The representative household model is based on the assumption that all households are identical. An alternative class of models allows for households to differ. 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 may have differences in accumulated wealth and/or different time horizons. 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 model of overlapping generations of Diamond (1965). This model is analyzed in discrete time, i.e we assume that time is divided in 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, since they live in the last period of their life. 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.
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.
While the Diamond model is analyzed in discrete time, a more recent category of overlapping generations models is usually analyzed in continuous time (see Blanchard (1985) and Weil (1989)). In this more recent class of models, new households are being born continuously. All households, irrespective of their time of birth, have an infinite time horizon. In the original version of these models by Blanchard, 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 overlapping generations models from a representative household model do not depend so much on the assumption of a positive probability of death, as in the Diamond and Blanchard models, but on the assumption that different generations have been born at different times in the past and thus hold different amounts of accumulated assets, which affect their savings behavior differently.
Savings behavior in overlapping generations models is not characterized by social efficiency, as in the representative household model. Moreover, in economies without a representative household, comparing utility across households is largely arbitrary. Furthermore, in the Diamond model, 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, since the competitive equilibrium is not necessarily optimal.