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Unformatted text preview: Noah Williams Economics 714 Department of Economics Macroeconomic Theory University of Wisconsin Spring 2009 Problem Set 4 Solutions (Sketch) 1. (a) Under consumption taxes, households FOC are u c ( c t +1 , 1- N t +1 ) u c ( c t , 1- N t ) = q t +1 (1 + c t +1 ) q t (1 + c t ) u c ( c t , 1- N t ) u l ( c t , 1- N t ) = 1 + c t w t q t q t +1 = r t + (1- ) Under a labor and capital income taxes, we have u c ( c t +1 , 1- N t +1 ) u c ( c t , 1- N t ) = q t +1 q t u c ( c t , 1- N t ) u l ( c t , 1- N t ) = 1 w t (1- N t ) q t q t +1 = r t (1- k t ) + (1- ) From this, you can derive the conditions for the tax schemes to yield equivalent marginal utilities. (b) The equations describing the transitional dynamics are u c ( c t +1 ) u c ( c t ) = [1- + f k ( k )](1 + g )(1 + ) c t + k t +1- (1- ) k t + G = f ( k t ) The steady state is c * = f ( k * )- k *- G and 1 = [1- + f k ( k * )](1 + g )(1 + )....
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This note was uploaded on 06/19/2011 for the course ECON 714 taught by Professor Staff during the Spring '08 term at Wisconsin.
- Spring '08