Elastic labor supply, variable markups, and spatial inequalities

• Author: Hajime Takatsuka,Dao‐Zhi Zeng
• DOI: http://doi.org/10.1111/roie.12350
• Published date: 01 November 2018
• Date: 01 November 2018

ORIGINAL ARTICLE

Elastic labor supply, variable markups, and spatial

inequalities

Hajime Takatsuka

1

|

Dao-Zhi Zeng

2,3

1

Kagawa University, Takamatsu,

Kagawa, Japan

2

Tohoku University, Sendai, Miyagi, Japan

3

Zhejiang University, Hangzhou,

Zhejiang, China

Correspondence

Hajime Takatsuka, Graduate School of

Management, Kagawa University,

Saiwai-cho 2-1, Takamatsu, Kagawa

760-8523, Japan.

Email: takatsuka@gsm.kagawa-u.ac.jp

Funding information

JSPS KAKENHI, Grant/Award Numbers:

16K03629 and 17H02514; National

Natural Science Foundation of China,

Grant/Award Number: 71733001

Abstract

Assuming an inelastic labor supply, existing studies show

that a larger country has a higher wage rate and a higher

individual income. We reexamine these results using a

model with an endogenous labor supply and variable mark-

ups. We find that these results can be reversed. Specifically,

in the larger country, the wage rate is lower but the individ-

ual income is higher if the love for variety is strong and

trade costs are high. In contrast, the wage rate is higher but

the individual income may be lower if the love for variety is

weak and trade costs are low.

1

|

INTRODUCTION

This paper examines the effect of an elastic labor supply on spatial inequalities across countries.

Assuming an inelastic supply of labor, the existing literature suggests that the wage rate and the indi-

vidual income in a larger country are both higher than those in a smaller country. We show that it is

not necessarily true when the labor supply is endogenously determined.

Since the studies of Krugman (1980) and Helpman and Krugman (1985), the issue of country-size

effects in intra-industry models has been examined in various settings. Many researchers have espe-

cially focused on the home market effect (HME) in terms of firm share, which is defined as a phenom-

enon in which a country with a relatively larger local demand attracts a more-than-proportionate share

of industry with positive transportation costs (Krugman, 1980, section III; Helpman & Krugman,

1985, section 10.4).

1

The HME is also defined in terms of wages, that is, other things being equal, a

larger country has a higher wage rate (Krugman, 1980, section II; Krugman, 1991, p. 491). The litera-

ture shows that the HME in terms of wages is more pervasive than that in terms of firm share. For

example, Davis (1998), Yu (2005), and Takatsuka and Zeng (2012b) introduce trade costs of homoge-

neous goods into Helpman and Krugman (1985) and show that a larger country has a higher wage

rate, although it might not have a more-than-proportionate share of firms. Furthermore, this result holds

Received: 9 May 2017

|

Revised: 4 January 2018

|

Accepted: 11 March 2018

DOI: 10.1111/roie.12350

1084

|

wileyonlinelibrary.com/journal/roie Rev Int Econ. 2018;26:1084–1100.

© 2018 John Wiley & Sons Ltd

even when we introduce mobile capital (Takatsuka & Zeng, 2012a; Takahashi, Takatsuka, & Zeng,

2013) and/or preferences of the variable elasticity of substitution (VES) (e.g., Chen & Zeng, 2018;

Bykadorov, Molchanov, & Kokovin, 2015).

2

In summary, it is believed that a larger country has the

advantages of a higher wage r ate and a higher individual inco me.

In the present paper, we show that the advantages of the larger country may disappear if the labor

supply is elastic and firm markups are variable. Specifically, when the love for variety is weak and

trade costs are low, individual income may be lower in the larger country. Meanwhile, when the love

for variety is strong and trade costs are high, a large country has a lower wage rate. We will show that

these results can be attributed to the fact that the labor supply difference across countries depends on

the love for variety. The individual labor supply is larger in the larger country if the love for variety is

stronger. This is because variety consumption is more attractive for workers in the larger country as

the country has more firms and thus they have better access to varieties. However, if the love for vari-

ety is weaker, this tendency diminishes and we may even see the opposite, that is, the individual labor

supply is smaller in the larger country. As shown later, this possibility is related to our framework

based on a quasilinear utility function generating variable markups.

In the completely free trade case, production costs (wages) are the only driver of firm location since

two countries are indifferent in market access. Thus, firms eventually relocate to eliminate any wage

differential. When trade costs increase marginally, the wage rate in a larger country goes up to offset

its advantage in market access. However, if the love for variety is weaker, the individual labor supply

in the larger country can be smaller than that in the smaller country, so that individual wage income

(5wage rate 3labor supply) may be lower there. In contrast, the larger country has a higher individ-

ual income when trade costs are sufficiently high. If the love for variety is strong, the individual labor

supply becomes relatively large in the larger country as mentioned before, so that the wage rate (5

individual income/labor supply) may be lower there.

The impacts of elastic labor supply on trade and agglomeration are explored by Ago, Morita, Tabuchi,

and Yamamoto (2017, 2018) based on two different frameworks, from which our setup takes the appro-

priate parts to derive new findings. First, since Chen and Zeng (2018) show that variable markups are

important in studying agglomeration, we borrow the quasilinear utility function of Ago et al. (2017) to

capture the pro-competitive effect. Second, i n their setting of one factor of labor, trade in goods is neces-

sarily balanced so that the HME in terms of firm share is never observed. Thus, we introduce mobile

capital as another production factor as in Ago et al. (2018). Since Ago et al. (2018) use a constant-

elasticity-of-substitution (CES) subutility function, our results originating from variable markups are

never observed in their setting. Finally, while Ago et al. (2017, 2018) focus on symmetric countries, our

model is based on countries having different sizes in order to examine various home market effects.

The remainder of this paper is organized as follows. We present the model in Section 2. In Section

3, we analytically examine the country-size effects when trade costs are small. We show that the indi-

vidual income in the larger country is not necessarily higher. Section 4 considers the country-size

effects when trade costs are large. The result shows that the wage rate in the larger country is not nec-

essarily higher. Finally, Section 5 reaches conclusions.

2

|

THE MODEL

The economy consists of two countries, called countries 1 and 2, and one differentiated goods sector.

The total number of workers in the world is normalized to one, and the share of country 1 is denoted

as u2ð1=2;1Þ, which implies that country 1 is the larger one. While labor is immobile between coun-

tries, capital is mobile across countries and is evenly held by all workers. The measure of the total

amount of capital is assumed to be one.

TAKATSUKA AND ZENG

|

1085