Economic growth and economic development 483

Introduction to Modern Economic Growth
that gives an expected life of 50 years, and gw corresponding to the rate of wage
growth holding the human capital level of the individual constant, which should
be approximately about 2%. Thus we should expect an estimate of γ around 0.10,
which is consistent with the upper range of the empirical estimates.

10.3. The Ben Porath Model
The baseline Ben Porath model enriches the model studied in the previous section by allowing human capital investments and non-trivial labor supply decisions
throughout the lifetime of the individual. In particular, we now let s (t) ∈ [0, 1] for

all t ≥ 0. Together with the Mincer equation (10.12) (and the model underlying

this equation presented in the previous section), the Ben Porath model is the basis
of much of labor economics. Here it is sufficient to consider a simple version of this
model where the human capital accumulation equation, (10.2), takes the form
(10.13)

h˙ (t) = φ (s (t) h (t)) − δ h h (t) ,

where δ h > 0 captures “depreciation of human capital,” for example because new
machines and techniques are being introduced, eroding the existing human capital
of the worker. The individual starts with an initial value of human capital h (0) >
0. The function φ : R+ → R+ is strictly increasing, continuously differentiable
and strictly concave. Furthermore, we simplify the analysis by assuming that this
function satisfies the Inada-type conditions,
lim φ0 (x) = ∞ and

x→0

lim φ0 (x) = 0.

x→h(0)

The latter condition makes sure that we do not have to impose additional constraints
to ensure s (t) ∈ [0, 1] (see Exercise 10.5).

Let us also suppose that there is no non-human capital component of labor, so

that ω (t) = 0 for all t, that T = ∞, and that there is a flow rate of death ν > 0.

Finally, we assume that the wage per unit of human capital is constant at w and
the interest rate is constant and equal to r. We also normalize w = 1 without loss
of any generality.
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