TwoSec_SL

TwoSec_SL - Two Sector Models Prof. Lutz Hendricks August...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Two Sector Models Prof. Lutz Hendricks August 7, 2009 L. Hendricks () Two Sector Models August 7, 2009 1 / 28
Background image of page 1

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

View Full DocumentRight Arrow Icon
Two Sector Models We relax the assumption that there is only one good at each date. There are no major changes in methods. Multi-sector models are used to study issues such as: technical change that is &embodied±in capital goods, human capital, international trade. L. Hendricks () Two Sector Models August 7, 2009 2 / 28
Background image of page 2
Planning Problem There is a unit mass of households who live forever. Preferences are t = 0 β t u ( c t , 1 & v t ) ν is work; 1 & ν is leisure. L. Hendricks () Two Sector Models August 7, 2009 3 / 28
Background image of page 3

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

View Full DocumentRight Arrow Icon
Planning Problem Consumption goods are produced according to Y 1 = F ( K 1 , L 1 ) and capital goods according to Y 2 = G ( K 2 , L 2 ) The resource constraints are L 1 t + L 2 t = ν t K 1 t + K 2 t = K t Y 1 t = c t Y 2 t = K t + 1 & ( 1 & δ ) K t L. Hendricks () Two Sector Models August 7, 2009 4 / 28
Background image of page 4
Planning Problem The planner maximizes t = 0 β t u ( c t , 1 & v t ) subject to the resource constraints. The planner chooses c t , L 1 t , L 2 t , and ϕ t . ϕ t is the fraction of capital employed in sector 1: K 1 t = ϕ t K t K 2 t = ( 1 & ϕ t ) K t The planner&s state variable is K t . We would need 2 states ( K 1 t , K 2 t ) if there were a cost of reallocating capital. L. Hendricks () Two Sector Models August 7, 2009 5 / 28
Background image of page 5

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

View Full DocumentRight Arrow Icon
Planning Problem The Bellman equation is V ( K ) = max u ( F ( ϕ K , L 1 ) , 1 & L 1 & L 2 ) + β V ( K ( 1 & δ ) + G ([ 1 & ϕ ] K , L 2 )) where the choice variables are L 1 , L 2 , and ϕ . L. Hendricks () Two Sector Models August 7, 2009 6 / 28
Background image of page 6
Planning Problem FOCs: u l = β V 0 ( K 0 ) G L = u c F L u c F K = β V 0 ( K 0 ) G K Envelope: V 0 ( K ) = ϕ F K u c + β V 0 ( K 0 ) f 1 & δ + ( 1 & ϕ ) G K g L. Hendricks () Two Sector Models August 7, 2009 7 / 28
Background image of page 7

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

View Full DocumentRight Arrow Icon
Planning Problem Euler equation u c F K G K = β u c ( . 0 ) F K ( . 0 ) G K ( . 0 ) f 1 & δ + G K ( . 0 ) g Static condition F K / F L = G K / G L L. Hendricks () Two Sector Models August 7, 2009 8 / 28
Background image of page 8
Planning Problem Solution Sequences f c t , ν t , K t + 1 , ϕ t , L 1 t , L 2 t g that satisfy: 2 FOCs; 4 feasibility conditions; TVC: lim t !
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/29/2009 for the course ECON 720 at UNC.

Page1 / 28

TwoSec_SL - Two Sector Models Prof. Lutz Hendricks August...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online