Lecture 11 Example 4.1 -- Consumption Saving Choice -- Blank

Lecture 11 Example 4.1 -- Consumption Saving Choice --...

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Unformatted text preview: !"# %&' ()*+ ,-.%/0%1,2.% 02&/'%&'-'0,&3 !"#$%&'( *+,-.$%/0+,12#30,4 56+05' #")*")*!* 456789965 :8;<5=> 4;;? :/: (@!!A B56789965B;;?CDE;[email protected] GH!)I AJHKLH(! .M% '4.,02+ &'-3N04.,'-"32O,-P &M',&%Q 2- 2-2+R.,&2+ %S204+% No t a t ion r e mind e r y : pre-tax income during the current period y f : pre-tax income during the future period n t : per capita net tax (tax minus transfer) in the current period n t f : per capita net tax in the future period a : initial assets. y = y ± n t : after-tax income during the current period (income minus net tax) f y " y f ± n t f : after-tax income during the future period c : current consumption c f : future consumption ݑሺܿǡ ܿ ௙ ሻ : utility function Exampl e 1: Ini t ial Si t ua t ion /HW WKH KRXVHKROG¶V XWLOLW\ IXQFWLRQ EH ( , ) 4ln 6ln f f u c c c c ¡ ,Q WKH LQLWLDO VLWXDWLRQ¡ VXEVFULSWHG ZLWK ¢¡ WKH KRXVHKROG¶V DIWHU-tax incomes and initial assets are given by 1 1 12 60 4 f y y a ¢ And the real interest rate is 1 25% r 7KH KRXVHKROG¶V 39/5 DQG )9/5 FDQ EH calculated as %&' ()*+T 456789965 :8;<5=> 4;;? %>;EB?8Q &6U9VEB<=6U"3;W=UD FX6=F8 )"# PVLR = 60 12 4 56 1 1.25 48 f y y a r ¡ ¡ ¢ ¡ ¡ FVLR = ( ) ( 1 ) ( 1 2 4 ) 1 . 2 5 6 7 10 f y a r y ¡ ¡ ¡ ¢ ¡ , or FVLR = (1 + r ) PVLR = 1.25 56 70 £ The budget set of the household is illustrated in the figure below: B A C ܿ ௙ 56 12 ± 4 = 8 60 70 ܿ %&' ()*+T 456789965 :8;<5=> 4;;? %>;EB?8Q &6U9VEB<=6U"3;W=UD FX6=F8 )"# PVLR = 60 12 4...
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Lecture 11 Example 4.1 -- Consumption Saving Choice --...

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