Home > Macro, Solow Model > Why the saving rate is important

## Why the saving rate is important

The saving rate shows the proportion of national income which is saved, and therefore available in the form of loanable funds for firms to use for investment, which is what adds new capital stock to the economy and increases its productive capacity.

We saw here how the economy reaches a point of steady state, where the amount of investment just equals the amount of old capital that depreciated, so the capital stock (in per capita terms) stays constant:

At point labelled C on this diagram, the economy has reached steady state, and it cannot grow its output per worker past the level of yC as it is impossible to increase the amount of capital per worker beyond point C. Any increase in capital will just mean that next year there is more depreciation than investment, so the capital stock will slip back to the steady state level. You can express a relationship between steady state capital and steady state output algebraically like this: $k* = \frac{s}{(n +\delta)}y*$.

So this tells us that the economy has got stuck at steady-state. But there is a way of breaking out.

If you increase the saving rate, then it shifts the saving (or investment) function on the diagram upwards:

Here we have a new saving rate, which means there is a new investment function, the purple line. So the economy can move past the old capital per worker (k*) which was at point C and continue to grow until it reaches a new steady state k* at point D. This means that there will be a new output per worker (y*), which has gone up (not by much on the diagram, because the production function was diminishing quite sharply at this stage) from yC to yD.

However this will still mean we are at a new steady state, just at a higher level of k* and y*.

So the moral of the story is in this form of the Solow model, which does not include technological progress, an increase in the saving rate can get you to a higher steady state level of output per worker, but you will still reach a new steady state, and you will get stuck again.