TAsection03sol

TAsection03sol - TA section 04 solution 1 Neoclassical...

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Unformatted text preview: TA section 04 solution February 16, 2009 1 Neoclassical Growth problem with labor Social planner&s problem in per capita term is the following: max f c t ;k t +1 ;l t g 1 X t =0 & t (log c t + ¡ log (1 & l t )) c t + k t +1 = k & t & (1 + g ) t l t ¡ 1 & & + (1 & ¢ ) k t 1.1 Lagrangian setup max f c t ;k t +1 ;l t g L = 1 X t =0 & t ¢ (log c t + ¡ log (1 & l t )) + £ t £ k & t & (1 + g ) t l t ¡ 1 & & + (1 & ¢ ) k t & c t & k t +1 ¤¥ 1.2 FOC Derive FOCs [ c t ] : 1 c t = £ t [ k t +1 ] : £ t = &£ t +1 £ ¤k & & 1 t +1 & (1 + g ) t +1 l t +1 ¡ 1 & & + (1 & ¢ ) ¤ [ l t ] : ¡ 1 & l t = £ t (1 & ¤ ) (1 + g ) t k & t & (1 + g ) t l t ¡ & & [ £ t ] : c t + k t +1 = k & t & (1 + g ) t l t ¡ 1 & & + (1 & ¢ ) k t 1 Eliminating & t 1 c t = ¡ 1 c t +1 & ¢k & & 1 t +1 ¡ (1 + g ) t +1 l t +1 ¢ 1 & & + (1 & £ ) £ ¤c t 1 & l t = (1 & ¢ ) (1 + g ) t k & t ¡ (1 + g ) t l t ¢ & & c t + k t +1 = k & t ¡ (1 + g ) t l t ¢ 1 & & + (1 & £ ) k t 1.3 Stationary equilibrium conditions...
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This note was uploaded on 05/13/2010 for the course ECON 110D taught by Professor Schmitt-grohe during the Spring '08 term at Duke.

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TAsection03sol - TA section 04 solution 1 Neoclassical...

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