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\f. Monetary policy in the overlapping generations model with ex ante heterogeneity Time: discrete, innite horizon, t = 1. 2,3... Demography: A mass 2N of newborns enter in every period. Everyone lives for 2 periods except for the rst generation of old people who live for 1 period. 1iui'lz'ithin the population there are two types of household A and B who di'er according to their endowments {see below}. The population is split exactly in half between the groups. Preferences: for the generations born in and after period 1; rtfcie- Elie\") = lnfiel + 31nfit+1l 1-: 24,3 where cg, is consumption in period t and stage 9 of life for type i = A. B individuals. For the initial old generation {11:23]} = Int-:31} for i = A. B Endowments: Except for the initial old, in the rst period of life type A people receive 1 unit of the consumption good and type B people receive 2 units. No one gets any endowment in their second period of life. In period 1 the rst generation of old are endowed with Hg units of money spread equally among them which can be stored but provides no utility in consumption. The money supply grows each period so that the aggregate money supply in period t is Hn + G'Jt. The new money transfers occur by helicopter drop Il:i.e. lump sum} to each old person at the beginning of the period in which they are old. Information: There is complete information with perfect foresight. Solution concept: Competitive equilibrium. Each period there are markets for the con sumption good and money. Let, pt, be the price for goods in terms of money in period t which is taken as given by every participant