A Change in the Population Growth Rate

We consider the effect of an increase in the population growth rate:

The line representing population growth and depreciation shifts upward. The new steady state has a lower level of capital per worker than the initial steady state. Thus, the model predicts that economies with higher levels of population growth will have lower levels of capital per worker and therefore lower incomes.

Population growth also affects the Golden Rule level of capital. Because steady state investment is $(\delta + n) k^*$, we can express steady state consumption as:

$c^* = f(k^*) - (\delta + n) k^*$

Using an argument largely the same as before, the Golden Rule steady state is one at which the following condition is satisfied:

$MPK = \delta + n$