Economic growth and economic development 523

Introduction to Modern Economic Growth
1
c˙ (t)
= (A − δ − ρ),
c (t)
θ

(11.9)

lim k(t) exp (−(A − δ − n)t) = 0.

(11.10)

t→∞

The important result immediately follows from equation (11.9). Since the righthand side of this equation is constant, there must be a constant rate of consumption
growth (as long as A − δ − ρ > 0). The rate of growth of consumption is therefore
independent of the level of capital stock per person, k (t). This will also imply
that there are no transitional dynamics in this model. Starting from any k (0),
consumption per capita (and as we will see, the capital-labor ratio) will immediately
start growing at a constant rate. To develop this point, let us integrate equation
(11.9) starting from some initial level of consumption c(0), which as usual is still to
be determined later (from the lifetime budget constraint). This gives
ả
à
1
(A − ρ)t .
(11.11)
c(t) = c(0) exp
θ
Since there is growth in this economy, we have to ensure that the transversality

condition is satisfied (i.e., that lifetime utility is bounded away from infinity), and
also we want to ensure positive growth (the condition A − δ − ρ > 0 mentioned
above). We therefore impose:
(11.12)

A > ρ + δ > (1 − θ) (A − δ) + θn + δ.

The first part of this condition ensures that there will be positive consumption
growth, while the second part is the analogue to the condition that ρ + θg > g + n
in the neoclassical growth model with technological progress, which was imposed
to ensure bounded utility (and thus was used in proving that the transversality
condition was satisfied).
11.1.3. Equilibrium Characterization. We first establish that there are no
transitional dynamics in this economy. In particular, we will show that not only
the growth rate of consumption, but the growth rates of capital and output are also
constant at all points in time, and equal the growth rate of consumption given in
equation (11.9).
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