CIA_RQ - Review Questions: Money in discrete time Prof....

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Review Questions: Money in discrete time Prof. Lutz Hendricks. August 6, 2009 1 Money and leisure Consider the following version of a Sydrauski model. A representative household solves max 1 X t =0 t u ( c t ; m t +1 =p t ; 1 n t ) subject to the budget constraint k t +1 + m t +1 =p t + c t = F ( k t ; n t ) + m t =p t + x t where x t is a (money) transfer from the government and n t is labor time. The government hands out money according to the rule x t = g t m t =p t where f g t g is an exogenous sequence. Assume that F ( k; n ) (a) State the household±s Bellman equation. Derive a system of equations that solves the house- hold problem. (c) Now assume that g t = g in all periods. Derive a system of equations that characterizes the steady state. (d) Prove that money is super-neutral, if the utility function is of the form u ( c; m=p; 1 n ) = U ( c; 1 n ) + W ( m=p ) . 1.1 Money and leisure (a) The household±s Bellman equation is given by V ( k; m ) = u ( c; m 0 =p; 1 n ) + ( k 0 ; m 0 ) + ± f F ( k; n ) + m=p + x m 0 =p c k 0 g u c ( t ) u m ( t ) = ( p t =p t +1 ) u c ( t + 1) (1) u n ( t ) = u c ( t ) F n ( k t ; n t ) u c ( t ) = c ( t + 1) F k ( k t ; n t ) A solution to the household problem is a set of sequences f c t ; m t ; n t ; k t g that solves the 3 FOCs and the budget constraint. The transversality conditions are lim t !1 t u c ( t ) k t = 0 and lim t !1 t u c ( t ) m t =p
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CIA_RQ - Review Questions: Money in discrete time Prof....

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