<p>In that case, I think you can try to approximate the value of the steady-state <span class="math-container">$k^*$</span>. If your capital accumulation function is implicitly defined, say <span class="math-container">$k_{t+1}=\phi(k_{t+1},k_t)$</span>:</p>
<ul>
<li>You can still prove the existence of a steady state by using the Intermediate Value Theorem.</li>
<li>To show the convergence of dynamics, maybe it is enough to prove <span class="math-container">$\phi' &gt; 0, \phi'' &lt; 0$</span>. (see Galor, O., &amp; Ryder, H. E. (1989). Although the theory was developed for the class of OLG model, I think its relevance can still be applied here).</li>
</ul>
<p>After making sure that you indeed have a steady state, you are entitled to use a numerical solution. I think you can use the <code>fsolve</code> function in Matlab to obtain a numerical approximation of that point, and then it's possible to create a grid as usual.</p>
<p>Please correct me if I'm wrong.</p>

CC BY-SA 4.0
2023-08-23T12:13:48.420Z
2023-08-23T12:20:29.683Z
2023-08-23T12:20:29.683Z
teddi
<p>I already know that expanding the grids of state variables around the steady states works, however in my toy model it's hard to get steady states analytically, so I cannot determine the boundary for variables. Is there any other method to set the grid even without steady states?</p>

<dynamic-programming>
Technical question about grid setting in dynamic programming models
Barry
# Technical question about grid setting in dynamic programming models

(Asked by: username_0 on 2023-04-17)

I already know that expanding the grids of state variables around the steady states works, however in my toy model it's hard to get steady states analytically, so I cannot determine the boundary for variables. Is there any other method to set the grid even without steady states?

**Tags:** dynamic-programming

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## 1 answers

### Answer by username_1 on 2023-08-23. Score: 1

In that case, I think you can try to approximate the value of the steady-state $k^\*$. If your capital accumulation function is implicitly defined, say $k\_{t+1}=\phi(k\_{t+1},k\_t)$:

* You can still prove the existence of a steady state by using the Intermediate Value Theorem.
* To show the convergence of dynamics, maybe it is enough to prove $\phi' > 0, \phi'' < 0$. (see Galor, O., & Ryder, H. E. (1989). Although the theory was developed for the class of OLG model, I think its relevance can still be applied here).

After making sure that you indeed have a steady state, you are entitled to use a numerical solution. I think you can use the `fsolve` function in Matlab to obtain a numerical approximation of that point, and then it's possible to create a grid as usual.

Please correct me if I'm wrong.


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