Paul Samuelson's (1958) overlapping generations model has turned 50. Seldom has so simple a model been so influential. The paper, in spite of its ripe age, still elicits wonder. Starting from the uncontroversial observation that "we live in a world where new generations are always coming along," Samuelson built a model that violates the credo of the first fundamental welfare theorem with which we still inculcate undergraduates 50 years later. According to Samuelson, all is not necessarily well in the best of market economies: with overlapping generations, even absent the usual suspects such as distortions and market failures, a competitive equilibrium need not be Pareto efficient. Worst of all, this failure of the first welfare theorem in an overlapping generations model occurs in a framework that is, in many ways, more plausible and realistic than the world of agents living synchronous and finite existences in which the theorem is usually proved. Like Mona Lisa's enigmatic smile, the mysterious welfare properties of the overlapping generations model are, to a significant extent, responsible for its popularity -- along with the many economic issues it has illuminated in the last half-century. I take it as my brief in this celebratory paper to provide, after a short exposition of the main results of the overlapping generations model under certainty, an explanation of why the welfare properties of the overlapping generations model differ so much from the canonical Arrow-Debreu framework and to review, in a deliberately nonencyclopedic mode, a few striking applications and extensions of Samuelson's deceptively straightforward model.
