Output per worker yy is divided between consumption per worker cc and investment per worker ii:

y=c+iy = c + i

We ignore government purchases and net exports (as we assume a closed economy). Every year, people save a fraction ss of their income yy and consume a fraction 1s1 - s. We hence have the following per worker consumption function:

c=(1s)f(k)c = (1-s)f(k)

where ss, the saving rate, is between zero and one. Similarly, we have the per worker investment function:

i=sf(k)i = sf(k)

This equation states that investment equals saving and thus, the rate of saving ss is also the fraction of output devoted to investment to form new captial. For any given kk, the production function y=f(k)y = f(k) determines output per worker, and the savings rate ss determines the allocation of that output between consumption and investment:





At the current level of capital and savings rate, ouptut per worker is 1.00, of which 0.70 units are consumed and the remained 0.30 are saved and invested into the capital stock.

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