Lecture_17_2009_M - Intermediate Macroeconomics Bruce...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 +...
View Full Document

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.

Page1 / 9

Lecture_17_2009_M - Intermediate Macroeconomics Bruce...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online