<p>Given the production function:</p>
<p><span class="math-container">$$Y = K^\alpha (AL)^\beta R^{1-\alpha -\beta}$$</span>.</p>
<p>Where <span class="math-container">$L, A$</span> grow at exogenously given rates <span class="math-container">$n, g$</span> respectively. <span class="math-container">$R$</span> is land and is constant in supply and given that <span class="math-container">$\alpha + \beta &lt;1$</span>. Investment is a fixed fraction <span class="math-container">$s$</span> of income so, <span class="math-container">$$\dot K/K = sY/K - \delta$$</span>.</p>
<p>Question:</p>
<ol>
<li>Show that there are two possible values (one positive and one negative) for <span class="math-container">$g_K$</span>.</li>
</ol>
<ul>
<li>I applied the usual aproach to find that <span class="math-container">$$g_K = \frac{\beta (g+n)}{1-\alpha}$$</span> at steady state. I think I didn't understand the question here because I don't see which two values are being referred to.</li>
</ul>
<ol start="2">
<li>Does this economy have a unique and stable BGP? If so what are those growth rates and if not why?</li>
</ol>
<ul>
<li>Again I could find the steady state growths buy it assumes that it exists. How to check whether it exists at all or not?</li>
</ul>
<ol start="3">
<li>Does R being constant imply that permanent growth is not possible? Answer this using positive value of <span class="math-container">$g_K$</span> and deriving an expression for <span class="math-container">$\dot Z/ Z$</span> where, <span class="math-container">$Z$</span> is <span class="math-container">$Y/L$</span>.</li>
</ol>
<ul>
<li>No idea what happened here as couldn't solve (1).</li>
</ul>

CC BY-SA 4.0
2022-03-14T14:31:02.300Z
Could you please show us the attempt for 2 and 3 per our homework/self-study question policy?
1muflon1
CC BY-SA 4.0
2022-03-15T05:30:32.103Z
@1muflon1: as mentioned in the post the three parts are connected and I couldn't solve even the first part properly. For third part I am blank and for second I found rates as mentioned in the first bullet point. This isn't exactly homework but yes it is self study as I am trying to solve some questions. Would appreciate either: full solution or a good hint.
Dayne
CC BY-SA 4.0
2022-03-15T16:01:33.847Z
A good starting point would be defining $g_K$. Is that the growth rate at time t or the steady state growth rate?
jpfeifer
CC BY-SA 4.0
2022-03-15T16:56:38.880Z
As per question it is simply defined as $\dot K / K$. However it doesn't say that need not be a function of t
Dayne
<macroeconomics><self-study><solow><steady-state><balanced-growth>
Solow Model With Land as Factor
Dayne
# Solow Model With Land as Factor

(Asked by: username_0 on 2022-03-14)

Given the production function:

$$Y = K^\alpha (AL)^\beta R^{1-\alpha -\beta}$$.

Where $L, A$ grow at exogenously given rates $n, g$ respectively. $R$ is land and is constant in supply and given that $\alpha + \beta <1$. Investment is a fixed fraction $s$ of income so, $$\dot K/K = sY/K - \delta$$.

Question:

1. Show that there are two possible values (one positive and one negative) for $g\_K$.

* I applied the usual aproach to find that $$g\_K = \frac{\beta (g+n)}{1-\alpha}$$ at steady state. I think I didn't understand the question here because I don't see which two values are being referred to.

2. Does this economy have a unique and stable BGP? If so what are those growth rates and if not why?

* Again I could find the steady state growths buy it assumes that it exists. How to check whether it exists at all or not?

3. Does R being constant imply that permanent growth is not possible? Answer this using positive value of $g\_K$ and deriving an expression for $\dot Z/ Z$ where, $Z$ is $Y/L$.

* No idea what happened here as couldn't solve (1).

**Tags:** macroeconomics, self-study, solow, steady-state, balanced-growth
> **Comments:**
> **username_1**: Could you please show us the attempt for 2 and 3 per our homework/self-study question policy?  
> **username_0**: @1muflon1: as mentioned in the post the three parts are connected and I couldn't solve even the first part properly. For third part I am blank and for second I found rates as mentioned in the first bullet point. This isn't exactly homework but yes it is self study as I am trying to solve some questions. Would appreciate either: full solution or a good hint.  
> **username_2**: A good starting point would be defining $g_K$. Is that the growth rate at time t or the steady state growth rate?  
> **username_0**: As per question it is simply defined as $\dot K / K$. However it doesn't say that need not be a function of t  

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## 0 answers

