upgrading is intensive in the intermediate inputs). One of

our main findings is that when the upgrading process is intensive in the overhead factors, in equilibrium each firm will

choose to produce either the high‐quality product, or the low‐quality product, but not both. Another major finding is

that, under this cost configuration, an increase in the market size will increase the number of high‐quality producers,

decrease the number of low‐quality producers, leading to a fall in the relative price and relative markup of the high‐

quality product and an increase in the market share of high‐quality firms. When, on the contrary, quality upgrading is

intensive in intermediate inputs and fixed cost is independent of quality, each firm will produce both the high‐and low‐

quality products, and an increase in market size will increase the relative price, relative markup, and the market share

of the high‐quality product in value terms, while leaving the ratio of high‐to low‐quality outputs unchanged.

Concerning the effects of partial trade liberalization between two countries, we find that, in broad outlines, the

results are similar to that of an increase in market size. However, when the two countries are of different sizes, we find

that as the trade costs decrease, in the small country, the ratio of high‐to low‐quality firms may change in a non-

monotonic fashion. This is due to the relocation decision of high‐quality firms from the small country to the large

country, which depends on trade costs. Indeed, firms choose their location based on the balance of market demand and

market competition intensity.

Our paper is an extension of the model of strategic product‐line choice by J. P. Johnson and Myatt (2006). Different

from J. P. Johnson and Myatt (2006), our model assumes more general cost structures. Thus, while J. P. Johnson and

Myatt (2006) assumethat all firms have the same fixed cost,

2

we consider two different cost scenarios. In the first scenario,

firms that want to producethe high‐quality product must incur a higher‐quality‐adjusted fixedcost, and this enables them

to produce the high‐quality product at a smaller quality‐adjusted marginal cost than that of the lower‐quality product. In

the second scenario, all firms have the same fixed cost but marginal costs differ: The high‐quality product requires much

more expensive raw materials, such that the quality‐adjusted marginalcost of the high‐quality product is higher thanthat

of the low‐quality product. In this alternative scenario, we find that all firms will produce both products.

3

Our results are broadly consistent with the empirical literature. Berry and Waldfogel (2010) examine descriptive data

on the relationship between product quality and market size. Theyfind that in one industry (restaurants),where quality is

created largely through variable costs, such as food ingredients and skilled labor time, an increase in market size will

increase the number of varieties, and while there will be more high‐quality restaurants per capita, there is “no evidence

that average quality increases as well (p. 25).”In contrast, in the newspaper industry, where quality is produced by fixed

cost rather than marginal cost, Berry and Waldfogel (2010) find that larger market sizes areassociatedwithhigheraverage

quality in the market. Our results on decreasing markups and increasing product quality under trade liberalization are

also consistent with empirical studies. Indeed, using a model where intermediate good producers are oligopolists,

Edmond, Midrigan, and Xu (2015) report their calibration result that increased exposure to trade reduces the markup

distortion by one‐half. Using data from different countries, Levinsohn (1993), Harrison (1994), and Krishna and Mitra

(1998) reach the similar conclusion that exposure to foreign competition leads to lower markups, and this effect is more

pronounced for larger firms. Along the same veins, using highly disaggregated firm–product‐level data from China over

the period 2000–2006, Li and Miao (2017) find that market expansion in the form of trade liberalization induces China's

high‐productivity firms to increase the fraction of high‐quality goods they export.

Our analysis has implications for firms’strategies. Should a firm that is capable of producing both high‐and low‐

quality products offer a large range of quality to cater for all types of consumers, or should it focus on the high‐quality

end of the product spectrum? According to our model, if quality is produced mainly by fixed cost, and if there are other

firms in the industry that choose to incur the low fixed cost (which disqualify them from producing the high‐quality

product), then the high‐quality firms should specialize in the high‐quality product, because supplying both types of

products will create an adverse cannibalization effect, reducing consumers’demand for their high‐quality good.

4

This

result seems to be applicable to the newspaper industry, where, as argued by Berry and Waldfogel (2010), quality is

produced mainly by fixed cost. We do not observe newspaper companies that sell low‐quality versions of their high‐

quality products. For industries that operate under a different cost configuration, where quality is produced by variable

costs while fixed cost is independent of quality, our model predicts that each firm would sell both the high‐and low‐

quality versions. This is consistent with the case of plasma televisions. Indeed, Sony, Samsung, and Mitsubishi all offer

product lines with varying degrees of resolution.

VAN LONG AND MIAO

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