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OLG_Money_RQ

# OLG_Money_RQ - Review Problems Money in OLG Models Econ720...

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Review Problems: Money in OLG Models Econ720. Fall 2009. Lutz Hendricks 1 Government Purchases Consider a two-period OLG model with money. At each date t a cohort of size N t = (1 + n ) t is born. Each household lives for two periods and derives utility from consumption at both ages according to u ( c y t ;c o t +1 ) Households receive endowments of goods when young ( e t ) that cannot be stored. The only as- set available is money which is injected into the economy through government purchases. The government buys G t = g t N t goods in each period and throws them into the ocean. (a) Write down the government budget constraint. is. Show that it can be written as P t =P t +1 = (1 + n m t +1 g t +1 ) = m t where m = M= ( PN ) denotes real, per capita money balances. function. (d) The money market clearing condition is m t = s ( P t =P t +1 ) where s is a saving function. For what follows assume that g is constant over time and that s (1 + n ) > 0 (Samuelson case). Also assume that the o/er curve is convex, but not backward bending. Using m t = s ((1 + n m t +1 g t +1 ) = m t ) ; (1)

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OLG_Money_RQ - Review Problems Money in OLG Models Econ720...

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