<p>$dk_{it}/dt = (W(\tilde K,\tilde l)/\tilde K)[(1+1/n)(\tilde k_i - \theta_i)(l_t - \tilde l)] + B(k_{it} - \tilde k_i)]$</p>

<p>This is a differential equation of individual capital stock $k_{it}$ linearized arond the steady states of $k_{it}$ &amp; $l_t$. How do I go about finding the stable solution solution to this equation? Considering that there are fewer equations than variables, how is it even possible? (Or am I getting my differential math completely wrong!) The papers states that the stable path is: </p>

<p>$k_{it} = \tilde k_i + (1/(u- B))(W(\tilde K,\tilde l)/\tilde K)[(1+1/n)(\tilde k_i - \theta_i)(l_0 - \tilde l)](k_{it} - \tilde \theta_i)e^{ut}$</p>

<p>Where u is the eigenvalue. Can I get help in deriving this? Just a nudge to right kind of solution method would do, thanks! </p>

<p>Edit: The <a href="http://www.vcharite.univ-mrs.fr/PP/penalosa/workingpapers/TurnRamsey1.pdf" rel="nofollow noreferrer">paper</a> in question.</p>

<p>Search for (A.13) (1st equation) &amp; (A.14) (the stable solution). </p>

CC BY-SA 3.0
2016-11-08T14:20:39.657Z
This question would be greatly improved by linking to the paper in question.
Giskard
CC BY-SA 3.0
2016-11-08T14:50:16.303Z
Edit: paper in question: http://www.vcharite.univ-mrs.fr/PP/penalosa/workingpapers/TurnRamsey1.pdf

Search for (A.13) (1st equation) & (A.14) (the stable solution). Going through a lot of his papers, and he's really... terse, at times.
user795028
<macroeconomics>
Unable to resolve this linearized equation from a macro growth theory paper
user795028
# Unable to resolve this linearized equation from a macro growth theory paper

(Asked by: username_0 on 2016-11-08)

$dk\_{it}/dt = (W(\tilde K,\tilde l)/\tilde K)[(1+1/n)(\tilde k\_i - \theta\_i)(l\_t - \tilde l)] + B(k\_{it} - \tilde k\_i)]$

This is a differential equation of individual capital stock $k\_{it}$ linearized arond the steady states of $k\_{it}$ & $l\_t$. How do I go about finding the stable solution solution to this equation? Considering that there are fewer equations than variables, how is it even possible? (Or am I getting my differential math completely wrong!) The papers states that the stable path is:

$k\_{it} = \tilde k\_i + (1/(u- B))(W(\tilde K,\tilde l)/\tilde K)[(1+1/n)(\tilde k\_i - \theta\_i)(l\_0 - \tilde l)](k\_{it} - \tilde \theta\_i)e^{ut}$

Where u is the eigenvalue. Can I get help in deriving this? Just a nudge to right kind of solution method would do, thanks!

Edit: The [paper](http://www.vcharite.univ-mrs.fr/PP/penalosa/workingpapers/TurnRamsey1.pdf) in question.

Search for (A.13) (1st equation) & (A.14) (the stable solution).

**Tags:** macroeconomics

> **Comments:**
> **username_1**: This question would be greatly improved by linking to the paper in question.  
> **username_0**: Edit: paper in question: http://www.vcharite.univ-mrs.fr/PP/penalosa/workingpapers/TurnRamsey1.pdf  Search for (A.13) (1st equation) & (A.14) (the stable solution). Going through a lot of his papers, and he's really... terse, at times.  

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## 0 answers

