Lecture_17_2009_M

# Lecture_17_2009_M - Intermediate Macroeconomics Bruce...

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Unformatted text preview: Intermediate Macroeconomics Bruce Preston March 30, 2010 Today Micro ounda ions: Op imizing wo-period model o consump ion Theory o inves men Deriving he IS curve Formal Two-Period Model Asump ions Two periods: he curen period and he u ure Household akes income, weal h and prices as given Can borow or lend a cons an real in eres ra e Formal Two-Period Model I Le y = curen income y f = u ure income a = real ini ial weal h r = real in eres ra e c = curen consump ion c f = u ure consump ion Household Op imiza ion Supose household pre erences are given by u c; c f = u ( c ) + u c f where = subjec ive ime pre erence and u ( c ) concave unc ion Household Problem Household wishes o ma imize by choice o c and c f u c; c f = u ( c ) + u c f subjec o c f = ( y + a c ) (1 + r ) + y f quivalen Problem Ma imize by choice o c u c; c f = u ( c ) + u ( y + a c ) (1 + r ) + y f Firs -order condi ions Taking deriva ives provides @u c; c f @c = @u ( c ) @c (1 + r ) @u ( y + a c ) (1 + r ) + y f @c = 0 Hence u ( c ) = (1 + r ) u c f In erpre a ion Grow h in marginal u ili y u c f u ( c ) = 1 (1 + r ) Posi ive grow h more likely when ei her or bo h r and smal Implica ions or consump ion grow h? Ques ion Under wha condi ions is consump ion cons an over ime? Sovling he Model Asume u ili y unc ion o he orm u c; c f = u ( c ) + u c f where u ( c ) = c c 2 u c f = c c f 2 Sovling he Model I Hence u ( c ) = 2 c u c f = 2 c f and 2 c = (1 + r ) 2 c f Toge her wi h in er emporal budge cons rain : wo equa ions in wo unknowns: c and c f Sovling he Model I Special case: (1 + r ) = 1 implies c = c f Using he IBC gives c + c f 1 + r = c 1 +...
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## This note was uploaded on 02/27/2011 for the course ECONOMICS 201 taught by Professor P during the Spring '11 term at Columbia College.

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Lecture_17_2009_M - Intermediate Macroeconomics Bruce...

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