Heterogeneous firms, urban costs and agglomeration

• Date: 01 September 2020
• Author: Yiming Zhou
• DOI: http://doi.org/10.1111/ijet.12194
• Published date: 01 September 2020

doi: 10.1111/ijet.12194

Heterogeneous firms, urban costs and agglomeration

Yiming Zhou∗

This paper explores how the interaction between firm heterogeneity, urban costs and transport

costs determines spatial configuration across regions within a simple general equilibrium model.

Weshed light on how firm heterogeneity affects the centrifugal and centripetal forces and reshapes

the spatial configuration of an urban space economy. We show analytically that an increase in

firm heterogeneity increases the range in which a symmetric equilibrium is stable. In addition,

full agglomeration is shown to be always sustainable, which complements existing results in

literature.

Key wor ds firm heterogeneity, urban cost, agglomeration

JEL classification F12, F22, R12

Accepted 18 June2018

1 Introduction

The canonical model in the new economic geography (NEG) literature (Krugman 1991a) demon-

strates that firms and workers tend to concentrate spatially in order to take advantage of large

local markets and save on the transport costs of goods across regions. Yet, the literature in urban

economics, dating back to Alonso (1964), Mills (1967) and Muth (1969), emphasizes that spatial

concentration generates urban costs within regions: people spend a large proportion of income on

land rents and a lot of time on commuting.1Indeed, the striking importance of urban costs for

economic agglomeration is evident, as noted by Behrens et al. (2014): “cities result from a trade-off

between agglomeration economies and urban costs.”

Regional scholars have long attempted to integrate urban costs into NEG models. For instance,

Helpman (1998) introduced a housing market into an economic geography model in which workers

were mobile. However, commuting costs were not considered in his model because of the absence

of spatial extension in his setting. P߬

uger and Tabuchi (2010) provided a theoretical framework in

which land is used in production. Independently,Tabuchi (1998) attempted to unify economics `ala

Alonso (1964) and NEG by developing a model allowing for the interplay between urban commuting

costs and transport costs. However, his analysis is limited to two extreme cases of zero and infinite

transport costs. Murata and Thisse (2005) overcame this difficulty and proposed a tractable

∗School of International Trade and Economics, Jiangxi University of Finance and Economics, Nanchang, China. Email:

zhouchn@hotmail.com.

I am grateful to the editor,Kazuo Nishimura, and an anonymous referee for helpful suggestions. This paper has also ben-

efited from comments by Jos´

e M. Gaspar, Tatsuhito Kono and Jian Wang.The usual disclaimers apply. Financial support

from the National Natural ScienceFoundation of China (71663023, 71773042, 71503110) is gratefully acknowledged.

1For instance, as argued by Proost and Thisse (2017), in the United States, the average expenditure share on housing is

24%, while it is 27% in France. Meanwhile, the opportunity cost of time spent commuting accounts for 3–6 weeks of

work for a Manhattanite and, on average, 4 weeks of work for a resident of GreaterParis.

International Journal of Economic Theory xx (2018) 1–20 © IAET 1

International Journal of Economic Theory

International Journal of Economic Theory 16 (2020) 329–348 © IAET 329

Heterogeneity, urban costs and agglomeration Yiming Zhou

framework with iceberg commuting costs that affect the effective labor supplied by a worker and

thus her income. Their results concur with what Krugman (1991a) obtained in the core–periphery

model, except that the sequence of spatial configuration is reversed. To be specific, agglomeration

causes higher commuting costs and land rents. Hence, mobile workers are unwilling to bear higher

urban costs by being dispersed unless the transport costs across regions are so high that the net

benefit of having all varieties locally produced is sufficiently large to outweigh the higher urban costs

that they must bear by being agglomerated. By introducing an idiosyncratic production function into

Murata and Thisse (2005), Zhou (2017) confirmed their spatial configuration results and showed

analytically how the interplay between transport costs and urban costs affects urban wage inequality.

This paper aims to contribute to the literatureby integrating fir m heterogeneity `alaMelitz(2003)

into the framework of Murata and Thisse (2005). Bydoing so, it enables us to explore analytically how

the interaction between firm heterogeneity, urban costs and transport costs determines the spatial

configuration of an urban space economy. In particular, one of the main features of our approach

is that it allows us to investigate how an increase in firm heterogeneity affects the interplaybetween

transport costs across regions and interregional urban costs that determines the outcomes of the

spatial equilibrium.

In this vein of research, Baldwin and Okubo (2006) marry the footloose capital model (Martin

and Rogers 1995) with firm heterogeneity `alaMelitz (2003) in which each firm is associated with

a particular labor input coefficient (i.e. marginal cost). They show that the most efficient firms in

the small region are the first to relocate from the small region to the large one. In other words, firm

heterogeneity leads to a sorting of the most productive firms into larger regions. However, based

on the footloose capital model where mobile factor repatriates all of its earnings to its region of

origin, their approach does not exhibit the demand-linked and cost-linked circular causality as in

Krugman (1991a). Okubo (2009) further introduces intermediate input linkages into the model of

Baldwin and Okubo (2006) and suggests that, rather than the catastrophic agglomeration, gradual

trade liberalization causes gradual agglomeration. In a linear model, Okubo et al. (2010) assume

two types of firm productivity and study how heterogeneous firms respond to trade liberalization

by choosing different locations. They show that the more productive firms are selected into the

large markets when trade costs fall, but the less productive firms also find it profitable to locate

in the large market if trade costs fall even further. In other words, it gives rise to a bell-shaped

relationship between trade liberalization and the international productivity gap. Also assuming two

typesoffirmproductivity,Saitoet al. (2011) find that trade liberalization induces low-productivity

firms to relocate away from the region where high-productivity firms agglomerate. Saito (2015)

further examines the organization and location decisions of heterogeneous firms with multi-plant

operations and their consequences for regional productivity. He showsthat a reduction in transpor t

costs induces the transformation from multi- to single-plant operations for high-productivity firms

and entices the relocation of low-productivity, single-plant firms to the small region.

This paper differs from this line of research in that wedo not consider relocation of firms. Instead,

and more in accordancew ith Krugman (1991a) and Murataand Thisse (2005), agg lomeration works

here via exit and entry of firms in each region, stimulated by labor migration and thus changes in

market size. We also refrain from setting the number of the firms exogenously, but endogenously

determine it in a general equilibrium model. In these respects, our settings are closer to the work

of Ehrlich and Seidel (2013) who introduce Melitz-type firm heterogeneity into the framework of

Krugman (1991a). They shed light on the role of firm heterogeneity in agglomeration and were the

first to show that an increase in firm heterogeneity works in favor of agglomeration. In contrast, our

results indicate that an increase in firm heterogeneity increases the range in which the symmetric

equilibrium is stable. Intuitively, the differences originate from the existence of urban costs. To be

2International Journal of Economic Theory xx (2018) 1–20 © IAET

International Journal of Economic Theory 16 (2020) 329–348 © IAET

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