Introduction to Modern Economic Growth Proposition 9.8 Consider the above-described overlapping generations economy and suppose that the decentralized competitive equilibrium is dynamically inefficient Then there exists a feasible sequence of unfunded Social Security payments {d (t)}∞ t=0 which will lead to a competitive equilibrium starting from any date t that Pareto dominates the competitive equilibrium without Social Security Proof See Exercise 9.13 Ô Unfunded Social Security reduces the overaccumulation and improves the allocation of resources The similarity between the way in which unfunded Social Security achieves a Pareto improvement in this proposition and the way in which the Pareto optimal allocation was decentralized in the example economy of Section 9.1 is apparent In essence, unfunded Social Security is transferring resources from future generations to initial old generation, and when designed appropriately, it can so without hurting the future generations Once again, this depends on dynamic inefficiency; when there is no dynamic inefficiency, any transfer of resources (and any unfunded Social Security program) would make some future generation worse off You are asked to prove this result in Exercise 9.14 9.6 Overlapping Generations with Impure Altruism Section 5.3 in Chapter demonstrate that altruism within families (for example of parents towards their offspring) can lead to a structure of preferences identical to those of the representative household in the neoclassical growth model In contrast, in this section we have so far ignored altruistic preferences in order to emphasize the effect of finite lives and the economic implications of the arrival of new agents in the economy As briefly noted in Section 5.3, the exact form of altruism within a family matters for whether the representative household would provide a good approximation In particular, a potentially empirically relevant form of altruism is one in which parents care about certain dimensions of the consumption vector of their offspring instead of their total utility These types of preferences are often referred to as “impure altruism” to distinguish it from the pure altruism discussed in Section 5.3 A particular type of impure altruism, commonly referred to as “warm glow preferences”, plays an important role in many growth models because of its tractability 436