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Unformatted text preview: Economics 302 - Macroecononomic Theory II Fall 2008 Jean-Paul Lam Chapter 3 October 20, 2008 Overlapping Generations 1 Introduction The Solow model with and without human capital relies on the assumption that the savings rate is exogenous. This assumption as we have discussed is one of the weaknesses of the Solow growth model. In this lecture, we will introduce a model of growth where the saving decisions of individuals are optimal. 1 Unlike the Solow model where all agents are assumed to be identical, the overlapping generations model (OLG) or sometimes known as the life-cycle model is a framework where multiple generations coexist. That is agents are heterogeneous. Besides being highly tractable, this feature of the life-cycle model or the OLG model is appealing because we can study many policy issues related to social security, investment in education, transfer payments, bequests and taxes. These issues are easier to analyze when agents are not homogeneous in the model. Moreover, the interactions and decisions of heterogeneous agents in the model allow us to analyse several pertinent questions about the importance of savings and technology for economic growth, in the short and long-run. The model we will study in this lecture assumes two generations only: a young cohort and an old cohort. Individuals in the model live for two periods. In period 1, they are born and are described as being young, whereas in the second period, they become old and die at the end of that period. Although individuals eventually die in this framework, the economy itself lasts forever since at each period in time, a new generation is born. Hence the OLG model is perpetually inhabited by two different generations but people do not live forever . We begin by describing the OLG model. We then show how to solve for the optimal decisions of agents. As in the previous lectures, we find the equilibrium of the model or the steady-state and analyze the implications for economic growth. 2 An Endowment Economy We assume as before that time is discrete and is indexed by t . Time can take values from to , that is the economy has always existed and never dies. We will however, start a time t = 1. We assume that all the history that has happened before t = 1 is given or predetermined and that history determines the initial conditions of the model. We assume that each generation lives for two periods only. Each period t , a new generation/cohort is born and this generation is assumed to be young. The young generation becomes old in period t + 1 and dies at the end of that period. We further assume that all members of a generation are identical (members of the same generation are identical) but the young and old generations are different. At any point in time, there are N t members of the young generation, that is there are N t young agents and N t +1 old agents (born in period t 1). The pattern of endowments is illustrated in Table 1....
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- Fall '08