Economic growth and economic development 232

Introduction to Modern Economic Growth
The expression in (5.1) ignores uncertainty in the sense that it assumes the sequence of consumption levels for individual i, {ci (t)}∞
t=0 is known with certainty.
If instead this sequence were uncertain, we would need to look at expected util-

itymaximization. Most growth models do not necessitate an analysis of growth
under uncertainty, but a stochastic version of the neoclassical growth model is the
workhorse of much of the rest of modern macroeconomics and will be presented in
Chapter 17. For now, it suffices to say that in the presence of uncertainty, we interpret ui (·) as a Bernoulli utility function, so that the preferences of household i at
time t = 0 can be represented by the following von Neumann-Morgenstern expected
utility function:
Ei0

∞
X

β ti ui (ci (t)) ,

t=0

where

Ei0

is the expectation operator with respect to the information set available

to household i at time t = 0.
The formulation so far indexes individual utility function, ui (·), and the discount
factor, β i , by “i” to emphasize that these preference parameters are potentially
different across households. Households could also differ according to their income
processes. For example, each household could have effective labor endowments of

∞
{ei (t)}∞
t=0 , thus a sequence of labor income of {ei (t) w (t)}t=0 , where w (t) is the

equilibrium wage rate per unit of effective labor.

Unfortunately, at this level of generality, this problem is not tractable. Even
though we can establish some existence of equilibrium results, it would be impossible to go beyond that. Proving the existence of equilibrium in this class of models is
of some interest, but our focus is on developing workable models of economic growth
that generate insights about the process of growth over time and cross-country income differences. We will therefore follow the standard approach in macroeconomics
and assume the existence of a representative household.
5.2. The Representative Household
When we say that an economy admits a representative household, this means
that the preference (demand) side of the economy can be represented as if there
were a single household making the aggregate consumption and saving decisions
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