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Introduction to Modern Economic Growth
for the first part of the book, where our focus will be on competitive economies.
They will not be as relevant (at least if used in their current form), when we turn
to models of technological change, where product markets will be monopolistic or
when we study certain classes of models of economic development, where various
market imperfections will play an important role.
Second, the most general class of dynamic general equilibrium models will not
be tractable enough for us to derive sharp results about the process of economic
growth. For this reason, we we will often adopt a range of simplifying assumptions.
The most important of those is the representative household assumption, which
enables us to model the demand side of the economy as if it were generated by the
optimizing behavior of a single household. We saw how this assumption is generally
not satisfied, but also how a certain class of preferences, the Gorman preferences,
enable us to model economies as if they admit a representative household. We also
discussed how typical general equilibrium economies can be modeled as if they admit
a representative firm.
In addition, in this chapter we introduced the first formulation of the optimal
growth problems in discrete and in continuous time, which will be useful as examples
in the next two chapters where we discuss the tools necessary for the study of
dynamic optimization problems.

5.11. References and Literature
This chapter covered a lot of ground and in most cases, many details were omitted
for brevity. Most readers will be familiar with much of the material in this chapter.
Mas-Colell, Winston and Green (1995) have an excellent discussion of issues of
aggregation and what types of models admit representative households. They also
have a version of the Debreu-Mantel-Sonnenschein theorem, with a sketch proof. The
representative firm theorem, Theorem 5.4, presented here is rather straightforward,
but I am not aware of any other discussion of this theorem in the literature. It is
important to distinguish the subject matter of this theorem from the Cambridge
controversy in early growth theory, which revolved around the issue of whether

different types of capital goods could be aggregated into a single capital index (see,
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