Investment sf(k)s f(k) causes the capital stock to rise, whilst depreciation δk\delta k causes the capital stock to fall. Hence we can express the aggregate impact of theses two forces on the capital stock as the difference between investment and depreciation:

Δk=sf(k)δk\Delta k = s f(k) - \delta k

At the current depreciation and saving rate, we are adding 0.55 units of capital through investment, whilst 0.25 units vanish through depreciation. Hence, there is an overall change in the capital stock of 0.22. We can explore how the saving rate affects the change in the capital stock:

ss

0.55
01

For a sufficiently high savings rate, more capital is added through investment than what is lost through depreciation, leading to an increase in the capital stock.

For a sufficiently low savings rate, the level of investment is not sufficient to cover capital depreciation, leading to a fall in the capital stock.


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