Economic growth and economic development 537

Introduction to Modern Economic Growth
in the production process, making the production process itself more productive.
Alternatively, the knowledge stock of the economy could be a function of the cumulative output that the economy has produced up to now, thus giving it more of a
flavor of “learning-by-doing”.
In any case, substituting for (11.35) into (11.34) and using the fact that all firms
are functioning at the same capital-effective labor ratio, we obtain the production
function of the representative firm as
Y (t) = F (K (t) , BK (t) L) .
Using the fact that F (·, ·) is homogeneous of degree 1, we have
Y (t)
= F (1, BL)
K (t)
= f˜ (L) .

Output per capita can therefore be written as:
Y (t)
L
Y (t) K (t)
=
K (t) L
= k (t) f˜ (L) ,

y (t) ≡

where again k (t) ≡ K (t) /L is the capital-labor ratio in the economy.

As in the standard growth model, marginal products and factor prices can be
expressed in terms of the normalized production function, now f˜ (L). In particular,
we have
(11.36)

w (t) = K (t) f˜0 (L)

and
(11.37)

R (t) = R = f˜ (L) − Lf˜0 (L) ,

which is constant.
11.4.2. Equilibrium. An equilibrium is defined similarly to the neoclassical
growth model, as a path of consumption and capital stock for the economy, [C (t) , K (t)]∞
t=0
that maximize the utility of the representative household and wage and rental rates
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