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208-2011-L11

# 208-2011-L11 - Econ208 MarekKapicka Lecture11...

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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
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
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 τ λ 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 β τ β 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
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 τ 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  to the government’s budget constraint n First Order Condition: = = - + + + - + - 0 0 } { ] 1 ) 1 1 ( [ 1 ln ln max 0 t t t t t t t W G r W t t τ τ μ β τ β τ 1 - = μ τ t
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208-2011-L11 - Econ208 MarekKapicka Lecture11...

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