Introduction to Modern Economic Growth This discussion therefore illustrates that overaccumulation results when there are overlapping generations and a strong motive for saving for the future Interestingly, it can be shown that what is important is not finite lives per se, but overlapping generations indeed In particular, Exercise 9.30 shows that when n = 0, overaccumulation is not possible so that finite lives is not sufficient for overaccumulation However, k∗ > kgold is possible when n > and ν = 0, so that the overlapping generations model with infinite lives can generate overaccumulation 9.9 Taking Stock This chapter has continued our investigation of the mechanics of capital accumulation in dynamic equilibrium models The main departure from the baseline neoclassical growth model of the last section has been the relaxation of the representative household assumption The simplest way of accomplishing this is to introduce two-period lived overlapping generations (without pure altruism) In the baseline overlapping generations model of Samuelson and Diamond, each individual lives for two periods, but can only supply labor during the first period of his life We have also investigated alternative non-representative-household models, in particular, overlapping generations with impure altruism and models of perpetual youth In models of overlapping generations with impure altruism, individuals transfer resources to their offspring, but they not care directly about the utility of their offspring and instead derive utility from the act of giving or from some subcomponent of the consumption vector on their descendent In models of perpetual youth, the economy features expected finite life and overlapping generations, but each individual still has an infinite planning horizon, because the time of death is uncertain All of these models fall outside the scope of the First Welfare Theorem As a result, there is no guarantee that the resulting equilibrium path will be Pareto optimal In fact, the extensive study of the baseline overlapping generations models were partly motivated by the possibility of Pareto suboptimal allocations in such models We have seen that these equilibria may be “dynamically inefficient” and feature overaccumulation–a steady-state capital-labor ratio greater than the golden rule capital-labor ratio We have also seen how an unfunded Social Security system 453