Consumption and Investment

Output per worker $y$ is divided between consumption per worker $c$ and investment per worker $i$:

$y = c + i$

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

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

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

$i = sf(k)$

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