Economic growth and economic development 593
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Introduction to Modern Economic Growth
Therefore, given the BGP interest rate we can simply determine the long-run growth
rate of the economy as:
(13.20)
g∗ =
1
(ηβL − ρ)
θ
We next assume that
(13.21)
ηβL > ρ and (1 − θ) ηβL < ρ,
which will ensure that g∗ > 0 and that the transversality condition is satisfied.
We then obtain:
Proposition 13.1. Suppose that condition (13.21) holds. Then, in the abovedescribed lab equipment expanding input-variety model, there exists a unique balanced
growth path in which technology, output and consumption all grow at the same rate,
g ∗ , given by (13.20).
Proof. The preceding discussion establishes all the claims in the proposition
except that the transversality condition holds. You are asked to check this in ExerÔ
cise 13.6.
An important feature of this class of endogenous technological progress models
is the presence of the scale effect, which we encountered in Section 11.4 in Chapter
11: the larger is L, the greater is the growth rate. The scale effect comes from a very
strong form of the market size effect discussed in the previous chapter. As illustrated
there, the increasing returns to scale nature of the technology (for example, as
highlighted in equation (13.12)) is responsible for this strong form of the market
size effect and thus for the scale effect. We will see below that it is possible to have
variants of the current model that feature the market size effect, but not the scale
effect.
13.1.4. Transitional Dynamics. It is also straightforward to see that there
are no transitional dynamics in this model. To derive this result, let us go back to
the value function for each monopolist. Substituting for profits, this gives
r (t) V (ν, t) − V˙ (ν, t) = βL.
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