Chapter4 OLG_and_Social_Security

Chapter4 OLG_and_Social_Security - Overlapping Generations...

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1 Overlapping Generations and Social Security The goal of this chapter is to develop a framework whereby we can evaluate policy regarding social security. For this purpose, the overlapping generations construct is ideal. There are two main constructs in economics: the overlapping generations construct and the infinite-lived (dynastic) construct. In the dynastic construct, a household lives forever. Surely, no individual can live forever, but the idea is that a family can go on forever, and provided that parents care about the utility of their children, the dynastic construct is a reasonable one to use for certain economic issues. The study of retirement and social security, however, is not one of these issues. The overlapping generations construct is the ideal construct. I. The Overlapping Generations Model The overlapping generations model was developed by Paul Samuelson in 1957. In this model, people not only live for a finite number of years or periods, but in any period, there are people of different ages or generations alive. The simplest of OLG models assumes that people live two periods. Thus, at any point in time, there are some old people and young people alive. Let N t be the number of people
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2 born in period t. Thus, these people are young in period t and old in period t+1. In the OLG framework there are N t young people and N t-1 people alive in period t. Each generation enjoys consumption when they are young, c y and consumption when they are old, c old .. Eventually, we will assume that each generation t values leisure when young and old. For now, however, we will deal with utility the simpler case where utility does not depend on leisure, namely old y old y c c c c U log log ) , ( + = (1) Notice that we have implicitly set the discount factor β =1. This just simplifies the algebra. None of the results would change if we were to allow for β <1. II. ENDOWMENT ECONOMIES We begin with a very simple world with no production. Instead, each person starts each period of their life with a certain quantity of the consumption good. We call this an endowment economy. For the present purpose, let us assume that each consumer is endowed with 7 units of the consumption good when young and 1 unit of the consumption good when old. The numbers are not so important. What is important is the household is much better endowed when young than old. We will now solve the equilibrium for this economy for different government policies. Model 1. AUTARKY.
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3 In this first economy, there is no government policy. Given the disparities in endowments between their two life periods, each young person would ideally like to lend so as to smooth out consumption. But can they do this? Here is the beauty or trick of the overlapping generations model: Who are they going to lend to? The only possible agents are the old people alive in the period. But this would be a stupid idea to lend to the old. Why? Because they won’t be around in period t+1 to pay back the loans.
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This note was uploaded on 05/23/2011 for the course ECON 509 taught by Professor Villamil during the Spring '08 term at University of Illinois, Urbana Champaign.

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Chapter4 OLG_and_Social_Security - Overlapping Generations...

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