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ps4_solutionsketch

ps4_solutionsketch - Noah Williams Department of Economics...

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Noah Williams Economics 714 Department of Economics Macroeconomic Theory University of Wisconsin Spring 2009 Problem Set 4 Solutions (Sketch) 1. (a) Under consumption taxes, household’s FOC are β u c ( c t +1 , 1 - N t +1 ) u c ( c t , 1 - N t ) = q t +1 (1 + τ c t +1 ) q t (1 + τ c t ) u c ( c t , 1 - N t ) u l ( c t , 1 - N t ) = 1 + τ c t w t q t q t +1 = r t + (1 - δ ) Under a labor and capital income taxes, we have β 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 - τ N t ) q t q t +1 = r t (1 - τ k t ) + (1 - δ ) ¿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 - δ + f k ( k )](1 + g )(1 + ρ ) c t + k t +1 - (1 - δ ) k t + G = f ( k t ) The steady state is c * = f ( k * ) - δk * - G and 1 = [1 - δ + f k ( k * )](1 + g )(1 + ρ ). Taking G and g as given without worrying about the government’s BC, increasing them has the effect of decreasing both steady state consumption and capital stock.

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