The representative household model is based on the assumption that all households are identical and that they internalize the welfare of future generations.
An alternative class of models allows for households to differ and for the absence of such intergenerational links. As young households are being born and old households die, there is a succession of overlapping generations.
At any given time, households represent different generations. The savings behavior across generations generally differs, as households belonging to different generations have differences in accumulated wealth. Thus, such models do not necessarily imply the homogeneity or economic efficiency that characterizes the basic representative household model.The standard model in this category is the overlapping generations (OLG) model of Diamond [1965]. This model, which is a generalization of the two-period Fisherian model, is analyzed in discrete time (i.e., we assume that time is divided into discrete time periods rather than being a continuous variable). In each time period, two types of households coexist. The young, who are in the first period of their lives, and the old, who are in the second and last period of their lives. Young households supply labor but own no capital. Thus, they only earn labor income. Old households are not working and consume the income from the capital they accumulated during their first period of life, as well as their capital stock itself, because they are in the last period of life and are not concerned with the welfare of future generations. In the following period, the old households have passed away, young households have become old, and a new generation of young households has entered the economy.
In the Diamond OLG model, no generation of households internalizes the welfare of future generations. Thus, the competitive equilibrium is not socially optimal.1
The production technology and the structure of markets is similar to that assumed in the Solow and Ramsey models. There are many competitive firms, the technology of production is described by a neoclassical production function, capital and labor markets are competitive, and capital and labor are paid their marginal product.
The Diamond model is analyzed in discrete time, but a more recent category of OLG models, due to Blanchard [1985] and Weil [1989], is usually analyzed in continuous time. In this more recent class of OLG models, new households are being born continuously. All households, irrespective of their time of birth, have an infinite time horizon. In the original Blanchard [1985] version of these models, at every instant there is also a constant probability of death, which is independent of the age of households. In the model of Weil, the probability of death is zero.
What emerges is that the differences of these OLG models from a representative household model do not depend on the assumption of a positive probability of death but on the assumption that current generations do not internalize the welfare of future generations. Thus, generations that have been born at different times in the past, and thus hold different amounts of accumulated assets, have differences in their savings behavior.
Savings behavior in OLG models is not socially optimal, as in the representative household model. Moreover, in economies without a representative household, comparing utility across different generations of households is largely arbitrary. Furthermore, in OLG models, it is theoretically possible that the competitive equilibrium is not even Pareto efficient, as the possibility of dynamic inefficiency cannot be ruled out a priori. In any case, in models of overlapping generations, policy interventions that can improve social efficiency can be justified, because the competitive equilibrium is not necessarily optimal.2
5.1