208-2011-L11

208-2011-L11 - Econ208 MarekKapicka Lecture11 RamseyTaxation

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Econ 208 Marek Kapicka Lecture 11 Ramsey Taxation
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Ramsey Approach to Taxation n Choose optimal (welfare maximizing)  sequences of taxes (and debt) given  that only distortionary tax instruments  are available n Tax instruments are given n Lump sum taxation not allowed
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Ramsey Taxation n We will analyze a problem of a  government that n Face a given sequence of expenditures  { Gt } t ≥0   n Choose a sequence of consumption  (sales) taxes  { τt } t ≥0 n Similar logic applies to labor taxation
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Ramsey Taxation Household Problem n Maximize lifetime utility n Subject to PVBC = 0 } { ) ln( max t t t C C t β = = + = + + 0 0 ) 1 1 ( ) 1 ( ) 1 1 ( t t t t t t t Y r C r τ
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Ramsey Taxation Household Problem n The Lagrangean n Assume that  β =1/(1+ r ): n where  W C t t = = + λ τ 1 ) 1 ( = = = + + - + + 0 0 0 } { ] ) 1 ( ) 1 1 ( ) 1 1 ( [ ) ln( max t t t t t t t t t t C C r Y r C t β = + + = 0 ) 1 1 ( 1 t t t Y r r r W
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Ramsey Taxation Household Problem n Indirect Utility: β τ - + + - = + = = = = = 1 ln ) 1 ln( ) 1 ln( ) ln( ) , } ({ 0 0 0 * 0 W W C W V t t t t t t t t t t t
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Ramsey Taxation Government’s Problem n PV Budget Constraint n Define  = = = + + = + = + 0 0 * 0 1 ) 1 1 ( ) 1 1 ( ) 1 1 ( t t t t t t t t t t t W r C r G r τ t t t G r G = + = 0 ) 1 1 (
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Ramsey Taxation Government’s Problem n Ramsey Problem: Choose a sequence of  tax rates to maximize agent’s utility, subject 
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This note was uploaded on 12/26/2011 for the course ECON 208 taught by Professor Staff during the Fall '08 term at UCSB.

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208-2011-L11 - Econ208 MarekKapicka Lecture11 RamseyTaxation

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