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Unformatted text preview: Homework 3 Macroeconomic Theory I. Viktor Tsyrennikov Question 1. Government needs to finance a stream of government pur chases g t > , ∀ t . It can raise tax revenue T t in any period t up to the total income Y t > 1. Government seeks to minimize the welfare cost imposed on the economy: ∞ summationdisplay t =0 β t . 5 T 2 t . Government can borrow and lend at a constant interest rate R . a) Compute the optimal tax and borrowing plan { T t , D t } for the govern ment that starts with no debt: D = 0. Solution. Government’s budget constraint is: D t +1 = R t +1 ( D t + T t g t ) . The system of FOCs is: T t : 0 = β t T t + λ t R t +1 , D t +1 : 0 = λ t + λ t +1 R t +2 . They can be combined to obtain the following Euler equation: T t = βR t +1 T t +1 . When R t = R, ∀ t then T t = ( βR ) − t T . Using the intertemporal budget constraint: summationdisplay t R − t T t = T / (1 βR 2 ) = summationdisplay t R − t g t ≡ G....
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This note was uploaded on 11/10/2011 for the course ECONOMICS 601 taught by Professor Viktortsyrennikov during the Spring '11 term at Cornell.
 Spring '11
 ViktorTsyrennikov

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