CIA_PSA - Problem Set 4 Cash-in-Advance Model Econ720 Fall...

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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 ) to a °rm, so that income is (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 and de°ne 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: 1 = l t + n t + s t Firms:
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