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 219