foreign capital inflow, fiscal policies and incidence of child labour in a developing economy...

FOREIGN CAPITAL INFLOW, FISCAL POLICIES ANDINCIDENCE OF CHILD LABOUR IN A DEVELOPING

ECONOMY*

bySARBAJIT CHAUDHURI

Department of Economics, University of Calcuttaand

JAYANTA KUMAR DWIBEDI†

Department of Economics, B.K.C. College

Empirical evidence suggests that the incidence of child labour taken as awhole has declined in the developing countries with economic growth dueto foreign capital. But, in some high-growth-prone areas, the problemhas been on the rise. A pertinent question is why liberalized investmentpolicies have produced dissimilar results in different cases. The presentpaper is intended to provide an answer to the above question using athree-sector general equilibrium framework with two informal sectorsand a non-traded final commodity. The paper is also designed to inves-tigate the efficacy of an education subsidy policy and a lump-sum tax onthe richer people in controlling the problem of child labour. We find thatthe effects of different policies on child labour crucially hinge on therelative intensities in which child labour and adult labour are used in thetwo informal sectors. However, we find that on the whole a policy ofsubsidy on education is more effective in comparison with the policy ofeconomic growth with foreign capital in eradicating the prevalence of theevil in the system.

1 Introduction

Child labour is presently a phenomenon pervasive mainly in the transitionalsocieties of the developing economies. India is one among these countrieswhere the concentration of child labour is the highest in the world. In recentyears, particularly after globalization, the issue of child labour has assumedcentral importance in the social policy discussions and statutory provisionsand efforts have been directed towards its eradication and prevention.According to ILO (2002) one in every six children aged between 5 and 17, or246 million children, are involved in child labour.1 Out of 246 million about170 million child workers were found in different hazardous works. Some 8.4

* Manuscript received 21.9.04; final version received 20.4.06.† The authors are indebted to an anonymous referee of this journal for his/her interesting and

constructive comments on an earlier version of the paper. Helpful editorial suggestionsfrom Professor Chris Orme are also gratefully acknowledged. However, the usual dis-claimer applies.

1If the ‘invisible’ workers who perform unpaid and household jobs are included, it is likely thatthe estimate would shoot up significantly further.

The Manchester School Vol 75 No. 1 January 20071463–6786 17–46

© 2007 The AuthorsJournal compilation © 2007 Blackwell Publishing Ltd and The University of ManchesterPublished by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK, and 350 Main Street, Malden, MA 02148, USA.

17

million children were caught in the worst forms of child labour includingslavery, trafficking, debt bondage and other forms of forced labour, forcedrecruitment for armed conflict, prostitution, pornography and other illicitactivities.

It is a very commonly held view that child labour is fundamentally aby-product of abject poverty, strongly suggesting that policy should focus oneconomic development and increasing income. A distinctive paper in thisregard is that of Basu and Van (1998). They have shown that if child labourand adult labour are substitutes (substitution axiom) and if child leisure is aluxury commodity to the poor households (luxury axiom), unfavourableadult labour markets, responsible for a low adult wage rate, are the drivingforce behind the incidence of child labour. The World Development Report1995 (World Bank, 1995) also recognized poverty as the greatest single forcewhich creates the flow of children into the work place.2

The last two decades have witnessed revolutionary changes in liberal-izing trade and investment policies across countries, whether developed ordeveloping. The developing countries have chosen free trade as their devel-opment strategy and been able to attract a huge amount of foreign directinvestment in the same period.3 It was believed that growth with foreigncapital would take the developing countries into higher growth orbits, thebenefits of which would definitely percolate down to the bottom of society,thereby leading to reduction of poverty and poverty-driven child labourincidence. The intuitive argument is as follows. Inflows of foreign capitallead to an overall expansion of the economy. Formal sectors expand at thecost of the informal sectors. Thus, more and more workers would now beengaged in the higher-wage-paying formal sectors and the number of poorworking families from which children are sent out to work would decrease.The consequence would be a decrease in the overall supply of child labourin the economy. Although the prevalence of child labour in the developingcountries has in general decreased with economic growth, in some cases theproblem has been on the rise. In this connection, it is worthwhile mention-ing the empirical finding of a study by Swaminathan (1998) in a city inGujarat, India. The economy of Gujarat, India, has grown at a very highrate mainly due to large inflows of foreign investment in the post-reformperiod. Despite high economic growth, Swaminathan (1998) has found thatthe incidence of child labour has increased significantly in the city ofBhavnagar after globalization. A pertinent question is therefore why

2Bonnet (1993) and Basu (1999, 2000) also support the same view.3According to the World Development Report 1998–99, the amount of foreign direct investment

to the low-income countries has increased from 1502 million dollars in 1980 to 9433million dollars in 1996. The corresponding figures for South Asian countries are 464 and3479 million dollars, respectively. Besides, as per the UNCTAD (1999) and Oxfam Inter-national (2002) reports, foreign capital accounts for 11 per cent of fixed capital invest-ment (10 times the share in 1980), and almost one-third of that in the manufacturingsector.

The Manchester School18

© 2007 The AuthorsJournal compilation © 2007 Blackwell Publishing Ltd and The University of Manchester 2007

growth with foreign capital has failed to lessen the gravity of the problemof child labour in some cases while in general the incidence has decreased inthe developing countries in the liberalized regime. Unfortunately, econo-mists have so far paid very little attention to analysing the effects of theliberalized trade and investment policies on the incidence of child labour ina developing economy. However, mention should be made of a paper byChaudhuri and Gupta (2004) where an attempt has been made to examinethe implication of a tariff reduction on the incidence of child labour in theset-up of a two-sector general equilibrium model with child labour. Theyhave found that the effect of trade liberalization on the incidence of childlabour crucially hinges on the relative factor intensities of the two sectors.However, the analysis of Chaudhuri and Gupta (2004) is based on theassumptions that both the sectors use child labour in production activities,all households supply child labour, there are no non-traded commoditiesand adult labour and child labour are perfect substitutes. Some of theseassumptions may not be quite realistic in the context of a developingeconomy. Also, they have not examined the implication of an inflow offoreign capital on the incidence of child labour in the economy.

There is a theoretical literature, including Baland and Robinson (2000),Ranjan (2001) and Jafarey and Lahiri (2002), which emphasizes the impor-tance of capital-market imperfection as a contributing factor to inefficientchild labour. According to this line of thinking, the cost of providing educa-tion to children including the opportunity cost, expected return to educationand the borrowing terms in the capital market are important determinants ofhuman capital accumulation and hence of children’s labour supply. Byacquiring education, children are able to enhance their wage-earning poten-tial in later life. However, during the period of skill formation, the householdforgoes the income the child labour could have earned by working instead. Inorder to calculate the pecuniary returns to education, the head of the workingfamily discounts the future increase in wages by a discount factor and com-pares this return with the forgone child wages in the current period. If thehousehold has access to the credit market, the discount rate should be theinterest rate on borrowing. Therefore, given the discount rate, increasededucational opportunities are expected to lower the supply of child labour byincreasing the discounted returns in future. On the other hand, given thereturns to education, a provision of credit at a subsidized rate is also likely toproduce the same result. However, the explanation of the child labour inci-dence in terms of credit market imperfection crucially hinges on the presup-position that returns to education are sufficiently high, which, in turn,assumes that the quality of schools is also satisfactory. But a few importantempirical studies4 have reported the abysmal state of the existing primary

4A study of India by PROBE (1999) found that the state of basic education was appalling and,even though parents valued education in its own right, they believed that their offspring

Foreign Capital and Incidence of Child Labour 19


education system in the developing countries, including India. Besides, thistheory of child labour is based on the notion of a mutually altruistic house-hold. It is implicitly assumed that when parents borrow against the futureincomes of their children, the repayment of the loan is a shared burden.However, Baland and Robinson (2000) have argued that, in the absence ofmutual altruism, the provision of credit at a reasonable rate might not beenough to rectify the occurrence of excessive levels of child labour. Prevailinglaws and attitudes in most societies do not allow parents to undertake debtsthat can be passed on by them as the responsibility of their children in future.

What has been the impact of the liberalized trade policies on the inci-dence of child labour across developing countries in the era of globalization?To find an answer to this question, we should go through the empirical workof Cigno et al. (2002). While analysing the cross-country data, they havefound that globalization can contribute to reducing child labour by increas-ing the returns to education. According to them, the effect of globalization onchild labour will be much more pronounced in the developing countrieswhich take part in world trade with a comparatively larger share of educatedworkforce than those with a largely uneducated workforce.

Although the relation of child labour to education and human capitalformation should ideally be analysed in a dynamic framework, the role ofeducation on the incidence of child labour can be examined even in a staticframework in an indirect way. We have already argued how an increase in thereturn to education and/or a decrease in the interest rate in the capital marketand/or a reduction in the cost of education including the opportunity cost cancause the child labour to decline. Thus, it can be argued that, given the returnto education and the discount rate (interest rate), the incidence of child labouris expected to fall owing to a reduction in the cost of education. As the costof education includes the opportunity cost of not sending children to work, asubsidy policy on education consisting of mid-day meals and/or provisionsfor a cash stipend should tend to lower the effective child wage and hencelower the cost of education indirectly. Moreover, in a society with highfertility rate, poor perception of the parents about future benefits of chil-dren’s education, low quality of schooling and households’ objectives tomaximize present income, one of the main motives behind the decision of thepoorer households in sending some of their offspring to public school is toderive the immediate benefits of an education subsidy policy.5

were unlikely to benefit from education in its current state. UNICEF (1997) cited lowquality of schooling as an important reason for high dropout rates among primary schoolstudents in the developing countries. Based on this observation, Jafarey and Lahiri (2002)have shown that child labour can coexist with child schooling even if credit markets areperfect.

5In this context, mention should be made of an empirical paper by Ravallion and Wodon (2000)who have found that the school enrolment subsidy substantially increased the number ofschool-going children from the poorer section of the households in Bangladesh. But themagnitude of the decline in the incidence of child labour as a proportion of the total amountof enrolment subsidy was not very significant.



The present paper is designed to examine the implications of capitalaccumulation through inflows of foreign capital and an education subsidypolicy on the poverty-induced child labour incidence in a developingeconomy in a general equilibrium set-up. We consider a three-sector full-employment model with child labour. The economy is divided into oneformal and two informal sectors. One of the two informal sectors (sector 1)produces an exportable agricultural commodity using adult labour, childlabour and capital, while the other (sector 2) produces a non-traded finalcommodity6 for the richer section of the population with the help of two typesof labour only. On the other hand, the formal sector (sector 3) produces amanufacturing commodity using adult labour and capital and this is theimport-competing sector of the economy. So, in the two informal sectors,adult labour and child labour are substitutes. In this set-up, we shall examinethe effects of an inflow of foreign capital and an education subsidy policy onthe aggregate supply of child labour in the economy. As the non-traded finalcommodity produced in sector 2 is consumed only by the richer section of thepopulation, an imposition of a lump-sum tax on this group of the populationis expected to provide a desirable impact on the incidence of child labourthrough a decrease in the demand for the commodity. The efficacy of thispolicy has also been studied. It is found that the effects of all these policiescrucially hinge on the relative child labour intensities of the two informalsectors with respect to adult labour. When the export sector is more childlabour intensive vis-à-vis the non-traded sector, an inflow of foreign capitalunambiguously lowers the incidence of child labour in the society. The edu-cation subsidy policy is also expected to produce the same result. However,an imposition of a lump-sum tax on the richer section of the populationproduces a perverse effect. In contrast, an inflow of foreign capital may becounterproductive when the non-traded sector is child labour intensive. But,an education subsidy policy and/or a lump-sum tax on the richer people arelikely to produce the desired result on the supply of child labour in theeconomy. A balanced-budget change in the education subsidy and the lump-sum tax fortifies the possibility of a reduction in the incidence of child labourin this case. So, the present theoretical analysis despite its limitations7

explains why a policy of growth with foreign capital may produce dissimilarresults on child labour under different circumstances and points to an edu-cation subsidy policy as a possible solution to the problem of child labour inthe developing countries.

6Domestic services, shoe shining, collection of seashells and prostitution in urban areas areclassic examples of such production activities.

7We admit that, in terms of the present static framework, we are unable to capture the relationof child labour to education and human capital formation in a satisfactory way. However,we have taken over the role of education on the incidence of child labour in an indirect way.We have explained this point in detail in the previous paragraph.



2 The Model

The economy we consider is a small open less developed economy, which isdivided into two informal sectors and one formal sector. There are two typesof labour available in the economy: adult labour and child labour. One of thetwo informal sectors (sector 1) produces an agricultural commodity, X1, withthe help of adult labour, child labour and capital. However, there is substi-tutability between adult labour and child labour. Sector 2 (another informalsector) produces a non-traded final commodity, X2, with the help of childlabour and adult labour. Domestic services, prostitution, collection of sea-shells and shoe shining are some of the classic examples of such productionactivities.8 Generally these types of goods and services are consumed (used)by the richer section of the working class employed in the higher-wage-payingformal sector and by the owners of capital.9 The formal sector (sector 3) thatproduces a manufacturing commodity, X3, is the import-competing sector ofthe economy. It uses adult labour and capital in its production.10 Owing toeffective wage legislation and unionization of labour, the adult wage rate inthe formal sector is fixed at W*, which is greater than the competitive infor-mal sector adult wage, W.11 The very low adult wage rate in the informalsector (a developing economy phenomenon) forces the poor families to sendsome of their offspring to the job market.

Production functions satisfy constant returns to scale with positive butdiminishing returns to each factor. Markets, except the formal sectorlabour market, are perfectly competitive. The adult labour allocationmechanism is of the following type. Adult workers first try to get employ-ment in the formal manufacturing sector and those who are unable to findemployment in the said sector are automatically absorbed in the two infor-mal sectors, as there is complete wage flexibility in the latter sectors. Adultlabour and child labour are completely mobile between the two informalsectors but adult labour is imperfectly mobile between the formal and theinformal sectors. On the other hand, capital is completely mobile betweensectors 1 and 3. Owing to the small open economy assumption, prices of X1

and X3 are given internationally. As the commodity produced by sector 2 isproduced and consumed domestically, its price is determined within theeconomy by demand and supply forces. The formal sector (sector 3) is morecapital intensive vis-à-vis the agricultural sector (sector 1) with respect toadult labour in the physical sense. However, we at this stage do not make

8These production activities use very little capital and so we can ignore capital as an input in thissector.

9See footnote 17 in this context.10The use of child labour is strictly prohibited in sector 3, as it is the formal sector of the economy.11Assuming that each formal sector firm has a separate trade union, the unionized wage function

may be derived as a solution to the Nash bargaining game between the representative firmand the representative union in the formal sector industry. For details see Chaudhuri(2003).



any assumption regarding the relative intensities at which child labour andadult labour are used in the two informal sectors. In a subsequent section,we shall consider both the cases separately and see how the results of themodel change under alternative factor intensity conditions. Finally, com-modity 1 is chosen as the numéraire.

The following symbols will be used in the formal presentation of themodel.

aLi adult labour–output ratio in the ith sector, i = 1, 2, 3aCi child labour–output ratio in the ith sector, i = 1, 2aKi capital–output ratio in the ith sector, i = 1, 3P1 1 (commodity 1 is the numéraire)P2 price of the non-traded final commodity (determined endogenously)P3 world price of commodity 3W adult wage in the two informal sectorsW* unionized adult wage in the formal sectorWC child wageR return to capitalL adult labour endowment of the economylC supply of child labour by each poor working familyLC aggregate supply of child labourLI number of adult workers engaged in the two informal sectorsKD domestic capital stock of the economyK economy’s aggregate capital stock (foreign plus domestic)qji distributive share of the jth input in the ith industry, j = L, K, LC and

i = 1, 2, 3lji proportion of the jth input employed in the ith industry, j = L, K, LC

and i = 1, 2, 3S ji

k the degree of substitution between factors j and i in the kth sector, j,i = L, LC, K and k = 1, 2, 3. For example, S W a a WL C L L CC

11 1≡ ( ) ∂ ∂( ),

S W a a WL L LL

11 1≡ ( ) ∂ ∂( ) etc. S ji

k > 0 for j � i and S jjk < 0.

Y aggregate income of the richer section of the populationCi level of consumption of the ith commodity by each poor household,

i = 1, 3∧ proportional change

2.1 Supply Function of Child Labour

In this section, we derive the supply function of child labour from theutility-maximizing behaviour of the representative altruistic poor house-hold. We assume that each working family consists of one adult worker anda certain number of children. There are a L numbers of working famil-ies, which are classified into two groups with respect to the earnings oftheir adult members. The adult workers who work in the higher paidformal manufacturing sector comprise the richer section of the working



population. In contrast, labourers who are engaged in the two informalsectors constitute the poorer section. There is now considerable evidenceand theoretical reason for believing that, in developing countries, parentssend their children out to work out of sheer poverty. A distinctive paper inthis regard is that of Basu and Van (1998). Following their ‘luxury axiom’,12

we assume that there exists a critical level of family (or adult labour)income, W , from non-child labour sources, such that the parents will sendtheir children out to work if and only if the actual adult wage rate is lessthan this critical level. We can easily assume that each worker in the formalmanufacturing sector earns a wage income, W*, sufficiently greater thanthis critical level. So, the workers belonging to this group do not let theirchildren go to work. On the other hand, each adult worker in the informalsectors earns W amount of wage income, which is less than W , and there-fore send off many of their children to the job market to supplement lowfamily incomes.

The altruistic adult member of the family (guardian) decides the numberof children to be sent to the work place. The rest of the children are sent toschool. We also assume that there is only a public educational system13,14

available to the children in the economy and that it is entirely financed bygovernment subsidy on this account. The richer workers do not send theirchildren to the job market. In the public education system in the developingeconomies, there are provisions for the children from the poorer families toget stipend, free educational goods and free mid-day meals. It is sensible toassume that the higher the subsidy on education, E, the higher would be thefree educational facilities and the related benefits, B, associated with childschooling. On the other hand, the larger the number of children sent toschool, the higher would be the aggregate benefits accruing to the poorfamilies. We make the simplifying assumption that the money value of suchbenefits is strictly proportional to the number of children sent to school. Theutility function of the household is given by

12An empirically testable hypothesis of Basu and Van’s model is that child labour arises if adulthousehold income falls below some benchmark level. This hypothesis has been tested bydifferent economists for different countries. Studies by Ray (1999) for India, Ray (2000) forPakistan and Peru, Addision et al. (1997) for Ghana and Pakistan and Bhalotra (2000) forPakistan have found the ‘luxury axiom’ of Basu and Van (1998) to be more or lessstatistically valid.

13Governments all over the world devote substantial resources to their education sector. This isespecially true in developing countries. In 1995, public spending on education accountedfor 15.7 per cent of total government expenditure in developing countries (see Bedi andGarg, 2000). Furthermore, the majority of students in developing countries are educated inpublicly funded and publicly managed educational institutions. According to Jimenez andLockheed (1995), almost 90 per cent of all primary and 70 per cent of all secondaryenrolments in developing countries are in public schools.

14The analysis in this paper, being static in nature, does not deal with an important aspect of childlabour—its relation to education and human capital formation. We have already discussedthis point in detail in Section 1.



U U C C n lC= −( )( )1 3, ,

The household derives utility from the consumption of the two traded(final) commodities and from the children’s leisure. As the poor householdsdo not consume the non-traded final commodity, it is not included in theirutility function. However, children’s leisure here does not imply that thechildren who are not sent out to work are kept at home. They are sent toschool. The altruistic guardian of the family derives utility from this sourcebecause at least some of his children have been kept out from the workhazards. Besides, by sending some of the children to school, the familysecures current income gain from access to the different incentives that thesubsidized education scheme provides. For analytical simplicity let us con-sider the following Cobb–Douglas type of utility function:

U A C C n lC= ( ) ( ) −( )1 3α β γ (1)

with A > 0 and 1 > a, b, g > 0; and a + b + g = 1. It satisfies all the standardproperties and is homogeneous of degree 1. The parameter g denotesthe degree of altruism of the guardian towards the well-being of hischildren.

Ruling out the possibility for any child worker attending school toundertake any part-time job, the budget constraint of the representative poorhousehold is given by the following:

C PC W l W n l B EC C C1 3 3+ = +( ) + −( ) ( ) (2)

where W is the income of the adult worker, WClC measures the income fromchild labour and (n - lC)B(E ) is the money value of the benefits derived by thehousehold from sending n - lC number of children to school. Note that B′(.)is positive. Here the effective child wage rate is WC - B(E ).15

Maximization of the utility function subject to the above budget con-straint gives us the following first-order conditions:

α β γU C U PC U n l W B EC C1 3 3= = −( ) − ( )[ ] (3)

From (3) we get the following expressions:

C n l W B EC C1 = −( ) − ( )[ ]α γ (4)

C n l W B E PC C3 3= −( ) − ( )[ ]β γ (5)

Substitution of the values of C1 and C3 into the budget constraint andsimplification give us the following labour supply function:

ln W B E W

W B EC

C

C

=+( ) − ( )[ ]−

− ( )α β γ

(6)

15We assume that WC > B(E). Otherwise, no children are sent to the job market.



This is the supply function of child labour by each poor family. We nowanalyse its properties. First, lC varies negatively with the adult wage rate, W.A rise in W produces a positive income effect so that the adult worker sendsa larger number of children to school and therefore decides to send a lowernumber of children to the work place. An increase in WC (or an increase inWC - B(E)), on the other hand, produces a negative price effect, whichincreases the supply of child labour from the family.16

There are L L a XI L= −( )3 3 adult workers engaged in the two informalsectors and each of them sends lC number of children to thejob market. Thus, the aggregate supply of child labour in the economy isgiven by

Ln W B E W

W B EL a XC

C

CL=

+( ) − ( )[ ]−− ( )

−( )α β γ3 3 (7)

2.2 The General Equilibrium Analysis

Given the assumption of perfectly competitive markets, the usual price–unitcost equality conditions relating to the three sectors of the economy are givenby the following three equations, respectively:

Wa W a RaL C C K1 1 1 1+ + = (8)

Wa W a PL C C2 2 2+ = (9)

W a Ra PL K* 3 3 3+ = (10)

The demand for the commodity produced in sector 2 comes from the richersection of the society.17 Hence the demand function for commodity 2 is asfollows:

D D P Y= ( )2 , (11)

with usual price and income effects, i.e. ∂D/∂P2 < 0 and ∂D/∂Y > 0. It may bepointed out that prices of the other two commodities also figure in thedemand function for commodity 2. However, as these are exogenously given,they have not been included in the demand function.

Total income of the richer section of the society consists of wage incomeof the formal sector workers and the rental income of the owners of domestic

16One may verify that the results of this paper hold for any utility function that satisfies these twoproperties.

17It may be checked that the qualitative results of this model hold under different sufficientconditions even if the poorer section of the working class is allowed to consume thiscommodity.



capital. Denoting Y as the income of the said class, the expression for Y canbe written as18

Y W a X RK TL D= + −* 3 3 (12)

where T is the lump-sum tax on the richer section of the population.In equilibrium, the supply of the non-traded final commodity must equal

its demand. So, we have

X D P Y2 2= ( ), (13)

Using (12), equation (13) may be rewritten as follows:

X D P W a X RK TL D2 2 33= + −( ), * (13.1)

Complete utilization of adult labour, capital and child labour implies thefollowing three equations, respectively:

a X a X a X LL L L1 2 31 2 3+ + = (14)

a X a X KK K1 31 3+ = (15)

a X a X LC C C1 21 2+ = (16)

Using (7), one may rewrite equation (16) as follows:

a X a Xn W B E W

W B EL a XC C

C

CL1 2 31 2 3+ =

+( ) − ( )[ ]−− ( )

−( )α β γ(16.1)

In this general equilibrium model, we have 10 endogenous variables(namely, W, WC, R, P2, D, Y, X1, X2, X3 and LC) and the same number ofindependent equations (namely, equations (7)–(12), (13.1), (14), (15) and(16.1)). The policy parameters are K, E and T. Equations (8)–(10) togetherconstitute the price system with four endogenous variables: W, WC, R andP2. Clearly, this is an indecomposable production structure. R is obtainedfrom (10) as W* is given. It should be noted that, once R is known, sectors1 and 2 can effectively be viewed as a Heckscher–Ohlin subsystem (HOSS).So, W and WC can be obtained from equations (8) and (9) as functions ofP2. Then solving equations (14), (15) and (16.1) simultaneously, one canfind X1, X2 and X3 as functions of P2. The equilibrium value of P2 can beobtained from (13.1). Y is now found from (12). One can get D from (11).Finally, LC is obtained from equation (7). Note that once factor prices areknown the factor coefficients aji are also known as these are functions of theinput prices.

18We assume that the rental income from foreign capital is fully repatriated and therefore it is notincluded in Y.



3 Comparative Statics

According to the conventional wisdom, an overall economic expansioninduced by an inflow of foreign capital is likely to take the developingcountries into higher growth orbits, the benefits of which would percolatedown to the poor people. Thus, this policy is expected to exert downwardpressure on the incidence of poverty-induced child labour. On the other hand,a policy of education subsidy is expected to reduce the supply of child labourdirectly while a lump-sum tax on the richer section of the population, whoconsume the non-traded final commodity produced using child labour (andadult labour), is likely to lessen the gravity of the problem from the demandside through a decrease in their disposable income. In this section, we shallexamine the efficacy of these policies to control the supply of child labour inthe given set-up.

Totally differentiating equations (8), (9) and (10) and solving byCramer’s rule, the following expressions can be obtained:

R = 0 (17)

ˆ ˆW PC= −1

1 2θθ (18)

ˆ ˆW PC L=1

1 2θθ (19)

where θ θ θ θ θ= −L C C L1 2 1 2.Differentiating equations (14), (15) and (16.1), solving by Cramer’s rule

and using (17)–(19), one can get the following expressions:19

ˆ ˆ ˆ ˆX K Z P G EL CL

LL K1 1 2 3

113 2

2

3

2 3= −−

⎛⎝⎜

⎞⎠⎟

+ −⎡⎣⎢

⎤⎦⎥λ

λ λλ

λλ λ (20)

ˆ ˆ ˆ ˆX K Z P G ELL

LC L K K L2 2 2 3

113

1

3

1 1 3 1 3=−

−⎛⎝⎜

⎞⎠⎟

+ + −( )⎡⎣⎢λλ

λλ

λ λ λ λ λ ⎤⎤⎦⎥

(21)

and

ˆ ˆ ˆ ˆX K Z P G EL C L C L K3 3 2 31

2 1 1 2 2 1= −( ) − +⎡⎣ ⎤⎦λλ λ λ λ λ λ (22)

where

λ λ λ λ λλ λ

λ= −( ) −

−L C L CK L

L2 1 1 2

3 3

31(23.1)20

19See Appendix A for derivation.20Actually, the expression for |l| is somewhat different but may be simplified to this present form.

See Appendix E in this context.



A S S S

A S

L L L L L C L L C

KK C

C C K

L

11 2 1

21

1 2 1 1 1 1

11

1= +( ) +( ) +[ ]

=

λ λ θ θ λ θθ

λθ

θ −−( ) =+ ( )[ ]

− ( )[ ]>

=− ( )[ ]

>

S GW W nB E

l W B E

GW

l W B E

K LC

C C

C C

C

11 2

2

1 0

0

θ γ

γGG

B E W nW

l W B E

A S S

C

C C

C C C L C CL L

3 2

31 2

0

11 1 1 2

= ′ +[ ]− ( )[ ]

>

= +( ) +

γ

θλ θ θ λ θθ θ λ θ θ θ

λ λ λ λ

C L C C L C L

K C L L

S G G

Z A A

K1 1 1 1 1 1

3 2 2 3

12 1

1 1 3

+( ) + + +[ ]

= +( ) + AA

Z A A

CL

L

LL

LC L K

2

2 2 3

22

3

31

3

1 1 3

1

1

λλ

λ

λλ

λλ λ λ λ

−−

⎛⎝⎜

⎞⎠⎟

=−

−⎛⎝⎜

⎞⎠⎟

− − KK LK L

LK C

L C L C

A

Z A A

1 31 3

3

3 1

2 1 1 2

1

3 2

1λ

λ λλ

λ λ

λ λ λ λ

( ) +−

−⎛⎝⎜

⎞⎠⎟

= − −( ) + 33 12 1 1 2λ λ λ λL K K CA+

(23.2)

Differentiating equation (11) and using (22) and (23.1), it is easy to check21

that the stability condition in the market for the non-traded final commodityis as follows:

EE W L

YZ

ZP

Y L2

33

2 0− − = <λ

λλ

*Δ (24)

where EP2 and EY are the own price and income elasticities of demand forcommodity 2, respectively.

Differentiating equation (11) once more, using (21) and (22) and simpli-fying, one can find22

ˆ ˆ ˆ ˆP Q K Q E Q T2 1 2 3= + + (25.1)

where

QE W L

YL

L

LC

Y LL C L C1

1 113

1

3

13

2 1 1 2=−

−⎛⎝⎜

⎞⎠⎟

− −( )⎡⎣⎢

⎤⎦λ

λλ

λλ

λλ λ λ λ

Δ*

⎥⎥

= −( ) −⎡⎣⎢

⎤⎦⎥

−( ) +( ) +( )

QG E W L

Y

Q

L K K LY L

L K23

3

11 3 1 3

32 1λ

λ λ λ λλ

λ λΔ

*

== < ( )( )

−( ) +( )

⎫

⎬

⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪

E TY

Y

Δ0 24using

(25.2)

21This is derived in Appendix B.22See Appendix C for the derivation of equation (25.1).



Finally, differentiating equation (7) and using (18), (19) and (22), the follow-ing expression23 may be obtained:

ˆ ˆ ˆ ˆ

ˆ

LG

PG

P G E

K Z

C L C

L

LL C L C

= + −

−−

−( ) −

12

22 31 1

3

3

2 1 1 211

θθ

θθ

λλ λ

λ λ λ λ 33 2 32 1ˆ ˆP G EL K+⎡⎣ ⎤⎦λ λ (26.1)

Now substituting P2 from (25.1) into (26.1) and simplifying, we get

ˆ ˆL I I I Q K I I I QC W W LL

K LW W L

L

C C= + +( ) −−

⎡⎣⎢

⎤⎦⎥

+ + +( )⎡⎣⎢

− +

1 23

3 3

1

λλ λ

λ 33

3

2 1

13 3−

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

+ + +( )[ ]λ

λ λλL

L KW W LG E I I I Q TC

ˆ ˆ (26.2)

where

IG

IG

I ZW L W C LL

LC = = =

−1 2

31 13

311

θθ

θθ

λλ λ (27)

We are now in a position to analyse the consequences of different poli-cies on the incidence of child labour in the society. Any changes in the policyparameters affect the aggregate supply of child labour in the society bothdirectly and indirectly. The indirect effects arise due to a change in the priceof the non-traded commodity and take place through changes in the adultand child wage rates and the use of capital in the export sector (sector 1). Inorder to find the overall impact of a policy, we need to identify each effectseparately. For that purpose one can find equation (26.1) quite handy. Insome cases, the different effects work in opposite directions and it is notpossible to predict the net outcome of a policy on child labour unequivocally.However, we can at least find reasonable condition(s) under which qualitativeresults may be predicted. In such cases we shall use equation (26.2).

From equation (7) we should note that the aggregate supply of childlabour in the economy, LC, depends on three factors. It depends negatively onthe informal sector adult wage, W, and positively on both the child wage, WC,and the number of poor families supplying child labour, L a XL− 3 3 . So, adecrease in WC and/or an increase in W and/or a decrease in L a XL− 3 3 causesthe aggregate supply of child labour to decline and vice versa. These threebroad effects may, respectively, be termed the child wage effect, the adult wageeffect and the adult labour reallocation effect. The first two effects can only beof induced type while the last effect can be of both direct and induced types.

As sectors 1 and 2 together form a HOSS, the two wage rates change (inopposite directions) only if there occurs a change in the price of the non-

23Equation (26) is derived in Appendix D.



traded commodity, P2 (Stolper–Samuelson effect). So, the two wage effectsproduce only indirect effects on child labour. The first two terms on theright-hand side of equation (26.1) capture the child wage effect and the adultwage effect, respectively. Moreover, a change in P2 also produces a Rybczyn-ski type effect24 in the HOSS resulting in a change in the sectoral compositionof output. If sector 1 expands (contracts), it requires more (less) capital thanbefore which has to be released (absorbed) by sector 3. Consequently, sector3 contracts (expands) both in terms of output and employment. This is theinduced adult labour reallocation effect which arises owing to a change in P2

and is captured by the second term within square brackets on the right-handside of (26.1).

Policies like an inflow of foreign capital and an increase in the subsidyon education have both direct and indirect effects on the incidence of childlabour while an imposition of a lump-sum tax on the richer section of thepopulation has only indirect effects. An inflow of foreign capital produces aRybczynski effect and leads to an expansion of sector 3 and a contraction ofsector 1 as sector 3 is more capital intensive relative to sector 1 in thephysical sense. But the return to capital, R, does not change as it is deter-mined from the zero-profit condition for sector 3 (equation (10)). As moreadult workers are now employed in sector 3, the number of working familiessupplying child labour decreases. This is the direct adult labour reallocationeffect of an inflow of foreign capital that lowers the incidence of child labourgiven the two wage rates and is captured by the first term within squarebrackets on the right-hand side of (26.1). Sector 2 contracts in tandem withsector 1 as the availability of the two types of labour decreases in the HOSS.Now as the higher-wage-paying sector (sector 3) expands, the aggregateincome of the richer people rises which in turn raises the demand for thenon-traded final commodity. The price of the non-traded good, P2, risesunambiguously which generates a Stolper–Samuelson effect and causes thetwo wage rates to change. This produces two induced wage effects on thesupply of child labour. As explained above, an induced adult labour real-location effect will also take place. These are the three induced effects of aninflow of foreign capital that work through a change in P2.

On the other hand, an increase in the educational subsidy, E, ceterisparibus, lowers the effective child wage rate, WC - B(E), and hence the supplyof child labour. This is the first direct effect of this policy and is representedby the third term on the right-hand side of (26.1). This may be called theeffective child wage effect. It produces a Rybczynski effect in the HOSSleading to a (an) contraction (expansion) of the more (less) child-labour-intensive sector depending on the relative child labour intensities of the two

24A Stolper–Samuelson effect contains an element of the Rybczynski effect if the technologies ofproduction are of the variable coefficient type. This is a well-known result in the theory ofinternational trade.



sectors. If sector 1 contracts (expands), some amount of capital is released(absorbed) which is now absorbed in (released by) sector 3. So, sector 3expands (contracts) in terms of both output and employment of adult labourand consequently the number of working families supplying child labourdecreases (increases). This is the direct adult labour reallocation effect whichtakes place without any changes in P2. This second direct effect of an educa-tion subsidy policy is encapsulated by the third term within square bracketson the right-hand side of (26.1). This causes the aggregate income of thericher people to change and hence the demand for the non-traded finalcommodity. The supply of this commodity has also changed. Consequently,the price of this commodity changes and two induced wage effects on thesupply of child labour would take place.

Finally, a lump-sum tax on the affluent section of the population affectsthe aggregate supply of child labour only indirectly through a change in P2.We have already discussed in detail how a change in P2 generates a child wageeffect, an adult wage effect and an induced adult labour reallocation effect.

As both sectors 1 and 2 use adult labour and child labour and form aHOSS, these can be classified in terms of factor intensities.25 The signs ofdifferent effects, especially those of induced effects, depend crucially on therelative factor intensities of these two sectors. Depending on this classifica-tion there can arise two cases. We are now going to discuss these one by one.For analytical simplicity, we assume that the per unit requirement of capital,aK1, is given technologically.26

Let us first consider the case where the export sector (sector 1) is moreintensive in the use of child labour relative to the non-traded sector (sector 2).From equation (26.2) the following proposition can be proved.27

Proposition 1: When the export sector is more child labour intensive thanthe non-traded sector with respect to adult labour, the incidence of childlabour in the economy (i) falls unambiguously due to an inflow of foreign

25Available empirical evidence suggests that the concentration of child labour is the highest in therural sector of a developing economy and that child labour is used intensively directly orindirectly in the agricultural sector. On the other hand, most adult employment in devel-oping countries is still in agriculture. See the International Labour Office (2002) andGovernment of India (2000) reports in this context. But, whether the ratio of child labourto adult labour used in agriculture is greater than or less than that in non-agriculturalactivities is quite inconclusive. So, we consider both the cases here and see how the effectsof different policies on child labour change under different factor intensity conditions.

26It rules out the possibility of substitution between capital and other factors of production (i.e.adult labour and child labour) in sector 1. Although this is a simplifying assumption, it isnot totally unrealistic. For cultivation with high yielding variety seeds, frequently used inseveral areas of a developing economy, different inputs such as fertilizers, pesticides,herbicides and water should be used in recommended doses. In other words, there arecomplementarities between these inputs and these are not substitutable with the input,labour. See Dasgupta (1977) for a detailed discussion on this aspect. It may be checked,however, that the qualitative results of the model hold under different condition(s) even ifwe allow substitutability between labour and capital.

27See Appendix E for the mathematical proof.



capital, (ii) falls following an education subsidy policy ifλ λ λ λ λL K Y L L KE W L Y1 3 3 2 1≤ * , and (iii) increases unambiguously due to impo-sition of a lump-sum tax on the richer section of the population.

We have already explained how an inflow of foreign capital lowers theincidence of child labour through the direct adult labour reallocation effectand leads to an increase in the price of the non-traded commodity, P2. Anincrease in P2, in turn, lowers the child wage rate, WC, and raises the informaladult wage rate, W, following a Stolper–Samuelson effect as sector 2 isintensive in the use of adult labour vis-à-vis sector 1. So the two induced wageeffects also exert downward pressures on the supply of child labour. In thiscase, all the effects work in the same direction and together contribute to anunambiguous decrease in the incidence of child labour in the economy.

On the other hand, an increase in the subsidy on education raises themarginal benefit of sending children to school. Other things remainingunchanged, this lowers the effective child wage rate and hence produces adirect contractionary effect on child labour. A Rybczynski effect in the HOSStakes place leading to a (an) contraction (expansion) of the more (less)child-labour-intensive sector, i.e. sector 1 (sector 2). As sector 1 contracts,some amount of capital is released which is now absorbed in sector 3. So,sector 3 expands in terms of both output and employment of adult labour.This is the direct adult labour reallocation effect which lowers the supply ofchild labour. The aggregate income of the richer section of the populationrises as more adult workers are now employed in the higher-wage-payingsector. This leads to an increase in the demand for commodity 2. Thus, wefind that there are two opposite effects on the price of commodity 2, P2, asboth the demand and the supply of this commodity have increased. However,the positive effect of an increase in demand on P2 outweighs the negativeeffect of an increase in supply under the sufficient condition as stated inProposition 1. As P2 rises, the competitive adult wage, W, rises and the childwage, WC, falls following a Stolper–Samuelson effect. Thus, we find that allthe direct and indirect effects work in the same direction and together lead toa reduction in the incidence of child labour subject to the sufficient conditionas mentioned above. However, it should be pointed out that one may get thesame result under a few other sufficient conditions as well.

Finally, a lump-sum tax, T, on the richer people has no direct effects onchild labour. However, it lowers the aggregate disposable income, Y - T, ofthis section of the population and hence the demand for the non-tradedcommodity. This leads to a fall in P2. As P2 decreases, W falls and WC risesfollowing a Stolper–Samuelson effect as sector 2 is intensive in the use ofadult labour with respect to child labour relative to sector 1 in this case.Besides, sector 1 expands at the cost of sector 2 following a Rybczynski typeeffect. This leads to a contraction of sector 3 as it has to release capital to theexpanding sector 1. As a consequence, the number of working families



employed in sector 3 falls. This means that more working families will now besupplying child labour. In this case, all the three effects, namely the childwage effect, the adult wage effect and an induced adult labour reallocationeffect, work in the same direction and together contribute to an unambiguousincrease in the incidence of child labour in the society. This is an interestingresult as it is counterintuitive to the common wisdom.

Now, we are going to analyse the case where the non-traded sector ismore child labour intensive with respect to adult labour vis-à-vis the exportsector. In this case, unlike the previous one, different effects of a policychange work on the supply of child labour in opposite directions. Althoughunambiguous consequences cannot be predicted, some counter-intuitive results may be obtained subject to a few reasonable conditions.For this purpose, we consider equation (26.2) and derive the followingproposition.28

Proposition 2: In a situation where the export sector is less childlabour intensive vis-à-vis the non-traded final good sector, the incidenceof child labour (i) rises owing to an inflow of foreigncapital if I I QW L L K LC +( ) ≥ −( )1 3 3 3λ λ λ , (ii) falls due to a hike in subsidyon education if λ λ λ λ λL K L L K YE W L Y1 3 3 2 1≤ * and I I I QW W LC + +( ) ≤2

λ λ λ λ λL L K LG3 2 1 33 1−( )[ ] , and (iii) decreases following a lump-sum tax on thericher people if I I QW LC +( ) ≤3 0.

As explained previously, an inflow of foreign capital causes sector 3 toexpand in terms of both output and employment, exerts a downward pressureon child labour through the direct adult labour reallocation effect and causesboth sectors 1 and 2 to contract. Besides, the aggregate income of the richersection of the population, denoted Y, increases which raises the demand forcommodity 2. So, the price of commodity 2, i.e. P2, rises unambiguously.When P2 rises, the competitive adult wage, W, falls and the child wage, WC,rises owing to a Stolper–Samuelson effect as sector 2 is now more child labourintensive vis-à-vis sector 1. So, the supply of child labour by each poorworking family rises due to the two induced wage effects. Sector 1 contractsfurther following a Rybczynski type effect and releases some more capital tosector 3. This causes a supplementary expansion of sector 3. This is theinduced adult labour reallocation effect which arises following an increase inP2. Thus, we find that the two induced wage effects tend to increase theincidence of child labour while both the direct and indirect adult labourreallocation effects work in the opposite direction. The net result of theseeffects will be an increase in the aggregate supply of child labour in the societyunder the sufficient condition I I QW L L K LC +( ) ≥ −( )1 3 3 3λ λ λ . This condition

28This is proved in Appendix E.



implies that the strength of the induced child wage effect is greater than thejoint strength of the two adult labour reallocation effects.29

A hike in the education subsidy, ceteris paribus, lowers the effective childwage rate and hence lowers the supply of child labour by each poor familythrough the effective child wage effect. This produces a Rybczynski effect inthe HOSS leading to a (an) contraction (expansion) of sector 2 (sector 1). Thisalso causes sector 3 to contract in terms of both output and employment ofadult labour as it has to release capital to the expanding sector 1. This leadsto a decrease in the demand for commodity 2 through a decrease in Y. Thus,we find that both the demand and supply of commodity 2 fall and hence therearise two opposite effects on P2. However, P2 falls under the sufficient con-dition that λ λ λ λ λL K Y L L KE W L Y1 3 3 2 1≤ * . As P2 falls, W rises and WC falls dueto a Stolper–Samuelson effect. There will be an additional expansionaryeffect on sector 1 following a Rybczynski type effect in the HOSS thatrequires sector 3 to release some more capital to sector 1. Sector 3 contractsfurther in terms of both output and employment. This is the induced adultlabour reallocation effect. So, there are now more child-labour-supplyingfamilies with each of them sending out a lower number of children to workthan before. The net outcome will be a fall in the incidence of child labour inthe society if I I I Q GW W L L L K LC + +( ) ≤ −( )[ ]2 33 2 1 31λ λ λ λ λ . This conditionmeans that the two induced wage effects collectively dominate over the twoadult labour reallocation effects.30

Finally, the imposition of a lump-sum tax on the richer people lowers theprice of commodity 2, P2. This produces a Stolper–Samuelson effect in theHOSS and leads to an increase in the competitive adult wage, W, and adecrease in the child wage, WC, as sector 2 is now more child labour intensiverelative to sector 1. Thus, the supply of child labour by each poor familydecreases due to the two induced wage effects. Also, sector 1 expands andsector 2 contracts following a Rybczynski type effect. Sector 3 contracts as ithas to release capital to the expanding sector 1. The number of child-labour-supplying families, L a XL− 3 3 , increases as sector 3 contracts in terms of bothoutput and employment. This is the induced adult labour reallocation effectthat produces an upward pressure on child labour. The net outcome will be afall in the aggregate supply of child labour if I I QW LC +( ) ≤3 0. This restrictionimplies that the magnitude of the induced child wage effect is greater than theextent of the induced adult labour reallocation effect. However, this resultalso holds under an alternative sufficient condition as well (see Appendix E).

It is interesting to note that the effects of a lump-sum tax on the richerpeople on the incidence of child labour in the economy completely differ inthe two cases considered above. When the export sector is more intensive in

29This result holds even if the induced adult wage effect is stronger than the two adult labourreallocation effects. In mathematical terms this is expressed as I I QW L L K L+( ) ≥ −( )1 3 3 3λ λ λ .

30One may find other sufficient conditions incorporating the effective child wage effect.



the use of child labour vis-à-vis the non-traded sector, the policy worksunfavourably on child labour while it produces the desired result in theopposite case. Hence, an education subsidy policy cannot be financed byimposing a lump-sum tax when the export sector is more intensive in the useof child labour than the non-traded sector. However, when the non-tradedsector is relatively child labour intensive, both the policies should be under-taken concurrently and a balanced-budget change raises the possibility ofgetting the desired result on the problem of child labour.

4 Concluding Remarks

There are now considerable evidence and theoretical reason for believingthat, in developing countries, parents send their children to work out ofutter poverty. It is also believed that an inflow of foreign capital will leadto an overall economic expansion, benefits of which will percolate down tothe bottom of society, which in turn will put a brake on the incidence ofpoverty-induced child labour. Over the last two decades, the developingeconomies have been able to attract a considerable amount of foreign directinvestment by adopting liberalized investment policies. Although the inci-dence of child labour on the whole has decreased in the developing coun-tries with economic growth in relative terms, in some high-growth-proneareas the incidence has been on the rise. A pertinent question is why lib-eralized investment policies have produced contradictory results in differentcases. The present paper has made an attempt to provide an answer to theabove question using a three-sector general equilibrium model with twoinformal sectors and a non-traded final commodity. In the two informalsectors child labour is used along with adult labour. The non-traded com-modity is consumed by the wealthier section of the population. Apart fromthe analysis of foreign capital, the paper is also intended to investigatethe effectiveness of an education subsidy policy and a lump-sum tax on thericher people as a means of financing the subsidy on education to controlthe prevalence of the evil in the system.

The interesting results that emerge from the analysis of the paper areas follows. An overall economic expansion with foreign capital mightproduce paradoxical results on child labour under different circumstances.While the policy lowers the incidence of child labour in the situation wherethe traded sector is more child labour intensive than the non-traded infor-mal sector, it might produce a counterproductive effect in the opposite case.In contrast, an education subsidy policy is expected to produce the desiredresult on child labour in both situations. However, when the traded sectoris relatively intensive in the use of child labour, the subsidy on educationshould not be financed by a lump-sum tax on the more affluent people asthe latter policy might invalidate the favourable effect of the educationsubsidy policy. But, in the other case both the policies can be undertaken



concurrently and a balanced-budget change is the best policy option in thegiven set-up. So, the paper finds that an education subsidy policy is a moreeffective instrument in comparison with the policy of economic growth withforeign capital in combating the problem of child labour in a developingeconomy. But, whether the subsidy on education should be financed by alump-sum tax on the wealthier people depends on the technological andinstitutional factors of the economy.

Appendix A: Derivation of Certain Expressions

Totally differentiating (14) yields

a X X aL i i Li id d∑ ∑= −

or

X a L X X L a W W a W W a R R

X

i L i L L C C Li( ) = −( ) ∂ ∂( ) + ∂ ∂( ) + ∂ ∂( )[ ]

−∑ ˆ

1

2

1 1 1d d d

LL a W W a W W

X L a R RL L C C

L

( ) ∂ ∂( ) + ∂ ∂( )[ ]− ( ) ∂ ∂( )[ ]

2 2

33

d d

d (A1)

Using the result that R = 0 (see (17)) from the above expression we can write

λ λ λ λ λ λ λL L L L L L L L L L LX X X S S W S SL L C C1 2 3 1 2 1 21 2 31 2 1 2ˆ ˆ ˆ ˆ+ + = − +( ) − +( ))WC (A2)

Substituting the values of W and WC from (18) and (19) into (A2) and simplify-ing, we get the following:

λ λ λL L LX X X A P1 2 31 2 3 1 2ˆ ˆ ˆ ˆ+ + = − (A3)

where

A S S SL L L L L C L L CC C K11 2 1

1 2 1 1 1 1

1= +( ) +( ) +[ ]λ λ θ θ λ θ

θ

(Note that S S S S S SL L L L L LL C K L C K1 1 1 1 1 10+ + = ⇒ = − +( ) and S SL LL C

2 2 0+ = .)

Now differentiating (15) we get

λ λ λK K K K K CX X K S W S WL C1 3 11 31 1ˆ ˆ ˆ ˆ ˆ+ = − −( )

Substituting the values of W and WC from (18) and (19) into the above expression andsimplifying one gets the following:

λ λ λθ

θ θK KK

K C K LX X K S S PL C1 31

1 11 31 1

2ˆ ˆ ˆ ˆ+ = + −( )

or

λ λK KX X K A P1 31 3 2 2ˆ ˆ ˆ ˆ+ = + (A4)



where

A S SKK C K LL C21 11

1 1= −( )λθ

θ θ

Similarly differentiating equation (16.1) we get

λ λ λλ

λ λ λ

C CL

L

C C C C C C

X X X

S S G W SL L C

1 23

3

1 2 1

1 2 3

1 22

1

1ˆ ˆ ˆ

ˆ

+ +−

= − + +( ) − + λλC C CS G W G EC22

1 3−( ) −ˆ ˆ (A5)

Substituting the values of W and WC into (A5) and simplifying, we get the following:

λ λ λλ θ

λ θ θ λ θC CL

LC C C L C C CX X X

PS SL L1 2

3

3

1 1 1 2 11 2 32 1 2

1ˆ ˆ ˆ

ˆ+ +

−= +( ) + + θθ

λ θ θ θ

L

C C L C LS G G G EK

1

1 1 1 11

2 1 3

( )[

+ + + ] − ˆ

This is rewritten as follows:

λ λ λλC CL

L

X X X A P G E1 23

3

1 2 3 3 2 31

ˆ ˆ ˆ ˆ ˆ+ +−

= − (A6)

where

GW W nB E

l W B EG

Wl W B E

GB E W nW

C

C C C C1 2 2

3

0 0=+ ( )[ ]

− ( )[ ]> =

− ( )[ ]>

= ′ +

γ γ

γ CC

C Cl W B E

( )− ( )[ ]

>2 0

and

A S S S G GC C C L C C C L C C L CL L K31 2 1

2 11

1 1 1 2 1 1 1 1 1= +( ) + +( ) + + +θ

λ θ θ λ θ θ λ θ θ θθL1[ ]

(A3), (A4) and (A6) can be written in matrix notation as follows:

λ

λ

λ

λ

λ

λ

λλ

λ

L

K

C

L

C

L

K

L

L

X

X

X

1

1

1

2

2

3

3

3

3

0

1

1

2

3−

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

⎛

⎝

⎜⎜⎜

ˆ

ˆ

ˆ⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

=

−

+

−

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟

A P

K A P

A P G E

1 2

2 2

3 2 3

ˆ

ˆ ˆ

ˆ ˆ

(A7)

Solving (A7) by Cramer’s rule and simplifying, one gets

ˆ ˆ ˆ ˆX K Z P G EL CL

LL K1 1 2 3

113 2

2

3

2 3= −−

⎛⎝⎜

⎞⎠⎟

+ −⎡⎣⎢

⎤⎦⎥λ

λ λ λλ

λ λ (20)



ˆ ˆ ˆ ˆX K Z P G ELL

LC L K K L2 2 2 3

113

1

3

1 1 3 1 3=−

−⎛⎝⎜

⎞⎠⎟

+ + −( )⎡⎣⎢λλ λ

λλ λ λ λ λ ⎤⎤

⎦⎥(21)

and

ˆ ˆ ˆ ˆX K Z P G EL C L C L K3 3 2 31

2 1 1 2 2 1= −( ) − +⎡⎣ ⎤⎦λλ λ λ λ λ λ (22)

where

Z A A A

Z A

K C L L CL

L

LL

L

1 1 3 2

2 2

3 2 2 3 22

3

31

1

1

= +( ) + −−

⎛⎝⎜

⎞⎠⎟

=−

λ λ λ λ λ λλ

λ λλ 33

1 1 3 1 31 3

3

3 13 11

−⎛⎝⎜

⎞⎠⎟

− −( ) +−

−⎛⎝⎜

⎞⎠⎟

λ λ λ λ λ λ λλ

λ λ

λ

C L K K LK L

LK CA A

== −( ) +−

−( ) −[ ]

= −


λ λ λ

λ λ λ

K L C L CK L

LC L L

L C L

3 2 1 1 21 3

3

2 3 2

2 1

11

11 23 3

31λ λ λ

λCK L

L

( ) −−

( )see Appendix E (23.1)

and

Z A A AL C L C L K K C3 2 3 12 1 1 2 2 1 1 2= − −( ) + +λ λ λ λ λ λ λ λ

Appendix B: Stability Condition in the Market for Commodity 2

Differentiating the demand function for commodity 2 given by equation (11), we canderive

ˆ ˆ ˆ ˆX E P EW L

YX

TY

E TDP Y

LY2 2 32

3= + −* λ

(A8)

Substituting X3 from (22) and simplifying, one obtains the following:

ˆ ˆ ˆ ˆ ˆX E PE W L

YK Z P G ED

PY L

L C L C L K2 2 3 2 323

2 1 1 2 2 1= + −( ) − +⎡⎣λλ λ λ λ λ λ λ*

⎤⎤⎦

−TY

E TYˆ (A9)

Allowing only P2 to change and keeping all parameters unchanged, we find that

ˆ

ˆX

PE

E W LY

ZD

PY L2

232

3= −λ

λ*(A10)

Similarly, from equation (21) one obtains the following:

ˆ

ˆX

P

Z2

2

2=λ (A11)



For static stability we require that

ˆ

ˆ

ˆ

ˆX

P

X

PE

E W LY

ZZD

PY L2

2

2

23

22

3 0− = − − = <λ

λλ

* Δ (24)

Appendix C: Derivation of Equation (25.1)

In equilibrium in the market for commodity 2, we have ˆ ˆX XD2 2= . Now using (A9) and

(21) we can write

E PE W L

YK Z P G E

TY

PY L

L C L C L K23

2 1 1 2 2 12 3 2 3ˆ ˆ ˆ ˆ+ −( ) − +⎡⎣ ⎤⎦−

λλ λ λ λ λ λ λ*

EE T

K Z P G E

Y

LL

LC L K K L

ˆ

ˆ ˆ ˆ=−

−⎛⎝⎜

⎞⎠⎟

+ + −( )⎡113

1

3

1 1 3 1 32 2 3λλ λ

λλ λ λ λ λ

⎣⎣⎢⎤⎦⎥

or

EE W L

YZ

ZP

E W L

PY L

LL

LC

Y

23

31

3

1

32

2

11

− −⎛⎝

⎞⎠

=−

−⎛⎝⎜

⎞⎠⎟

−

λλ

λ

λλ λ

λλ λ

*

*

ˆ

LLL C L C

L K K LY L

L

YK

E W LY

32 1 1 2

1 3 1 33

2

1

λ λ λ λ

λλ λ λ λ λ λ

−( )⎡⎣⎢

⎤⎦⎥

+ −( ) −

ˆ

* λλK YG ETY

E T1 3⎡⎣⎢

⎤⎦⎥

+ˆ ˆ

Using (24) the above expression may be rewritten as follows:

ˆ ˆ ˆ ˆP Q K Q E Q T2 1 2 3= + + (25.1)

where

QE W L

YL

L

LC

Y LL C L C1

1 113

1

3

13

2 1 1 2=−

−⎛⎝⎜

⎞⎠⎟

− −( )⎡⎣⎢

⎤⎦λ

λ λλ

λ λ λ λ λ λΔ

*⎥⎥

= −( ) −⎡⎣⎢

⎤⎦⎥

= <

⎫

QG E W L

Y

QE T

Y

L K K LY L

L K

Y

23

3

1

0

1 3 1 33

2 1λλ λ λ λ λ λ λ

Δ

Δ

*⎬⎬

⎪⎪⎪

⎭

⎪⎪⎪

(25.2)

Appendix D: Derivation of Equations (26.1) and (26.2)

Differentiating equation (7), we get

ˆ ˆ ˆ ˆ ˆL GW G W G E XC CL

L

= − − −−1 2 3 3

3

31λ

λ (A12)

Substitution of W, WC and X3 from (18), (19) and (22) into (A12) yields



ˆ ˆ ˆ ˆ

ˆ

LG

PG

P G E

K Z

C L C

L

LL C L C

= + −

−−

−( ) −

12

22 31 1

3

3

2 1 1 211

θθ

θθ

λλ λ

λ λ λ λ 33 2 32 1ˆ ˆP G EL K+⎡⎣ ⎤⎦λ λ (26.1)

Rearranging terms we write

ˆ ˆLG G

Z PC L CL

L

L

LL C= + +

−⎛⎝⎜

⎞⎠⎟

−−

−1 23 21 1

3

3

3

3

2 111

11

θθ

θθ λ

λ λλ

λ λλ λ λLL C

L

LL K

K

G E

1 2

3

3

2 111

13

λ

λλ λ

λ λ

( )

− +−

⎛⎝⎜

⎞⎠⎟

ˆ

ˆ

Now substituting P2 from (25.1) into the above expression, using (23.1) and simpli-fying, one finally gets

ˆ ˆL I I I Q K I I I QC W W LL

K LW W L

L

C C= + +( ) −−

⎡⎣⎢

⎤⎦⎥

+ + +( )⎡⎣⎢

− +

1 23

3 3

1

λλ λ

λ 33

3

2 1

13 3−

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

+ + +( )[ ]λ

λ λλL

L KW W LG E I I I Q TC

ˆ ˆ (26.2)

where

IG

IG

I ZW L W C LL

LC = = =

−1 2

31 13

311

θθ

θθ λ

λ λ (27)

Appendix E: Proof of Propositions 1 and 2

In this model, sector 3 has been assumed to be more capital intensive (in a physicalsense) vis-à-vis sector 1 with respect to adult labour. This implies the following:

λλ

λλ

λλ

λλ λ

λ λλ

λ λ λ λK

L

K

L

K

K

L

L K

L L

LL K L L

3

3

1

1

3

1

3

1 1

3 1

1

1 1 3 1

1> ⇒ > ⇒ >

+⇒ > +(( ) (A13)

and

λλ

λλ

λ λλ λ

λ λλ λ

λ λL

L

K

K

L L

L KK

L

L LK L

1

3

1

3

1 3

3 3

33

1 3

3 3

1> ⇒

+> ⇒ >

+⇒ > (A14)

(Note that lL1 + lL3 < 1.)

The expression for |l| is as follows:

λ λ λ λ λ λ λ λλ

λ λ λ= −( ) +−

−( ) −[ ]K L C L CK L

LC L L3 2 1 1 2

1 3

3

2 3 211 (A15)

Substitution of lL1 + lL2 in place of 1 - lL3 in (A15) and simplification yield




= −( ) −−L C L C

K L

L2 1 1 2

3 3

31 (23.1)

From the stability condition in the market for commodity 2, we have

EE W L

YZ

ZP

Y L2

33

2 0− − = <λ

λλ

* Δ (24)

As both sectors 1 and 2 use adult labour and child labour as inputs, these togetherform a HOSS given the rental to capital, R. So, these sectors can be classified in termsof relative factor intensities.

Case I

We first consider the case where the export sector is more child labour intensivevis-à-vis the non-traded sector with respect to adult labour. In other words,

aa

aa

C

L

C

L

C

L

C

LL C L C

1

1

2

2

1

1

2

2

2 1 1 2 0> ⇒ > ⇒ − >λλ

λλ

λ λ λ λ (A16)

In this case, we also have

θ θ θ θ θ θ θ θ θC L C L L C C L1 2 2 1 1 2 1 2 0> ⇒ = − < (A17)

From (A16) it is easy to find that

λλ

λλ

λλ λ

λ λλ

L

L

C

C

L

L CC

L

L

2

1

2

1

3

1 1

11

3

1 11

> ⇒−

> ⇒ >−

Alternatively

λλ

λλ λ

λλ

λλ

λC

C

L

L C

L

L

L

LC

1

2

1

2 2

3

2

2

3

2

1 11

> ⇒ >−

⇒−

> (A18)

Assuming aK1to be technologically given and using (24), (A13), (A14) and (A16)–

(A18), from (23.1), (23.2) and (25.2) it is easy to check that

i

ii

iii

iv

v

vi if

( ) >( ) <( ) =( ) <( ) >

( ) > ≤

λ

λ λ

0

0

0

0

0

0

1

2

3

1

2 1 3

A

A

A

Q

QE W

L KY **

vii

viii

ix , ,

LY

Z

Z

I I I

LL K

W W LC

λ λ λ32 1

1

3

0

0

0

( ) <( ) <( ) <

⎫

⎬

⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪

(A19)



With the help of (A19), from (20) and (25.1) we get the following results:

a when

b when

c when

d

( ) < >

( ) < >

( ) < >( ) > <( )

( )

ˆ ˆ

ˆ ˆ

ˆ ˆ

X K

X E

X P

1

1

1 2

0 0

0 0

0 0ˆ ˆ

ˆ ˆ

ˆ

P K

P EE W L

YL K

Y LL K

2

2

0 0

0 0 1 33

2 1

> >

( ) > > ≤

( )

when

e when if*

f

λ λ λ λ λ

PP T2 0 0< >

⎫

⎬

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪when ˆ

(A20)

Using (A16), (A18) and (A19), from (21) and (22) we find that X2 decreases (increases)while X3 increases (increases) following an inflow of foreign capital (an educationsubsidy policy). Besides, an increase in P2 raises X3. We will use these results whileexplaining Proposition 1 verbally.

Finally, using (A14) and (A19), from equation (26.2) the following results trivi-ally follow:

(R.1) LC < 0 when K > 0.(R.2) LC < 0 when Ê > 0 if Q2 3 0, i.e. if λ λ λ λ λL K

Y LL K

E W LY1 3

32 1≤

*.

(R.3) LC > 0 when T > 0.

Note that, in (R.2),

λ λ λ λ λL KY L

L KE W L

Y1 33

2 1≤*

is only a sufficient condition for LC to fall following an education subsidy policy.

Case II

Let us now consider the case where sector 2 is more child labour intensive relative tosector 1 with respect to adult labour. This implies the case where

aa

aa

C

L

C

L

C

L

C

L

1

1

2

2

1

1

2

2

< ⇒ <λλ

λλ

(A21)

In this case, we find that



θ θ θ θ θ θ θ θ θλλ

λλ

λλ λ

C L C L L C C L

L

L

C

C

L

L C

1 2 2 1 1 2 1 2

2

1

2

1

3

1 1

0

1 1

< ⇒ = − >

< ⇒−

< ⇒⇒ <−

< ⇒ <−

⇒ >−

<

λ λλ

λλ

λλ λ

λλ

λ λλ

λ

CL

L

C

C

L

L C

L

LC

L

L

A

11

3

1

2

1

2 2

3

2

22

3

1

1 11

0

11

2

3

1

2

0

0

0

0

0

1

>= ( )>>

<

A a

A

Q

Q

Kassuming to be given technologically

iff*

, > 0

λ λ λ λ λL KY L

L K

W W L

E W LY

Z

Z

I I IC

1 33

2 1

1

3

0

0

0

≤

>>

<

⎫

⎬

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

(A22)

Using (A22), from (20) and (25.1) the following results are obtained:

a when

b when

c when

d

( ) < >

( ) > >

( ) < >( ) > <( )

( )

ˆ ˆ

ˆ ˆ

ˆ ˆ

X K

X E

X P

1

1

1 2

0 0

0 0

0 0ˆ ˆ

ˆ ˆ

ˆ

P K

P EE W L

YL K

Y LL K

2

2

0 0

0 0 1 33

2 1

> >

( ) < > ≤

( )

when

e when if*

f

λ λ λ λ λ

PP T2 0 0< >

⎫

⎬

⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪when ˆ

(A23)

Using (A21) and (A22), from (21) and (22) we find that X2 decreases (decreases)while X3 increases (decreases) following an inflow of foreign capital (an educationsubsidy policy). Besides, an increase in P3 raises X3. These results will be useful inexplaining Proposition 2 intuitively.

Using (A14) and (A23), from (26.2) it is easy to derive the following results:

(R.4) LC > 0 when K > 0 if

I I QW LL

K LC +( ) ≥

−13

3 3

λλ λ

or if

I I QW LL

K L

+( ) ≥−1

3

3 3

λλ λ



(R.5) LC < 0 when Ê > 0 if (i)

λ λ λ λ λL K

L L K YE W LY1 3

3 2 1≤*

and (ii)

I I I QG

W W LL L K

LC + +( ) ≤

−( )233 2 1

31λ λ λ

λ λ

(R.6) LC < 0 when T > 0 if I I QW LC +( ) ≤3 0 or if (IW + IL)Q3 2 0.

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