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Unformatted text preview: University of Minnesota Macroeconomic Policy 4731H, Spring 2011 Problem Set # 2 Instructor: Justin Barnette Due date: 03 / 8 / 2011 Question 1 (40 points) This question is about the Ramsey problem in the Neoclassical Growth Model. Suppose the government imposes taxes on consumption, labor and capital income { τ c t ,τ l t ,τ k t } ∞ t =0 . 1 Given taxes, prices and k , the representative household solves max { c t ,l t ,k t +1 ,x t } ∞ X t =0 β t u ( c t ,l t ) s.t. ∞ X t =0 p t [(1 + τ c t ) c t + x t ] = ∞ X t =0 p t [(1 τ l t ) w t l t + (1 τ k t ) r t k t ] and k t +1 = (1 δ ) k t + x t where c t is time t consumption, l t is time t labor, x t is time t investment and k t is time t capital, p t is time t price of consumption, w t is time t wage and r t is time t rental rate of capital. On the other hand, given prices, the representative firm solves at any t max ( y t ,l t ,k t ) y t w t l t r t k t 1 Again, the government does not have access to taxes on investment, just to make it simpler. 1 University of Minnesota Macroeconomic Policy 4731H, Spring 2011 s.t. y t = F ( k t ,l t ) In addition, government balances its lifetime budget constraint ∞ X t =0 p t g t = ∞ X t =0 p t [ τ c t c t + τ l t w t l t + τ k t r t k t ] As derived in class, the Implementability Constraint in the Neoclassical Growth Model is ∞ X t =0 β t [ u c ( t ) c t + u l ( t ) l t ] = A (1) where A ≡ u c (0) (1 τ k ) (1+ τ c ) k ( r + 1 δ ) , u c ( t ) ≡ ∂u ( c t ,l t ) ∂c t and u l ( t ) ≡...
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This note was uploaded on 03/26/2011 for the course ECON 4731H taught by Professor Justinbarnette during the Spring '11 term at Minnesota.
 Spring '11
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