Economic growth and economic development 233

Introduction to Modern Economic Growth
(and also the labor supply decisions when these are endogenized) subject to a single
budget constraint. The major convenience of the representative household assumption is that instead of thinking of the preference side of the economy resulting from
equilibrium interactions of many heterogeneous households, we will be able to model
it as a solution to a single maximization problem. Note that, for now, the description concerning a representative household is purely positive–it asks the question
of whether the aggregate behavior can be represented as if it were generated by a
single household. We can also explore the stronger notion of whether and when an
economy admits a “normative” representative household. If this is the case, not only
aggregate behavior can be represented as if it were generated by a single household,
but we can also use the utility function of the normative representative household
for welfare comparisons. We return to a further discussion of these issues below.
Let us start with the simplest case that will lead to the existence of a representative household. Suppose that each household is identical, i.e., it has the same
discount factor β, the same sequence of effective labor endowments {e (t)}∞
t=0 and

the same instantaneous utility function

u (ci (t))
where u : R+ → R is increasing and concave and ci (t) is the consumption of house-

hold i. Therefore, there is really a representative household in this case. Consequently, again ignoring uncertainty, the preference side of the economy can be
represented as the solution to the following maximization problem starting at time
t = 0:
(5.2)

max

∞
X

β t u (c (t)) ,

t=0

where β ∈ (0, 1) is the common discount factor of all the households, and c (t) is the

consumption level of the representative household.

The economy described so far admits a representative consumer rather trivially;
all households are identical. In this case, the representative household’s preferences,
(5.2), can be used not only for positive analysis (for example, to determine what
the level of savings will be), but also for normative analysis, such as evaluating the
optimality of different types of equilibria.
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