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CHAPTER 5

Foundations of Neoclassical Growth
The Solow growth model is predicated on a constant saving rate. Instead, it
would be much more satisfactory to specify the preference orderings of individuals,
as in standard general equilibrium theory, and derive their decisions from these preferences. This will enable us both to have a better understanding of the factors that
affect savings decisions and also to discuss the “optimality” of equilibria–in other
words, to pose and answer questions related to whether the (competitive) equilibria
of growth models can be “improved upon”. The notion of improvement here will
be based on the standard concept of Pareto optimality, which asks whether some
households can be made better off without others being made worse off. Naturally,
we can only talk of individuals or households being “better off” if we have some
information about well-defined preference orderings.

5.1. Preliminaries
To prepare for this analysis, let us consider an economy consisting of a unit
measure of infinitely-lived households. By a unit measure of households we mean
an uncountable number of households, for example, the set of households H could

be represented by the unit interval [0, 1]. This is an abstraction adopted for simplicity, to emphasize that each household is infinitesimal and will have no effect on
aggregates. Nothing we do in this book hinges on this assumption. If the reader
instead finds it more convenient to think of the set of households, H, as a countable

set of the form H = {1, 2, ..., M } with M = ∞, this can be done without any loss of

generality. The advantage of having a unit measure of households is that averages
and aggregates are the same, enabling us to economize on notation. It would be
even simpler to have H as a finite set in the form {1, 2, ..., M } with M large but
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