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Gainful Effects of Foreign Capital Inflow in the Presence of

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					       Gainful Effects of Foreign Capital Inflow in the Presence of
         Intermediate Goods and Technical Efficiency of Labour



                             Anindita Basu (Chowdhury)
                              Department of Economics
                               Mahishadal Raj College
                                     Mahishadal
                                   Midnapur(East)
                                    West Bengal
                                       INDIA

                                          and

                                    Kausik Gupta
                               Department of Economics
                              Rabindra Bharati University
                                       Kolkata
                                     West Bengal
                                        INDIA


Keywords: Foreign capital inflow, Import-competing sector, Technical efficiency,
Intermediate goods, Foreign enclave, Non-traded intermediate goods.

JEL classification: F10, F11, F13, F21, F23


ADDRESS FOR COMMUNICATION:

                         ANINDITA BASU (CHOWDHURY)
                                  AL-79, SECTOR-II
                                    SALT LAKE
                                 KOLKATA-700091
                          Telephone No (R): (033)23580470
                         Email: basu_anindita@rediffmail.com




The present paper is part of the doctoral dissertation of Anindita Basu(Chowdhury) which
is in progress at the Department of Economics, Burdwan University, West Bengal, India.
Any remaining error, however, are the sole responsibility of the authors.
           Gainful Effects of Foreign Capital Inflow in the Presence of
            Intermediate Goods and Technical Efficiency of Labour




Abstract:

The paper attempts to examine the impact of foreign capital inflow in the presence of an
intermediate goods sector which may be traded or non-traded using a general equilibrium
trade model for a small open economy. Here it has been shown that the welfare
improving effects of foreign capital inflow is valid in an economy with intermediate
goods sector irrespective of whether it is traded or non-traded sector. Our results support
the challenges of Marjit and Beladi (1997) and Marjit, Broll and Mitra (1997), Chaudhuri
(2001) etc, regarding the conventional wisdom in the context of foreign capital inflow,
though our framework is quite different from the frameworks of the above mentioned
authors.
            Gainful Effects of Foreign Capital Inflow in the Presence of
                intermediate goods and Technical Efficiency of Labour



1. Introduction:


The formation of world trade organization (W.T.O.) brought some revolutionary changes
in liberalizing international trade across countries, whether developed or developing.
Liberalization includes both inflow of foreign capital as well as reduction of protection to
domestic industries. Empirically it has been observed that many developing economies
notably the non-OECD countries, have not implemented tariff reforms to any significant
extent, even after formally choosing free trade as their development strategy. This fact
appears to be puzzling at the first sight. However, this phenomenon can be explained by
“tariff jumping theory”1. It suggests a positive correlation between the amount of foreign
direct investment (FDI) in a country and tariff rates imposed by it. So the countries which
welcome huge inflow of foreign capital may be reluctant to implement tariff reform
seriously.


The effects of inflow of foreign capital in the developing countries have been
investigated intensively by both trade and development theorists. According to both trade
and development theorists the effects of inflow of foreign capital in developing
economies in the presence of full repatriation of foreign capital income are, in general,
discouraging. Brecher and Alejandro (1977) have analyzed the welfare effects of foreign
capital inflow in a two-commodity, two-factor full employment model. Khan (1982) has
re-examined this proposition in a mobile capital Harris-Todaro model with urban
unemployment. Both of them have reached the conclusion that inflow of foreign capital,

1
    The higher rate of return on foreign capital is the major driving force behind foreign direct investment by
the multinational corporation. Along with this the protected domestic markets creates an additional
incentive for the multinational corporations to invest in these countries. It helps them to jump the tariff
walls and to reap a good return by serving the markets of developing countries. See for example, Motta
(1992) and yanagawa (1990) for details.
with full repatriation of its earning, is necessarily immiserizing if the import-competing
sector is capital-intensive and is protected by a tariff. However, in the absence of any
tariff, foreign capital inflow with full repatriation of its earnings does not affect welfare.


An interesting question in this regard is the willingness of the developing countries to
invite foreign capital inspite of its immiserizing results on welfare due to foreign capital
inflow. There are a quite large number of works2 that have re-examined the Brecher-
Alejandro (1977) proposition. Most of these have attempted to find out the impact of
inflow of foreign capital to the final goods sector. Two interesting papers by Marjit and
Beladi (1997), Marjit, Broll and Mitra (1997)3 are however exceptions in this regard. In
both these works a protected intermediate goods sector, using sector specific foreign
capital, has been considered. They have shown, contrary to the conventional wisdom,
foreign capital inflow into the tariff distorted intermediate goods sector with full
repatriation of foreign capital income is welfare improving under some reasonable
conditions4. Chaudhuri (2001) has shown that the economy may experience an
improvement in its welfare due to foreign capital inflow when the non-traded
intermediary goods sector is sufficiently capital intensive relative to the import
competing sector and a sufficiently large amount of the output of this sector is used in the
export sector of the economy. Using a three-sector general equilibrium framework with
two informal sectors Chaudhuri and Mukhopadhyay (2002) have shown that in the
presence of labour market distortions, foreign capital inflow may be desirable both in the
presence and absence of tariff protection due to its favourable impact on welfare.

2
    See the works of Grinols(1991), Beladi and Marjit(1992), Datta Chaudhuri and Adhikari(1993), Chandra
and Khan(1993), Gupta(1994), Gupta(1997) etc.
3
    The basic difference between these two model is that former is based on a neo-classical full employment
framework whereas the latter is based on a structure with Harris- Todaro(1970) unemployment. Again in
case of the former it is only the intermediate goods sector, which is protected whereas in case of the latter
one of the final goods sectors along with the intermediate goods sector are protected.
4
    Gupta (1998) however, has considered general equilibrium framework to show that the effects of inflow
of foreign capital to the tariff distorted intermediate goods sector is generally, immisering, under some
reasonable conditions, in the presence of full repatriation of foreign capital income.
The impact of foreign capital inflow in the presence of intermediate goods and technical
efficiency of labour is relatively neglected in the literature. Though Marjit and
Beladi(1997), Marjit, Broll and Mitra (1997) have considered intermediate goods they
have ignored technical efficiency of labour. In this paper we first consider a tariff
distorted intermediate goods sector. In the second part of the paper, however, we consider
a non-traded intermediate goods sector.


To capture improvement in technical efficiency we have introduced a technical efficiency
function, which depends on foreign capital. The rationale behind this function is that an
increase in foreign capital inflow implies foreign direct investment in the home country.
As a result of foreign direct investment, resident of the host country come into contact
with foreign entrepreneurs who posses superior technical skills and know-how. These
new ideas lead to transfer of technology from the foreigners to the residents of the host
country and it takes place through observation, discussion, and training. This
transmission can be considered as a spillover effect on the residents of the host country
leading to improvement in technical efficiency of labour force5.



The analysis of the present paper is based on a static full employment framework of the
Heckscher-Ohlin-Samuelson type where the economy is broadly divided into domestic
enclave and a foreign enclave6. The first part of our paper shows that, under some
reasonable conditions, inflow of foreign capital is welfare improving when the
intermediate goods sector is protected and there is full repatriation of foreign capital
income. These results support the challenge of Marjit and Beladi (1997) and Marjit, Broll
and Mitra (1997) regarding the conventional wisdom in the context of foreign capital
inflow. However, here we have used a framework which is different from the frameworks
of the above mentioned authors.
5
    See Koizumi and Kopecky (1977). Findlay (1978) has also used this ‘contagion hypothesis’ in his
theoretical analysis of technology transfer and relative backwardness.
6
    This inclusion of measurement of labour in efficiency unit makes a difference from Gupta’s (1998) model.
Contrary to Gupta (1998) we find that introduction of technical efficiency function gives us results which
are opposite to that of conventional wisdom.
In recent years, many developing countries are interested to attract foreign capital into
non-traded intermediate goods sector the products of which are required to produce
manufacturing product. Unfortunately, economists have given little attention to analyze
the impact of foreign capital inflow in the presence of non-traded intermediate goods. In
the second part of the paper our objective is to analyze the welfare effects of foreign
capital inflow when such capital flows to both the final goods producing and non-traded
intermediate goods producing foreign enclave. This inclusion of foreign enclave makes a
difference from Chaudhuri’s (2001) model. Contrary to Chaudhuri (2001) here we have
used Heckscher-Ohlin-Samuelson type full employment framework instead of Harris-
Todaro frame work with urban unemployment. Welfare effects of foreign capital inflow
have been examined in this set-up. It has been found that, contrary to the conventional
immiserizing result, inflow of foreign capital is welfare improving under some reasonable
conditions.


The plan of the paper is as follows. Section 2 deals with the model of foreign capital,
traded intermediary and technical efficiency of labour. The comparative static analysis
regarding the effects of increase in foreign capital inflow of the above model is also
considered in this section. Section 3 specifies the model of foreign capital with non-
traded intermediate goods. The comparative static analysis regarding the effects of
increase in foreign capital inflow of the above model is also considered in this section.
Finally the concluding remarks are made in section 4.


2. Foreign Capital, Traded Intermediary and Technical Efficiency of Labour:


2.1 The Model:


We consider a small open economy consisting of three sectors in a Heckscher- Ohlin-
Samuelson Framework. One of these three sectors produces intermediate goods and the
other two sectors produce final goods. All these three sectors use labour (L), which is
perfectly mobile among the sectors. Domestic capital (KD) has been considered as mobile
only between agricultural goods sector, A and intermediate goods sector, I, but foreign
capital (KF) is specific to manufacturing goods sector, M7. Thus agricultural sector uses
domestic capital, labour and intermediate goods as inputs whereas manufacturing sector
uses foreign capital, labour and intermediate goods as inputs. Here endowment of L and
KD are exogenously given. Due to the assumption of small open economy the economy is
a price taker in the world market. All the prices are normalized to unity. All the products
are traded. Here two final products are exported and that amount of intermediate goods
which fails to meet-up the entire demand generated by the two final goods sector is
imported. The intermediate goods is protected by a tariff. All markets are assumed to be
perfectly competitive. The entire foreign capital income is repatriated. Thus most
interesting part of the paper is the introduction of the technical efficiency function of
labour8 and it is assumed to be a function of foreign capital.


For specifying our model on the basis of the above assumption we use the following
notations.
Xi = product produced by the ith sector, i = A, M, I
XI* = amount of import of intermediate goods
w = common wage rate of labour in all sectors
r = rate of return on domestic capital
rF = rate of return on foreign capital9

7
    The fact that foreign capital is sector- specific is a common assumption in the existing literature. See the
works of Young and Miyagiwa (1987, 1992), Datta Chowdhury and Adhikari(1993) Gupta and Gupta
(1998) e.t.c. The existence of a joint sector, where foreign capital and domestic capital exist side by side is
not considered here. This is nothing more than a simplifying assumption.
8
    See the works of Gupta (1999), Chaudhuri (2005) e.t.c. in this regard.
9
    Our implicit assumption is that rF ≥ rFw, where rFw is the exogenously given world rate of return on foreign
capital. For this reason foreign capital will be invested in the small open economy but due to government
control the amount of foreign capital which enters in this country is also fixed at a particular point of time.
It may be noted in this connection that in many developing countries we find that the shift towards more
liberalized regime is a gradual one instead of drastic shift. Drastic policy changes may lead socio-political
tension in the economy in the short run. The assumption of exogenously given foreign capial stock can thus
be justified as the government directly regulates the entry of foreign capital. See Marjit (1994) for details.
See also Gupta and Gupta (1998).
L = fixed endowment of labour
h(.) = technical efficiency function of labour
KD = fixed endowment of domestic capital
KF = Fixed amount of foreign capital
aji =quantity of jth factor for producing one unit of output in the ith sector. j = L, K and i=
A, M, I (we consider variable coefficient technology)
ji = proportion of jth factor used in the production of the ith sector
 = Proportional change
 = the measure of real national income
t = rate of tariff on the intermediate goods sector


Competitive equilibrium condition in the product market for the three sectors implies the
following equations.
waLA + raKA + (1+t)aIA= 1                                                                  (1)
waLI + raKI = (1+t)                                                                        (2)
waLM + rFaKM + (1+t) aIM = 1                                                               (3)


The sector specificity of foreign capital is given by the following equation
aKMXM = KF                                                                                 (4)
Mobility of domestic capital can be expressed as
aKIXI+aKAXA=KD                                                                             (5)


The technical efficiency of each worker is assumed to be a positive function of the
amount of foreign capital in the economy and is given by h(KF), h>0 i.e. Labor
endowment is expressed in efficiency unit and it is thus a function of foreign capital.
We write the labor endowment of the economy in efficiency units as
aLAXA+ aLIXI + aLMXM =Lh(KF)                                                              (6)
Here equation (4), (5), and (6) imply that there exists full employment in the factor
market.
Demand-supply equilibrium for the intermediate goods gives us
aIAXA + aIMXM = XI + XI*                                                                   (7)
It is important to mention that our measure of welfare in this small open economy is
national income at world prices10, , and it is expressed in the presence of full
repatriation of foreign capital income as follows.
 = wLh(KF) + rKD + tXI*                                                                               (8)
Given (1 + t) from equation (1) & (2) we can determine w & r and then from equation (3)
we can determine the value of rF. Thus the factor prices are determined independently of
factor endowments i.e. the model is completely decomposable. Hence we can solve for
the equilibrium values of the input output coefficients. From equation (4) we can
determine XM as KF is given and then equation (5) & (6) can be used to find out the value
of XA & XI. From equation (7) we can thus determine XI* and finally from equation (8)
the value of national income can be obtained.


2.2. The Comparative Static Effects:


In this section we want to examine the impact of foreign capital inflow on the level of
output of each sector as well as on the national income of the domestic economy.
From equation (4) we get dXM/dKF = 1/aKM.
                               ˆ     ˆ
                    It implies X M / K F = (KF /XMaKM)                                                 (9)
                         ˆ     ˆ
Since aKM is positive so X M / K F >0.
Now using this result and differentiating (5) and (6) we can get [see appendix 1]
ˆ     ˆ
X I / K F = -[KA{(hKF/h) - LM}]/                                                               (10)
ˆ     ˆ
X A / K F = [KI{(hKF/h) - LM}]/                                                                (11)

Where  = KILA-KALI >0 iff KI/LI > KA/LA. This implies that the intermediate goods
sector is more capital intensive compared to final goods sectors, which uses domestic
capital.
                           ˆ     ˆ           ˆ     ˆ
Under the above assumption X I / K F < 0 and X A / K F > 0 iff (hKF/h) >LM.


10
     The indirect welfare function of the economy depends on prices and national income. In case of a small
open economy with given prices, real national income can be treated as a proxy for welfare. . See for
example, Chaudhuri (2001),Chaudhuri and Mukhopadhyay (2002a, 2002b), Gupta (1994, 1997) etc.
Using equation (9), (10) &(11) and after some simplification from equation (7) we can
get
ˆ       ˆ                    ˆ     ˆ         ˆ     ˆ     ˆ     ˆ
X I * / K F = [(XI/XI*) {IA X A / K F + IM X M / K F - X I / K F }]

       = (XI/XI*) [{(hKF/h) – LM}{(IAKI + KA)/ } + {IM(KF /XMaKM)}] [See appendix 1]
                                                       ˆ       ˆ
Under the assumption  =KILA-KALI>0 the value of X I * / K F >0 if (hKF/h) > LM.


From equation (8) we find that
d/ dKF = wLh + tdXI*/ dKF
The value d/dKF is dependent on the value of dXI*/dKF (since h is positive). Under
                                                           ˆ       ˆ
some reasonable assumption we have shown that the value of X I * / K F is positive i.e.
inflow of foreign capital leads to increase in import demand of intermediate goods. Thus
real national income increases due to inflow of foreign capital in the economy.


The economic intuition behind the results can be explained as follows. An increase in
foreign capital stock (KF) leads to an increase in the output of manufacturing sector (XM),
which draws labour away from other sectors as the input output coefficients remains
unchanged10. This increase in production of XM creates a shortage of effective labour
supply in the other two sectors. Under the assumption that the intermediate goods sector
(I-sector) is more capital intensive than the final agricultural goods sector (A-sector) we
find, following Rybczynski Theorem, that production of intermediate goods sector
increases and the production of agricultural goods sector falls. On the other hand, owing
to improvement in technical efficiency of the workforce associated with increase in
foreign capital, the labour endowment of the economy in efficiency unit increases. This
produces another Rybczynski effect, which leads to an expansion of agricultural sector
and a contraction of intermediate goods sector. Thus in this model two opposite
Rybczynski effects are generated. The net result, which is called net output effect, is
dependent on the relative strength of these two opposite effects. This net output effect
would be a contraction of the sector ‘I’ and expansion of the sector ‘A’if the former effect

11
     As the model is decomposable i.e. factor prices are determined independently of factor endowment.
is less than the effect of the latter. This happens if (hKF/h) > LM i.e. technical efficiency
functionwith respect to capital is highly elastic. Increase in the levels of XA and XM due to
foreign capital inflow implies an increase in the demand of intermediate goods. As the
output of sector I falls it implies an increase in the demand for imported intermediaries
due to an increase in inflow of foreign capital. Hence, under certain reasonable conditions
the amount of imported intermediate goods rises. As the tariff rate t on the intermediary is
given, it implies that there is an increase in tariff revenue from intermediate imports as a
result of inflow of foreign capital. The increase in foreign capital stock leads to an
increase of labour income through an improvement in technical efficiency. However this
inflow of foreign capital leads to no change in the domestic capital income. Thus total
domestic factor income [wLh(KF)+rKD] increases. The combined result implies an
increase in real national income of the economy. In case of a small open economy with
given prices, real national income can be treated as a proxy for welfare. Hence an inflow
of foreign capital raises welfare under some reasonable assumptions. We summarise our
results in the form of the following proposition.


Proposition 1: Given the assumption that (i) there is full repatriation of foreign capital
income, (ii) there is tariff protection to the intermediate goods sector, I, which uses
domestic capital and (iii) technical labour efficiency is a positive function of foreign
capital, an inflow of foreign capital to the manufacturing goods sector is welfare
improving if and only if intermediate goods sector is more domestic capital intensive than
agricultural goods sector and (hKF/h)>LM i.e. technical efficiency function with respect
to capital is highly elastic.


3. Foreign Capital and Non-traded Intermediary:


3.1. The Model:

We consider a small open economy consisting of four sectors in a Heckscher-Ohlin-
Samuelson Framework. One of these four sectors produces intermediate goods and the
other three sectors produce final goods. All these four sectors use labour (L), which is
perfectly mobile among the sectors. Domestic capital (KD) has been considered as mobile
only between domestic manufacturing sector, M and the agricultural sector, A and
foreign capital (KF) has been considered as specific to the foreign enclave though it is
mobile between two sectors of foreign enclave, the non-traded intermediate goods sector,
F1 and a final goods sector, F2. Here the domestic manufacturing sector, M produces its
commodity (XM) with the help of labour, domestic capital and non-traded intermediate
goods. The agricultural sector, A produces agricultural commodity (XA) with the help of
labour and domestic capital. Both the sectors within foreign enclave use labour and
foreign capital to produce their product. The per-unit requirement of the intermediate
input is assumed to be technologically fixed in the manufacturing sector12. Let us now
assume that labour in the manufacturing sector earns a contractual wage rate w , while the
wage rate in the other three sectors and the payment to capital are market determined.
Here contractual wage rate is assumed to be higher compared to competitive wage rate.
Owing to our small open economy assumption, we consider prices of all final goods to be
given internationally. On the other hand, the price of the non-traded intermediary
produced in sector F1 is endogenously determined. We assume that the manufacturing
sector is the import-competing sector of the economy and is protected by a tariff. Price of
the agricultural product is considered as the numeraire and its price is set equal to unity.
Production functions exhibit constant returns to scale with diminishing marginal
productivity to each factor. All inputs are fully employed. The entire foreign capital
income is repatriated.


For specifying our model on the basis of the above assumptions we use the same
notations as used in section 2 of this paper. Here we just mention the additional notations
relevant for the present model.
Xi = product produced by the ith sector, i = A, M, F1, F2
w = contractual wage rate of manufacturing sector
Pi = world price of the ith commodity, i = M, A and F2
PF1 = endogenously determined price of the non-traded intermediary
θij = distributive share of the jth input in the ith industry

12
     It is just a simplifying assumption. It rules out the possibility of substitution between the non-traded
intermediary and other factors of production in the final goods sector.
The general equilibrium is represented by the set of following equations.
w aLM + raKM + aF1MP F1 = PM (1+ t )                                                       (12)
waLA + raKA = 1                                                                            (13)
waLF1 + rFaKF1 = PF1                                                                       (14)
waLF2 + rFaKF2 = PF2                                                                       (15)


Equations (12), (13), (14) and (15) are the competitive equilibrium conditions. They
imply that unit cost of production of each commodity must equal its domestic price in
equilibrium.


The demand for the non-traded intermediary must equal to its supply, so we have
aF1MXM = XF1                                                                               (16)
Here only aF1M is fixed though other aji are variable and are functions of relevant factor
prices.
Full employment of labour implies the following equation
aLMXM + aLAXA + aLF1XF1 + aLF2XF2 = L                                                      (17)


Full utilization of domestic capital in the economy implies that
aKMXM + aKAXA = KD                                                                         (18)


Full utilization of foreign capital inflow in the capital recipient economy implies that
aLF1XF1 + aLF2XF2 = KF                                                                     (19)
There are eight endogenous variables in the system: w, r, rF, PF1, XM, XA, XF1, XF2. The
parameters of the system are: PM, aF1M, L, KD, KF, t, which are exogenously given. Thus
we have eight independent equations [equations (12) to (19)] to solve for eight
unknowns. Given the prices of the products of sectors M, A, F2 from equations (12), (13),
(14) and (15) we can determine the values of four variables r, PF1, w, rF. Here the factor
prices are determined independently of factor endowments. Thus the decomposability
property is valid in our model. Once factor prices are known the input-output coefficients
are also known. Equations (16), (17), (18) and (19) then can be solved for XM, XA, XF1 and
XF2.
Before going into comparative statics, we note that national income at world prices, ,
expressed in the presence of full repatriation of foreign capital income as follows.
           = w aLM.XM + w (aLAXA + aLF1XF1 + aLF2XF2) + r.KD – t.XM.PM
             = w.L + ( w - w).aLM.XM + r.KD – t.XM.PM                                                 (20)
In equation (19) [w.L + ( w - w).aLM.XM] is the aggregate wage income of the workers.
The term r.KD is the income from domestic capital stock. Here t.X M.PM measures the cost
of tariff-protection to the import-competing sector13.


3.2. The Comparative Static Effects:


In this paper we are interested to reanalyze the impact of increase in foreign capital
inflow on the level of output of each sector as well as on the level of welfare in a small
open economy.
Given the fact that aF1M is fixed we get from equation (16) the following relation
ˆ    ˆ
XM  X       F1                                                                                       (21)
Totally differentiating equation (17), (18), and (19), using equation (21) and after some
algebraic simplifications (see appendix 2 for details) we get the following three
expressions.
    ˆ         ˆ
KM X M + KA X A = 0                                                                                 (22)
     ˆ          ˆ     ˆ
KF1 X M + KF2 X F2= K F                                                                             (23)
            ˆ         ˆ          ˆ
(LM+ LF1) X M + LA X A + LF2 X F2= 0                                                               (24)
Solving equations (22), (23) and (24) by Cramer’s rule and after some algebraic
simplification we can get [see appendix 2 for details]
  ˆ     ˆ
( X M / K F ) = LF2/[(KF1LF2 – KF2(LF1 - |λ|/KA)]

                  = LF2/[(LF1LF2 {(KF1/LF1) – (KF2/LF2)}+ |λ|(KF2/KA)]                        (25)

13
     The imposition of a tariff on the import-competing sector artificially raises the domestic price of the
formal sector’s product from its world price, which lead to a misallocation of resources between the two
sectors. Producers would produce more (less) of the importable (exportable) commodity vis-à-vis their free
trade levels. t.XM.PM measures the loss in the economy’s welfare resulting from this inefficiency in
production.
  ˆ     ˆ
( X F2/ K F ) = {|λ| -(LF1KA)}/[KA{(KF1LF2) – (KF2LF1)} + KF2|λ|]

             = {(LAKM - LMKA) - (LF1KA)}/
                               [KALF1LF2{(KF1/LF1)–(KF2/LF2)+ KF2|λ|]              (26)
  ˆ     ˆ                     ˆ     ˆ
( X A / K F ) = - (KM/KA) ( X M / K F )

            = -LF2KM/KA[(LF1LF2 {(KF1/LF1) – (KF2/LF2)}+ |λ|(KF2/KA)]           (27)
where |λ| = LAKM - LMKA>0 as manufacturing sector is assumed to be more capital
intensive compared to agricultural sector i.e. (KM /LM) >(KA /LA).


Again it is to be noted that manufacturing sector uses labour both directly as well as
indirectly through use of non-traded intermediary goods as production of one unit of
manufacturing sector requires aF1M units of non- traded intermediary goods which also
requires aLF1 units of labour in its production. Thus domestic capital-labour ratio for
manufacturing sector is given by KM/(LM+LF1). We assume that not only (KM/LM) >
(KA /LA) but also KM/(LM+LF1)>(KA/LA).


Finally we assume that the non-traded intermediate goods sector is more (foreign)
capital-intensive than the final goods sector that uses foreign capital i.e. (KF1/LF1) >
                    ˆ     ˆ           ˆ     ˆ              ˆ     ˆ
(KF2/LF2). Thus ( X M / K F ) >0, ( X F2/ K F ) >0 and ( X A / K F ) <0. As from equation (21)
             ˆ     ˆ
we find that X M  X      F1
                                                 ˆ     ˆ
                               we can say that ( X F1/ K F ) >0.


Since the system posses the decomposable property, factor prices and hence factor
coefficients remain unaltered owing to foreign capital inflow. However, inflow of foreign
capital produces a change in the output composition of the economy. In order to interpret
the impact of foreign capital inflow on welfare of the economy we need to find out the
impact of such an inflow on the output level of sectors F1 and F2. Under the assumption
that sector F1 is more (foreign) capital-intensive than sector F2 we find that, for given XM
and XA, output of sector F1 increases and output of sector F2 falls. We can refer to it as
Rybczynski effect. However, it is to be noted that the output level of sectors M and A do
not remain constant. In fact due to the fixed coefficient nature of subcontracting we find
that aF1M is fixed so that the output of manufacturing sector increases as much as the
                                                                 ˆ     ˆ
increase in output of non-traded intermediary. This implies that X M  X F1. Increase in
output of the M sector should be matched by decrease in output of the A sector as
domestic capital stock is given. However, if we argue that as the output of sector F2 falls
due to an increase in foreign capital we can say that the effective labour endowment for
sector M, A, and F1 increases. This is because reduction in XF2 implies reduction in aLF2XF2
so that (L-aLF2XF2) increases. Here we assume not only sector M is more (domestic)
capital-intensive than sector A so that (aKM/aLM)>(aKA/aLA) but also aKM/(aLM+aLF1)>(aKA/aLA).
            ˆ     ˆ
Noting that X M  X         F1
                                                                                       ˆ     ˆ
                                 we can express the change in output level in terms of X M , X A and
ˆ
X F2. As a reduction in XF2 implies an increase in effective labour endowment we can
argue that this increase in effective labour endowment is actually meant for sectors M, A.
Thus, by applying Rybczynski theorem we can say output of sector M will increase and
output of sector A will fall. Combining the two Rybczynski effects we thus finally
                ˆ     ˆ           ˆ     ˆ           ˆ     ˆ              ˆ     ˆ
conclude that ( X M / K F ) >0, ( X F2/ K F ) >0, ( X A / K F ) <0 and ( X F1/ K F ) >0.


If inflow of foreign capital with full repatriation of foreign capital income takes place
welfare of the economy would be affected owing to two possible effects: labour
reallocation effect and distortionary effect due to tariff protection. From equation (20) it
follows that
d/dKF = (dXM/dKF)[( w - w).aLM - t.PM]                [see appendix 2]                                 (28)


As a result of foreign capital inflow we find that the output of the domestic import-
competing manufacturing sector increases. An expansion of this sector has two opposite
effects on national income. On one hand an expansion of the import-competing sector
‘M’ implies an increase in employment14 aLM.XM. Thus aLM(dXM/dKF) implies increase in
employment in sector ‘M’ due to an increase in KF. The workers of sector ‘M’ enjoy a
wage rate w , which is higher than the wage rate w, in rest of the economy. As the
increase in employment in sector ‘M’ is at the cost of reduction in employment15 in

14
     aLM remains unchanged as a result of increase in KF due to decomposability property.
15                          ˆ     ˆ
  It is to be noted that as X M  X       F1,   an increase in employment in sector ‘M’ implies an increase in
employment in sector F1.
sectors A and F2, the labour reallocation effect due to a change in output (and hence
change in employment ) measured in terms of wage differential ( w - w) is given
by( w - w)aLM. In other words ( w - w).aLM..(dXM/dKF) measures the increase in national
income due to ‘labour reallocation effect’. We can thus interpret ( w - w).aLM as the
marginal impact of gain in national income due to ‘labour reallocation effect’ for one
unit increase in output of sector ‘M’ due to unit increase in foreign capital.


So far we have considered the favorable effect of an increase in output of sector ‘M’ on
national income. However, it is to be noted that sector ‘M’ is the import-competing sector
and it is protected by a tariff. Hence, its expansion raises the distortionary cost of
protection given by t.PMdXM/dKF. Here t.PM is the distortionary cost of protection when
output of sector ‘M’ increases by one unit due to unit increase in foreign capital inflow.
We refer to it as the ‘distortionary effect due to protection’. Hence, the net effect of
increase in output of sector ‘M’ depends on the relative strength of the two effects: the
“labour reallocation effect” and “distortionary effect due to protection”.


       ˆ     ˆ
Thus ( X M / K F ) >0 implies (dXM/dKF) >0 which again implies from equation (27) that

d/dKF >0 if and only if ( w - w)aLM > t.PM. It is to be noted that in the presence of full
tariff liberalization (a situation of free trade) we have t=0 and (d/dKF) is unambiguously
positive. We have already mentioned earlier that in case of small open economy national
income can be considered as a proxy for welfare. Thus we can interpret that an inflow of
foreign capital raises welfare iff ( w - w)aLM > t.PM. We summarize our results in the form
of the following proposition


Proposition 2: Under the assumptions (i) the import-competing manufacturing sector
is   more(domestic) capital–intensive than the agricultural sector (ii) the non-traded
intermediate goods producing sector of the foreign enclave is more (foreign) capital
intensive than the final goods producing sector of the foreign enclave, an inflow of
foreign capital raises the level of welfare of a small open economy if and only if the
“labour reallocation effect” dominates over the “distortionary cost of tariff protection”
as a result of this inflow.
4. Concluding Remarks:


In this paper we have shown that given full repatriation of foreign capital income, the
effect of foreign capital inflow is welfare improving under some reasonable conditions in
the presence of an intermediate goods sector irrespective of whether it is traded or non-
traded. Marjit and Beladi (1997), Marjit, Broll and Mitra (1997) have challenged the
immiserizing effects of inflow of foreign capital by considering sector specific foreign
capital for the tariff-ridden intermediate goods-sector. By ruling out this assumption of
sector specificity of foreign capital to the tariff ridden intermediate goods sector, under
certain reasonable conditions Gupta (1998) has shown that the immiserising effects of
foreign capital inflow is still valid. In the first part of our paper we have introduced the
technical efficiency function in a general equilibrium model proposed by Gupta (1998)
and have shown that the welfare improving effects of foreign capital inflow are still valid
in an economy with tariff ridden intermediate goods sector. In the second part of our
paper we have introduced a four sector general equilibrium model with foreign enclave
which comprises non-traded intermediate goods sector and a final goods sector and have
shown that the welfare improving effects of foreign capital inflow are still valid in an
economy with intermediate goods sector.


Our results may influence the policy makers who are interested to drive the economy
towards full liberalization to get favourable impact on national welfare. Our results are
specially significant for developing economies which are interested to invite foreign
direct investment for the intermediate goods sector like infrastructure. This paper would
have been more interesting if it has been assumed that the supply of foreign capital to our
small economy is a positive function of the net rate of return of capital. In this case we
can examine the impact of the change in tax rate on foreign capital income on welfare.
We shall take up this issue in our future research agenda.
                                          Appendix 1


                                         ˆ     ˆ            ˆ     ˆ
1.1. Derivation of the expressions for ( X I / K F ), and ( X A / K F ) .
Totally differentiating equation (5) and (6) we get the following two expressions.
    aKIXI +aKAXA=KD                                                                       (5)
    aLIXI + aLAXA+ aLMXM = Lh(KF)                                                         (6)


Now differentiating (5) & (6) we get
(aKMXI/KD)(dXI/XI) + (aKMXA/KD)(dXA/XA)=0
{aLMXI/Lh(KF)} (dXI/XI) + {aLXXA/Lh(KF)} (dXA/XA) + {aLYXM/Lh(KF)} (dXM/XM)
                                                               =(LhdKF/KF)/{Lh(KF)/KF}
        ˆ         ˆ
or, KI X I + KA X A = 0
        ˆ           ˆ         ˆ         ˆ
    LI X I + + LA X A + LM X M = (h K F KF)/h(KF)
       ˆ         ˆ
  KI X I + KA X A = 0
        ˆ         ˆ         ˆ                   ˆ
    LI X I + LA X A = (h K F KF)/h(KF) - LM X M


    ˆ     ˆ         ˆ     ˆ
KI X I / K F + KA X A / K F = 0
    ˆ     ˆ         ˆ     ˆ                        ˆ     ˆ
LI X I / K F + LA X A / K F = (hKF)/h(KF) - LM X M / K F


                                     ˆ     ˆ
From equation (4) of the text we get X M / K F = (KF /XMaKM)
     ˆ     ˆ         ˆ     ˆ
KI X I / K F + KA X A / K F = 0
      ˆ     ˆ         ˆ     ˆ
  LI X I / K F + LA X A / K F = (hKF)/h(KF) – (LM KF)/( XMaKM)
By using Cramer’s rule we get
ˆ     ˆ
X I / K F = -[KA{(hKF/h) - LM}]/ 
ˆ     ˆ
X A / K F = [KI{(hKF/h) - LM}]/ 

Here  = KILA-KALI
                                         ˆ      ˆ
1.2. Derivation of the expressions for ( X I */ K F )
Now we can consider equation (7)
aIAXA + aIMY = XI + XI*
(XAaIA/KF)(dXA/dKF) (KF/XA)+ (XMaIM/KF)(dXM/dKF) (KF/XM) =
                    (XI/KF)(dXI/dKF)(KF /XI) + (XI*/ KF)(dXI*/dKF)( KF /XI*)

        ˆ     ˆ         ˆ     ˆ     ˆ     ˆ               ˆ      ˆ
    IA X A / K F + IM X M / K F = X I / K F + (XI*/XI)( X I */ K F )
  ˆ      ˆ                   ˆ     ˆ            ˆ     ˆ         ˆ     ˆ
 X I */ K F = (XI/XI*)[(IA X A / K F ) + (IM X M / K F ) – ( X I / K F )]
           ˆ      ˆ
It implies X I */ K F = (XI/XI*)[(IAKI/ ){(hKF/h) - LM} + IM(KF/XMaKM)

                                                                  + (KA/){(hKF/h) - LM}]
  ˆ      ˆ
 X I */ K F = (XI/XI*)[{(hKF/h) – LM}{(IAKI + KA)/ } + {IM(KF /XMaKM)}]
             ˆ      ˆ
          So X I */ K F > 0 If {(hKF/h) > LM}




                                              Appendix 2


                                         ˆ     ˆ        ˆ     ˆ           ˆ     ˆ
2.1. Derivation of the expressions for ( X M / K F ), ( X F2/ K F ) and ( X A / K F ) .
Totally differentiating equation (17), (18), and (19), using equation (21) we get the
following three expressions.
    ˆ         ˆ
KM X M + KA X A = 0                                                                            (22)
     ˆ          ˆ     ˆ
KF1 X M + KF2 X F2= K F                                                                        (23)
             ˆ         ˆ          ˆ
(LM + LF1) X M + LA X A + LF2 X F2= 0                                                        (24)


                                ˆ                 ˆ
From equation (22) we can write X A = - (KM/KA) X M                                        (22)´
Putting the value of (22)´ and rearranging the above equation (24) we can get
                                   ˆ          ˆ
[(LMKA + LF1KA - LAKM) /KA] X M + LF2 X      F2 =   0
                     ˆ          ˆ
(LF1KA - |λ|)/KA] X M + LF2 X   F2   =0                                                  (24)´
where |λ| = LAKM - LMKA>0 as manufacturing sector is more capital intensive compared
to agricultural sector.


Solving equation (23) and (24)´ by crammer’s rule we can get
  ˆ     ˆ
( X M / K F ) = LF2/[(KF1LF2) – (KF2/KA)(LF1KA - |λ|)]

            = LF2/[(KF1LF2 – KF2(LF1 - |λ|/KA)]
            = LF2/[(LF1LF2 {(KF1/LF1) – (KF2/LF2)}+ |λ|(KF2/KA)]
                                                                         ˆ     ˆ
Under the assumption (KF1/LF1) > (KF2/LF2) and |λ| >0 we find that ( X M / K F ) >0.
   ˆ     ˆ
 ( X F2/ K F ) = -[(LF1KA - |λ|)/KA]/[(KF1LF2) – (KF2/KA)(LF1KA - |λ|)]

             = {|λ| -(LF1KA)}/[KA{(KF1LF2) – (KF2LF1)} + KF2|λ|]
             ={(LAKM - LMKA)-(LF1KA)}/[KALF1LF2{(KF1/LF1)–(KF2/LF2)+KF2|λ|]
Under the assumption (KF1/LF1) > (KF2/LF2)}, |λ| >0 and KM / (LM+LF1) > (KA/LA) we
            ˆ     ˆ
find that ( X F2/ K F ) >0.
  ˆ     ˆ
( X A / K F ) = -LF2KM / KA[(LF1LF2 {(KF1/LF1) – (KF2/LF2)}+ |λ|(KF2/KA)]
                                                                         ˆ     ˆ
Under the assumption (KF1/LF1) > (KF2/LF2) and |λ| >0 we find that ( X A / K F ) <0.


2.2. Derivation of the expressions for (d/dKF)
 = w.L + ( w - w).aLM.XM + r.KD – t.XM.PM
d/dKF = ( w - w).aLM.dXM/dKF - t.PMdXM/dKF
         = (dXM/dKF)[( w - w).aLM - t.PM]
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