<p>I have a question on Ramsey Model.</p>
<p>Consider the following one-sector, closed, representative household economy.</p>
<p>I have the following Cobb Douglas production function in intensive form</p>
<p><span class="math-container">$$f(k)=Ak(t)^{\alpha}$$</span></p>
<p>A is the constant technology level: There is no technological progress: Let  denote n the population growth rate. This production function displays constant returns to scale in both Capital and labor ; hence each factor is paid its marginal product.</p>
<p><span class="math-container">$\delta$</span> is depreciation rate for capital. And <span class="math-container">$p$</span> is time preference rate.</p>
<p>I found the characteristics of the equilibrium in this model as follows</p>
<p>Euler equation is</p>
<p><span class="math-container">$$\frac{\dot{c}}{c}=A\alpha k^{\alpha -1}- \delta -p$$</span></p>
<p>Resource constraint is</p>
<p><span class="math-container">$$\dot{k} = Ak^{\alpha} - (\delta +n) k - c $$</span></p>
<p>The question asks that</p>
<p>suppose at some t = 0, a permanent shock raises technological level A to <span class="math-container">$A&gt;A^*$</span>. Show the effect of this shock on the phase diagram of the model. In your answer, be sure to compare the equilibrium paths for capital stock and consumption in the economies with and without technological shock.</p>
<p><strong>My answer</strong>
The economy is initially at <span class="math-container">$E_0$</span>.</p>
<p>If <span class="math-container">$A$</span> increases, then the return to saving <span class="math-container">$A\alpha k^{\alpha -1}- \delta $</span> increases, so saving increases, this implies that capital accumulates. So the <span class="math-container">$\dot{c}=0$</span> locus shifts to right.  As capital accumulates, consumption jumps up and so, consumption rises to point B.</p>
<p>If <span class="math-container">$A$</span> increases, then the Output <span class="math-container">$f(k)$</span> is much higher than the break even investment <span class="math-container">$ (\delta +n)k$</span>, so c will be also increasing such that <span class="math-container">$\dot{k}=0$</span> holds. Then the locus <span class="math-container">$\dot{c}=0$</span> shifts up.</p>
<p>At the end, the economy reaches the new equilibrium point <span class="math-container">$E_N$</span>.</p>
<p>The graph is as follows.</p>
<p><a href="https://i.sstatic.net/ujNru.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ujNru.jpg" alt="enter image description here" /></a></p>
<p>However, my instructor gives such a feedback about my answer. And my answer is not enough for her.</p>
<blockquote>
<blockquote>
<p>you need to show the old and new stable arms and also show that at the time of the shock the c jumps up and the new path remains above the old path.</p>
</blockquote>
</blockquote>
<p><strong>How can I correct my answer according to this feedback?</strong></p>
<p>Please help me to answer this question correctly. Thank you.</p>
<p>Edit: I add the original question.
<a href="https://i.sstatic.net/Vy2Gi.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Vy2Gi.jpg" alt="enter image description here" /></a></p>
<p>Now suppose at some t = 0, a permanent shock raises technological level A to
<span class="math-container">$A^* &gt; A$</span>. Show the effects of this shock on the phase diagram of the model. Please compare the equilibrium paths for capital stock and consumption in the economies with and without the technological shock on the phase diagram.</p>

CC BY-SA 4.0
2022-07-21T17:24:33.243Z
With no technological progress and $α<1$, how does your economy achieve the initial steady state?
Alalalalaki
CC BY-SA 4.0
2022-07-21T17:47:47.870Z
@Alalalalaki I have no idea. This is past exam question which I sit. And the question is asked like that.
studentp
CC BY-SA 4.0
2022-07-23T13:54:22.980Z
I suggest you write down exactly the same question as the one in your exam with all the context. Otherwise no one can help with a broken question.
Alalalalaki
CC BY-SA 4.0
2022-07-23T15:00:15.413Z
This is the whole question @Alalalalaki
studentp
<macroeconomics><economic-growth><self-study><endogenous-growth><ramsey>
Question on Ramsey model with shock on technological level
studentp
# Question on Ramsey model with shock on technological level

(Asked by: username_0 on 2022-07-19)

I have a question on Ramsey Model.

Consider the following one-sector, closed, representative household economy.

I have the following Cobb Douglas production function in intensive form

$$f(k)=Ak(t)^{\alpha}$$

A is the constant technology level: There is no technological progress: Let denote n the population growth rate. This production function displays constant returns to scale in both Capital and labor ; hence each factor is paid its marginal product.

$\delta$ is depreciation rate for capital. And $p$ is time preference rate.

I found the characteristics of the equilibrium in this model as follows

Euler equation is

$$\frac{\dot{c}}{c}=A\alpha k^{\alpha -1}- \delta -p$$

Resource constraint is

$$\dot{k} = Ak^{\alpha} - (\delta +n) k - c $$

The question asks that

suppose at some t = 0, a permanent shock raises technological level A to $A>A^\*$. Show the effect of this shock on the phase diagram of the model. In your answer, be sure to compare the equilibrium paths for capital stock and consumption in the economies with and without technological shock.

**My answer**
The economy is initially at $E\_0$.

If $A$ increases, then the return to saving $A\alpha k^{\alpha -1}- \delta $ increases, so saving increases, this implies that capital accumulates. So the $\dot{c}=0$ locus shifts to right. As capital accumulates, consumption jumps up and so, consumption rises to point B.

If $A$ increases, then the Output $f(k)$ is much higher than the break even investment $ (\delta +n)k$, so c will be also increasing such that $\dot{k}=0$ holds. Then the locus $\dot{c}=0$ shifts up.

At the end, the economy reaches the new equilibrium point $E\_N$.

The graph is as follows.

[![enter image description here](https://i.sstatic.net/ujNru.jpg)](https://i.sstatic.net/ujNru.jpg)

However, my instructor gives such a feedback about my answer. And my answer is not enough for her.

> > you need to show the old and new stable arms and also show that at the time of the shock the c jumps up and the new path remains above the old path.

**How can I correct my answer according to this feedback?**

Please help me to answer this question correctly. Thank you.

Edit: I add the original question.
[![enter image description here](https://i.sstatic.net/Vy2Gi.jpg)](https://i.sstatic.net/Vy2Gi.jpg)

Now suppose at some t = 0, a permanent shock raises technological level A to
$A^\* > A$. Show the effects of this shock on the phase diagram of the model. Please compare the equilibrium paths for capital stock and consumption in the economies with and without the technological shock on the phase diagram.

**Tags:** macroeconomics, economic-growth, self-study, endogenous-growth, ramsey
> **Comments:**
> **username_1**: With no technological progress and $α<1$, how does your economy achieve the initial steady state?  
> **username_0**: @Alalalalaki I have no idea. This is past exam question which I sit. And the question is asked like that.  
> **username_1**: I suggest you write down exactly the same question as the one in your exam with all the context. Otherwise no one can help with a broken question.  
> **username_0**: This is the whole question @Alalalalaki  

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## 0 answers

