TAsection03sol

# TAsection03sol - TA section 04 solution 1 Neoclassical...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

### Page1 / 3

TAsection03sol - TA section 04 solution 1 Neoclassical...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online