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Unformatted text preview: Suggested Solutions to EC 2102 Macroeconomic Analysis I Tutorial 4 , Week 8 (March 7 11 , 2011 ) ( i ) Since the production technology is Y t = z t F ( K t ;N t ) = z t K a t N 1 & a t (0 < a < 1) , the marginal product of capital in time period t , MPK t : MPK t = @Y t =@K t = z t F 1 ( K t ;N t ) = az t K a & 1 t N 1 & a t > 0; (1) and the marginal product of labor in time period t , MPN t : MPN t = @Y t =@N t = z t F 2 ( K t ;N t ) = (1 & a ) z t K a t N & a t > : (2) ( ii ) The &rm¡s maximization problem in period 1 is: max f N 1 ;K 2 g & 1 + & 2 1 + r 1 + & 3 (1 + r 1 )(1 + r 2 ) + ¡ ¡ ¡ Since & t = z t F ( K t ;N t ) & w t N t & I t = z t F ( K t ;N t ) & w t N t & [ K t +1 & (1 & ¡ ) K t ] Therefore, we can rewrite the &rm¡s maximization problem in period 1 as: max f N 1 ;K 2 g z 1 F ( K 1 ;N 1 ) & w 1 N 1 & [ K 2 & (1 & ¡ ) K 1 ]+ z 2 F ( K 2 ;N 2 ) & w 2 N 2 & [ K 3 & (1 & ¡ ) K 2 ] 1 + r 1 + ¡ ¡ ¡ F:O:C: ( N 1 ) : z 1 F 2 ( K 1 ;N ¡ 1 ) & w 1 = 0 (3) F:O:C: ( K 2 ) : & 1 + 1 1 + r 1 [ z 2 F 1 ( K ¡ 2 ;N 2 ) + (1 & ¡ )] = 0 (4) 1 Substituting equation (1)and (2) into equation (3) and (4), we have z 1 F 2 ( K 1 ;N & 1 ) = (1 & a ) z 1 K a 1 ( N & 1 ) ¡ a = w 1 z 2 F 1 ( K & 2 ;N 2 ) = az 2 ( K & 2 ) a ¡ 1 N 1 ¡ a 2 & & = r 1 : The economic meaning of F.O.C.s: equation (3) tells &rm how muchThe economic meaning of F....
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This note was uploaded on 01/18/2012 for the course ECONOMICS 2102 taught by Professor Tan during the Spring '11 term at National University of Singapore.
 Spring '11
 Tan

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