<p>I don't know how this can be answered without any recourse to at least basic mathematics, since the question itself refers to movement along some curves which is mathematical concept. Hence I will go over some math and then provide intuition at the end.</p>
<p><strong>Explanation Including Math</strong></p>
<p>The investment curve in Solow model is defined as <span class="math-container">$sf(k)$</span> where <span class="math-container">$f(k) = Y$</span> and it is assumed that when we have zero capital per effective worker <span class="math-container">$k$</span> output is also zero <span class="math-container">$f(0)=0$</span>.</p>
<p>The curve appears to shift upwards due to change in its slope. The investment curve will have to go through the origin no matter what it's <span class="math-container">$s$</span>  changes the slope of the investment curve. For example, if <span class="math-container">$s_1=0.5$</span> and <span class="math-container">$f(k)=k$</span> the investment curve will be: <span class="math-container">$0.5k$</span>. If we change <span class="math-container">$s$</span> to <span class="math-container">$s_2=0.7$</span> investment curve would be now <span class="math-container">$0.7k$</span>. This would work for any investment curve that goes through the origin and by our assumption it has to (you can try to verify this for <span class="math-container">$f(k) = \sqrt{k}$</span> or other valid functions.</p>
<p><strong>Non Mathematical Explanation:</strong></p>
<p>The investment function is by definition the <strong>proportion</strong> of output that is being saved (and hence invested). Here <span class="math-container">$s$</span> is the proportionality constant that determines what proportion of output is invested. Increasing that proportionality constant has to change the slope of investment function as now at any level income higher proportion of income is invested. For example, with <span class="math-container">$s_1=0.5$</span>  if <span class="math-container">$Y=100$</span> the investment will be <span class="math-container">$50$</span>, with <span class="math-container">$Y=200$</span>, the investment will be <span class="math-container">$100$</span> etc. Now if you change that proportion not only the investment will be higher at any income but also rate of change of that investment will be higher. With <span class="math-container">$s_2=0.7$</span> at income <span class="math-container">$Y=100$</span>, investment will be <span class="math-container">$I=70$</span>, at <span class="math-container">$Y=200$</span> investment will be <span class="math-container">$I=140$</span>.</p>

CC BY-SA 4.0
2020-11-13T19:26:11.803Z
Thanks. What I don't understand is that if the returns on capital for any capital per worker  ratio hasn't changed then why does the rate of change in investment change?
user3280937
CC BY-SA 4.0
2020-11-13T19:44:05.917Z
@user3280937 but higher saving changes the capital per worker ratio $K/L$. However, it does change the level of $K/L$ instead of growth rate of $K/L$. This is by the way addressed in my previous answer to your other question at the bottom.
1muflon1
CC BY-SA 4.0
2020-11-13T19:07:11.640Z
2020-11-13T19:17:16.300Z
2020-11-13T19:17:16.300Z
1muflon1
<p>In the solow model why does an increase in the savings rate shift the investment curve instead of move along it? Intuitively not mathematically</p>
<p>Thanks</p>

CC BY-SA 4.0
2020-11-13T18:57:50.370Z
Why does it change the slope then?
user3280937
CC BY-SA 4.0
2020-11-13T19:16:20.207Z
actually never mind I just realized that some authors also call this shift although thats not very rigorous so I am retracting my previous comment
1muflon1
<macroeconomics><saving><solow>
Solow model and a change in the savings rate
user3280937
# Solow model and a change in the savings rate

(Asked by: username_0 on 2020-11-13)

In the solow model why does an increase in the savings rate shift the investment curve instead of move along it? Intuitively not mathematically

Thanks

**Tags:** macroeconomics, saving, solow
> **Comments:**
> **username_0**: Why does it change the slope then?  
> **username_1**: actually never mind I just realized that some authors also call this shift although thats not very rigorous so I am retracting my previous comment  

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## 1 answers

### Answer by username_1 on 2020-11-13. Score: 2

I don't know how this can be answered without any recourse to at least basic mathematics, since the question itself refers to movement along some curves which is mathematical concept. Hence I will go over some math and then provide intuition at the end.

**Explanation Including Math**

The investment curve in Solow model is defined as $sf(k)$ where $f(k) = Y$ and it is assumed that when we have zero capital per effective worker $k$ output is also zero $f(0)=0$.

The curve appears to shift upwards due to change in its slope. The investment curve will have to go through the origin no matter what it's $s$ changes the slope of the investment curve. For example, if $s\_1=0.5$ and $f(k)=k$ the investment curve will be: $0.5k$. If we change $s$ to $s\_2=0.7$ investment curve would be now $0.7k$. This would work for any investment curve that goes through the origin and by our assumption it has to (you can try to verify this for $f(k) = \sqrt{k}$ or other valid functions.

**Non Mathematical Explanation:**

The investment function is by definition the **proportion** of output that is being saved (and hence invested). Here $s$ is the proportionality constant that determines what proportion of output is invested. Increasing that proportionality constant has to change the slope of investment function as now at any level income higher proportion of income is invested. For example, with $s\_1=0.5$ if $Y=100$ the investment will be $50$, with $Y=200$, the investment will be $100$ etc. Now if you change that proportion not only the investment will be higher at any income but also rate of change of that investment will be higher. With $s\_2=0.7$ at income $Y=100$, investment will be $I=70$, at $Y=200$ investment will be $I=140$.

> **Comments:**
> **username_0**: Thanks. What I don't understand is that if the returns on capital for any capital per worker  ratio hasn't changed then why does the rate of change in investment change?  
> **username_1**: @user3280937 but higher saving changes the capital per worker ratio $K/L$. However, it does change the level of $K/L$ instead of growth rate of $K/L$. This is by the way addressed in my previous answer to your other question at the bottom.  

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