TAILIEUCHUNG - Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 9

Chapter 9 Overlapping Generations Models This chapter describes the pure-exchange overlapping generations model of Paul Samuelson (1958). We begin with an abstract presentation that treats the overlapping generations model as a special case of the chapter 8 general equilibrium model with complete markets | Chapter 9 Overlapping Generations Models This chapter describes the pure-exchange overlapping generations model of Paul Samuelson 1958 . We begin with an abstract presentation that treats the overlapping generations model as a special case of the chapter 8 general equilibrium model with complete markets and all trades occurring at time 0. A peculiar type of heterogeneity across agents distinguishes the model. Each individual cares about consumption only at two adjacent dates and the set of individuals who care about consumption at a particular date includes some who care about consumption one period earlier and others who care about consumption one period later. We shall study how this special preference and demographic pattern affects some of the outcomes of the chapter 8 model. While it helps to reveal the fundamental structure allowing complete markets with time-0 trading in an overlapping generations model strains credulity. The formalism envisions that equilibrium price and quantity sequences are set at time 0 before the participants who are to execute the trades have been born. For that reason most applied work with the overlapping generations model adopts a sequential trading arrangement like the sequential trade in Arrow securities described in chapter 8. The sequential trading arrangement has all trades executed by agents living in the here and now. Nevertheless equilibrium quantities and intertemporal prices are equivalent between these two trading arrangements. Therefore analytical results found in one setting transfer to the other. Later in the chapter we use versions of the model with sequential trading to tell how the overlapping generations model provides a framework for thinking about equilibria with government debt and or valued fiat currency intergener-ational transfers and fiscal policy. - 258 - Time-0 trading 259 . Endowments and preferences Time is discrete starts at t 1 and lasts forever so t 1 2 . There is an infinity of agents named i 0 1

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