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homework4 2010

# homework4 2010 - ECN/APEC 7240 Spring 2010 Homework 4 Due 1...

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ECN/APEC 7240 Spring 2010 Homework 4 Due 2/24/10 1) We augment the Consumption RBC Model with Cobb-Douglas production and CRRA utility by including government spending financed by lump-sum taxes. Let T t be the tax at t with τ t = ln T t = τ t 0 + τ t 1 . We assume that τ t 0 = τ 0 + gt and τ t 1 is an AR(1) process such that , 1 1 1 1 τ ε φτ τ + + + = t t t where φ ( - 1,1) and ε t τ is i.i.d and uncorrelated with ε t a . ζ = T 0 / Y 0 is exogenous. a) What are the Euler equation and budget constraint for this model? b) How do C 0 / Y 0 , K 0 / Y 0 , and r 0 depend on the exogenous parameters of the model? c) Derive the log-linearized Euler equation and budget constraint assuming now that c t 1 = η ck k t 1 + η ca a t 1 + η c τ τ t 1 and similarly for k t +1 1 and y t 1 . d) Does the introduction of the lump-sum tax change the equation that determines η ck ? What about the equations that determine η ca , η kk , η ka , η yk , or η ya ? 2) Consider the following discrete-time model. A continuum of identical households with unit measure maximize , ) exp( 1 0

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homework4 2010 - ECN/APEC 7240 Spring 2010 Homework 4 Due 1...

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