# lecture8 - Lecture 8 Transition Dynamics and Public Policy...

This preview shows pages 1–9. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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: Lecture 8 Transition Dynamics and Public Policy in the Cass-Koopmans- Ramsey Model ECON 7240 VIII - 2 Intensive Equations of Motion Instantaneous budget constraint: Euler equation: ) ( ) ( ) ( )) ( ( ) ( t k g n t c t k f dt t dk + +-- = g t k f dt t c d--- = )) ( ( ' ) ( ln ECON 7240 VIII - 3 Balanced Growth Path For any k (0), there is a unique c ( k (0)) such that the solution to the equations of motion satisfies Starting the system at k (0) and c (0) = c ( k (0)) , k ( t ) will converge to k * and c ( t ) to c * where g k f + + = *) ( ' * ) ( *) ( * k g n k f c + +- = ( 29 . *) ( exp ) ( lim = + +- t r g n t k t ECON 7240 VIII - 4 Difference Equations There is no analytic solution to this system of differential equations. We can solve them numerically by approximating them by difference equations. For small t , define k i = k ( i t ) and c i = c ( i t ). t k g n c k f k k i i i i i + +-- + = + ) ) ( ) ( ( 1 --- + = + t g k f c c i i i ) ( ' 1 1 ECON 7240 VIII - 5 Shooting Method Given k , choose a large T at which we believe k ( T ) k *. We have to find c = c ( k ). If c &gt; c ( k ), household will not save enough and k T &lt; k *. If c is too much larger than c ( k ), k i will be negative for some i and k T is undefined. If c &lt; c ( k ), household will save too much and k T &gt; k *. ECON 7240 VIII - 6 Dynamics of k ( = 1) 4 4.2 4.4 4.6 4.8 5 5.2 5.4 10 20 30 40 50 60 70 80 90 100 CKR Solow t k ECON 7240 VIII - 7 Dynamics of c ( = 1) 1.1 1.15 1.2 1.25 1.3 1.35 10 20 30 40 50 60 70 80 90 100 CKR Solow t c ECON 7240 VIII - 8 Balanced Growth Welfare Suppose the economy is at the steady state at T ....
View Full Document

## lecture8 - Lecture 8 Transition Dynamics and Public Policy...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online