Comparing Steady States

Let's assume that a policymaker can choose the economy's saving rate. By doing so, the policymaker determines the steady state level of capital and output. Hence, we must ask which steady state the policymaker must choose to maximise the well-being of people in the economy.

People only care about the amount of goods and services they consume and are indifferent about the amount of capital or output in the economy. Thus, the policymaker would want to choose the steady state $k^*$ that maximises the steady state level of consumption $c^*$. We obtain an expression for $c^*$ by writing consumption as output minus investment:

$c = y - i$

Because we want to find steady-state consumption, we substitute steady-state values for output and investment. In the steady state, output is $f(k^{*})$ and since the capital stock is fixed, investment equals depreciation $δ k^*$. Plugging in these values, we can express steady state consumption as:

$c^* = f(k^{*}) - δ k^*$

Steady state consumption is what is left of output after paying for depreciation, and can be seen graphically as the gap between output and depreciation. As a benevolent policymaker would, we can select $k^*$ to maximise $c^*$:

At the current steady state level of capital, consumption per worker is 0.800. We can maximise $c^*$ by setting $k^*$ to 1.43, in which case steady state consumption is equal to 0.860.

Thus, a higher steady state level of capital and output is not always a good thing. There is an optimal level of capital accumulation and production from the standpoint of economic well-being.