Inequalities, Economic Development and Growth
Diana Loubaki[1]
Université de Paris1
Abstract
We establish whether inequalities can generate economic growth in developing countries. However poverty often lead poor families decide not to put their children in the schooling system to supplement the household’s income, most educated parent’s altruism makes them choosing full time education. Thereby, perpetuating both poverty and the highest social condition in the same society. Indeed, the necessary public investment in human capital respectively expressed by training periods abroad for the scholars endowed with highest productivity levels and families financial supports for the other part of the society at the whole, increase the efficiency of productivity labour in developing country’s at the first step. At the second step, the developed country’s human capital externalities generated by the most educated scholars create also positive effects in increasing the average amount of units of the labour productivity of the others children once more leading progressively to the cease of poverty and to the reduction of inequalities while growth generated implies also development of productive capacities.
JEL: J20, K31, D60
1-Introduction
The International Labour Organisation (ILO) reports that, in 1993, the percentage of children meaning, the persons between the age of 10 to 14 years, who work is 13.7 percent in the world and in some part of central Africa, it can be as high as 32.9%.
This phenomenon is relates theoretically, to the analysis of child labour which is associated to the household’s behaviour in general. Also, two specific approaches of this literature can be listed: the bargaining models and the multiple equilibriummodels with the government intervention.
The bargaining models of child labour can be divided in two distinct approaches: the intra household bargaining which origins come from the failure of the concept of characterisation of the household by a single unit decision making(Becker(1964)) giving birth to the collective bargaining models like Bourguignon-Chiappori(1995)) which represent the household as one parent and one child and the decision making provides from an amalgam of the members of the household is similar to say that, the decision provides from the average weighted utilities of the members of the family. But the models which explicitly explain child labour are: Extra-Household Bargaining approach like the model of Gupta(1998) in which it is argued that the child’s bargaining power is low in the household. The bargaining occurs now between parent and employer concerning the wage paid for the child work. Gupta(1998) introduces the selfish notion of the parent such in assuming that he takes all the component of the household’s wage for himself.
In all the preceding approaches, the notion of a unique equilibrium is central. New horizons are then opened with the inclusion of multiple equilibrium concept(K.Basu-P.H.Van(1998)) giving several policy questions. The multiplicity of the equilibrium is introduced in child labour analysis through two hypothesis. The luxury axiom which takes account of parental altruism towards the child in saying that, a parent won’t send his child work if the household’s income were sufficiently high to live. Secondly, the substitution axiom which assumes that adults can do what children can do. Hence, children work arguments are follow, it is because of poverty according to Anderson(1971) and Vincent(1981), it is because of parental callousness according to Burra(1995). What is more relates to the phenomenon of Africa, is the justification given by Alaka Basu(1993) saying that, the mother takes her child such a girl out of school in order to have her do the housework. But if the mother’s wage rises enough, she’ll get her child back school. The interesting idea of this argue is the explanation of child labour as a consequence of a non sufficient income of the household without making a substitution assumption between the adults and the children work in the labour market. Making the two types of labour inputs substitutes in good production, means that the demand of work is high which is not really the case of our study concerning Africa less efficiency labour forces. Hirschman(1995) then, justifies child labour work by social norms which have many interpretations(Dasgupta(1993)). The others kinds of justifications are unemployment problems and are thus relate to income distribution(Gupta(1997)).
The Economists who introduce the government intervention, justified this action by the existence of externalities to child labour meaning that, private returns to education are smaller that social returns to education. This is also the explanation we use to conduct our study concerning growth and development. Our model precisely follows the most recent approach of child labour literature initiated by Dessy(2000) such for the possibility of the poverty trap existence. Dessy(2000) shows that, there are poverty trap with an unstable equilibrium with low productivity and high fertility steady state, and a high productivity with a low fertility rate. Till then, there is not a real contribution dealing with both the stationary and a growth equilibrium which are just after, introduced by Clive Bell and Hans Gersbach(2000) through taxes and transfers programs.
This paper focuses on the dynamics implications of child labour and its relation between education and growth through inequalities in the basis of Clive Bell and Hans Gersbach(2000).
The study of the paper is as follows, section 2 presents the basic model starting with the technology of human capital and goods and pursue with the definitions of the notions of growth, education and work. Finally, it stops with utility optimisation. The third section deals with the dynamics of human capital and the fourth section apply the preceding theory to the real case where functions are explicitly given. After the presentation of the whole theory, section 5 formulates the economic policy in three stages. The first stage introduces the government action to justify the increase of income necessary to supplement the household’s income to permit the adults to let the children have partial schooling leading to the rise of the average efficiency of the whole society. The first step increases inequalities whereas, the second step creates convergence through the spread over of the developed country’s human capital externalities in the least levels increasing once more the level of the whole society. Finally, suitable mechanics of economic development are given through the study of the impact of parameters on the dynamical system. Section 6 concludes on the study and gives recommendations for growth and development.
2-The Basic Model
Consider a developing country’s overlapping generations economy in which individuals live for two periods, the childhood and the adulthood respectively and dye at the end of the second period. Each generation consists on several households or several families represented by one mother and her child who born at the beginning of the second period. More precisely, each mother gives birth to one child, so that, the population remains constant over time. We denote, Nt the children(or the population) who enter in the system. We assume,: Nt =N at each period t also, N is composed of Et and Vt who are the children of the educated and of the non educated adults respectively. The preceding relation can also be expressed in terms of proportions such that: et + vt=1, which is per-capita child devoted to schooling and per-capita child devoted to work respectively. Indeed, at each period t, there are educated adults, non educated adults and their children who spend most of their time working.
2.1 The technology of human capital and the technology of goods in terms of efficiency units of labour
To express human capital law of motion, let an adult in period t possesses t efficiency units of labour, where tN/{0} (the set of integers minus zero) measures human capital accumulation, t=1 corresponds to a non literate adult. The idea is that, the average efficiency labour of the whole society should be greater than t.=1 to avoid complete backwardness. Agents within a generation inherited their parents efficiency labour. Then the children efficiency labour is composed of their parent’s endowment and formal education which is composed of: reading, writing and calculating abilities. Therefore, the child’s endowment of efficiency units labour while reaching adulthood at time t+1 is given by,
(1)
Note that the preceding formula concerns only the child of the educated mother and h(,) is assumed to be a continuous, increasing and differentiable function on {0,1} with h(0)=0. Equation (1) means that, if human capital is also composed of formal education, then t+1>1 necessarily. Without any education chosen by the mother concerning the non educated household, because she doesn’t win enough money and she needs her child working to increase the family’s income, the children ability stagnate. Ad we also assume in that case that, the child supplies at most one unit of labour. Doing so, illiteracy is perpetuating through the next generations keeping the country in economic backwardness state. To express all so, let: be the supply of the child efficiency unit labour, where {0,1}. The upper limit is reached when the child work full time. Therefore, the non educated household supplies a total of [t +vt] efficiency units labour to the production of the aggregate good. Whereas the child of the educated adult goes to school and doesn’t work at the first period.
Under the above assumptions on the technology and on the level of output produced by a household who is endowed of t units of efficiency labour, per-capita income of the educated and of the non educated adults are respectively,
Equation (2) expresses that the level of output produced by a household where education is not chosen for the child. Whereas, equation (3) corresponds to the production of the educated adult minus the cost of education chosen, >0 for human capital investment. It indicates also that these categories of persons have the highest human capital endowment in the society and this human abilities are not assumed to be bounded for instance. Later on, we’ll see that, this efficiency is lower than the developed country’s human capital endowments of the same kind of individuals in the society. Also, A and B are constants per-capita efficiency units of labour of the educated and of the non educated adults respectively.
2.2 Growth, Education and Work
We denote the growth rate g, such that:
Indeed, assuming t+1 = t ,all pairs, (t, et) satisfies
et =0, which is a non schooling decision and, vt=1 which is full time working for all t bounded, as well as the poverty case for the family. Then, t tends asymptotically to the steady state t =1 and the growth rate, g tends to zero.
et =1 for all t non bounded is full time schooling decision it provides from the technology satisfying, h(1)>1 implying that, t tends asymptotically to an unstable steady state at the rate 1/[h(1)-1].
Indeed, if h(1)<1, two cases can be distinguished corresponding to the cases where the child’s efficiency units labour are higher than which one of his parent and the case where, the child’s efficiency units labour are lower than which one of his parent. Meaning that, t tends asymptotically to the steady state, * in the first case which mathematical expression is, *, then * is a fixed stable point for each t. Indeed, human capital will increase if it began from .
In contrast to the preceding case, or concerning the first case where: * then, * is not surely a fixed stable point for each t without additional hypothesis concerning the pair (et,t). Therefore, human capital will decrease to if it goes from *.
2.3 Utility Maximisation
The decision to allocate resources between education and consumption are made by the adults such that, the child consumes a positive fraction of the adult’s consumption, ct in the same family. Then, the budget’s constraints for the poor or the non educated and for the rich or the educated are,
equation (6) depends on the level t of the adult. Indeed, for the poor and for the rich, the constraints are respectively,
equation (7) means that, current consumption is the only good which as a cost for poor families. Whereas, equation (8) presents two goods, current consumption and education. We can see that schooling is cost on income in (8) but child working is an income in (7).
where pv = (1+)/A and pe = (1+)/ are constant relative price of current consumption also, tv = t / for all t =1 and te = Bt / for all t>1 are the households full income measured in real terms.
From equations (7) and (8), the budget constraints defining the poor and the rich choices respectively are,
equation (9) is the feasible set in the space (c,v) for =1, the units of productivity labour endowment of the non educated adult.
equation (10) is the feasible set in the space (c,e) for >1 the units of productivity labour endowment of the educated adult.
Because income is an increasing function of units productivity labour endowment, the feasible plan also increases with the budget line. Thus, a small units of productivity labour endowment is similar to poverty. This is why, the poor families often put their children to full time working. It is then for the process of economic development, use full to analysis the household’s strategy, in formulating economic development issues to help poor families put these children schooling.
For that purpose, we denote: and the pair of maximum and minimum consumption of the poor and the rich respectively which exact expressions are:
and
Assuming these different situations, the economic policy we’re going to establish should cease poverty in the long run.
The poor adult behaviour is now summed up by three decisions variables which are: consumption, work and education expressed by equation (11) such that,
Thus, the advantage of this policy comes from partial time schooling possibility for the poor adult’s child instead of not schooling at all. The aim of this paper is to study eventualities given to the social planer not to let poverty perpetuate in the long run. Also, as we’ll see, the best way is to look for politics which prevent illiteracy for future generations in giving financial supports to the whole families. Because we want to see the most human capital endowed scholars as a positive thing for the nation and in that way, inequalities are exploited for the better off of the while nation.
Concerning the educated adult, two situations can also appear summed by equation (12) such that,
Like we did for the preceding case, we introduce partial time working for the educated child meaning that human capital accumulation is not necessary an increasing function of time inside the same family. This allow a medium social class in the society because, the path of a child can be different of his parent. This is why, several choices done by the adults depend also on the motivations known by them, concerning their child schooling motivation and the household income situation. Equations (13) and (14) express the above preferences of the poor and of the rich respectively such that,
In the above expression, we introduce the assumption of the existence of both partial education and partial working. Indeed, we reject the case of full time working or zero education for the child.
Assuming that the preference ordering is representative by a continuous, strictly increasing differentiable and strictly quasi concave function, wi=w(c,i) where i=v,e, the problem of decision of the non educated parent for the child is expressed such that,
In view of the assumptions on the utility function, the poor adult problem, has a unique solution denoted by, (c*,v*) continuous and increasing function of units productivity labour. Therefore, the associated curve (drawn as n°1) is expressed like following,
The above formula expresses the arbitrage which can be done between consumption and schooling. A highest consumption level leads to full time working choice whereas a lowest consumption leads to partial time working choice, inducing only partial working. The specification of the impact of schooling in units labour productivity shows that, inter generationnel poverty can be avoid if the child of the non educated adult can reach a higher units productivity labour than that of his parent in one generation to an other.
In the same kind of ideas, the problem of decision of the educated parent for his child can be expressed such that,
where
The preceding preference introduces work notion concerning the educated adult’s child, but the particularity of this work is that it can’t be a full time working. But, this child can be concerned with full time schooling depending on his parent decision related to the child’s motivation. Consequently, like before, the assumptions on the utility function lead the educated adult problem determined a unique solution denoted by, (c*,e*) continuous and increasing function of units productivity labour where the associated curve is expressed like following,