Effectiveness of Trade and Non-trade Policies on the Incidence of Child Labour—A Three-Sector General Equilibrium Framework

Abstract

This chapter considers a 3 × 3 × 3 competitive general equilibrium framework of a small open economy which exports product produced by child labour. In the first part, we abstract from unemployment to begin with and assume that adult labour market maintains full employment. Our objectives have been to investigate the effectiveness of trade and non-trade policies in the presence of child labour problem and also to examine the impacts on national welfare and trade balance of such an economy. In particular, in this chapter, we have examined the effectiveness of three different kinds of policies on the incidence of child labour. Among these three, one is trade policy and the rest are non-trade policies. First part of this chapter reveals that economic expansion via increase in adult labour endowment is ineffective in curtailing the incidence of child labour. The other two policies seem to be efficient in this ground. However, any policy designed to control child labour incidence must have an impact on welfare and trade balance situation of the economy. Trade balance situation worsens in case of economic expansion via increase in domestic capital stock. However, the other non-trade policy leaves it as unchanged. But the impact is ambiguous for the case of trade policy. Again, welfare impact is positive only in case of economic expansion via increase in adult labour endowment but ambiguous in the other two cases. Hence, from the above analysis, we observe that none of the policies simultaneously can have favourable impact on child labour supply, trade balance and welfare of the small open economy. In part two of the chapter, we introduce unemployment problem in the adult labour market on one hand, and retain the existence of a child labour market on the other hand. The economy is divided into one rural and two urban sub-sectors. Four inputs are used in the model among which three are specific in nature. The representative adult worker in this model not only supplies his own labour but also sends his children out to work. Factor market distortion in this model is captured by the existence of a factor price differential between urban and rural sectors. The model is used to analyse the effects of imposition of various forms of trade restrictions on the unemployment of adult workers on the one hand and on the incidence of child labour on the other. Alternative trade policy prescriptions to combat child labour as well as adult market unemployment problem have been analysed. An interesting result obtained from the exercise of trade policy suggests that supply of child labour is shown to vary inversely with the level of unemployment in the adult labour market. In part three, we focus on an important non-trade policy, namely education subsidy to find its effects on the incidence of child labour.

Note:

I. This chapter draws from and reuses with permission the materials contained in the following papers of the author(s):

(a) Runa Ray (2014): “Import Restrictions, Capital Accumulation and Use of Child Labour—A General Equilibrium Analysis”, Chapter 5 of the book edited by Ambar Nath Ghosh and Asim K. Karmark (eds.), Analytical Issues in Trade, Development and Finance, Essays in Honour of Biswajit Chatterjee, Springer India, 2014, as Part I of Chapter 6 of the present book;

(b) Runa Ray and Biswajit Chatterjee (2010a), “Child Labour and Restrictive Trade Policy—A Three Sector General Equilibrium Framework”, Vol. 52, No. 1, April 2010, Asian Economic Review, Journal of The Indian Institute of Economics, Pages 179–190, as Part I of Chapter 6 of the present book;

(c) Runa Ray and Biswajit Chatterjee (2010b), “Impact of Restrictive Trade Policy on Adult Unemployment, Welfare and the Incidence of Child Labour—A Three Sector General Equilibrium Analysis,” Journal of Quantitative Economics, The Indian Econometric Society, vol. 8(1), pages 148–161, January 2010 as Part II of Chapter 6 of the present book;

(d) Biswajit Chatterjee and Runa Ray (2013), “Trade Restriction, Adult Unemployment and Incidence of Child Labou: A Three Sector General Equilibrium Analysis”, Artha Vijnana Journal of The Gokhale Institute of Politics and Economics, Vol. LV No. 3, September 2013 Page No. 239–251 as Part II of Chapter 6 of the present book;

(e) Runa Ray and Biswajit Chatterjee (2010c),“Education Subsidy, Adult Unemployment and the Incidence of Child Labour in an Open Economy: A Three Sector General Equilibrium Analysis”, Vol. 57, No. 4, Jan–March 2010, The Indian Economic Journal, pages 37–59, as Part III of Chapter 6 of the present book;

(f) Biswajit Chatterjee and Runa Ray (2016), “Impact of Trade versus Non-trade Policies on the Incidence of Child Labour, A Two-sector General Equilibrium Framework”, Foreign Trade Review, July 2016, pp. 287–297;

(g) Biswajit Chatterjee and Runa Ray (2016), “Impact of Trade Restriction on Child Labour Supply and the Role of Parents’ Utility Function: A Two Sector General Equilibrium Analysis “ in Malabika Roy and Saikat Sinha Roy (eds.), International Trade and International Finance, Springer 2016.

(h) Biswajit Chatterjee and Runa Ray (2007), “Growth, National Welfare and Trade Balance in a Small Open Economy: A General Equilibrium Analysis,” Artha Vijnana, vol. XLIX, Nos. 3 and 4, pp. 203–222, September–December, 2007.

(i) Biswajit Chatterjee and Runa Ray (2008), “A Three Sector Model With Child Labour And Adult Market Unemployment: Impact Of Trade Restriction On National Welfare and Trade Balance” Artha Beekshan, vol. 17, No. 3, December 2008.

II. The notational and structural similarity follows from the pioneering papers on General Equilibrium Analysis by Ronald W. Jones (1965, 1971), which have been used widely in the literature on trade and development.

Appendices

Appendix 6.1

In specific factor model, we will prove that

$$ \hat{a}_{LaY} = - {\theta }_{KY} {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) > {0} $$

$$ \hat{a}_{KY} = {\theta }_{LaY} {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) < 0 $$

$$ \left[ {{Where }\;{\sigma }_{Y} = {\text{Elasticity of substitution}} = \left( {\frac{{\hat{a}_{KY} - \hat{a}_{{{{{L}_{a} {Y}}} }}}}{{\widehat{W}^{A} - {\hat{r}}}}} \right)} \right] $$

Proof

The zero profit conditions for the economy is shown by the following two equations:

$$ {a}_{{{L}_{C} {X}}} \left( {\frac{{{W}^{A} }}{\beta }} \right) + {a}_{{{L}_{a} {X}}} {W}^{A} = {P_x} $$

(6.193)

$$ {a}_{{{L}_{A} {Y}}} {W}^{A} + {a}_{KY} {r} = {P}_{Y} $$

(6.194)

Cost minimization condition for the producer of Y entails that

$$ \frac{{{da}_{KY} }}{{{da}_{{{L}_{a} {Y}}} }} = - \frac{{{W}^{A} }}{r} $$

(6.195)

or,

$$ {rda}_{KY} + {W}^{A} {da}_{{{L}_{a} {Y}}} = 0 $$

or,

$$ {\theta }_{KY} \hat{a}_{KY} + {\theta }_{{{L}_{a} {Y}}} \hat{a}_{{{{{L}_{a} {Y}}} }} = 0 $$

(6.196)

Now $\sigma_{Y} = \frac{{\hat{a}KY - \hat{a}_{{L_{a} Y}} }}{{\widehat{W}^{A} - \widehat{r}}}$

$$ \therefore \;\hat{a}_{KY} = {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) + \hat{a}_{{{{{L}_{a} {Y}}} }} $$

(6.197)

Substituting the value of $\widehat{aKY}_{KY}$ in (6.196), we get

$$ {\theta }_{{{L}_{a} {Y}}} \hat{a}_{LaY} + {\theta }_{KY} \hat{a}_{{{{{L}_{a} {Y}}} }} + {\theta }_{KY} {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) = 0 $$

or,

$$ \hat{a}_{{{{{L}_{a} {Y}}} }} = - {\theta }_{KY} {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) $$

$\therefore$ From (6.197)

$$ \begin{aligned} \hat{a}_{KY} & = \left( {1 - {\theta }_{KY} } \right){\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) \\ & = {\theta }_{{{L}_{a} {Y}}} {\sigma }_{Y} \left( {\widehat{W}^{A} - {\hat{r}}} \right) \\ \end{aligned} $$

(6.198)

$$ \because \;\hat{a}_{LaY} - \hat{a}_{KY} = - {\sigma }_{Y} (\widehat{W}^{A} - {\hat{r}}) $$

(6.199)

Appendix 6.2

In specific factor model, we will prove that

$$ \begin{aligned} \hat{a}_{LaZ} & = - {\theta }_{YZ} {\sigma }_{Z} \left[ {\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})} \right] \\ \hat{a}_{YZ} & = {\theta }_{LaZ} {\sigma }_{Z} \left[ {\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})} \right] \\ \end{aligned} $$

where

$$ \begin{aligned} {\sigma }_{Z} & = {\text{Elasticity of substitution}} \\ & = \left( {\frac{{\hat{a}_{YZ} - \hat{a}_{LaZ}}}{{\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})}}} \right) \\ \end{aligned} $$

Proof

The zero profit conditions for the economy are shown by the following two equations:

$$ {a}_{LaY} {{W}^{*}} + {a}_{KY} {r} = {P}_{Y} (1 + {t}) $$

(6.200)

$$ {a}_{LaZ} {{W}^{*}} + {a}_{YZ} {P}_{Y} (1 + {t}) = {P}_{Z} $$

(6.201)

Cost minimization condition for the producer of Z entails that

$$ \frac{{{da}_{YZ} }}{{{da}_{LaZ} }} = - \frac{{{{W}^{*}} }}{{{P}_{Y} (1 + {t})}} $$

(6.202)

or,

$$ {P}_{Y} \left( {1 + {t}} \right){da}_{YZ} + {{W}^{*}} {da}_{LaZ} = 0 $$

or,

$$ {\theta }_{YZ} \hat{a}_{YZ} + {\theta }_{LaZ} \hat{a}_{LaZ} = 0 $$

(6.203)

Now ${\sigma }_{Z} = \left( {\frac{{\hat{a}_{YZ} - \hat{a}_{LaZ}}}{{\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})}}} \right)$

$$ \therefore \;\hat{a}_{YZ} = {\sigma }_{Z} [\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})] + \hat{a}_{LaZ} $$

(6.204)

Substituting the value of $\hat{a}_{YZ}$ in (6.203), we get

$$ {\theta }_{YZ}{\sigma }_{Z} [\widehat{W}^{*} - \widehat{P}_{Y}(1 + {t})] + {\theta }_{YZ} \hat{a}_{LaZ} + {\theta }_{LaZ} \hat{a}_{LaZ} = 0 $$

or,

$$ \hat{a}_{LaZ} = - {\theta }_{YZ} {\sigma }_{Z} \left[ {{{W}^{*}} - {P}_{Y} (1 + {t})} \right] $$

(6.205)