OLG_Money_PSA

OLG_Money_PSA - Problem Set 2: OLG Models With Money...

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Problem Set 2: OLG Models With Money Econ720. Fall 2009. Lutz Hendricks 1 Money and Storage follows: The old enter period t holding aggregate capital K t = N t 1 k t and nominal money balances of M t = m t N t 1 . Each old person produces f ( k t ) . All capital is used up in production (complete depreciation). Assume that f ( : ) obeys Inada conditions. The government pays a lump-sum transfer of x t p t units of money to each old person: M t +1 = M t + N t 1 x t p t . N t = (1 + n ) t young households are born. Each is endowed with e units of a single good. The young buy money ( m t +1 =p t ) from the old, consume c y t and save k t +1 . The old consume their income. The utility function is u ( c y t ) + ( c o t +1 ) . (a) State the household±s budget constraints when young and old. (c) The government±s only role is to grow the aggregate money supply at the constant rate ± : M t +1 = (1 + ± ) M t (e) Find the money growth rate ( ± ) that maximizes steady state consumption per young person, ( N t c y t + N t 1 c o t ) =N t . 2 Money in the Utility Function in an OLG Model Consider a two-period overlapping generations model with money. Each generation is of constant size N . Young households supply one unit of labor when young and earn the wage w t . Each consumes c y t and saves the remainder either as capital ( s t +1 ) or as real money ( m d t =p t ). Old households consume their savings, including interest income ( c o t +1 ) . The utility function is

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This note was uploaded on 10/29/2009 for the course ECON 720 at UNC.

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OLG_Money_PSA - Problem Set 2: OLG Models With Money...

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