Economics Letters 117 (2012) 600–603

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Economics Letters

journal homepage: www.elsevier.com/locate/ecolet

Inflow of labour, producer services and wage inequalityJingjing Zhang ∗

School of Business, University of Western Sydney, Locked Bag 1797, Penrith NSW 2751, Australia

a r t i c l e i n f o

Article history:Received 9 February 2012Received in revised form15 July 2012Accepted 20 July 2012Available online 1 August 2012

JEL classification:F22J31O24

Keywords:GlobalisationLabour mobilityProduct varietiesMonopolistic competitionSkilled–unskilled wage inequality

a b s t r a c t

This paper examines the issue of skilled–unskilled wage inequality in the shortrun when varieties ofproducer services are traded. It is shown that, irrespective of the relative size of income share of capital,inflow of neither skilled nor unskilled labour affects skilled–unskilled wage inequality. However, anincrease in (i) the level of competition in the services sector and (ii) relative price of the varieties ofproducer services can affect the level of wage inequality.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

A number of recent studies have considered the issue ofskilled–unskilled wage inequality. For example, Marjit and Kar(2005) showed that, as long as the income shares of capital are notidentical across industries, outflow of either skilled or unskilledlabour would have the same effect on wage inequality. Anwar(2006) extended this result by showing that in the presenceof a services sector that produces non-traded varieties of anintermediate good, outflow of labour can affect the level of wage inequality even if the income shares of capital are identical. Yabuuchiand Chaudhuri (2007) showed that in the presence of labourmarket imperfections, a reduction in import tariff on low-skilledmanufacturing sector can result in an unambiguous increase inwage inequality. Wälde andWeiß (2007) and Anwar (2009) arguethat globalisation led to increased competition which resultedin downsizing and that industrial downsizing is an importantdeterminant of skilled–unskilled wage inequality. Beladi and Chao(2010) use a simple model of a developing economy that is subjectto Harris-Todaro type unemployment. Their model includes anurban and a rural sector. They showed that downsizing of the urbanfirms can reduce the level of skilled-unskilled wage inequality,which can enhance the economy’s social welfare. Gupta and Dutta(2010) consider the issue of wage inequality in the presence of

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non-traded goods. However theirmodel does not include a servicessector.1

However, except for Anwar (2010), most available studiesutilise theoretical models that are relevant in the longrun. Anwarshows that the shortrun and longrun effect of factors such as tradeliberalisation on skilled–unskilled wage get can be very different.However, this paper is based on the assumption that the servicessector produces non-traded goods. Given the current emphasison further liberalisation of international trade in services, resultsbased on this assumption need to be re-evaluated.

This paper aims to examine the issue of skilled–unskilled wageinequality in the shortrun where a small open economy producesone industrial and one agricultural good. The industrial good pro-duction involves a large number of varieties of producer servicesthat are internationally traded. It is shown that inflow or outflow ofneither skilled nor unskilled labour affects skilled–unskilled wageinequality in the shortrun.

2. A simple model where producer services are traded

Consider a small open economy that produces two final goods;Y and Z . Y , which is an industrial good, is produced by means

1 Recent studies that consider the issue of wage inequality include Yabuuchi andChaudhuri (2007), Epifani and Gancia (2008), Chaudhuri (2008), Beladi et al. (2008),Fang et al. (2008), Afonso and Leite (2010), Breau and Rigby (2010), Chowdhury(2010), Gupta and Dutta (2010) and Kurokawa (2010).

J. Zhang / Economics Letters 117 (2012) 600–603 601

of skilled labour, capital and varieties of producer services (X).Varieties of producer services are produced by skilled labour andcapital under conditions of monopolistic competition.2 The finalgood Z , which is an agricultural good, is produced by unskilledlabour and capital under conditions of perfect competition.Following the existing studies, factor intensity differences arecaptured in this paper in an extreme fashion. The productionfunctions for the final goods are as follows:

Y = g

Ky, Lsy,

n

i=1

xδi

1δ

Z = h(Luz, Kz)

where δ is a parameter in the range [0, 1]; xi is the output of the i-thvariety produced by the services sector; n is the number of varietiesproduced; Lsy and Luz respectively are skilled and unskilled labourused in the production of Y and Z;Ky andKz respectively are capitalused in the production of Y and Z .

Due to the presence of internal economies, each firm specialisesin the production of a single variety. The cost function of the ithfirm/variety is as follows:cx(ws, r, xi) = [λ + µxi] ex(ws, r)where r and ws respectively are the price of capital and the skilledwage rate and λ and µ respectively are positive parameters.

This paper considers a symmetric-equilibrium where allvarieties, that are produced, are equally priced. Accordingly, theaggregate output of the services sector equals nx. Accordingly, theindustrial good production function can be re-written as follows:

Y = g

Ky, Lsy,

n

i=1

xδi

1δ

= gKy, Lsy, n

1−δδ X

.

Each firm in Y industry takes the number of producer servicesvarieties as given. Accordingly, the industrial good sector is subjectto external economies of scale where (1−δ)

δis the size of these

economies (which is positive but less than unity). Because theservices sector produces a large number of varieties, the priceelasticity of demand for each variety is 1

1−δ. In the shortrun the

number of firms is exogenous and hence the economic profit maynot be zero.

Eq. (1) determines the equilibrium output of the industrial goodsector, where p is the equilibrium price of producer services.3

1 = cy

ws, r,p

n1−δδ

. (1)

Eq. (2) determines the shortrun profit maximising output ofeach variety of services as follows:4

δp = λex(ws, r). (2)Equilibrium output of the agricultural good is determined by

the following zero profit condition:

q = cz(wu, r) (3)where q, which is relative price of the agricultural good isdetermined in the international market; and wu is the unskilledwage rate.

The market clearing condition for skilled and unskilled labour,both assumed to be in fixed supply, are as follows:

2 Following Markusen and Strand (2007), we assume that these services aremainly used by the industrial sector and therefore do not enter as input in theproduction of non-industrial goods.3 The right hand side of each of Eqs. (1)–(3) is marginal cost of production

whereas the left hand side is marginal revenue. In the case of Eqs. (1) and (3),the underlying market structure is perfectly competitive and hence the unit priceequals marginal cost.4 Because the price elasticity of each variety is 1

1−δ, marginal revenue equals δp.

Ycyw

ws, r,

p

n1−δδ

+ n [µ + λx] exw(ws, r) = Ls (4)

Zczw(wu, r) = Lu. (5)

The capital market clearing condition is as follows, where thesupply of capital (K ) is fixed:

Ycyr

ws, r,

p

n1−δδ

+ n [µ + λx] exr(ws, r) + Zczr (wu, r) = K . (6)

As the producer services are internationally traded, p is deter-mined in the international market. Accordingly, Eqs. (1)–(6) in-volve six endogenous variables: ws, wu, r, x, Y and Z . n, q, K , Luand Ls are the exogenous variables. The impact of changes in any ofthe exogenous variables on skilled–unskilledwage inequality

wswu

can be examined by totally differentiating Eqs. (1)–(6)with respectto the relevant variable.

3. Analysis of the shortrun equilibrium

The results presented in this section are derived by totallydifferentiating Eqs. (1)–(3) as follows:

ζ ywws + ζ y

r r = −ζ yp p +

1 − δ

δ

ζ yp n (7)

ζ xwws + ζ x

r r = p (8)

ζ zwwu + ζ z

r r = q (9)

where w, p, r, n and q are percentage change in the relevantvariable.

Eqs. (7)–(9) can be used to explore the link between labourmobility and wage inequality as follows:∂

wswu

∂ Lu

Luwswu

= 0 (10)

∂

wswu

∂ Ls

Lswswu

= 0. (11)

Eqs. (10) and (11) indicate that inflow or outflow of either typeof labour has no effect on skilled–unskilled wage inequality in theshortrun.

While examining properties of the longrun equilibrium, Marjitand Kar (2005) showed that, as long as the relative income sharesof capital and labour are not identical, inflow/outflow of eithertype of labour (i.e., skilled or unskilled) would have the sameeffect on wage inequality.5 Anwar (2006) extended this resultby demonstrating that in the presence of specialisation-basedexternal economies, inflow of capital or either type of labour canaffect wage inequality even if the income shares of capital wereidentical.

The impact of an increase in the level of competition in producerservices industry on skilled–unskilled wage inequality can beexamined as follows:∂

wswu

∂n

nwswu

=

1 − δ

δ

ζypζ zwζ x

r − ζ zr ζ x

w

ζ zw

ζywζ x

r − ζyr ζ x

w

. (12)

5 In other words, inflow of either type of labour inflow/outflow would eitherincrease or decrease the skilled–unskilled wage inequality.

602 J. Zhang / Economics Letters 117 (2012) 600–603

Eq. (12) shows that the impact of increased competition inproducer services industry on skilled–unskilled wage inequalitydepends on income shares of primary factors of production. Thenumerator of Eq. (12) is positive if the income share of capital inservices industry

ζ xr

is greater than the income share of capital in

agricultural industryζ zr

. However, if the income share of capital

in the services sector is also greater than the income share of capitalin the industrial good industry

ζyronly then does the impact of

increased competition in services sector increase skilled–unskilledwage inequality. It can be easily confirmed that

ζ xr > ζ z

r ⇔ ζ xw < ζ z

w

ζ xr > ζ y

r ⇔ ζ xw < ζ y

w

where

ζ xr =

∂ex(·)

∂r

r

ex(·)

> 0; ζ x

w =

∂ex(·)∂w

w

ex(·)

> 0;

ζ zw =

∂cz(·)∂w

w

cz(·)

> 0;

ζ zr =

∂cz(·)

∂r

r

cz(·)

> 0; ζ y

w =

∂cy(·)∂w

w

cy(·)

> 0;

ζ yr =

∂cy(·)

∂r

r

cy(·)

> 0.

Using the above inequalities, it is clear that if the incomeshare of capital in the industrial sector is greater than the incomeshare of capital in the services sector then the effect of anincrease in competition in the services industry decreases theskilled–unskilledwage inequality. This can be attributed to the factthat increase in the level of competition in the services sector leadsto a relatively small increase in skilled wage rate. This result is inline with the work of Kurokawa (2010). Within the context of aproduct variety model, Kurokawa has argued that the number offirms can also affect the level of skill-premium.

While there has been a significant increase in price of producerservices, none of the existing studies have considered its affect onskilled–unskilled wage inequality:∂

wswu

∂p

pwswu

= −

ζ zwζ z

r

ζ yw + ζ

yp ζ x

w

ζ zw

ζywζ x

r − ζyr ζ x

w

ζyp ζ x

r + ζyr

ζyp ζ x

w + ζyw

−ζ zr

ζ zw

(13)

where ζyp =

∂cy(·)

∂p

p

cy(·)

> 0.

The denominator of the first term on the right hand side ofEq. (13) is positive if the income share of capital in the producerservices industry is greater than the income share of capital in theindustrial good industry. However, the sign of the second term onthe right hand side of the same equation depends on whether ornot the combined income share of capital in industrial good andproducer services industry

ζyp ζ x

r + ζyris greater than the income

share of capital in the agricultural sectorζ zr

.

An increase in the price of producer services reduces skilled–unskilled wage inequality, if (i) the combined income share ofcapital in industrial and services sectors is greater than the incomeshare of capital in the agricultural sector and (ii) the incomeshare of capital in the services sector is greater than the incomeshare of capital in the industrial good industry. On the otherhand, an increase in the price of producer services increasesskilled–unskilledwage inequality, if (i) the combined income share

of capital in industrial and services sectors is less than the incomeshare of capital in the agricultural sector and (ii) the income shareof capital in the services sector is greater than the income share ofcapital in the industrial good industry.

4. Conclusion

A number of studies have considered the determinants ofskilled–unskilled wage inequality.6 However, most studies arebased on models that are relevant in the longrun. Within thecontext of a product varieties model, this paper examines theissue of skilled–unskilled wage inequality in the shortrun. Inaddition, unlike the existing studies, this paper assumes thatvarieties of producer services are traded.Within the context of thismodel, inflow of either skilled or unskilled labour has no effecton skilled–unskilled wage inequality. Marjit and Kar (2005) andAnwar (2006) have shown that the impact of labour inflow onskilled–unskilled wage inequality depends on income shares ofcapital. This paper extends the existing literature by showing that,in the shortrun, the relative size of income shares of capital isirrelevant.

This paper also examines the impact of an increase in the level ofcompetition in the producer services industry on skilled–unskilledwage inequality. It is shown that depending on the relative size ofincome shares of capital, an increase in competition can increaseskilled–unskilled wage inequality. An increase in the price ofproducer services reduces skilled–unskilled wage inequality aslong as (i) the combined income share of capital in industrialand services sectors is greater than the income share of capitalin the agricultural sector and (ii) the income share of capital inthe services sector is greater than its share in the industrial goodindustry.

Acknowledgements

The author was grateful to A/Professor Partha Gangopadhyayfor encouragement and a referee for very helpful comments andsuggestions. All errors are my responsibility.

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