ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E13-2

Environment and Labor Transfer of Skilled Laborand Unskilled Labor between Sectors
byXiaochun Li
Yuanting Xu
Dianshuang Wang

March 2013

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Environment and Labor Transfer of Skilled Laborand Unskilled Labor between Sectors
Xiaochun Li1, Yuanting Xu2, Dianshuang Wang2

Abstract:
In this paper, we divide the labor into skilled and unskilled labor to investigate theimpact that the heterogeneous labor transfer between sectors has on the environment
under the international skilled and unskilled labor movements and the price change ofthe agricultural products. The main conclusions are: under certain conditions, skilledlabor inflow deteriorates the environment while its outflow improves the environment;
unskilled labor inflow improves the environment while its outflow deteriorates theenvironment; the increasing price of the agricultural products improves theenvironment while the decreasing price deteriorates the environment.

Keywords:
Harris-Todaro; Environment; Heterogeneous Labor Transfer; Product Price Change

JEL classification:
O24; Q56; R23

1. Introduction
The transfer of heterogeneous labor force between different sectors is often
considered in studies of income disparity and employment. Marjiit and Kar (2005)
divided labor force in an economy into skilled and unskilled labor, and established a1: Professor, School of Economics, Nanjing University
Visiting Fellow (Dec 20, 2012-Mar 19, 2013), Economic Research Center, Graduate School of Economics,
Nagoya University
2: School of Economics, Nanjing University
1

general equilibrium model of a two-sector economy. They studied the income
disparity with the assumption that there is no unemployment or flow of capital
between sectors. Yabuuchi and Chaudhuri (2007) took skilled labor as a specificfactor whereas unskilled labor could move freely between sectors. Based on theassumption of non-existence of unemployment in either sector, they analyzed theimpact of international factors on changes of income. Beladi et al (2008) analyzed theimpact of inflow of international factors on the wage disparity between the skilledlabor and unskilled labor through a two-sector general equilibrium model. This paper
is based the assumptions of full employment and free movement of skilled labor
between sectors, and existence of unemployment of the unskilled labor. Gupta andDutta (2010) made an assumption that skilled labor move between trade and non-trade
sectors, while unskilled labor do not, upon which they established a generalequilibrium model and studied the impact of changes in factor endowments and inprice of tradable goods on unemployment and the relative wages of skilled andunskilled labor. Chaudhuri and Banerjee (2010) divided the rural sector into theadvanced and the backward subsectors and established a general four-sector
equilibrium model. They studied the income effect of capital inflow under the premiseof existence of unemployment of skilled labor and immobility of them between
sectors, as well as full employment and full mobility of the unskilled labor between
the two rural sectors and immobility of unskilled labor between the rural and urban
sectors. However, with regard to the real-world economic activities in the developing
countries, the impact of the transfer of heterogeneous labor is not limited to income
disparity and employment.
On the other hand, since the 1990s, there have been many studies in the academia
on the impact of inter-sector labor transfer in developing countries on the environment2

from different perspectives, particularly the impact of labor transfer on pollution
based on the Harris-Todaro Model, such as Beladi and Rapp (1993), Beladi and
Frasca (1999), Daitoh (2003), Daitoh (2008), Tawada and Sun (2010), Daitoh andOmote (2011) and Kondoh and Yabuuchi (2012), which involve taxation,
environmental policy and improvement of labor market. However, we note that all theaforesaid studies on the labor transfer and environment are based on a common
premise, namely, labor is homogeneous, which is different from the reality wherelabor is actually heterogeneous. As a result, the impact of labor quality on
environment is a focus of academic studies in developing countries. Some Chinese
scholars pointed out that increasing skilled labor endowment would have an impact ofimproving the environment.3 Therefore, we would like to study the impact of thetransfer of heterogeneous labor between sectors on the environment.
In this paper, we will divide the entire labor force into the skilled and unskilled
sectors and studied the impact of heterogeneous labor transfer between sectors on theenvironment under the conditions of free flow of international labor factors andchange of agricultural products prices. The main conclusion of this paper is that,
under certain circumstances, inflow of skilled labor could deteriorate the environment;on the other hand, the outflow of labor could improve the environment. The inflow of
unskilled labor would, however, improve the environment; and the outflow would
deteriorate the environment. In the following, we will establish an analytical a modelin the second part, made a theoretical analysis in the third part, and draw a conclusion
thereupon the last part would.

3

See: Li, P.Y. and Ding L., 2012. Evaluation Index and Multivariate Statistical Analysis of Urban
Inhabiting Environment. Journal of Harbin Industry University 5, 116-124.
3

2. The Model
We consider a small open developing economy with two sectors, namely, theurban sector and the agricultural sector. The economy uses four production factors,
which are skilled labor LS , unskilled labor LU , capital K and land N . The urban
sector uses skilled labor, unskilled labor and capital to produce the import-competing
goods. The agricultural sector uses skilled labor, unskilled labor and land to produce
exportable goods. The urban sector is skilled labor intensive and the agricultural
sector is unskilled labor intensive. The production functions of the urban andagricultural sectors are given by:
X 1  F 1 ( LS 1 , LU 1 , K )(1)

X 2  eF 2 ( LS 2 , LU 2 , N )(2)

F 1 and F 2 are production functions increasing corresponding to each factor andsatisfying linear homogenous and strictly quasi-concave properties.
In the production function of the agricultural sector,eE   X1
E

(3)

where e represents the environment of the economy. When e  1 , the environmentis in the best condition. It becomes worse when e decreases. E represents theenvironment endowment when there is no pollution in the economy.  is thepollution that the urban sector discharges for producing one unit of good. We assume
that only the production of the urban sector causes pollution emission to make theenvironment worse. The harmful substance emitted, such as waste gas, waste residue
and waste water, pollute water and soil for agricultural use through atmosphere, rivers
and other media. Hence, the product efficiency of the agricultural sector decreases.
Under the condition that the markets are perfectly competitive, we could obtain4

that:

p1  aS1wS1  aU 1 wU  aK1r(4)

p2  aS 2 wS 2  aU 2 wU 2  aN 2 R(5)Where aij (i  S , U , K , N ; j  1, 2) represents that the factor i used in producing one
unit of goods in the j th sector. wS1 is the wage rate of skilled labor in the urban
sector. wS 2 is the wage rate of skilled labor in the agricultural sector. wU is thewage rate of unskilled labor in the urban sector. wU 2 is the wage rate of unskilledlabor in the agricultural sector. r is the interest rate of capital in the urban sector. R
is the rent of land used in the agricultural sector. p j ( j  1, 2) represent the productprices of the urban sector and the agricultural sector, respectively. In this paper, we
assume that all the products are tradable and hence the product prices are given
internationally.
Generally, developing countries lack skilled labor. Therefore, we assume thatskilled labors are fully employed with no unemployment and they move freely
between the urban and agricultural sectors. This paper assumes that the wage rate of
unskilled labor in the urban sector is given exogenously, which means that it isdownward rigid. However, in the agricultural sector, the wage rate of unskilled labor

w is fully elastic. We use LUU to denote the number of unemployed unskilled laborin the urban sector and  to denote the unemployment rate of unskilled labor in this
sector. Hence,   LUU / LU 1  LUU / aU 1 X 1 . Therefore, in the unskilled labor market
equilibrium, the wage rate in the agricultural sector equals the expected wage incomein the urban sector, which equals to the downward rigid wage rate wU multiplied by
the probability of obtaining a job in this sector LU 1 / ( LU 1  LUU ) . Thus, the allocation
5

mechanism of the skilled labor and unskilled labor are shown as:
wS 1  wS 2
wU 2 

(6)

LU 1
wU
LU 1  LUU

(7)

Or:

(1   ) wU 2  wU

(7’)

The market clearing conditions of the four production factors: skilled labor,
unskilled labor, capital and land, could be shown as follows:

aS1 X1  aS 2 X 2  LS

(8)

aU 1 X1  aU 2 X 2   aU 1 X1  LU

(9)

aK1 X1  K(10)

aN 2 X 2  N(11)Where LS , LU , K , N represent the endowment of skilled labor, unskilled labor,
capital and land, respectively.
The basic theoretical model has been built, which consists of nine equations, (3),(4), (5), (6), (7’), (8), (9), (10) and (11). Nine endogenous variables are determined,
and they are wS 1 , wS 2 , wU 2 , r , R ,  , e , X 1 and X 2 .

3. Environment and Labor Transfer between Sectors
Differentiating the equations (4), (5), (6), (7’), (8), (9), (10) and (11) and writing
in a matrix notation, we can obtain the following equation:6  S1 S 2
 A
 B
1
 S KS
 2
 S NS

 K1

0

U 2

0

N 2

0
0

S 2 S

 S

2
S 2 S SN2
U 2 SUNS 1(1   )U 1

0

1

2
NN

0

0
2
SU

1
S 1 SK

C
0
S

D
1
S KK

2
NU

0

S

0   wˆ S 1   pˆ1   
0   wˆ U 2   pˆ 2 
S 2   rˆ   LˆS 
U 2   Rˆ   LˆU   
0   Xˆ 1   Kˆ 
1   Xˆ   Nˆ  2  (12)

And differentiating the equation (3), we can get the following:eeˆ  (1  e ) Xˆ 1  0(13)

Where “  ” represents the rate of change, ,  ij (i  S , U , K , N ; j  1, 2) is the
distributive share of factoriin thej th sector (e.g.  S 1  aS 1wS 1 / p1 ),ij (i  S , U , K , N ; j  1, 2) is the allocated share of factor i in the j th sector (e.g.

S1  aS1 X 1 / LS ), Sijh (i, j  S ,U , K , N ; h  1, 2) is the partial elasticity of substitution
2
between factors i and j in the h th sector (e.g. S SUaS 2 wU 2), Sijh  0(i  j )wU 2 aS 2

and Sijh  0(i  j ) . We also have:1
2
A  S 1S SS
 S 2 S SS
01
2
, B  (1   )U 1SUS  U 2 SUS  0 ,2
C  U 2 SUU
 (1   )U 1  0

1, D  (1   )U 1SUK  0 .

The partial elasticity of substitution between factors plays an important role in thefollowing discussion. Therefore, in this paper, we make the following assumptions:
Assumption 1.

1
SUK

K1



1
SUS

 S1

Assumption 1 implies that unskilled labor is more substitutable with capital thanwith skilled labor in the urban sector.
Assumption 2.

2
S SN

N 2



2
S SU

U 2
7

Assumption 2 implies that skilled labor is more substitutable with land than withunskilled labor in the agricultural sector.

3.1 Labor transfer between sectors under the international skilled labor movement
Skilled labor in developing countries will sometimes leave because of low wages.
In reality, there are also some situations in which skilled labor moves to developing
countries from outside. Recently, high unemployment rate in some developed
countries results in unemployed and retired skilled labor moving to the developing
countries to find job opportunities. Therefore, in this paper we not only consider
skilled labor outflow, but also their inflow.
We can obtain the following by solving the equation (12):
1
1
2
2
2
) U 2 U 2 ( SUN)   N 2 (C  U 2 S NU
)  /   0 (14)  S 1S KK S NNXˆ 1 / LˆS  ( K 1S KS

2
2
2wˆ S 1 / LˆS   K 1 U 2 U 2 ( SUN)   N 2 (C  U 2 S NU
)  /   0
 S NN(15)222
 S NNrˆ / LˆS   S 1 U 2 U 2 ( SUN)   N 2 (C  U 2 S NU
)  /   0

(16)

2
2
2
)   K 1 N 2 U 2 S NSwˆ U 2 / Lˆ S  { K 1 S 2 U 2 ( S UN S NN(17)11]   S 1 N 2 [ D  (1   ) U 1 S KK]} / 
 K 1 N 2 [ B  (1   ) U 1 S KS

Where  is the determinant of the matrix in equation (12) and   0 (seeAppendix).
Using the equations (15) and (17) and Assumption 1, we could get the following:22( wˆ U 2  wˆ S 1 ) / LˆS  { K 1U 2 ( SUN)( S 2  U 2 )   K 1 N 2 (1   )U 1
 S NN11
1
122)   K 1 N 2 U 2 ( S NN)} /   0
 (1   ) N 2 U 1 ( K 1S KS
  S 1SUK  K 1SUS  S 1S KK
 SUN

(18)

Differentiating the equation aS1 X1  LS1 , we could obtain the following from theequations (14), (15) and (16):
ˆ S1
LˆS 1 Xˆ 1
rˆ
1 w
1

 S SS S SK
0
Lˆ
Lˆ
Lˆ
Lˆ
S

S

S

(19)

S

8

Xˆ 1 Xˆ 1 LˆS 1, we could get that:

Lˆ
Lˆ Lˆ

According to equations (13), (19) and

S

S1

S

Xˆ 1 / LˆS 1  0(20)eˆ / LˆS 1  0(21)

Differentiating the equation aU 1 X1  LU 1 , we could obtain the following equationfrom the equations (14), (15) and (16) and Assumption 1:

ˆ S1
LˆU 1 Xˆ 1
rˆ
1 w
1

 SUS
 SUK
0
Lˆ
Lˆ
Lˆ
Lˆ
S

S

S

(22)

S

Xˆ 1 Xˆ 1 LˆU 1, we could get that:

Lˆ
Lˆ Lˆ

According to equations (13), (22) and

S

U1

S

Xˆ 1 / LˆU 1  0(23)eˆ / LˆU 1  0(24)

With the seven equations (18), (19), (20), (21), (22), (23) and (24) andAssumption 1, we can obtain the following proposition:

Proposition 1. Under Assumption 1, the skilled labor inflow increases employment ofskilled labor of the urban sector and causes the skilled and unskilled labor from theagricultural sector migrate to the urban sector, which deteriorates the environmentand decreases the skilled-unskilled wage inequality. Conversely, the skilled labor
outflow decreases the employment of skilled labor of the urban sector and causes theurban unskilled labor move to the agricultural sector, which improves theenvironment and increases the skilled-unskilled wage inequality.

The urban sector is more skilled labor intensive than the agricultural sector.
Therefore, the skilled labor inflow increases the skilled labor endowment in the9economy. According to the Rybczynski Theorem, skilled labor inflow leads to an
expansion of the urban sector and a contraction of the agricultural sector following the
Rybczynski effect. With the unchanged capital endowment, the urban sector should
employ more skilled and unskilled labor to increase the output. Hence, the rural
skilled and unskilled labor migrates to the urban sector. With the unchanged unskilledlabor endowment, the demand for them increases because of the unskilled labor
migrates to the urban sector, which decreases the skilled-unskilled wage inequality.
The increasing output of the urban sector increases pollution and deterioration of theenvironment. Conversely, using the same method, we could also analyze the impactsof the skilled labor outflow.

3.2 Labor transfer between sectors under the international unskilled labor movement
We consider the impacts of both the outflow and inflow international unskilledlabor on the wage disparity and unemployment rate in the developing countries.
Although the former situation (outflow) is common in the developing countries, thelatter (inflow) also exists in the real developing economies.4
Under Assumption 2, we could obtain the following by solving the equation (12):
1
1
2
2
2
2
Xˆ 1 / LˆU  S 2 ( S 1S KK
  K 1S KS
  N 2 S SU U 2 S NN  N 2 S NU)(U 2 SSN) /   0 (25)2222wˆ S 1 / LˆU   K 1S 2 (U 2 S SN  N 2 S SU U 2 S NN  N 2 S NU)/ 0

(26)

2
2
2
2
rˆ / LˆU   S 1S 2 (U 2 S SN  N 2 S SU U 2 S NN  N 2 S NU
)/0

(27)

1
1
2
2
wˆ U 2 / LˆU  [  S 1 N 2 S 1 ( S SK S KK S NN)  K 1 S 2 S 2 ( S SN)
21
  K 1 N 2 S 2 S NS  K 1 N 2 ( A  S 1S KS)] /   0(28)

Using the equations (26) and (28), we could get that:

4

See: Frédéric Docquier and Hillel Rapoport, 2012. Globalization, Brain Drain and Development.
Journal of Economic Literature 50, 681–730.
10

( wˆ U 2  wˆ S 1 ) / LˆU  0(29)

Differentiating the equation aS1 X1  LS1 , we could obtain the following from theequations (25), (26) and (27):
ˆ S1
LˆS 1 Xˆ 1
rˆ
1 w
1

 S SS S SK
0LˆU LˆU
LˆU
LˆU

(30)

According to equations (13), (30) andXˆ 1 Xˆ 1 LˆS 1, we could get that:

Lˆ
Lˆ Lˆ
U

S1

U

Xˆ 1 / LˆS 1  0(31)eˆ / LˆS 1  0(32)

Differentiating the equation aU 1 X1  LU 1 , we could obtain the following
equation from the equations (25), (26) and (27) and Assumption 1:

ˆ S1
LˆU 1 Xˆ 1
rˆ
1 w
1

 SUS
 SUK
0
Lˆ
Lˆ
Lˆ
Lˆ
U

U

U

(33)

U

According to equations (13), (33) andXˆ 1 Xˆ 1 LˆU 1, we could get that:

Lˆ
Lˆ Lˆ
U

U1

U

Xˆ 1 / LˆU 1  0(34)eˆ / LˆU 1  0(35)

With the seven equations (29), (30), (31), (32), (33), (34) and (35), Assumption 1
and Assumption 2, we can obtain the following proposition:

Proposition 2. Under Assumptions 1 and 2, the inflow of unskilled labor causes theurban unskilled as well as skilled labor migrates to the agricultural sector, which
improves the environment and increases the skilled-unskilled wage inequality.
Conversely, the outflow of unskilled labor outflow increases the employment of11

unskilled labor of the urban sector and causes the agricultural skilled labor migrate
to the urban sector, which deteriorates the environment and decreases the
skilled-unskilled wage inequality.

The agricultural sector is more unskilled labor intensive than the urban sector.
Therefore, the unskilled labor inflow increases the unskilled labor endowment in theeconomy. According to the Rybczynski Theorem, unskilled labor inflow leads to an
expansion of the agricultural sector and a contraction of the urban sector following the
Rybczynski effect. With the unchanged land endowment, the agricultural sector
should employ more skilled and unskilled labor to increase the output. Hence, demandfor both production factors increase, and both the urban skilled and unskilled labor
migrate to the agricultural sector. The decreasing output of the urban sector decreases
the pollution and improves the environment. With the unchanged skilled laborendowment, the wage of the skilled labor increases because of the skilled labor
migrates to the agricultural sector. At the same time, the wage of the unskilled labordecreases because of the increasing endowment, which increases the skilled-unskilled
wage inequality. Conversely, using the same method, we could also analyze thesituation of decreased unskilled labor endowment.

3.3 Labor transfer between sectors under the price change of agricultural products
We consider the impacts that the labor transfer between sectors has on theenvironment under the condition of change of price of agricultural products. We canobtain the following by solving the equation (12):1
1Xˆ 1 / pˆ 2  S 2 ( S1S KK
  K 1S KS)V /   0(36)wˆ S 1 / pˆ 2  S 2 K 1V /   0

(37)
12

rˆ / pˆ 2  S 2 S 1V /   0

(38)

2
2
2
2
2
2
2
2
2
2
Where V  U 2 [ SUN( S SU S NS)  S NN( S SU SUS)  S NU
S SN
]  (1   )U 1S NN
 CS SN0.

Differentiating the equation aS1 X1  LS1 , we could obtain the following from theequations (36), (37) and (38):ˆ S1
LˆS 1 Xˆ 1
rˆ
1 w
1

 S SS S SK
0
pˆ 2
pˆ 2
pˆ 2
pˆ 2

(39)

According to equations (13), (39) andXˆ 1 Xˆ 1 LˆS 1, we could get that:pˆ 2 LˆS 1 pˆ 2

Xˆ 1 / LˆS 1  0(40)eˆ / LˆS 1  0(41)

Differentiating the equation aU 1 X1  LU 1 , we could obtain the following
equation from the equations (36), (37) and (38) and Assumption 1:
ˆ S1
LˆU 1 Xˆ 1
rˆ
1 w
1

 SUS
 SUK
0
pˆ 2
pˆ 2
pˆ 2
pˆ 2

(42)

According to equations (13), (42) andXˆ 1 Xˆ 1 LˆU 1, we could get that:pˆ 2 LˆU 1 pˆ 2

Xˆ 1 / LˆU 1  0(43)eˆ / LˆU 1  0(44)

With the six equations (39), (40), (41), (42), (43) and (44) and Assumption 1, we
can obtain the following proposition:

Proposition 3. Under Assumptions 1, increase of agricultural product price causes
the urban skilled and unskilled labor migrate to the agricultural sector, which
improves the environment; conversely, decrease of agricultural product price causes
13the agricultural skilled and unskilled labor migrate to the urban sector, which
deteriorates the environment.

The agricultural sector is more unskilled-labor intensive than the urban sector.
Therefore, according to the Stolper-Samuelson effects, increase of agricultural
product price raises wage rate of unskilled labor in the agricultural sector, which
attracts unskilled labor in the urban sector migrates to the agricultural sector. Increaseof unskilled labor employment of the agricultural sector increases the output and thedemand for skilled labor in this sector. This also attracts the skilled labor in the urban
sector to migrate to the agricultural sector. The decrease of employment of bothskilled and unskilled labor in the urban sector decreases the output of the urban sector
as well as pollution. Hence, the environment of the economy improves. Conversely,
using the same method, we could analyze the impacts of decreasing agricultural
product price.

4. Conclusion
This article analyzed the impact of labor transfer between the skilled and unskilled
sectors on the environment, considering free flow of international labor factor andprice change of agricultural products. Our study expands the practicality of theoreticalstudies of the impact of labor transfer on the environment. Nonetheless, it is just a
beginning, and we shall proceed to the other related topics, such as taxation,
environmental policies and labor market reform in our future studies.

Appendix
Under the present model, the dynamic adjustment process for the supply side is14

as follows:X 1  d1 ( p1  aS 1wS 1  aU 1wU 1  aK 1r )(A1)

X 2  d 2 ( p2  aS 2 wS 1  aU 2 wU 2  aN 2 R )(A2)w S1  d3 (aS1 X1  aS 2 X 2  LS )(A3)w U 2  d 4 (aU 1 X 1  aU 2 X 2 

wU  wU 2
aU 1 X 1  LU )
wU 2

(A4)

r  d5 (aK1 X1  K )(A5)R  d 6 ( aN 2 X 2  N )(A6)

Where “.” represents differentiation with respect to time and d j ( j  1, 2, 3, 4, 5, 6, 7,8)
is the positive coefficient measuring the speed of adjustment and d j  0 .
Marshallian adjustment process is assumed for quantities when the demand pricediffers from the supply price in the goods markets. A Walrasian adjustment
mechanism is assumed for the factor prices with the fixed endowment in the factor
markets. The determinant of the Jacobian matrix of equations (A1) - (A6) is:00
J  d1d 2  d 6 p1 p2 KNLS LU

0
0

S1
S 2
(1   )U 1 U 2
1
0

0
1

 S 1 S 2A

U 2
2
S 2 S SU

 K 1
01
S 1S SK

B
1
S KS
2
S NS

C
0
2
S NU

D
1
S KK
0

0

0
 N 22
S 2 S SN2
U 2 SUN02
S NN

It can also be written as follows:J  d1d 2  d 6 p1 p2 KNLS LU 

Therefore, according to the Routh-Hurwitz Theorem, a necessary condition forthe local stability of the system is that the determinant of the Jacobian matrix is
positive. Hence, it is assumed that the equilibrium in this paper is stable under the15

condition that J  0 . We could obtain that   0 .

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