tence of wage differentials over the life cycle. Individuals can invest in human
capital or invest in financial assets. Investment in human capital is costly and
specific to each individual, and it is therefore concentrated at the beginning of
the life cycle and ends when retirement sets in.7 Human capital depreciates at
a constant rate, and the wage rate per unit of working time thus declines when
learning ends.
There are two different types of individuals in the model: conscripts (indexed
by subscript c) and non-conscripts (subscript n). Conscripts are subject to draft
and are forced to spend their time on work in the first period of the life cycle,
possibly with a low income. Non-conscripts do not face the time constraint or
the supplementary tax.
2.1 Intertemporal Optimization
In each period of the life cycle, individuals divide time between work, q, learning,
s, and leisure, υ. The economic life-span of each individual consists of 60 periods,
each period representing one year, and the periods are indexed from 0 to 59.
Total use of time in each period cannot exceed the endowment of time:
vi,t + qi,t + si,t ∙ e, (1)
where e is the constant endowment of time in each period. The endowment of
time denotes hours available to work, learning and leisure, and it is therefore
interpreted as the normal length of a work week, say 40 hours. Subscript t refers
to the person’s age, and subscript i indicates whether the individual is or has
been subject to conscription (i = c) or not (i = n).
Gross investment in human capital is determined by learning, and the stock
of human capital evolves according to the following law of motion:
hi,t+ι = (1 - Sh) ¢ hijt + s^, (2)
where h is the individual stock of human capital, Sh is the rate of depreciation
with respect to human capital, and η measures the elasticity of new human capital
with respect to learning, where 0 < η ∙ 1. This specification implies that learning
is spread more evenly across time when η falls. The initial stock of human capital,
h0, is positive and every person enters the economy with some productive skills.
The effective supply of labor services depends on time devoted to work and
the stock of human capital:
Iu = q<t hu, (3)
where I is the individual supply of labor services, and β denotes the elasticity
of labor services with respect to the stock of human capital. We assume that
7 New human capital can be produced through education and formal/informal on-the-job
training, together referred to as learning.