Wage Determination of Child Labor and Effect of Trade Reform

Saibal Kar1 and

Basudeb Guha-Khasnobis2

September 2003

Abstract

This study examines the interaction of a small open economy engaged in trade in goods and services with the process of household decision-making, where

individuals are characterized by a degree of relative risk aversion. In particular, we determine the demand for child labor originating in the small open economy and compare that against child labor supply determined by household decisions.

In the process, we determine the equilibrium child wage endogenously, as a fraction of the equilibrium adult wage. Trade reform policies affect both demand

and supply of child labor and the equilibrium child wage through its effects simultaneously on the production pattern and on household labor market

decisions. Based on these demand and supply movements generated through various parametric shifts, we offer our propositions on the incidence of child labor.

1 Address for Correspondence: Dr. Saibal Kar, Research Officer, Reserve Bank Of India Endowment, Centre For Studies In Social Sciences, Calcutta. R 1, B.P. Township, Calcutta 700 094, India. PH. 91-33-2462 5794/ 5795/7252. EXT. 230. FAX. 91-33-2462 6183. E-mail: skar<econcsss@giascl01.vsnl.net.in> / skar1801@yahoo.com 2 UNU-WIDER, Katajanokanlaituri 6 B, Helsinki 00160, Finland. E-mail: basudeb@wider.unu.edu.

1. Introduction In almost all the recent studies on the existence of child labor in developing

countries, its alarming extent and magnitude has been carefully documented and

highlighted. The entrenchment of the practice of child labor in developing societies3has

unanimously been declared problematic and upsetting.4 Various policy propositions in

favor of eradicating child labor has at best produced inconclusive results, which in turn

has made implementation of any or all of these policies rather difficult.

As the extensive literature suggests, the issue of the prevalence of child labor

has been approached from many angles. Grootaert and Kanbur (1995) provides an

elegant compendium of how the economics of child labor may be approached, and in

later studies we find a number of points mentioned here being taken up for further

investigation. Apparently, such studies have been successful in creating a large number

of explanations behind incidence of child labor, whether demand determined or supply

determined. Demand for child labor is generated by several factors. Segmentation of

the economy between formal and informal sectors and the degree of informalization is

an important factor in generating such demand. Formal sector of an economy, which

adheres more closely to labor laws prevailing in the country cannot for understandable

3 Although child labor is a much more visible phenomenon for developing nations, a decade or so ago even the United States had more than 4 million children in the working class (Corbin, 1988). Child labor by definition of ILO pertains to children below the age of 15 years. We also include children working for the household at the expense of school time. 4 Child labor is not necessarily considered ‘bad’ in every society. Work instead of education is believed to instill survival skills in the children (Bekombo, 1981; Agiobu-Kemmer, 1992). A related question may be: does every child need formal education? On the job training or apprenticeship and skill acquisition from an early age can provide them with an adequate means of living. Quoting Agiobu-Kemmer, (1992, p.7), “ Education broadens your mind but it does not teach you how to survive”. There is no doubt a problem with such arguments. Every child does not have to excel in educational attainments and neither is that practically feasible. However, every child must have at least primary education to take advantage of possible socio-economic developments around him/her. This not only enables the child to communicate with the outside domain but also acts as insurance against future shocks when such skills may be in considerable need. Moreover, education generates self-esteem and capacity of bargaining in the face of hostile socio-economic situations.

reasons engage in child labor employment. 5 Demand for child labor mostly originate in

the informal sector which itself bypasses legal regulations for various interests of its

own. This moreover has much to do with the technology used in production under the

behest of the informal economy. Children in developing countries are largely engaged

in production of goods and services where adult labor are imperfect substitutes. This

can range from employment of boys in quarries (where adult labor finds it difficult to

do mining in the narrow tunnels) to chimney sweeps or of children for weaving carpets

with their ‘nimble’ fingers (Grootaert and Kanbur, 1995, p. 195, also see Guha-

Khasnobis et al, 1999). Apart from that there is high demand for children workers in

the agriculture and allied sector, involving delicate plantations and harvesting or cattle

herding. Use of children as domestic helps/servants is also a common feature in these

countries. However, despite such widespread evidence on child labor, the problem

remains in estimating the demand for child labor properly, simply because once child

labor is prohibited by law, it does not exist legally and thus obtaining a positive demand

for child workers becomes rather impossible.

On the other hand, there are many supply-side determinants of the occurrences

of child labor, ranging from cultural factors to poverty-related causes. In this

connection Grootaert and Kanbur (1995) raise the issue of household responses towards

risk. If households face income risk, they might send their children to work to better

manage such risks, especially at income levels where any negative fluctuations could

mean disaster. We pursue this point further. While the objective of this study is laid

out shortly, we can elaborate a little bit more on this ground presently.

In the absence of savings, liquid assets or ability to borrow (Mendelievich,

5 Exceptions are plantation farms (eg. Bonnet, 1993, for Africa; Goonesekere, 1993, for Sri Lanka).

1979) most individuals seem to be distributed on the higher scale of relative risk

aversion and decide to engage their children in work for supporting an unstable

household income. In the later part of the study, we obtain a critical degree of such

relative risk aversion, such that, all individuals distributed with a relative risk aversion

above the critical level would spontaneously trigger the decision to send their children

to work with or without possibilities of adverse shocks. It may be argued that if

individuals are characterized by varying degrees of relative risk aversion, then for

highly risk-averse decision-makers, such reactions are obvious; the reverse being true

for low risk-averse individuals. We show that attainment of the critical degree of

relative risk aversion will automatically classify individuals falling into groups of high

risk-averse individuals and low risk-averse individuals even if one begins with an

assumption of equally risk-averse individuals distributed uniformly over a scale of

measurement.

Grootaert and Kanbur (1995, p. 194) carefully distinguish between strategies to

insure against adverse income shocks and that between ensuring old-age care. In the

first case, parents decide to send their children to work, while in the second case they

would want to send their children to school so that old-age transfers are higher.

Although demand for having children would be high in both cases, there is a potential

conflict between short-run and long-run gains as realized by the parents. This should be

reflected in the expected utility facing the parents and as our analysis would show,

parents face a trade-off between high-risk and long run gains. Supply of child labor is

accordingly affected by distribution of parents between high-risk and low-risk choices,

or rather between short run income smoothing choice and long run income transfer.6

There are a number of other models of household decision to send children to

work. Basu and Van (1998) assume child labor to be bad in parental preference, such

that, as household income exceeds some threshold, children are withdrawn from the

labor force. They identify several factors such as price and returns to education, the

price of the goods that households consume and produces, adult wage, child wage as a

fraction of adult wage etc.7 Here as also in Basu (2000), child wage is an arbitrary

fraction of adult wage. Basu (1998) obtains equilibrium employment of child labor

through a demand-supply interaction, but it is based on exogenously given child and

adult wages. Empirically, child and adult labor are shown to be substitutes or

complementary depending on gender, age and country type (see for example, Ray,

2000). One of the contributions we make in this paper is providing a definitive method

of calculating the equilibrium child wage as a fraction of adult wage and obtaining the

nature of relationship between child and adult workers, that can be interpreted suitably

in accordance with the empirical results. Ray (2000) test for the luxury axiom in Basu

and Van (1998), which essentially says that as the family falls into poverty, children are

withdrawn from school. For Peru and Pakistan, the two countries with similar rates of

children living in poverty (approximately 30%), that Ray (2000) tests for, it is observed

that while the axiom is true for Pakistan (although with a gender discrimination against

girls) it is contradicted for Peru.8

6 Note that, this is not a dynamic model. Here all gains are static and can at best be viewed as pesent discounted value of all future earnings. 7 Also see Baland and Robinson (2000). Brown (2000), Dixit (2000) consider the effect of raising foreign country price of goods using child labor on the incidence of child labor in developing countries in a simplified Basu and Van (1998) framework. 8 A possible explanation for contradictory evidence in Peru may be found in Patrinos and Psacharopoulos (1997, p. 398), “working actually makes it possible for the children to go to school.”

Credit constraints may also play a significant role in influencing supply of child

labor in a household model. Ranjan (2001, also see Dehejia and Gatti, 2002) builds up

a connection between trade policy and child labor in a household model with credit

constraints. This paper shows that trade sanctions might not reduce the incidence of

child labor in a long-run model of trade based on differences in relative endowments

across countries.

Previously, Maskus (1997) shows that imposition of foreign tariff on the

exported good has ambiguous effect on the incidence of child labor. On the other hand,

if child labor serves as a specific factor to the export sector (Melchior, 1996), imposing

tariff on export price of the good lowers returns to child labor and therefore the supply

of child labor. These results seem to differ on the basis of peculiarities in the specific

model building and the study by Edmonds and Pavcnik (2002) takes up an empirical

connection between globalization of the rice price in Vietnam and reduction of the

extent of child labor in the country. The results display a positive causation such that, a

30% increase in relative price of rice helps reducing child labor by an average of 9

percentage points. In rural Vietnam especially, it accounted for 45% reduction in child

labor (about 1 million less child labor between 1993-98), with households having larger

land holdings experiencing larger reductions.

A brief encounter with the economics of child labor thus provides various

paradigms one can look further into. This study is an attempt to bring together the

interaction of a small open economy engaged in trade in goods and services with the

process of household decision-making, where individuals are characterized by a degree

of relative risk aversion. The importance of the study lies in the fact that here we

determine the demand for child labor originating in the small open economy and

compare that against child labor supply determined by household decisions. In the

process, we determine the equilibrium child wage endogenously as a fraction of the

equilibrium adult wage. Trade reform policies affect both demand and supply of child

labor and the equilibrium child wage through its effects simultaneously on the

production pattern and on household labor market decisions, channeled through the

wage movements. Based on these demand and supply movements generated through

various parametric shifts, we offer our propositions on the incidence of child labor. It

should, however, be noted that we are not trying to provide yet another theory of

determination of child wage and extent of child employment. Instead, we emphasize

the importance of observing the link between economic restructuring, wage and labor

mobility and labor market decisions by individuals characterized by relative risk

aversion, in order to focus on the incidence of child labor.

The plan of the paper is as follows. In section 2 we present the model. In

section 3 we provide an overview of the results and conclude.

2. The Model Let there be a three-sector small open economy producing three goods X, Y and

Z. X is an import-competing industrial good and is protected by a proportional tariff t.

It requires the use of Y as an intermediate good, which is produced and traded at world

prices, *YP . Z is an export good. Other than Y, X also requires the use of capital, K

(interest rate, R) and adult labor, L (formal and unionized, at an administered wage w ).

One can assume Y to be agricultural output, which is produced with adult labor

(informal, at market-determined wage, w), child labor,C (at a wage wLγ , 10 << Lγ )

and land (T, at rental rateτ ).9 On the other hand, production of Z requires the use of

adult labor, child labor and capital at per unit prices given above.10 Production is based

on fixed endowments of L, K and T and on the basis of given production technologies.

Demand for child labor (C), on the other hand is determined endogenously, such that it

is less than or equal to the stock of children (C ) in the economy, CC ≤ . We define

child labor wage as,

ww LC γ= , 10 << Lγ (1)

In standard literature (for example, Basu, 2000), γ , a general discounting factor,

is treated as an exogenous constant and thus Cw is readily determined once w is known.

We propose that, γ instead is an endogenous variable, which2 may be interpreted as the

equilibrium level of effort exerted by a child labor. A child may exert varying levels of

effort at work and at school. At the point, where such efforts are same, the child is

indifferent between going to school or to work. For sake of simplicity we assume that

the total level of effort exerted by the child in going to school ( Sγ ) and to work ( Lγ )

cannot exceed 1. In other words,

SL γγ −= 1 (2)

It directly follows that when the child is full-time in school and not spending any time

9 One can assume X to be food processing industry, using agricultural, dairy, poultry and marine inputs traded at world prices. Y is a direct example of agricultural product ranging from fruits or cereals to fish and meat production. Z is an industrial/ handicraft export, using child labor. In case of India, for example, a famous example is in the carpet industry. 10 Viewed alternatively, the economy consists of a formal (and urban, X) sector and an informal (rural and urban/semi-urban, Y and Z respectively) sector. Formal sector follows legal procedures and labor laws, while similar enforcements are not suitably applicable for production of Y and Z. We conceptualize the general equilibrium structure of the economy in this form that covers main sectors using the essential

in the labor market, Sγ = 1 and Lγ = 0. The reverse occurs when the child is employed

full-time and has zero school attendance. Any combination of both school time and

work time is possible under this structure.11

In our model, Lγ is endogenously determined by the interaction of demand and

supply for child labor. Demand originates from the general equilibrium structure of the

small open economy and supply from the household comparison of parental utilities

from sending the child to work or to school. While the intricacies of such determination

will be presented below, we first offer the general equilibrium system of the small open

economy under perfect competition following other neo-classical assumptions of full-

employment, diminishing marginal returns and so on.

Let )1(* tPX + = Tariff included price of X

=*ZP Price of export good Z

=ija Amount of ith factor for producing one unit of jth commodity.

The following equations display the zero-profit and full-employment

conditions for our economy:

)1(* * tPPaRawa XYYXKXLX +=++ (3)

*YTYCCYLY Pawawa =++ τ (4)

*ZKZCCZLZ PRawawa =++ (5)

LZaYaXa LZLYLX =++ (6)

factors of production. One can further introduce capital specificity across formal and informal sectors, but we believe that it does not change the main results of our model. 11 It is also possible to begin with a total effort level < 1 or > 1, as a function of the inherent capability of the child, since individuals across ethnicities or country types may have different total effort levels. This in turn is a function of the existing conditions (including infrastructure, access to public goods, average

CZaYa CZCY =+ (7)

KZaXa KZKX =+ (8)

TYaTY = (9)

Given world prices of traded goods and w , from (3) we determine, R*. Substituting

R* in equation (5) we obtain )(* Lww γ= and substituting w* in (4) we determine

)(* Lγττ = , given international prices and the ija ’s. Clearly, determinate solutions of

the above variables require determination of equilibrium Lγ . The physical equations, on

the other hand, solve in the following manner. From (9), we determine, Y, given total

land resources, T . Substituting Y in (6), we solve simultaneously for X and Z from (6)

and (8), given exogenous adult labor and capital stocks in the economy. We plough

back Y and Z in equation (7) to obtain the demand for child labor in the economy, C as a

function of Lγ . Also, it displays the normal demand function. Intuitively, as Lγ rises

child wage rises, and demand for child labor falls. Thus,

)( LC CD γ= 0<′CD (10)

We further assume that Lk)1( − share of the total labor force is in the

unorganized sector and would therefore be the source of child labor supply. This is

explained next. k varies from country to country, but given the world average

percentage of labor union affiliation one can safely assume k to be around 10% in most

countries.

Now in order to determine the equilibrium value of γ , we need to obtain the

extent of supply of child labor in the economy. Let the economy, and thus all

nutrition levels and health situations, dependence on climatic factors, etc) within the country. However,

individuals face two states of nature, good sate with probabilityα and bad state with

probability β , such that, 1=+ βα . Note that, organized workers keep earning w under

all states of nature, while unorganized workers are susceptible to wage fluctuations

depending on the state of nature prevailing in the economy. The level of unorganized

wage in the economy is the prime determinant of the supply of child labor in our study.

It is assumed that, )(* Lww γ= as determined from equation (5) also represents the

critical wage facing an unorganized worker. The reason for invoking this assumption

will be made clear as we lay out the details of the supply-side of the model. However,

we first comment on the potential size of the child labor supply. Since organized

workers always earn more than the critical wage, children belonging to these families

would not be a potential child labor subject to the state of nature. However, if labor

from the organized sector is relocated to the unorganized sector due to effects of

structural reform, children belonging to these parents would also add to the potential

child labor supply. Before such reallocating effects of reform sets in, the actual number

of children who could be potential child labor is obtained in the following manner. The

average number of children (from a stock ofC ) per adult worker is LC / , of which,

LCk /)1( − would be readily affected by swing in the state of nature.

In our model the supply of child labor is determined by parental decision.12 We

assume all parents to be equally risk averse distributed uniformly over a range of

relative risk aversion and individuals are characterized by a von-Neumann-Morgenstern

utility function. The parent (an individual decision-maker representing a household)

we restrict our attention to the case of total effort level equal to 1. 12 Children self-selecting themselves either to school or to work is a possibility we bypass. Orphans, for example, if not supported by bequests or by social institutions must engage in labor work for survival.

receives utility from sending the child to work and/or to school. The possibility of both

school and work for a child is kept alive because there may be a situation when an

individual would be indifferent between sending the child either to school or to work or

both. More specifically, the individual compares separate utilities from sending the

child to school or to work and at the intersection point of the two utility functions we

obtain the critical relative risk aversion for the group of individuals. Individuals are so

distributed that, those displaying a relative risk aversion greater than the critical level

send the children to work, while those falling in the range where individual relative risk

aversion is less than the critical level decide to send their children to school. The idea

behind such decision-making is simple. It is well documented in the literature that

parents send their children to work for smoothing out risk associated with income

variability. We offer a point of departure in this context. The ultimate decision to send

children to school or work would depend on the level of critical relative risk aversion

and the distribution of individuals around that critical point. Put simply, we propose

that the decision to send children to work for smoothing out income fluctuations is not

universal among all individuals who are subject to wage uncertainties. Instead, it is a

function of the distribution of individuals on the scale of relative risk aversion with

reference to the critical point. This critical level of relative risk aversion defined in the

range [0,1) is obtained next.13

w is the critical wage under steady state general equilibrium facing an

unorganized worker (see appendix for an alternative approach for determining supply of

13 However, Kanbur (1982, p. 18) comments that value of relative risk aversion between 1 and 2 seems to be reasonable one to take. We use the measure of relative risk aversion as an analytical tool here and such specifications as r belongs to [0,2) can easily be introduced to check the validity of the model and results.

child labor). This is obtained from equation (5) above. αw be the wage, such an worker

earns in good state, while he earns βw in bad state. The two states of nature are results

of economic shifts, engendered through economic reforms in the country. It is a

simplification that in good state, w jumps to αw and in bad state it falls to βw . In fact,

there can be an infinite number of wage levels between w and αw , and that between w

and βw . At w, an individual is indifferent between sending the child to work or to

school.14 The idea is that, as w increases above the critical level, parents decide in favor

of sending the children to school. On the other hand, if wage falls below w, children are

withdrawn from school and sent to work.

Based on this behavior, we conceive of two separate utility functions: one for

supporting the household by sending the children to work (USH), and the other for

increasing the educational attainment of the household by sending the children to school

(UHK). For each case there are two possible outcomes.

First, let us consider the case of supporting the household. In good state, which

comes with a probabilityα , the individual does not send the children to work and the

household does not gather an extra income from child work. Thus in good state, utility

is a function of the difference in αw and w alone. In bad state on the other hand, as adult

wage falls below the critical level, children are sent to work and they earn a fraction of

14 In other words, under steady state equilibrium when adult workers earn w, the economy still may have a positive supply of child labor as well as positive number of school goers. However, we are more interested in tracking the changes in the supply of child labor and school attendance that results from introduction of economic reform.

the prevailing adult wage, βγ wL . This is added to the household income in bad state.15

On the basis of the above discussion, we construct a Stone-Geary utility function of the

following type.

+−

−=

−

−

rL

r

www

wwUSH

1

1

)(

)(

ββ

α

γ (11)

From (10), we obtain the expected utility function for supporting the household.

rL

r wwwwwEUSH −− +−+−= 11 )()( ββα γβα (12)

where, 0)(,0)(2

2

<>r

EUSHr

EUSHδ

δδ

δ . In other words, EUSH is a concave and well-

behaved function.

Second, the flipside of the above situation reveals that, in good state the

individual decides in favor of sending the children to school with a view to increase the

educational attainment of the children and thus of the household. In good state, this

educational attainment enters the utility function of the parent. In bad state, the children

are simply withdrawn from school and thus utility becomes a function of w and βw only.

All children are endowed with an innate ability b. Administering individual effort at

15 As noted earlier, any wage level between w and αw , or that between w and βw may well trigger the decision to send the children to school or work. At precisely what level of income differences such decisions take-off possibly needs to be addressed in an empirical framework. Here it is assumed that ( αw -w) is large enough, so that parents decide against sending the children to work and subsequently

make schooling facilities available for them. Conversely, for a large ( βw -w), parents are hard pressed to withdraw children from school and send them to the labor market. Utility from work and school are, however, accounted for separately in our model. Finally, such households do not have any other source of income or capital assets other than market determined wage earnings. Once again, cost of capital borrowing or returns from land holdings by individuals can be introduced in this framework to provide the general equilibrium structure. We believe, adding other markets would extend the main results of the model without altering any basic findings.

school children acquire )1( Sb γ+ level of educational attainment.16 As already

mentioned, in bad state such return from schooling is zero, children being withdrawn

from school as soon as adult wage drops below the critical level.

The Stone-Geary utility function representing these choices is given below.

−

++−=

−

−

r

rS

ww

bwwUHK

1

1

)(

)]1([

β

α γ (13)

We denote the expected utility from sending or not sending the children to school by,

rrS wwbwwEUHK −− −+++−= 11 )()]1([ βα βγα (14)

Again, 0)(,0)(2

2

<>r

EUHKr

EUHKδ

δδ

δ depicting a continuous and well-behaved utility

curve.

At the point where the curves depicting equations (12) and (14) intersect and

using (2), we obtain the critical relative risk aversion of adult individuals

( )(** Lrr γ= ).17 Algebraically, this is obtained at the point where,

rL

r wwwww −− +−+− 11 )()( ββα γβα = rrS wwbww −− −+++− 11 )()]1([ βα βγα

One can check for the intercepts of EUSH and EUHK. It can be easily seen that,

−<>

== bwbiffEUSHEUHK Lrr αβ

αγβ

,,00

. (15)

Once again, given other parameters, condition (15) sets the upper limit for Lγ such that

a equilibrium point exists. Determination of unique equilibrium further requires that,

16 This may be considered equivalent to the net present discounted value of return from schooling. We do not explicitly consider the market for education, but this static educational attainment has a market value equivalent at that point in time. Also, schooling is free, so the only cost of schooling is the wage loss and other expenses incurred for supporting the children when in school. We believe that, even if these features are explicitly modeled here, it does not change the basic analysis and results.

rEUHK

rEUSH

δδ

δδ )()(

> .

Diagrammatically this is shown in figure (1). Individuals distributed to the left of the

critical relative risk aversion ( 0*),(** <′= rrr Lγ , point M) point choose to send their

children to school, whereas those distributed to the right send their children to work.

EUSH, EUHK

EUSH

M EUHK

0 r* r

Fig (1)

Intuitively, 0*),(** <′= rrr Lγ is explained as follows. As Lγ increases, child wage

increases. Subsequently, expected utility from household support increases and EUSH

curve shifts out. This leads to a drop in the level of critical relative risk aversion among

individuals. Looked at alternatively, as Lγ increases, Sγ falls and expected utility from

human capital formation falls, such that, EUHK shifts in. As a result, critical relative

risk aversion falls with an increase in labor market work effort of the children.

The attainment of the critical relative risk aversion, therefore, demarcates

individuals distributed with higher relative risk aversion from those distributed with

17At this stage, we do not rule out possibilities of multiple equilibria.

lower relative risk aversion. This further influences the decision to send the children to

school or to work. At the critical level, individuals are indifferent between sending the

children to school or to work.

This determines the number of individuals who send their children to work. For

those who are distributed with higher relative risk aversion than the critical level, the

decision is to send the children to work for smoothing out risk associated with variance

in income. All individuals with relative risk aversion in the range [r*, 1) belong to this

decision group. The actual number of such individuals is given by

LkrS )1*)(1( −−= (16)

Now, as noted earlier, the number of children belonging to the unorganized workers

is LCk /)1( − . Thus, using (16) the number of children who are sent to work is given

by,

CrkS LC )](*1[)1( 2 γ−−= , 0)( >′ LCS γ as 0)(* <′ Lr γ (17)

)( LCS γ in equation (17) represents the supply of child labor in the economy.

Now, one can straightaway determine the equilibrium value of *)( LL γγ = by equating

(10) and (17),

CrkC LL )](*1[)1()( 2 γγ −−= (18)

Once *Lγ is known, equilibrium values of other variables are also

determined *)(* Lww γ= , *)(* Lγττ = . Using these values we obtain the equilibrium

child labor wage in the economy,

*** ww LC γ= (19)

Comparative static

a. Reduction in tariff rate on commodity X, i.e. dt<0.

We show that a reduction in the price of X may change the incidence and

magnitude of child labor in the economy, through its effects on both demand for and

supply of child labor. The effect on demand for child labor is propagated primarily

through factor price adjustments in the economy and subsequently through the impact

of changing factor-prices on the production of goods and services. The supply effect,

on the other hand, operates through shifts in household decisions on labor supply owing

to factor-price movements - essentially, wage movements in the economy.

Proposition I: Demand for child labor rises while supply of child labor falls with a

tariff-cut on of X, if the respective conditions are satisfied :

a. Demand condition:

1)()]([ <−++−LY

CZ

TY

KZLZ

LYKX

KZLX

Y

ZCZLZKXLX

Y

XLX λ

λθθθ

λλλλ

σσ

θθθθσσ

λ

b. Supply conditions:

For EUSH: 1>−w

w L

δδγ

β , where, 0. >> wwβ and 0<w

L

δδγ

For EUHK: 1>w

b S

δδγ

, where, b>0 and 0>w

S

δδγ

Proof: The detailed mathematical proof of Proposition I is provided in the appendix.

Here, we explore intuitively if a tariff cut on the import of X leads to an increased

demand for and a decreased supply of child labor. A reduction in tariff lowers R in

sector X, along with a reduction in output and employment in sector X. Capital takes a

flight to sector Z increasing production, employment and return to adult labor in the

economy. If Lγ is high in equilibrium, child labor is a close substitute for adult labor

and employment of child labor rises. Again, even for a low equilibrium Lγ and based

on the structure of the industry and technique in production, there may be

complementarity between adult and child labor.18 Thus, increasing adult employment

also leads to an increase in demand for child labor. However, this does not portray the

complete picture of the economy. A reduction in the output in sector X is associated

with a drop in production and employment in sector Y, the agricultural commodity,

which serves as an intermediate good to the import-competing sector. Thus the overall

impact of trade liberalization on employment of child labor becomes a function of

condition (a) shown above. One may argue that, with a large agricultural sector and

high involvement of child labor in this sector, impact of a downsized food processing

industry on negative demand for child labor may not be very deeply entrenched.

Increased industrial demand for child labor dominates in the case of a tariff-cut,

resulting in a higher overall demand for child labor.

The supply of child labor on the other hand changes in the following manner.

Note that, change in children’s supply of effort at school or at work is a supply-side

phenomenon. We accommodate this feature here, while considering a constant effort

level for earlier determination of shifts in demand. As adult wage unambiguously rises,

parents prefer to withdraw children from the labor market. Consequently, children’s

supply of effort in the labor market falls. In other words 0<w

L

δδγ . Also, as rise in adult

wage lowers children’s work effort, expected utility of household support through child

18 In fact, we assume fixed technological proportionality or correspondence between adult and child labor in sector Y and Z, whether the factors are substitutes or complements in production.

income falls. The curve depicting EUSH shifts in with a rise in adult wage subject to

condition (b) stated above. Similarly, as adult wage rises children are sent to school by

parental decision. Children’s effort at school rises and households’ expected utility

from educational attainment/human capital formation increase. There is an outward

shift of EUHK. The adjusted critical relative risk aversion point (where new EUSP and

EUHK intersect) locates higher up in the scale of relative risk aversion. Thus, more

individuals compared to pre-trade reform situation are now distributed with a lower

relative risk aversion than the critical level. This leads to a drop in the supply of child

labor from the households. We display this supply-side shock with the help of the

following diagram.

EUSH, EUHK EUSH N EUSH’ EUHK’ M EUHK 0 r* r*’ r

Fig (2)

Subject to satisfaction of the conditions as in (b) above, EUSH curve shifts inward to

EUSH’, while EUHK shifts outward to EUHK’. Consequently, the critical relative risk

aversion point shifts from point M rightward to point N. This is indicative of an

increase in the proportion of individuals distributed with a relative risk aversion lower

than the critical level. Conversely, the proportion of individuals distributed with a

relative risk aversion higher than the critical level falls with these adjustments.

Therefore, the supply of child labor decreases as a direct consequence of these

movements.

Finally, we address the ultimate question that forms an important, if not the sole

motivation behind this paper. Whether the size of the child labor force declines in

equilibrium depends on the wage elasticity of demand for and supply of child labor. In

this particular example, we observe a conditional increase in the demand for child labor.

On the other hand, subject to fulfillment of conditions as under proposition I there may

be a decrease in the supply of child labor in the economy. Thus the extent and

magnitude of child labor in the post-reform economy would depend upon the relative

strength of these shifts.

b. Imposition of Import Ban on exports that use child labor

Suppose the rest of the world imposes an import ban on products made with the

use of child labor. In our model commodity Z is such an exportable. This sector is

therefore directly affected by the imposition of import ban. If the technology of this

sector is such that child labor is an indispensable factor input, then export of Z

completely stops. If instead child labor could be substituted by adult labor or some

other form of factor input, then the production and export of Z continues. However,

sector Z can operate at the world prices due to presence of cost advantage generated

from use of child labor. If child labor is replaced by an imperfect substitute, then the

cost advantage disappears and the export sector may cease to exist. This is referred to

as ‘jump’ and in models of international trade this feature can be quite clearly

displayed. The phenomenon of ‘jump’ provides interesting examples of discontinuity in

structures of production and exchange equilibrium. Essentially, jumps here show that

some sectors may completely cease to exist in the face of structural adjustments.19

Alternatively, in the absence of child labor laws stringently enforced within the

domestic economy, the sector may be producing non-traded instead. However, it must

produce at the world prices and thus may face insufficient demand within the country to

sustain previous production level. Thus in any case, output and employment in sector Z

must fall (continuous and interior solution) due to imposition of import ban. In the

extreme case (jump and corner solution), sector Z may cease to exist.

Therefore, capital must take a flight to sector X, where return to capital R falls.

Adult and child labor moves to sector Y. )(* Lww γ= must also fall, although return to

land )(* Lγττ = increases.

Let us now check the new demand situation for child labor. As capital moves to

sector X, output increases there. Also, since both adult and child labor moves to sector

Y, output increases in Y. Thus there are two cross-effects working on the aggregate

demand for child labor. There is lower demand as production of Z falls, while an

increased demand as production of Y rises. So the net effect on aggregate requirement

of child labor )( Ld CC γ= may go either way depending on the relative strength of the

production shifts in sectors Y and Z.

Next, we investigate the effect of import ban on the supply of child labor. As

19 A similar example can be obtained in Marjit, Kar and Beladi (2003), mimeo, CSSSC, India.

modeled above, parental decision to send child to work or school depends on the

equilibrium wage rate. A fall in wage shifts the EUSH curve outward. This implies

that when adult wage rate falls, at every level of relative risk aversion expected utility of

supporting the household is higher than before. On the same note, this shifts the EUHK

curve inward. Therefore the critical relative risk aversion point shifts to the left of the

previous equilibrium. This increases the supply of child labor in the economy.

This brings us to the determination of Lγ as in (18). Successive determinations

of other variables follow once Lγ is obtained in equilibrium. Once again, the size of the

child labor force employed in equilibrium depends on the adjusted demand and supply

levels in the economy.

4. Conclusions

Certain activities of children, usually those of the “helping-hand” variety confined

within the immediate family may be normal, but the excessive involvement of children

in hired labor segments is long-recognized as a social malaise and generally defined as

child labor. It has co-habited with adult labor in nearly all human societies for ages.

Globalization, still a relatively recent phenomenon, has added new and complicated,

chiefly trade-related economic dimensions, to child labor calling for intervention by

national governments and international institutions in this highly informal market.

Policies which are the best for the children themselves may be hard to come by, because

policymakers are influenced by two completely distinct groups of individuals, voicing

from the same platform their concerns about child labor. Admittedly, one of the groups

comprises genuine well-wishers of children who do not seem to have any vested

interests. The welfare of children, especially of those in other countries, may or may not

be of any real concern for the other group, but they certainly have a business interest in

talking about child labor. In dealing with child labor, the task of the policymaker is thus

not an enviable one.

In this paper, we brought together two distinct classes of economic models to

understand both the demand as well as the supply forces of child labor, operating in a

stylized “globalizing” economy. Changes in the demand for child labor are caused by

factor substitution, their reallocation between production sectors and concomitant

changes in output levels of each good triggered by trade policies that are commonly

associated with globalization. One such policy is tariff-reduction, its positive impact on

efficiency well-known and firmly grounded in the theory of international trade. The

distributional impact of tariff reduction, that is, its differential effect on various factor

prices using child wage, is context specific, depending mainly on factor intensities. In

our model, tariff reduction will increase the demand for child labor. The supply of child

labor is based on decisions taken by parents characterized by different degrees of risk-

aversion in an uncertain world. We show that tariff reduction reduces the supply of

child labor in our model. These two effects on demand and supply determine both the

wage rate as well as the incidence of child labor in the new equilibrium. Whether wages

and incidence rise or fall in the new equilibrium, depend on the relative strengths of the

two distinct changes.

We also discuss another important development associated with globalization, which is

the growing use of trade measures to achieve non-trade objectives such as core labor

standards, elimination of child labor or the protection of environment. Some countries

have decided to impose an import ban on goods that are produced with child labor. We

argue that such a policy can actually increase the supply for child workers in the

exporting country, which is not what the aforesaid group genuinely concerned with

child welfare would want.

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Appendix

Proof of Demand-side condition:

From equation (3) as dt < 0, 0ˆ <=KX

dtRθ

. From (5), using equilibrium Lγ as given,

such that, wwC ˆˆ = , we substitute R̂ to get (also see fn. 16 and the assumption that sector

X requires relatively more capital per unit of labor, compared to commodity Z),

0)(

ˆ >+

−=CZLZKX

KZ dtwθθθ

θ while from (4) 0ˆ <+

+=

CZLZKX

KZ

TY

CYLY dtθθθ

θθ

θθτ .

Now, we obtain the changes in the output and employment in various sectors. From (9)

0)ˆˆ(ˆˆ <−−=−= τθσ waY LYYTY and 0)ˆˆ(ˆˆˆˆˆ <−−=−=+= τθσ waaYaL LYYTYLYLYY .

On the other hand from (6) and (8), we get the respective changes,

0ˆˆˆˆˆ >=−−−=+ MLaaZX YLYLZLZLXLXLZLX λλλλλ , (A.1)

0ˆˆˆˆ <=−−=+ NaaZX KZKZKXKXKZKX λλλλ (A.2)

Substituting for Yij La ˆ,ˆ in (A.1) and (A.2), we get M >0 and N <0. We use Cramer’s

rule to solve for YX ˆ,ˆ .

=

NM

ZX

KZKX

LZLX

ˆˆ

λλλλ

(A.3)

We define 0<−=∆ KXLZKZLX λλλλ , such that,

0ˆ <∆−

=NMX LZKZ λλ and 0ˆ >

∆−

=MNZ KXLX λλ .

Also, equation (7) is rewritten as

CZaYa CZCZCYCYˆ)ˆˆ()ˆˆ( =+++ λλ (A.4)

Substituting ZY ˆ,ˆ in (A.4), and using the assumption that use of child labor in sector Y

and Z do not undergo any technological change following factor-price changes, we

obtain the change in the requirement of child labor in the economy.

Thus with CZCY aa ˆ0ˆ == , ∆−

+−−=MNwC KXLX

CZLYYCYλλ

λτθσλ )ˆˆ(ˆ .

This with suitable manipulations is reduced to the form of

1)()]([ <−++−LY

CZ

TY

KZLZ

LYKX

KZLX

Y

ZCZLZKXLX

Y

XLX λ

λθθθ

λλλλ

σσ

θθθθσσ

λ (A.5) QED.

Proof of supply-side conditions:

From (12)

)1())(1())(1()(w

wwwwrwwrw

EUSH LrL

r

δδγ

γβαδ

δβββα ++−−+−−−= −− (A.6)

such that forw

EUSHδ

δ )( < 0, it suffices to have )1( >−w

w L

δδγ

β , where,

0. >> wwβ and 0<w

L

δδγ .

Similarly from (14)

rSrS wwr

wbbwwr

wEUHK −− −−++−++−−= ))(1()1()]1()[1()(

βα βδδγ

γαδ

δ (A.7).

Once again, for 0)(>

wEUHKδ

δ , it suffices to have )1( >w

b S

δδγ

, where, b>0 and 0>w

S

δδγ .

QED.