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# Suppose you have a two-period model OLG in discrete time

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Suppose you have a two-period model OLG in discrete time. Lt agents are born in time t, where Lt = (1+n)tL0. Normalize L0 = 1 and let n > 0. Preferences of a young agent born in time t are time separable:
u(c1t,c2t+1) = 2(c1t)0.5 + 2(c2t+1)0.5,
where c1t denotes consumption in period t; c2t+1 denotes consumption in period t+1 of an old agent born in t. The initial old agents want to consume as much as possible. Each young agent is endowed with y units of the consumption good. The old have no endowment whatsoever. There is a storage technology that allows to convert one unit of period t goods into 1+r units of period t+1 goods. There is a social security system that is "pay-as-you-go". In each period t the government taxes the young and uses the receipts to make transfers to the old. We consider a per capita tax on the young that is constant over time, i.e. ?t = ? for all t = 0, 1, 2, ...

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