A key feature of the neoclassical growth model analyzed in the previous chapter is that it admits a representative household.
This model is useful as it provides us with a tractable framework for the analysis of capital accumulation. Moreover, it enables us to appeal to the First and Second Welfare Theorems to establish the equivalence between equilibrium and optimum growth problems.
In many situations, however, the assumption of a representative household is not appropriate. One important set of circumstances where we may wish to depart from this assumption is in the analysis of an economy in which new households arrive (or are born) over time. The arrival of new households in the economy is not only a realistic feature, but it also introduces a range of new economic interactions. In particular, decisions made by older “generations” will affect the prices faced by younger “generations”. These economic interactions have no counterpart in the neoclassical growth model. They are most succinctly captured in the overlapping generations models introduced and studied by Paul Samuelson and then later Peter Diamond.These models are useful for a number of reasons; first, they capture the potential interaction of different generations of individuals in the marketplace; second they provide a tractable alternative to the infinite-horizon representative agent models; third, as we will see, some of their key implications are different from those of the neoclassical growth model; fourth, the dynamics of capital accumulation and consumption in some special cases of these models will be quite similar to the basic Solow model rather than the neoclassical model; and finally these models generate new insights about the role of national debt and Social Security in the economy.
We start with an illustration of why the First Welfare Theorem cannot be applied in overlapping generations models. We then discuss the baseline overlapping generations model and and a number of applications of this framework. Finally, we will discuss the overlapping generations model in continuous time. This latter model, originally developed by Menahem Yaari and Olivier Blanchard and also referred to as the perpetual youth model, is a tractable alternative to the basic overlapping generations model and also has a number of different implications. It will also be used in the context of human capital investments in the next chapter.
9.1.