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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 { c t , l t , 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 t u ( c t ,l t ) s.t. X t =0 p t [(1 + c t ) c t + x t ] = X t =0 p t [(1 l t ) w t l t + (1 k t ) r t k t ] and k t +1 = (1 ) 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 [ c t c t + l t w t l t + k t r t k t ] As derived in class, the Implementability Constraint in the Neoclassical Growth Model is X t =0 t [ u c ( t ) c t + u l ( t ) l t ] = A (1) where A u c (0) (1 k ) (1+ c ) k ( r + 1 ) , u c ( t ) u ( c t ,l t ) c t and u l ( t )...
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 Spring '11
 JustinBarnette

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