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CIA_PS

# CIA_PS - 1 = l t n t s t Firms Firms produce output in...

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Problem Set 4: Cash-in-Advance Model Econ720. Fall 2009. Lutz Hendricks 1 Shopping time Consider the following monetary model. Households: There is a single representative household with preferences over consumption ( c ) and leisure ( l ) given by 1 X t =0 t u ( c t ; l t ); 0 1 : The household supplies capital ( k ) and labor ( n ) (1 + r t ) k t + w t n t . The household also brings M t units of money into the period. Let P t be the price level in period t m t = M t =P t . The household±s budget constraint is then (1 + r t ) k t + w t n t + m t = c t + k t +1 + m t +1 (1 + ± t +1 ) where 1 + ± t +1 = P t +1 =P 1 . Money is held to facilitate consumption transactions. The trans- actions technology is such that s t units of time are required to purchase c t given money balances m t : s t = g ( c t ; m t ) Obviously, g c > 0 and g m < 0 . The household is endowed with one unit of time in each period, which is split between leisure, work, and shopping:
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Unformatted text preview: 1 = l t + n t + s t Firms: Firms produce output in competitive markets, using labor and capital, both of which are hired from households on spot markets. Firms have access to a typical neoclassical production function: f ( k t ; n t ) . The depreciation rate is < ² < 1 . Questions: . 1. De&ne a solution to the household problem. 2. De&ne a competitive equilibrium. Assume that the money supply is constant. 3. Is money neutral in this economy? Prove your answer using the system of equations that de&ne a competitive equilibrium. 4. Would money still be neutral if the transactions technology used nominal money balances i.e., s t = g ( c t ; M t ) ? Explain the intuition. You need not derive your answer. 1...
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