An economic growth model with individual years of schooling is present. It is proved that there exist optimal individual years of schooling for fixed wage growth rate. On the other hand, the economy has balance growth path for given individual years of schooling. Finally, we prove that there exist optimal individual years of schooling and economic growth rate such that the individual lifetime utility reaches maximum and the economy grows on a balance growth path.
The relationship between economic growth and education has been deeply researched by economists. Barro and many others [
In [
Futagami and Nakajima [
In this paper, the individual years of schooling are integrated into the analysis framework provided by Futagami and Nakajima to inquire the relationship between the economic growth and the individual years of schooling. It is firstly proved that there exist optimal years of schooling for the individual such that the individual lifetime utility reaches maximum under the fixed wage growth rate. Then, the connection between wages and economic growth rate are obtained by using the aggregate economic balance condition
The paper is organized as follows. The problem of the individual optimal consumption and years of schooling are discussed in Section
For simplification, we follow the assumption given by Futagami and Nakajima [
The individual begins to work after ending his schooling at age
Following the assumption used by Blanchard [
The lifetime utility of the individual born at time
The individual optimal problem is to maximize (
The current value Hamiltonian to solve the optimization problem of individuals is
By (
Multiplying (
From (
From (
The optimal consumption path of individuals is
If the interest is fixed
For a fixed interest rate
If
Let
The optimal individual years of schooling increase strictly with respect to wage growth rate; that is,
By (
Following Futagami and Nakajima [
Following Romer [
Notice that profit maximization firm’s behaviour satisfies the following two conditions in perfectly competitive market: its marginal product of capital equals the real interest rate and its marginal product of labor equals the real wage rate; that is,
It is assumed as Futagami and Nakajima [
The wage rate grows at the same rate as total output and total physical capital; that is,
From
Substituting (
From
If we do not consider depreciation, the equilibrium condition in the output market is
The balance economic growth rate is determined by the equation
From (
If
Let
For
The intersection of curve
The assumption
In fact,
Let
When
When the parameters are taken the values
If
In fact, by
If
When the above parameters are taken the values
In this section, we inquire whether we can find the optimal individual years of schooling and an economic growth rate, such that individual lifetime utility reaches maximum and the growth of economy is balanced.
At steady state, the years of schooling decrease strictly with respect to wage growth rate; that is,
Let
At
From Corollary
Assume that there is
Under certain given conditions, the assumption
There is only a pair of individual years of schooling and economic growth rate, such that individual lifetime utility reaches maximum and the economy has balance growth path under some given parameters.
The relationship between individual years of schooling and economic growth has been inquired in this paper by using an overlapping generation model. From Theorem
Under given individual years of schooling, the total consumption, asset, and capital are aggregated into the production process and condition of having the balance growth is obtained. Theorems
Theorem
There are several limitations in our paper. Firstly, the uncertain survival schedule is not considered in this paper. Secondly, the individual’s age of retirement is fixed. Thirdly, the bequest motives are not put into the model.
The authors declared that they have no conflict of interests related to this work.
This work is supported by National Natural Science Foundation of China (71271158).