MIU_RQ - Review Questions: Money in Continuous Time Prof....

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Unformatted text preview: Review Questions: Money in Continuous Time Prof. Lutz Hendricks. August 7, 2009 1 Money in the production function Consider a standard Sidrauski model with a single representative household who maximizes R 1 e & &t u ( c t ; m t ) dt subject to the budget constraint _ a t = f ( k t ; m t ) & c t + & t & t m t . Here, a t = k t + m t denotes asset holdings, consisting of capital and real money balances, c t is consumption, and t = _ p t =p t is the in&ation rate. & t denotes lump-sum money transfers. Money transfers follow the rule & t = g m t for some exogenous money growth rate g t . (a) Dene a solution to the household problem. (b) Dene a competitive equilibrium. (c) Provide a system of equations that characterizes the steady state. Is money generally super-neutral? (d) Now assume that u ( c ) = ln( c ) + ln( m ) and f ( k; m ) = k m 1 & . The model now features endogenous growth. How does faster money growth rate a/ect the balanced growth rate?...
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