260 B.R. Hazari, P.M. Sgro International Review of Economics and Finance 9 2000 257–265
a
LI
w
I
1 a
KN
r 5 P 9
where r and w
I
denote the rental on capital and the wage rate for migrant labor, respectively. The market clearing equation [Eq. 10] for the non-tradable goods is:
D
N
[P, I] 5 Y
N
10 where D
N
denotes demand for the non-tradable and I total income. Note that the migrants consume the non-traded goods as well as the traded goods.
The national income from the expenditure side equals the value of total output, hence:
I 5 D
T
1 PD
N
5 Y
T
1 PY
N
11 resident income I
R
5 Y
T
1 PY
N
2 w
1
L
1
and D
T
denotes the demand for the tradable goods. This completes the specification of the model.
3. Results
3.1. Increased migration We first explore the impact of increased migration on employment, resident welfare
and factor returns. By differentiating Eq. 3 to Eq. 11 and by differentiating and using Eqs. 1 and 2 we obtain:
3
l
KT
l
KN
b
K
l
LT
2b
L
2 1
1 2
C 2
1 h
N
h
NI
2u
L
1
43
Y ˆ
T
Y ˆ
N
P ˆ
L ˆ
Iˆ
4
5
3
L ˆ
I
u
I
L ˆ
I
4
12
where l
ij’s
represents factor shares, b
j’s
and C are the elasticities of factor substitution, h
N
and h
NI
the price and income elasticities of the non-tradable goods h
N
, 0, h
NI
. 0. The term u
L
shows the share of domestic wages in national income, while u
I
the share of migrant income in national income.
The above system is solved for the endogenous variables of interest:
P ˆ 5
l
KT
3
m
n
wL
1
PY
N
2 1
4
2 h
NI
l
KN
u
L
D 13
L ˆ 5
A9
1
1 2 m
N
w
1
L
1
PY
N
2
D 1
B9 h
N
2 h
N 1
u
1
D 14
Iˆ
R
5 u
L
L ˆ
15 rˆ 5 2
u
LY
m
N
u
KY
P ˆ
16
B.R. Hazari, P.M. Sgro International Review of Economics and Finance 9 2000 257–265 261
w ˆ
I
5 a P
ˆ 17
D 5 l
KT
h
N
1 l
KT
C 1 h
NI
u
LKT
l
KT
b
L
1 l
LT
Cl
KN
h
NI
u
L
1 l
LT
b
K
u
L
h
NI
u
L
. as h
N
, 0 and C, b
L
b
K
are all positive. Also A9 5 l
KT
b
L
1 l
LT
b
K
. B9 5 l
KT
l
KN
. a 5
1 u
LI
3
1 1 u
KN
u
LY
m
N
u
KY
4
. b
L
5 s
T
m
N
b
K
5 l
KT
u
LT
s
N
m
N
u
KT
1 l
KN
s
N
u
LN
1
u KT
1 u
KN
u
LT
m
N
u
LN
u
KT
1 u
LT
m
N
u
KT
2
C 5 u
KI
s
T
1
u
KT
1 u
KN
u
LT
m
N
u
KT
u
LN
1 u
LT
m
N
u
KT
2
m
N
5 P
d D
N
d Y
N
where m
N
is the marginal propensity to consume the non-traded goods. On the basis of Eqs. 13–17 we obtain the following results:
Proposition 1. An increase in sector-specific migration necessarily lowers the relative price of the non-tradable and migrant wages and raises the return to
capital.
Proposition 2. An increase in sector-specific migration raises lowers domestic employment as:
3
A9
1
1 2 m
N
w
1
L
1
PY
n
2
1 B9
h
NI
u
1
4
. ,O
We proceed to discuss Proposition 2 using a variant of the Edgeworth-Bowley box diagram. In developing this explanation Proposition 1 is used. The dimensions of Box
1, in Fig. 1, OK
N
O
T
L ¯
I
show the quota-determined supply of immigrant labor and the allocation of K to the non-traded goods denoted by K
N
. The production equilibrium for the non-traded goods is shown by point O
T
isoquant omitted. In Box 2 we have the inelastically given supply of domestic labor O
T
L and the remaining supply of
capital K
N
M which is fully utilized in traded goods production. Because of wage
indexation, equilibrium occurs at point e isoquant omitted resulting in unemployment of domestic labor as shown by ee9. From Proposition 1 we know that an increase in
sector-specific migration raises the section to capital and lowers the migrant wages, hence, the labor intensity in sector N increases as shown by the slope of OO
″
T
. Also note that the output of Y
N
increases.
262 B.R. Hazari, P.M. Sgro International Review of Economics and Finance 9 2000 257–265
Fig. 1. Migration and increased domestic employment.
We represent two cases: first, the case of an increase in domestic employment Fig. 1; and second, the case of a decrease in domestic employment Fig. 2, respectively.
We only describe Fig. 1 in detail. Since wage indexation raises the real wage above the competitive level, unemployment results as shown by ee9. In a non-distortionary
model, full employment equilibrium would have been observed to show a higher labor capital ratio lower capital intensity. An increase in unskilled labor migration results
in a new box OK9
N
O ″
T
Q . Equilibrium in this sector is now shown by point O
″
T
. At this equilibrium point, all the migrants are employed and some capital is released to the
production of traded goods as shown by the distance K
N
K9
N
. The availability of more capital to the production of traded goods increases domestic employment as shown
by the difference between Te ″
2 O9
T
e . 0. In Fig. 2 we illustrate the case of increased
unemployment—this arises due to the reduction in the capital available for employ- ment in the production of traded goods. The above discussion provides the intuitive
explanation for the results.
3.2. Capital accumulation In this subsection we analyze the implications of domestic capital accumulation on
domestic and migrant welfare, unemployment and relative price of the non-traded goods. The left-hand side of Eq. 12 remains the same, but the right-hand side vector
changes and becomes [Eq. 18]:
B.R. Hazari, P.M. Sgro International Review of Economics and Finance 9 2000 257–265 263
Fig. 2. Migration and decreased domestic employment.
3
K ˆ
O O
O u
r
K ˆ
4
18 where u
r
5 rK
¯ I. By using the above right-hand side with the Eq. 12 we obtain:
P ˆ 5
h
NI
[l
KT
u
r
1 u
L
] D
K ˆ
19 Iˆ 5 2
h
N
2 C
Y
T
I K
ˆ 20
L ˆ 5
3
2h
N
1 1 2 u
r
m
N
C D
2 u
r
h
NI
[l
KT
b
L
1 b
K
] D
4
K ˆ
21 Iˆ
R
5 u
r
L ˆ
22 From Eqs. 19 and 20 we derive the following proposition:
Proposition 3. Capital accumulation necessarily raises total income and the rela- tive price of the non-traded goods.
264 B.R. Hazari, P.M. Sgro International Review of Economics and Finance 9 2000 257–265
It is clear that the availability of more capital raises total income and via the income effect also raises the relative price of the non-traded goods. The increase in total
income arises as capital is mobile between both sectors in contrast to migrant labor which is sector specific and has an ambiguous effect on total income. This explains
the non-ambiguous effect of capital accumulation on the relative price of non-traded goods. This increase in the relative price of the non-traded goods has obvious implica-
tions for structural adjustment within the economy.
From Eqs. 21 and 22 it is clear that resident welfare and employment respond ambiguously to an increase in capital accumulation. These results are consistent with
results in second best models.
4. Conclusions
