Modern Economy, 2011, 2, 39-44
doi:10.4236/me.2011.21006 Published Online February 2011 (http://www.SciRP.org/journal/me)
Informal Wage, Informal Price and Extortion under
Migration and Tariff Reform*
Biswajit Mandal1, Saswat i Chaudhu ri2
1Visva-Bharati University, Santiniketan, India
2St. Xavier’s College, Kolkata, India
Received January 9, 2011; revised January 20, 2011; accepted February 4, 2011
Abstract
In this paper we propose a theoretical model where formal and informal sectors co-exist in tandem. Trade
union segregates some labor from being formal. Capital is not allowed to freely move between formal and
informal sectors. Using this sort of framework it has been shown that immigration of unskilled workers re-
duces the return to informal labor and makes the informal good relatively cheap. A tariff slash also impinges
on similar kind of results. In both the cases informal capitalists gain. Moreover, what is more striking is that
both migration and tariff reform are equally bad for the economy as a whole since these policies enhance the
‘unproductive’ element or labor in the society which is really costly as these laborers could have been used
to produce some more consumable commodities.
Keywords: International Trade, Corruption/Extortion, Informal Sector, Migration, General Equilibrium
1. Introduction
Irrespective of the type of countries, be it developing or
developed, the existence of informal sector is an undeni-
able fact of real world. Informal sector mainly consists of
non-agricultural sector or any sector which is not regis-
tered and not legal, per se. In fact more than 50% in
South Asia, 30-50% in South East Asia, almost 50% in
Africa, 55% in Latin America and Caribbean, 24% in
Southern Europe, 10% in Western Europe, 18% in Can-
ada and 8% in USA employment come under the infor-
mal purview ([1-3]). Here we define informal sector by
the non-existence of trade union implying a perfectly
competitive labor market for unskilled informal workers.
Since informal sector is unlawful, it is beset with inter-
mediation related extortion1. At this point extortion is
defined by the set activities of a group of people who
intermediate with local governmental authority for the
survival of informal units. In return of this intermediation
extortionists get a wage equivalent to the wage of infor-
mal workers. Hence informal production and extortion
are complementary with each other in a sense.
Another important facet of factual world is migration.
It could be immigration of unskilled workers or emigra-
tion of skilled workers. The reasons might be a search for
better job opportunity (pull factor) or relatively poverty-
stricken native land (push factor). The issue of interna-
tional migration posits itself in causing major challenges
to the socio-economic condition of a country. For exam-
ple, India has a long history of receiving a constant in-
flow of migrants from Bangladesh. More than 56% of
the migrants to India are from Bangladesh. Though the
trend of Bangladeshi immigrants has decreased in recent
times, the absolute number is still huge and warrants
discussion. These migrants generally find work as cheap
labor in the informal sector of the receiving country.
Coupled with these issues trade protectionist policies are
gradually taking the backseat. Continuing demolition of
tariff has become the prime agendum of all economies
across the globe. Therefore, in this paper we will try to
look at the possible effects of all these policies in a trade
theoretic framework described in the next section. We
primarily focus on three things: informal wage, price of
the informal good and extortion activity due to immigra-
tion and tariff reform. Several papers have been written
in this line [8-14]. In a recent volume [15] emphasize has
been given on different facets of informal sector and
dealt with varied intricate issues. But none of the papers
*The authors like to thank the editor of this journal and two anonymous
referees for many insightful comments. However, the usual disclaimer
applies.
1Interested readers may look into [4,5,6,7] etc. for further understand-
in
g
of extortion and informal activi
t
ies.

B. MANDAL ET AL.
40
in the existing literature has attempted to focus on the
effects of migration on informal wage, informal price,
extortion etc.
The next section describes the model and provides
with the solution. Section 3 analyses the effects of mi-
gration and reform. Section 4 points to some possible
extensions which is followed by concluding remarks in
Section 5. However, relevant mathematical details are
relegated to the Appendix.
2. The Basic Model and Solutions
Here we have a small open economy producing three
goods: X, Y and Z. Out of these three goods X (export-
able) and Y (importable) are traded but Z is a non-traded
one. Hence
x
P and
y
P are determined in the interna-
tional market whereas
z
P is determined by the standard
Cobb-Douglas demand function. X and Y use skilled la-
bor (S) and unskilled labor (L) respectively as specific
factors but they share a common capital (K). Note that Y
is protected by a tariff and L is unionized there. Thus L
gets W as wage in Y. Therefore X and Y constitute the
formal segment of the economy. However, Y is not capa-
ble of absorbing all unskilled workers. Hence some
“unlucky” workers have to search for an alternative op-
tion and they find it in the informal sector (Z) where
wage rate is determined by the competitive pressure. Z
uses T as a specific factor. As informal sector is distorted
by the intermediation of local ‘tolapickers’ (n L) a certain
proportion (

) of the value of the good (
z
P) is appro-
priated by n L as the fee of extortion. Informal produc-
ers have to abide by this ‘system’ as informal units are
illegal by rules. We can easily term this extortion activity
as ‘corruption’ sector if we go by Bhagwati’s [16] con-
cept of directly unproductive profit seeking activities
(DUP). Since n L workers get the same wage as infor-
mal workers total expenditure on n L (= w. n L) has to
be equal with the lost value of output (=

z
P. Z). We
further assume competitive market for all goods and fac-
tors. Production of goods follows constant returns to
scale (CRS) and factors of production exhibit diminish-
ing marginal productivity (DMP).
Following Jones [17,18] we can describe the model by
the following symbols and the set of equations,
where, j P price of the jth commodity (j = X, Y, Z);
S
W skilled wage; W unskilled formal wage;
W unskilled informal wage; r rate of return to
K; R rate of return to T; ij a production re-
quirement of the ith factor in one unit of jth commodity ( i
= S, L, K, T and j = X, Y, Z); S  total supply of
skilled labor; L  total supply of unskilled labor; n L
 number of unskilled labor employed in extortion; K
 total supply of capital, K; T total supply of
capital, T.
The competitive price conditions are given by:
SSXKX x
Wa raP

 (1)

1
LYKY y
Wa raPt

 (2)

1
LZTZ z
Wa RaP


 (3)
2
Note that ww because of the trade union exercise
in the formal unskilled segment. Full employment of all
the factors guarantee the following equations,
.
SX
aXS

(4)
..
KX KY
aXaYK

 (5)
..
L
YLZ n
aYaZ LL

 (6)
.
TZ
aZT

(7)
Let us further assume that the demand for Z follows
standard Cobb-Douglas preference where

fraction of
consumers’ income is spent on the informal good. This is
denoted by



 
.1. 1.
xy z
PX tPYPZ   (8)
The value-cost equality of extortion is
.. .
z
PZ wLn


(9)
Here we have nine unknown variables (, , ,
S
WWr
, , , , and
z
n
RPX Y ZL)and nine equations. For given t
and
y
P, we solve r from (2). Given
x
P, we solve S W
from (1).The technological co-efficients for X and Y are
determined from the CRS assumption. X can be derived
from (4) for any given S. Equation (5) solves the value of
Y for given K and for the given value of X, calculated
from (4). Again for any given and positive n L, we get
the value of Z from (6). Consequently
z
P is solved
from (8). W and R are determined from (3) and (7).
Moreover, we can solve for equilibrium n L from (9).
So the system is solved. For a detailed technique one can
check [19,20].
3. Effects of Migration and Reform
3.1. Immigration of Unskilled Workers
An immigration of unskilled workers indicates an in-
crease in labor supply in Z. This is likely to influence the
output of Z, W and n L. However as
x
P and
y
P are
given, there would be no change in S W, r and .W
Through CRS assumption output of X and Y would not
change. This implies a constant


.1 .
xy
P
XtPY for
given t. Hence demand for Z remains same and
z
P cru-
cially depends on supply of Z.
2

implies the degree of extortion and 01.



B. MANDAL ET AL.
41
An increase in L immediately pushes W down and for
given Z (and hence unchanged
z
P) R must go up. Pro-
ducers will try to economize on the usage of T. This en-
sures an increase in the supply of Z from Equation (7).
For given ,
z
P

if Z goes up n L must increase from
(9) (also see Figure 1) again as Z rises and
 

.1 .
xy
PX tPY remains same
z
P must fall be-
cause

is constant.
When W falls, Wn L rotates down. But as L increases
some more L would also be employed as extortionists
and productive L in the informal sector will increase as
well. Thus ..
z
PZ

would shift up. These two effects
would result in an unambiguous increase in n
L.
By simple mathematical manipulation and using the
standard notation we can arrive at the following expres-
sions (see Appendix for detailed calculation).

1
ˆˆˆ
ˆ0,
ˆˆ
ˆ
as 0
xkx
xy
sxty ky
xy
tt
XPPt
PPt










(10)
Note that throughout the paper ‘Λ’ represents
proportional change.
i

= elastcity of substitution in ith commodity.
ij

= value share of ith factor in jth commodity.
ij

= quantity share of ith factor in jth commodity.

1ˆ
ˆˆˆ 0
kxx kx
xy
ky sxtyky
tt
YPPt

 







(11)



ln
1(1)
ˆˆˆˆ
0
nz
lzzlztz lztz
RLLP


 



(12)
For given
z
P, ˆ0R as ˆ
L can not be less than
ln ˆn
L  . Note that even if entire increased L is absorbed in
extortion, ln
ˆˆ
n
LL   as ln
01.





ln
(1 )
ˆˆˆˆ
() 0
tz
nz
lzzlztz lztz
WLLP


 

 

(13)
α
P
z
Z
O
L
n
L
n
L
'
n
αP
z
Z
(αP
z
Z)'
(WL
n
)'
WL
n
Figure 1. Change in the number of extortionists due to
immigration.

ln
ˆˆˆ
0
lz
n
lz tz
ZLL



 (14)
From (8)
0 (as
ˆˆ ˆˆ
() )0
z
PZ XY

 (15)
From (9) ˆˆˆˆ
ˆ
z
n
PZWL 

 
Or, as
ˆˆ ˆˆ
ˆ
()0 and ()0
nz
WL PZ 

  (16)
Or, 0 as
ˆˆ
() 0
ˆn
LW W

 (17)
Thus the following proposition is immediate:
Proposition I: An immigration of unskilled labor
a) Depresses the informal wage,
b) Expands the informal output,
c) Decreases the price of the informal good, and
d) Enhances the number of extortionists.
3.2. Tariff Reform
A reduction in tariff in the protected sector (Y) changes
the return of K as formal wage is already fixed at .W
The return to capital r will fall in both X and Y. But as
x
P is given S W must go up leading to an increase in X
and a fall in Y as these two goods share the same mobile
capital, K. The moment Y falls some unskilled labor
would be released from Y and would rush to Z to raise
the output of Z. In this process the informal wage rate
must fall as the supply of unskilled workers go up in the
informal sector. If we assume an unchanged




.1 .,
x
yz
PXtPY P should decline as Z has already
increased. A similar diagram like Figure 1 helps ex-
plaining the effect on n L which must increase.
Mathematically the effects of a tariff cut can be sum-
marized as follows:

ˆ
ˆˆˆ
0, aˆ s 0 and 0
xkx
xy
sx ky
tt XPPt









(18)
ˆ
ˆˆˆ
0, as 0 and 0
ˆ
kxx kx
xy
ky sxky
tt
t
YPP

 







(19)
ˆ0
ˆ
ky
t
rt


 (20)
ˆˆ
kx
S
ky sx
tt W



 (21)

.
ln
.
1
ˆ.0
.
ˆ
ˆlykxkx
n
lz zlztzkykysx
RLtt
 

  



 



(22)
R will increase for a given Ln and we prove later that
ˆ0
n
L, in that case ˆ R is not unambiguously positive.

B. MANDAL ET AL.
42
We need to put some more restrictions.

.
.
ˆ(). 0
.
ˆ
ly kx
tz kx
lzz lzlztzkykysx
tWt


 


 



(23)
ˆˆˆ
.( )0
lz x
ZRW   (24)
If there is no change in



.1 .,..
xyz
PXtPY PZ  
would also remain unaltered. Hence from (9)
0 as
ˆˆ ˆ
() 0
n
LW W (25)
And from
ˆˆ
() 0
z
PZ (26)
However, if
 
.1 .
xy
PX tPY does not remain
unaltered
ˆ
ˆˆ .( )
kx kx
z
yx
sx ky
tPZ t



 (27)
Where ..
.
x
x
z
PX
PZ


 and ..
.
y
y
z
PY
PZ



If
x
y

 and kx ky

  (likely to hold true).
z
P
must fall as Z has already increased. But for kx ky



the impact on
z
P is uncertain.
This leads to the follwoing proposition:
Prposition II: Due to trade reform informal workers
are worsened but informal output gets a boost. However
the number of extortionists must go up.
4. Some Possible Extensions
4.1. Capital Mobility
If capital is allowed to move among X, Y and Z an immi-
gration of L would not depress W (for given
z
P) like the
basic model. Because, r would not change (from Equa-
tion (2)) and it would be same for all the sectors. Hence
out put of Z will increase and that of Y would fall if
lz ly

  following Rybczynski argument. However,
when lz ly

 , Z would, in fact, contract. Depending
upon the output effect on Z,
z
P will change. Note that if
,
lz ly

 
 
.1 .
xy
PX tPY would fall as Y falls.
Thus
z
P must decrease as Z has already risen. And
again ..
z
PZ

should fall as
 
.1 .
xy
PX tPY has
fallen. We already know that W has not changed, there-
fore the effect on n L is certain and it would fall.
4.2. Skilled Emigration
If skilled workers emigrate, there will be a tendency for
S
W to rise. But since the system determines r from (2)
and it is unchanged, S W can not change because of
small country assumption. Therefore production of X
would fall due to shortage of specific skilled labor. Sub-
sequently, some capital would be released from X to
augment production of Y. Again in order to produce
more Y some more unskilled workers need to be relin-
quished from Z. This will induce an increase in W and
hence a fall in R for given P. As R falls, TZ a should
increase and subsequently Z will fall.
If we assume




.1 .
xy
PX tPY as constant even-
tually
z
P would go up. Thus from equation (9) n L has
to fall as ..
z
PZ

remains same through the constancy
of




.1 .
xy
PX tPY . Thus an outmigration of skilled
workers is good for the society as a whole as n
L falls
and is also good for informal workers in particular as W
goes up.
4.3. Foreign Capital Inflow
If foreign capital comes in the formal sector there will be
changes in the outputs but r, W and S W would re-
main unchanged because of the structure of the model.
Both X and Y would increase. X would expand more than
Y if distributive share of capital is higher in X than that of
in Y. In order to produce more X, skilled labor need to be
substituted by increased capital as supply of skilled labor
is fixed at S. However, as far as an increase in Y is con-
cerned, along with increased capital the necessity of an
increased employment of unskilled workers is also there.
These workers should come from informal sector and
hence W will rise. At given
z
P, R has to fall. This will
induce a reduction Z. From (8) the Left Hand Side (LHS)
has gone up and Z falls, therefore, subsequently
z
P
must increase. It should be noted that the effect on n L
is uncertain.
5. Conclusions
Here we have built a trade theoretic model where both
formal and informal sectors are embedded. Informal
sector is segregated from the formal world by the
non-existence of trade union. Since informal units are
illegal, they are distorted by extortion. In this framework
we have shown that both the immigration of unskilled
workers and a tariff cut lead to similar kind of results.
Under these two situations informal workers lose, infor-
mal output expands but informal capitalists gain. But
what is more worrying is that under both these cases
number of extortionists in the economy inflates. If we
allow for capital mobility between formal and informal
sectors, this would not matter much for the informal
workers under immigration of unskilled workers and
reform. Nevertheless, an outmigration of skilled workers
would raise the informal wage and reduce the number of

B. MANDAL ET AL.
43
extortionists. Informal wage would also go up if we al-
low foreign capital to come in.
We can easily invoke some other possibilities in this
set up. One is when the demand for informal good comes
only from formal unskilled sector. Under immigration of
unskilled workers, the wage rate of informal labor must
fall and there would also be a decline in the informal
commodity price. This assumption is quite sensible in
that skilled workers constitute the richer section of the
society and they do not usually consume informal goods.
The interesting point is that it does not matter whether
the richer segment of the society demands the informal
good, the effect of immigration of unskilled workers on
informal wage, price and extortion are identical. Another
interesting possibility is the introduction of new imported
substitutes of Z which, essentially, move away the de-
mand for Z. This may happen in the post reform period
(if we assume the existence of prohibitive tariff in the
pre-reform phase). In this situation, consequent upon
reform, the price of the informal good would fall by a
relatively large amount. The size of the extortion sector
would increase in this case also. Nevertheless, the extent
of increase would be relatively less.
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B. MANDAL ET AL.
44
Appendix
Differentiating Equation (2) one gets,

ˆˆ
ˆ1
ky y
rPttt   (A.1)
Differentiating (1) and substituting (A.1) into that,

ˆˆ
1ˆ
ˆkx kx
Ssxx y
ky ky
WPPt tt





  (A.2)
Differentiating equation (3)

ˆˆˆ ˆ
1
lztz z
WRP

  (A.3)
Given that the factor endowments remain constant,
from the full employment conditions we get,

ˆˆSX
X
a (A.4)
ˆˆ
0
kx ky
XY   (A.5)


ln
ˆˆ ˆ
ly lzn
YZL

  (A.6)

ˆˆTZ
Z
a (A.7)
Using the concept of elasticity of substitution in X and
the zero profit condition we have

ˆ
ˆˆ
SXXSkx
arW

  (A.8)
where,
ˆˆ
ˆ
ˆ
SX KX
x
S
aa
rW



Using the above equation one can easily calcultae that

1
ˆˆ
ˆ
ˆ
xkx
xy
s
xtyky
tt
XPPt













(A.9)

ˆˆ
1
ˆˆ
kxx kx
xy
ky sxtyky
t
tt
YPP

 











(A.10)


ln
1
ˆˆ
ˆ
1
ˆˆ
ˆ
tz
z
lztzlz lzz
ly
kx kxkx
n
kykyky sx
WP
LL tt





 










 








(A.11)
Substituting (A.10) in (A.6) and then using (A.3) we
have,
ln
ˆˆ ˆˆ
ly
lzkx kx
n
lz tzkykysx
Z
LL tt



 










(A.12)
From equation (8)
ˆˆ
.ˆ
kx kx
zyx
sx ky
PttZ









(A.13)
where ..
.
x
Px X
Pz Z


 and ..
.
y
Py Y
Pz Z



And again from (9)
ˆˆˆˆ
ˆ
nz
LPZW 

 (A.14)
We can use the above equations to find out the
specific effects of migration and tariff cut on informal
wage, informal price and extortion.