Economic growth and economic development 573

Introduction to Modern Economic Growth
It can be verified that depending on the form of the v (·) function, profits can
be increasing in the number of varieties (see Exercise 12.12). This may at first
appear somewhat surprising: typically, we expect a greater number of competitors
to reduce profits. But the love-for-variety effect embedded in the Dixit-Stiglitz
preferences creates a countervailing effect, which is often referred to as aggregate
demand externalities in the macroeconomics literature. The basic idea is that when
N increases, this raises the utility from consuming each of the varieties because of
the love-for-variety effect. The impact of the entry of a particular variety (or the
impact of the increase in the production of a particular variety) on the demand for
other varieties is a pecuniary externality. This pecuniary externality will play an
important role in many of the models of endogenous technological change and we
will encounter it again in models of poverty traps in Chapter 22.
12.4.2. The Dixit-Stiglitz Model with a Continuum of Products. As
discussed in the last subsection and analyzed further in Exercise 12.12, when N is
finite, the equilibrium in which each firm charges the price given by (12.12) may be
viewed as an approximation (where each firm only has a small effect on the ideal
price index and thus ignores this effect). An alternative modeling assumption would
be to assume that there is a continuum of varieties. When there is a continuum
of varieties, (12.12) is no longer an approximation. Moreover, such a model will be
more tractable because the number of firms, N, need not be an integer. For this
reason, the version of the Dixit-Stiglitz model with a continuum of products is often
used in the literature and will also be used in the rest of this book.
This version of the model is very similar to the one discussed in the previous
subsection, except that the utility function of the representative household now takes
the form

àZ

N
U [ci ]i=0 , y =

N

1


ci

0

di


ả ε−1

+ v (y) ,

where now N denotes the measure of varieties. The budget constraint facing the
representative household is

Z

0

N

pi ci di + y ≤ m.
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