Solow model and a change in the savings rate

Question

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

Answer 1

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 $I=140$.