Economic growth and economic development 701

Introduction to Modern Economic Growth
Let us also modify the baseline environment by assuming that total population,
in particular, the population of scientists, grows at the exponential rate n. With
a similar arguments to that in Section 13.3 in Chapter 13, it can be verified that
aggregate output in this economy will grow at the rate (see Exercise 15.15):
n
.
(15.42)
g∗ =
1−λ
Consequently, even with limited knowledge spillovers there will be income per capita
growth at the rate λn/ (1 − λ). As usual, this is because of the amplification to

the externalities provided by population growth. It can also be verified that when
λ = 1, there is no balanced growth and output would reach infinity in finite time
(see Exercise 15.16).
The important point for the focus here concerns the market size effect on the
direction of technical change. To investigate this issue, note that the technology
market clearing condition implied by (15.41) is (see Exercise 15.17):
(15.43)

η L NLλ π L = η H NHλ π H ,

which is parallel to (15.36). Exactly the same analysis as above implies that equilibrium relative technology can be derived as
à
ả
à
ả à ả 1

NH
1 γ 1−λσ H 1−λσ

1−λσ
(15.44)
=η
.
NL
γ
L
Now combining this with (15.19)–which still determines the relative factor prices
given technologywe obtain
ả
à
à ả 2+
ả (1)
à
1
1
1


H 1
w
H
= η 1−λσ
.
(15.45)
ω∗ ≡
wL
γ
L

This equation shows that even without scale effects we obtain exactly the same
results as before. Specifically:
Proposition 15.10. Consider the directed technological change model with no
scale effects described above. Then there is always weak equilibrium (relative) bias,

meaning that an increase in H/L always induces relatively H-biased technological
change.
Ô

Proof. See Exercise 15.8.
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