Child Labor and Economic Development

Transcription

1 Child Labor and Economic Developmen Ambar Ghosh Cenre for Economic Sudies, Presidency College, Kolkaa.. Chandana Ghosh* Economic Research Uni, Indian Saisical Insiue, Kolkaa. Absrac The paper develops an overlapping generaions model where he issue of child labor can be addressed in he shor as well as in he long run. I also capures he ransiional dynamics from he shor o he long run. In his model parens are he decision-making uni and are alruisic owards heir children. Since child labor is presen only in developing counries, we use his model o show how he major feaures of underdevelopmen, namely, backward echnology, inefficiency of he educaion sysem, parenal apahy ec. bind an economy in a child labor rap in he long run. The paper also seeks o derive he shor run and long run implicaions of a minimum wage law, which applies o boh adul and child workers. We find ha, if he minimum wage rae is se above he long run free marke seady sae wage rae and he parens perceive he impac of he law on employmen, he law eliminaes child labor alogeher in he long run. If, however, he wage rae is se below he seady sae wage rae, here are muliple equilibria. Submied for discussion paper series (2003)ERU, ISI,Kolkaa.

2 . Inroducion Child labor is presen only in developing naions and i disappears once a naion achieves a cerain degree of developmen. Informaion presened in Table, which shows how incidence of child labor has declined wih economic developmen in differen regions of he world, brings i ou quie clearly. Hence i is imporan o examine he relaionship beween child labor and hose aspecs of an economy ha are regarded as major indicaors of underdevelopmen. Recen lieraure on child labor, which has emerged following he conroversy creaed by child labor sandards, idenifies parens economic condiion as he single mos imporan causal facor responsible for child labor (see, for e.g., Basu and Van(998) and Basu(999)). I has no sough o go farher and link he incidence of child labor o he sage of economic developmen achieved by he economy. I is rue ha he low level of income of he parens is an imporan feaure of underdevelopmen, bu i is by no means he only index. More imporanly, i should be regarded as an endogenous variable a leas in he long run. One imporan purpose of his paper herefore is o explain he incidence of child labor in he long run in erms of cerain imporan feaures of developmen, which are responsible for boh low levels of parens income and child labor. In his sense he paper seeks o generalize one major resul of he recen heoreical lieraure and hereby ries o remove a major gap. 2

3 Child labor is obviously undesirable. Every child should ge he opporuniy o develop all her/his faculies o he fulles possible exen. However, as many Table Paricipaion Raes for Children, 0-4 Years World Africa Asia Europe Source: ILO (996) 3

4 wriers have argued, see, for e.g., Ranjan(999), Basu and Van (998), among ohers, a ban on child labor may be couner-producive. Under hese circumsances i may be advisable o search for an alernaive policy measure. This paper akes such a course and examines he impac on child labor of a minimum wage law ha is applicable o boh adul and child labor. I finds ha, when parens perceive he impac of he minimum wage law on unemploymen, he law removes he incidence of child labor alogeher in he long run if he minimum wage is se above he long run free marke seady sae wage rae. If, however, he minimum wage rae is se below his seady sae wage rae, here are muliple equilibria. The presen paper develops a simple overlapping generaions model where parens are alruisic owards heir children. Glomm (997) has also used an overlapping generaions model wih alruisic parens, bu he has focused only on he relaive efficacies of privae and public invesmen in human capial formaion. Ranjan (200) also uses an overlapping generaions model wih alruisic parens, bu his focus is on he relaionship beween inequaliy and he incidence of child labor and he evoluion of inequaliy over ime. This paper, however, absracs from he problem of inequaliy, assumes all individuals o be idenical and seeks o relae he problem of child labor o he major feaures of underdevelopmen. This paper is arranged as follows. Secion 2 develops he model and derives he condiions under which an economy ges caugh in a child labor rap in he 4

5 long run. Secion 3 examines he implicaions of he minimum wage law, while he final secion conains he concluding remarks. 2.Model The model consiss of a large number of idenical households and firms. Firms produce a single good wih only one inpu, labor. Households use i only for purposes of consumpion. There is no physical capial in he model. Markes for boh his consumpion good and labor are assumed o be perfecly compeiive. The only qualificaion is ha here he number of firms exising in he economy is assumed o be fixed. This implies ha here may exis posiive profi or loss even in he long run. This assumpion is made jus for simpliciy and wihou any loss of generaliy. I allows us o examine he implicaions of he minimum wage law in he simples possible framework. Thus firms and households are price akers in boh he markes. Household As we have already menioned, here are a large number of idenical households. Each household consiss only of wo members, one paren and one child. Each member lives for wo periods. In he firs period of an individual s life, he is a child. In he second period, he is a paren. An individual spends a par of he firs period of his life in schools and works in he remaining par. He spends he whole of he second period of his life working. In any given period in a represenaive household, he paren is he decision-making uni. He is assumed o be alruisic. He supplies inelasiciy he whole of his labor endowmen and 5

6 decides on how much ime or labor he child will devoe o curren producion and how much o schooling. In his model, i is assumed for simpliciy and wihou any loss of generaliy ha here is no child labor if he child is allowed o spend he whole of he firs period of his life in schools. Accordingly, we measure he incidence of child labor in erms of how much ime or labor endowmen he child devoes o schooling. The greaer he proporion of ime or labor endowmen he child devoes o schooling, he less is he incidence of child labor. In his model he household does no save. Here we also assume for simpliciy ha here is no cos of schooling oher han he amoun of curren producion foregone. There is no populaion growh. Households do no save and he economy produces a single consumpion good, which is reaed as he numeraire. We also posulae ha boh he paren and he child supply labor of he same qualiy. In any period,, he paren in he represenaive household maximizes he following uiliy funcion, which for simpliciy is assumed o be separable and addiive. log C + φ log h + ; φ > 0 () where C consumpion of he household in period, h human capial of he + child of period in period +,and paren s aiude or he degree of alruism owards he child. φ a shif parameer, which measures he C = W L + Π (2) where W wage rae in period, L amoun of labor supplied by he household 6

7 in period and Π profi income of he household in period. Value of h + is given by he following human capial formaion funcion: h ( + ) α + = + δ ; 0 α and δ > 0 (3) Le us explain eq. (3). Labor endowmen of he child is assumed o be uniy. α denoes he proporion of labor endowmen devoed by he child in period o schooling andδ, which measures he efficiency of schooling is a consan. For simpliciy we have no inroduced eiher he paren s human capial or he aggregae sock of human capial in period as an argumen in he human capial formaion funcion. Equaion (3) does no conain any mechanism o generae exernaliy or endogenous growh. From eq. (3) i follows L LF ( α ) = + (4) where LF labor endowmen of he paren in period and ( α ) gives he proporion of labor endowmen or amoun of labor devoed by he child o curren producion in period. Again, from eq. (3) and eq. (4) i follows ha LF ( + ) + B α ; B > 0 and 0 α (5) = δ + where α gives he amoun of labor devoed by he child in period ( - ) o schooling and B gives he amoun of labor ha an unskilled paren can supply over and above he uni amoun of labor ha an unskilled child can supply in one period if hey work over he whole period. However, for simpliciy and wihou any loss of generaliy we shall henceforh assume B o be equal o zero. Using equaions 7

8 (2), (3), (4) and (5), he paren s maximizaion exercise in period may be rewrien as max[log(.{ α ( + δ ) + + ( α )} + Π ) + φ log( + α ( + δ ))] α s.. W 0 α,0 α Firs order condiion for maximizaion, when here is an inerior soluion, is given by δ ( W.{ α ( + δ ) + + ( α )} + Π ). W = φ( α ( + δ ) + ).( + ) (6) If, however, he soluion of α as yielded by eq.(6) for he given value of α exceeds (falls shor of 0), we have a corner soluion and he soluion is (he soluion is 0). Given (), he second order condiion for maximizaion is saisfied. When here is an inerior soluion, we can solve eq. (6) for he opimum value of α as a funcion of α, δ, φ and Π. α ~ = α ( Π, α, δ, φ) (7) From equaions (4), (5), and (7) we ge he labor supply funcion of he household in period. Thus L [ + α ( )] { ~ + δ + α (.)} (8) = Firm There are a large number of idenical firms. Each firm produces he same good wih only labor. The producion funcion of he represenaive firm is given by β ( 0,) Q = L ; β (9) 8

9 where Q amoun of he good produced and L amoun of labor employed by he firm. The firm maximizes profi as shown below: L β max Π = L W L (0) Firs order condiion for profi maximizaion is given by β W β L = () From eq. () we ge he labor demand funcion. Denoing labor demand in period by L d, we ge L = g d W (, β ) W β β ; g < 0 and g > 0 2 (see eq.(9)) (2) Subsiuing eqs. (0) and (2) ino eq. (8) and using eqs. (2), (4) and (5), we can wrie he labor marke equilibrium condiion as.( + δ ) + { ~ α ( β [ g ( W, β )] W. g( W, β ), α, δ, φ)} = g( W, ) + α θ Walras law holds in our model. Subsiuing eq.(0) ino eq. (2), we ge C ( C Q ) + W ( L L ) = 0 = W L + Q LdW d The above equaion gives he Walras law. Hence labor marke equilibrium implies goods marke equilibrium. Therefore he labor marke equilibrium condiion gives he shor run equilibrium condiion, i.e., equilibrium condiion in any given period, in our model. Alernaively, he shor run equilibrium condiion may be derived as follows. Subsiuing ino eq. (6) equilibrium values of W and Π as given 9

10 respecively by equaions () and (0) and he value of L as given by equaions (4) and (5), we ge [{ + ( + δ ) α = { + ( + δ ) α } + ( α )} β ] ( + δ ) φ β{ + ( + δ ) α + ( α )} β Deerminaion of he Equilibrium Value of α, given α mlu, mgu mgu mlu α Figure 0

11 β{ + ( + δ ) α = { + ( + δ ) α } + ( α )} ( + δ ) φ [ β{ LF + ( α )} ] (3) Eq.(3) gives he shor run equilibrium condiion of our model, i.e., he equilibrium condiion in any given period. We can solve eq. (3) for he shor run equilibrium value of α as a funcion of [ α ( + δ )] + ( LF ),δ, β and φ. The soluion of eq. (3) is shown graphically in Figure where mlu and mgu schedules represen he LHS and RHS of eq. (3) respecively. In Figure mlu schedule or he LHS of eq. (3) gives he amoun of loss in uiliy due o he fall in C following a uni increase in α. We call his marginal loss in uiliy or mlu due o a uni increase in α. The slope of he mlu schedule is quie self-eviden. Again, he RHS of eq. (3) or he mgu schedule gives he amoun of increase in household s uiliy due o he rise in h + brough abou by a uni increase in α. We refer o his as he marginal gain in uiliy or mgu of a uni increase in α. Obviously, he shor run equilibrium value of α corresponds o he poin of inersecion of mgu and mlu schedules. Le us now solve eq.(3) mahemaically for he equilibrium value of α. From eq.(3) we ge + ( + δ ) α ( + δ ) φ = + ( + δ ) α + ( α ) β

12 or, α φ φ = ( + δ ) α + 2 φ + β φ + β ( + δ ) φ ( α ) β α (4) Eq.(4) is a linear firs-order difference equaion. Le us herefore derive he condiions under which i will have a unique and sable seady sae. Now, α (). is coninuous and differeniable over he domain α [ 0,] unique and sable inerior fixed poin if ( 0) eq.(4) we ge α ( 0) Therfore ( ) φ = 2 φ + β β δ ( + ) φ ( + δ ) φ 2( + δ ). Therefore i will have a 0 < α <, 0 < α < and α () <. From β β α 0 > 0 2 > φ > (5) Again, α ( 0) < φ 2 φ + β β δ ( + ) < φ < β + φ + δ (6) From (5) and (6) i follows ha ( 0) 0 < α < if and only if β 2 + δ ( ) < φ < β + (7) + δ Now, 0 < φ β < φ < (8) β + φ δ < α ( + δ ) φ β α() < 2 + ( + δ ) < φ < β (9) β + φ ( + δ ) φ + δ 2

13 If φ saisfies (9), i auomaically saisfies (8) ( ( + δ ) > δ ) Q and (6) ( Q [( /+ δ ) + ] > ( / + δ )). Therefore if [ β 2( + δ )] < φ < [ β /( + δ )] ( 0) 0 < α <, 0 < α < and α () <. From he above i follows /, hen Derivaion of he Seady Sae Value of α α αα α α Figure 2 3

14 Remark : If [ β 2( + δ )] < φ < [ β /( + δ )] inerior fixed poin. /, α (). will have a unique and sable The siuaion is shown in Figure 2, where αα represens α (). in he ( α, α ) plane. Le us now derive he seady sae value of α. Denoing i by α and subsiuing i in eq. (4), we ge φ β α = 2 (20) β φδ ( + δ ) φ The seady sae value of α is unique and globally sable. From eq. (20) i is clear ha paren s economic condiion is no a deerminan of he incidence of child labor in he long run. Obviously, paren s economic condiion is iself an endogenous variable in he long run. From eq. (20) we find ha in he long run he deerminans of child labor are δ, β and φ. Economic Developmen and Child Labor We shall here carry ou a few comparaive dynamic exercises. More precisely, we shall examine how δ, β and φ, which are all imporan indicaors of developmen affec he incidence of child labor in he shor and he long run. Paren s Economic Condiion Paren s economic condiion measured by LF in his model may be regarded as exogenous only in he shor run, i.e., only in a given period. I is obviously endogenous in he long run. Therefore we can examine he impac of an 4

15 increase in LF in he shor run only. I is clear from eq.(3) ha an increase in LF, given all oher variables, leaves is RHS unaffeced, bu lowers he LHS. This implies ha a he iniial α, marginal reward of sending children o school remains unchanged, bu is marginal cos falls. This obviously induces parens o increase α. The fall in marginal cos of schooling is due o diminishing marginal uiliy of he parens from household s income. In erms of Figure following an increase in LF mlu schedule shifs downward, while mgu schedule remains unaffeced. This leads o he following proposiion: Proposiion : An improvemen in parens economic condiion will reduce he incidence of child labor in he shor run. In he long run, however, paren s economic condiion is iself an endogenous variable and herefore canno be regarded as a deerminan of he incidence of child labor. The firs par of he above resul is perfecly in accord wih he resuls derived by Basu and Van (998) and Ranjan (999), among ohers. Parenal Alruism and Child Labor Consider now he effec of an increase in φ. Focus on he shor run firs. From eq. (4) i is clear ha an increase in φ implies an increase in he value of α, given he value of α. This resul may be explained wih he help of Figure. An increase in φ raises he value of he marginal gain from he child s educaion as measured by he RHS of eq.(3), given he value of α. I, however, leaves he LHS, which measures he marginal cos of sending he child o school unaffeced. Therefore he mgu schedule in Figure shifs upward, while he mlu schedule 5

16 remains unaffeced. Thus a he iniial equilibrium value of α marginal gain of sending children o school exceeds is marginal cos inducing he paren o increase α. From he above i follows ha, following an increase in φ, αα schedule in Figure will shif upward bringing abou an increase in α. This resul follows sraighway from eq.(20) also. I is clear from Figure 2 ha, following an increase in φ, α will rise seadily from is iniial seady sae value o is new seady sae value. This leads o he following proposiion: Proposiion 2: An increase in φ, which measures parenal alruism owards children will reduce he incidence of child labor in boh he shor and he long run. Efficiency of he Educaion Sysem and Child Labor Le us now examine he effec of an improvemen in he efficiency of he educaion sysem, which in our model implies an increase in δ, on he incidence of child labor in he shor and he long run. Le us focus on he shor run firs, i.e., le us firs examine how an increase in δ affecs he equilibrium value of α, given α in period. I is quie clear from eq. (4) ha an increase in δ leads o an increase in he equilibrium value of α, corresponding o any given value of α. This is he shor run implicaion. The long run implicaion can easily be derived wih he help of Figure 2. In erms of Figure 2, an increase in δ brings abou an upward shif in he α α schedule. Hence he seady sae value of α rises. This is obvious from eq. (20) 6

17 also. Therefore following an increase in δ, as mus be clear from Figure 2, incidence of child labor as measured by α will rise seadily from is iniial seady sae value o is new seady sae value. Thus we ge he following proposiion. Proposiion 3: An improvemen in he efficiency of schooling will reduce he incidence of child labor boh in he shor and he long run. This resul may be explained wih he help of eq.(3) and Figure. An increase in δ, given all oher variables, lowers he value of he LHS of eq. (3) due o diminishing marginal uiliy of he paren from household income. Therefore marginal reurn from sending he child o school falls and mlu schedule in Figure 2 shifs downward. On he oher hand, he value of RHS rises by ~ ~ ~ ( / ) φ[ {( B ) / B} ] dδ > 0 ~ B δα B, where + ( + ). This indicaes ha a rise in δ raises he marginal reurn from schooling. Accordingly, mgu schedule in Figure shifs upward. Thus mlu becomes less han mgu a he iniial equilibrium value of α inducing he paren o raise α. This explains he resul. Technology and Child Labor Here we shall examine he impac of an improvemen of echnology on child labor. This in our model we can capure hrough an increase in β. I follows sraigh from eq.(4) ha an increase in β lowers he equilibrium value of α, given α. Thus in he shor run i raises he incidence of child labor. We can examine he long run implicaion wih he help of figure 2 where, as follows from above, α α schedule shifs downward and hence he seady sae value of α falls following an increase in β. One can also derive his from eq. (20). From Figure 2 i is clear ha he equilibrium value of α will fall seadily 7

18 from is iniial seady sae value o is new seady sae value. This gives us he following proposiion: Proposiion 4: Technological improvemen will lead o an increase in he incidence of child labor in boh he shor and he long run. This resul may be explained wih he help of eq.(3) and Figure 2. From eq. (3) i follows ha an increase in β, given all oher variables, raises he LHS, which measures he marginal cos of sending he child o school. Bu marginal gain from he child s educaion as given by he RHS remains unaffeced. In erms of Figure 2 he mlu schedule shis upward, bu he mgu schedule remains unchanged. Thus a he iniial equilibrium value of α, mgu falls shor of mlu. Accordingly, he paren reduces α. This explains our resul. In course of developmen, parens aiude owards heir children changes. They derive more pleasure from and ake greaer ineres in heir children s educaion. Efficiency of he educaion sysem also increases seadily. These changes, as we have seen in our paper end o reduce he incidence of child labor. However, along wih he evens noed above, here also akes place seady improvemen in echnology, which by raising marginal produciviy of labor makes i coslier for he parens o send heir children o school. However, as experiences of differen counries show, he effec of he firs wo changes dominaes over ha of he hird one and he incidence of child labor falls seadily wih economic developmen. Proposiions 2,3 and 4 yield he final proposiion of his secion. Proposiion 5: Given he level of echnology, if parens are no sufficienly alruisic owards heir children and he educaion sysem is no sufficienly 8

19 efficien, he economy will be caugh in a child labor rap in he long run. If in course of developmen parenal aiude owards children and efficiency of he educaion sysem improve a a sufficienly faser rae han echnology, incidence of child labor will fall seadily over ime. 3. Wage Policies and Child Labor When a ban on child labor is inadvisable, he governmen can exend he scope of he minimum wage law o include child labor as well o proec hem from exploiaion. Here we examine he implicaions of such a law for child labor. Basu (2000) has explored he relaionship beween minimum wage law for adul workers and he incidence of child labor in he shor run. He has found he impac of he law o be ambiguous. In his model, incidence of child labor is a decreasing funcion of parens income. Minimum wage law for adul workers ends o make parens beer off by raising he wage rae. A he same ime i creaes unemploymen among adul workers. Therefore parens income may change eiher way. This explains he resul. In his paper, however, we seek o examine he impac of a minimum wage law, which applies o adul labor as well as o child labor. Here we consider he case where we assume ha parens perceive he impac of he minimum wage law on employmen. The assumpion may be jusified on following grounds. If minimum wage law causes persisen unemploymen which i cerainly will, if i is effecive- hen even if parens fail o idenify he cause of unemploymen, hey will find i difficul o find jobs for heir children. I is herefore quie likely ha hey will incorporae his in heir opimizing decision. No only ha, in poor counries 9

20 poor households operae in unorganized labor markes, which are characerized by he dominance of casual labor and a high degree of labor urnover. In such a scenario if here is unemploymen, almos every household will share i. For example, if unemploymen rae is en percen, mos of he households will no find work on en per cen of he days on which hey are willing o work. In hese circumsances, in he face of persisen unemploymen i only seems reasonable ha he alruisic parens on he average will ake his phenomenon of unemploymen ino accoun while deciding on heir children s educaion. Le us herefore examine he implicaions of he minimum wage law when parens realize ha a he sipulaed wage rae hey are quaniy consrained in he labor marke. We have modeled he opimizaion exercise of he parens in his siuaion following he line suggesed by sudies belonging o he so-called disequilibrium or fixed price macroeconomics such as Clower (967), Barro and Grossman (976), Malinvoud (977), Benassy (982) and ohers. In he absence of he minimum wage law, i.e., in he free marke siuaion eq.(3) yields he shor run equilibrium value of α, given α, φ, δ and oher exogenous variables, when here is an inerior soluion. This shor run equilibrium value of α is given by α( α )- see eq.(4). Accordingly, shor run equilibrium values of L and W ha prevail in he absence of he minimum wage law are given by ( α ))]( L( α )) [ + α ( + δ ) + ( α and β * ( ))) ( ) β ( + α ( + δ ) + ( α α W respecively (see eq. (), eq. (4) and eq. (5)). Suppose he minimum wage sipulaed by he governmen is denoed by W. We assume ha for some given, W > W * 20

21 β )) = β ( + α ( + δ ) + ( α( α ). Under he minimum wage law, given he assumpions, he paren s maximizaion exercise in he shor run, i.e., in any given period reduces o max[ U ( W.{ α ( + δ ) + + ( α )} + Π ) + U ( + α ( + δ ), φ)] α (2) s.. [( + α ( + δ ) + ( α )] g( W, β ) and 0 α (see eq. (2) Firs order condiion for he above maximizaion exercise, in case here is an inerior soluion, is given by eq. (6). In equilibrium he above firs order condiion reduces o eq.(3). We know ha he value of α ha saisfies eq. (3) is ( ) α. α Since by assumpion, in he period under consideraion, W > W * and g < 0 - see eq.(2)- labor supply a W * as given by ( ))] g( W, ) [ + α ( + δ ) + + ( α α > β (22) Therefore in equilibrium in he given period he above opimizaion exercise does no have an inerior soluion and by Kuhn-Tucker condiion he value of α ha saisfies he paren s opimizaion exercise in he given period is given by [ + α ( + δ ) + + ( α )] g( W, β ) (23) = From eq.(23) and (22) i follows ha ( α ) = 2 + α ( + δ ) g( W, β ) > α α (24) Eq.(24) gives he opimum value of α as long as he value of α ha saisfies he above equaion is less han or equal o uniy. If he value of α ha saisfies he 2

22 above equaion is greaer han uniy, hen by Kuhn-Tucker condiion he opimum value of α is uniy. From his we ge he following proposiion: Proposiion 6: When minimum wage law applies o boh adul and child workers and parens perceive is impac on employmen, he law induces he parens o sep up invesmen in human capial reducing he incidence of child labor in he shor run, i.e., in any given period. The inuiion behind proposiion 6 is quie simple. Since minimum wage law creaes unemploymen of child labor as well, he cos of sending children o school declines. This induces alruisic parens o do all he work ha is available and send he unemployed children o schools. This raises invesmen in human capial formaion and lowers he incidence of child labor in he shor run. Le us now focus on he long run. Suppose he governmen sipulaed minimum wage rae denoed by W is greaer han he seady sae wage rae, which is given β s by he expression, ( + α( + δ ) + ( α( α ))) ( W ) β (see eq. (), eq. (4) and 0 0 eq. (5)). Le us consider he shor run equilibrium pair ( α ) α, corresponding o 0 0 β = which he shor run equilibrium W = W, i.e., β ( + α ( + δ ) + ( α )) W. Now consider he schedule αα in Figure 3. This is he same αα schedule of Figure 2. Since he slope of αα - see Figure 2 - given by α is less han uniy, see eq.(4), shor run equilibrium value of L [ = ( α ( + δ ) + + ( α( α )))] rises as α and α increase along αα. Since equilibrium value of W is given by β ( + α β ( ) ( + δ ) + ( α α )) labor. Therefore shor run equilibrium value of, here is diminishing marginal produciviy of W falls as we move upward along 22

23 αα. This ogeher wih he assumpion ha W > W implies ha ( α, α )< α. 0 0 Thus, as shown in Figure 3, ( α ) s α, will be o he lef and below (α, α ) on αα. Under minimum wage law he opimizaion exercise of he paren is given by (2). When he opimizaion exercise has an inerior soluion, he firs order condiion for maximizaion in equilibrium is given by eq.(3). Given our assumpion abou W, we know ha, for allα 0 < α 0, (2) has an inerior 0 soluion. Hence for 0 < α α, shor run equilibrium combinaions of α and α under minimum wage law are given by αα schedule in Figure 3. However, for α 0 α, (2) does no have an inerior soluion. Therefore for 0 α α, as we have already shown, shor run equilibrium combinaions of α and α under he minimum wage law are given by he equaion [ α ( + δ ) + + ( α )] g( W, β ) + = or by he equaion β ( + α β ( + δ ) + ( α )) = W 0 0 β 0 0 ( +, = β α ( + δ ) + ( α )) ; α α < α i.e. by + α ( + δ ) + + ( α )] = ( + α ( + δ ) + ( α )) (25) [

24 Derivaion of he Seady Sae Value of α Under Minimum Wage Law A 4 A 3 C α B B α A A 6 αα 0 α A 5 A 2 0 α α α m ~ α α Figure 3 24

25 for 0 α, 0 α. If for any 0 α, opimum value of α, as given by eq. (25), is greaer han (less han zero), he opimum α is equal o (zero). These opimum combinaions of α and α are represened by he curve 0 0 A 5 A 4 A 3 C, which sars from he poin ( α ) α, on αα in Figure 3. The curve A 5 A 4 A 3 C shows ha he equilibrium value of α becomes uniy beforeα becomes uniy. This poin may be explained as follows. From eq.(25) i d follows ha ( α / α ) > d. Again, 0 0 > α α. These wo facs imply ha α, according o eq.(25), will be uniy a a α <. Le us denoe his α by α. For all α such ha ~ α α, α =. This explains he posiion of ~ A 5 A 4 A 3 C. Thus he locus of all he shor run equilibrium combinaions of α and α in he presen case is given by he curve A 2 A 5 A 4 A 3 C in Figure 3. Therefore in his case here is only one seady sae, C (see Figure 3) and his seady sae is sable. Thus we ge he following proposiion: Proposiion 7: If he minimum wage rae is se above he long run free marke seady sae wage rae ha prevails in he absence of he minimum wage law, he value of α in he long run will sele down o uniy eliminaing child labor. Le us now consider he case where he minimum wage rae, W consider he shor run equilibrium pair ( α ), s < W. Le us α corresponding o which he equilibrium W = W, i.e., β ( + α ( + δ ) + ( α )) = W (see eq. (4), eq. (5) and eq. ()). We have already shown ha, since α < along αα in Figure 2 or 3 (see eq.(4)), shor run equilibrium value of L rises and herefore ha of β 25

26 W falls as α and α increase along αα. Therefore, since W > ( α, α ). From he above i follows ha, for < α s < W, ( α α ), α opimizaion exercise, (2), has an inerior soluion in equilibrium. Therefore for α < α, shor run equilibrium value of α coninues o be given by αα. However, for α α, here does no exis any inerior soluion in equilibrium. Therefore for α α, shor run equilibrium combinaions of α and α under minimum wage law, by Kuhn-Tucker condiion, are given by β ( + α ( + δ ) + ( α )) β = W β β (, β + α ( + δ ) + ( α )) = β ( + α ( + δ ) + ( α )) ; α i.e., by ( +, α ( + δ ) + ( α ) = ( + α ( + δ ) + ( α ); α α > α From he above equaion we ge α > α 0 ( L ) + ( + δ ) α α ( α ); L + α ( + δ ) + ( α ); α, α α = 2 α > Eq.(26) gives he opimum value of α corresponding o any given value of α in he domain α 0 α α, if ( ) (26) α. If for any such value of α, value of α saisfying eq. (26) is greaer han uniy, he opimum value of ( α ) α is. Now, α, may be represened in Figure 3 by a poin such as A or by a poin such as A 6. Therefore, for α α, he shor run equilibrium value of α corresponding o any given α is given by he curve A B A 3 C or by he curve 26

27 A 6 B in Figure 3. Thus in he presen case he locus of all shor run equilibrium combinaions of α and α are given eiher by he curve A 2 A 5 A B A 3 C or by he curve A 2 A 5 A A 6 B in Figure 3. Le us now derive he condiions under which we have hese wo curves. Noe firs ha eq.(26) will definiely have a unique fixed poin over he domain ( ) α `, since α α > and α = ( + δ ) > 0. Le he value of his fixed poin be α m. We can ge he value of α m by solving eq.(26) afer subsiuing α m for α and α. Obviously, if α m <, α as given by eq.(26) will equal uniy a < 0 α. Therefore, if (, α ) α since = ( + δ ) > α is such ha α <, we have he siuaion depiced by A 2 A 5 A B A 3 C in Figure 3. If on he m oher hand ( α ) α is such ha α, we have he siuaion as depiced by, m A 2 A 5 A A 6 B in Figure 3. The value of α m as derived from eq.(26) is given by ( + δ ) α( α ) f ( α ); f = + ( α ) > α = α m (27) δ δ Le us now focus on ( ) f α. Since, as follows from eq.(4), α <, f >. We firs derive he condiions under which for α = α <, ( α ) = α α or ( ) f. Again, a m f α is less han uniy. Noe ha, = [{ }/ δ ] α, f ( ) = + α() α > (since α () < in his model). I is quie clear from eq.(27) ha ( ) coninuous and differeniable for every α [,] f α is α. Therefore, if α is sufficienly close o α, i.e., if W is sufficienly close o W, α < and we have s m 27

28 he siuaion depiced by A 2 A 5 A B A 3 C in Figure 3. If, however, W is sufficienly smaller han s W, we have he siuaion represened by A 2 A 5 A A 6 B in Figure 3. In he firs case, where opimum combinaions of α and α are given by A 2 A 5 A B A 3 C in Figure 3 here are muliple equilibria. As shown in Figure 3, here are wo oher seady saes besides A or (α, α ): one a B and he oher a C. Seady saes a A and C are sable, bu ha a B is unsable. Le us denoe he seady sae value of α and α a B by ~ α m. Subsiuing eq. (26), we can solve i for he value of ~ α m for α and α in ~ α m. However, his seady sae is unsable. If iniial α > ~ α m, hen α and α will go on rising and hereby move farher and farher away from ~ α m and will evenually converge o C, wih α = α =. On he oher hand, if < α m ~ α, α and α will go on falling over ime and converge o he long run seady sae value, α. In he second case, however, where he shor run equilibrium combinaions of α and α are given by he curve A 2 A 5 A A 6 B, here is only one seady sae, A, which is sable. In his case herefore he law has no impac on he incidence of child labor in he long run. The above discussion leads o he following proposiion: Proposiion 8: When W s < W, we have wo cases. In he firs case W is no significanly less han W s. In his case we have muliple equilibria. If in his case in he iniial siuaion he minimum wage law is binding, i.e., if he free marke shor run equilibrium wage rae is less han W in he absence of he law, he law will have wo ypes of effec on child labor. If in he iniial 28

29 siuaion he free marke shor run equilibrium wage rae is less, bu no very close o he governmen sipulaed minimum wage rae (so ha he iniial value of α is greaer han ~ α m ), he law will eliminae child labor alogeher. If, however, in he iniial siuaion he free marke equilibrium wage rae is less, bu very close o he minimum wage rae, i will have no impac on he incidence of child labor in he long run. If in he iniial siuaion he minimum wage law is no binding, i.e., if in he iniial siuaion he free marke shor run equilibrium wage rae is greaer han he sipulaed minimum, he law will have no impac on he child labor in he long run. In he second case W is sufficienly less han W s. In his case again he law will have no impac on he incidence of child labor in he long run. 4. Conclusion The paper develops a simple overlapping generaions model where parens are alruisic owards heir children. The model allows us o address he issue of child labor in he shor as well as in he long run and show he dynamics of ransiion from he shor o he long run. The paper uses his model o explain why he problem of child labor persiss in poor counries and how economic progress can alleviae he problem. More precisely, i derives he condiions under which he major feaures of underdevelopmen such as backward echnology, inefficien educaion sysem and parenal apahy owards heir children s educaion bind an economy in a child labor rap in he long run. I also idenifies he condiions under 29

30 which improvemens in all hese frons reduce he incidence of child labor and evenually eliminae i. I also examines he impac of a minimum wage law, which applies o boh adul and child labor. This exercise is carried ou for he case where parens perceive he impac of he law on employmen. In his case in he shor run he law will unambiguously reduce child labor. Siuaions in he long run are, however, much more complex. If he minimum wage rae is se above he long run free marke seady sae wage rae, he law will eliminae child labor alogeher. If, however, he minimum wage rae is se below he free marke seady sae wage rae, here are muliple equilibria. If he minimum wage rae is se subsanially below he free marke seady sae wage rae, i will have no impac on he incidence of child labor in he long run. However, if he minimum wage rae is no ha low, here will emerge wo differen siuaions. If in he iniial siuaion he free marke shor run equilibrium wage rae is less han and close, bu no very close, o he minimum wage rae, he law will remove child labor alogeher. On he oher hand, if in he iniial siuaion he free marke shor run equilibrium wage rae is less han, bu very close o or higher han he sipulaed minimum, he law will have no impac on child labor in he long run. Acknowledgemens We are indebed o he paricipans in he conference organized by he Jadavpur Universiy for many helpful commens and suggesions. However, all he remaining errors are ours. 30

31 References Barro, R. and H.Grossman (976). Money, Employmen and Inflaion, Cambridge: Cambridge Universiy Press. Basu, K (2000). The Inriguing Relaion beween Adul Minimum Wage and Child Labor, Economic Journal, Vol. 0, No. 462, pp. C 50-C (999). Child Labor : Cause, Consequence and Cure, wih Remarks on Inernaional Labor Sandards, Journal of Economic Lieraure, Vol. 37, No. 3, pp Basu, K and P.H. Van (998). The Economics of child labor, American Economic Review, Vol. 88, No. 3, pp Benassy, J. (982). The Economics of Marke Disequilibrium, New York: Academic Press. Clower,R. (967). A Reconsideraion of he Micro Foundaions of Moneary Theory, Wesern Economic Journal, Vol.6, pp. -9. Glomm, G. (997). Parenal Choice of Human Capial Invesmen, Journal of Developmen Economics, Vol. 53, Issue, pp ILO (996). Economically Acive Populaions: Esimaes and Projecions, , Geneva: ILO. Malinvaud, E. (977). The Theory of Unemploymen Reconsidered, New York: Halsed Press. Ranjan, P. (200). Credi Consrains and he Phenomenon of Child Labor Journal of Developmen Economics, Vol. 64. pp (999). An Economic Analysis of Child Labor Economics Leers, Vol. 64, pp

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