Economic growth and economic development 592

Introduction to Modern Economic Growth
and balanced growth path interchangeably when referring to endogenous growth
models.
13.1.3. Balanced Growth Path. A balanced growth path (BGP) requires
that consumption grows at a constant rate, say gC , which is only possible from
(13.16) if the interest rate is constant. Let us therefore look for an equilibrium
allocation in which
r (t) = r∗ for all t,
where “*” refers to BGP values. Combining (13.9), (13.10) and a constant interest
rate with (13.8), we also obtain that V˙ (t) = 0. Substituting this in either (13.7) or
in (13.8), we obtain
βL
,
r∗
where we have also substituted for the (constant) flow of rate of profits per period
V∗ =

(13.18)

from (13.11). This equation is intuitive: a monopolist makes a flow profit of βL,
and in BGP, this is discounted at the constant interest rate r∗ .
Let us next suppose that the (free entry) condition (13.14) holds as an equality,
in which case we also have

ηβL
=1
r∗
This equation pins down the steady-state interest rate, r∗ , as:
r∗ = ηβL
The consumer Euler equation, (13.16), then implies that the rate of growth of consumption must be given by

1
C˙ (t)
= (r∗ − ρ).
C (t)
θ
Moreover, it can be verified that the current-value Hamiltonian for the consumer’s
(13.19)

gC∗ =

maximization problem is concave, thus this condition, together with the transversality condition, characterizes the optimal consumption plans of the consumer.
In a balanced growth path, consumption cannot grow at a different rate than
total output (see Exercise 13.4), thus we must also have the growth rate of output
in the economy is
g ∗ = gC∗ .
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