Economic growth and economic development 684

Introduction to Modern Economic Growth
scarce factors will be relatively more expensive, the price effect tends to
favor technologies complementing scarce factors.
(2) The market size effect is a consequence of the fact that VH /VL is increasing
in H/L. The market for a technology is the workers (or the other factors)
that will be using and working with this technology. Consequently, an
increase in the supply of a factor translates into a greater market for the
technology complementing that factor. The market size effect encourages
innovation for the more abundant factor.
The above discussion is incomplete, however, since prices are endogenous. Combining (15.24) together with (15.18), we can eliminate relative prices and obtain the
relative profitability of the technologies as:
ả 1 à ả 1
à
ả à
H
1 NH
VH
=
.
(15.25)
VL
γ
NL
L
Note for future reference that an increase in the relative factor supply, H/L, will
increase VH /VL as long as σ > 1 and it will reduce it if σ < 1. This shows that
the elasticity of substitution between the factors, σ, regulates whether the price
effect dominates the market size effect. Since σ is not a primitive, but a derived
parameter, we would like to know when it is greater than 1. It is straightforward to
check that
σ T 1 ⇐⇒ ε T 1.

So the two factors will be gross substitutes when the two intermediate goods are
gross substitutes in the production of the final good.
Next, using the two free entry conditions (15.20) and (15.21), and assuming that
both of them hold as equalities, we obtain the following BGP “technology market
clearing” condition:
η L VL = η H VH.

(15.26)

Combining this with (15.25), we obtain the following BGP ratio of relative technologies
(15.27)

à

NH
NL

ả

=



à

1

670

ả à

H
L

ả1

,