Population and the Neoclassical Growth Model
|
Contents:
|
The Aggregate Production Function
Assuming a fixed stock of labor and other resources construct a total
product of capital curve (TPk) for the economy as a whole. It will rise
at a decreasing rate because the marginal product of capital (MPk) is positive
and decreasing as the capital stock (K) grows. The product of the capital
stock is the GDP (Y). |
 |
| |
|
The Savings Function
If we assume that the proportion of income saved (APS) is constant, the
savings function will be similar to the total product of capital function.
Thus the size of the capital stock (K) will determine both the level of
GDP (Y) and the level of Savings (S).
|
 |
| |
|
Per Worker Basis
These graphs can be put on a per worker basis by dividing the capital
stock (K), GDP (Y) and Savings (S) by the umber of workers (N).
The shapes of the curves will not change if we assume that there is constant
returns to scale. |
 |
| |
|
The Capital Requirements Curve
In order to maintain a constant capital-worker ratio (K/N), it is necessary
to replace depreciation and to equip new workers with the same amount of
capital per worker as the old workers. (This is called capital widening.)
The amount of new capital needed to maintain a constant capital-labor ratio
is shown by the red line. The slope of the red line is equal to the sum
of the population growth rate (n) and the depreciation rate (d). |
 |
| |
|
The Current Situation
At present all nations find themselves in a situation where the capital
stock per worker is below the equilibrium level. The result is that gross
savings exceeds the amount needed for depreciation and capital widening.
The net savings or net investment can go towards increasing the capital-labor
ratio. (That is called capital deepening.) |
 |
| |
|
The Steady State
The process of capital deepening will continue every year until at some
future time, all of gross savings goes to depreciation and capital widening.
At that point, there is no more capital deepening and the system is in equilibrium.
There will be no further growth in living standards. This is referred to
as a "Steady State". |
 |
| |
|
Time Path of Income Per-worker
As the economy moves toward a steady state level of capital per worker,
output per worker grows until it reaches its "Steady State" level.
After that, it remains constant. There are no further improvements in living
standards. |
 |
| |
|
A Lower Population Growth Rate
If the population grows more slowly, less saving and investment will
be required for capital widening, more will be available for capital deepening.
As a result the "Steady State" level of capital per worker will
be higher and the steady state level of output per worker will also be higher. |
 |
| |
|
The Effect of a Fall in the
Population Growth Rate
In the long run, the rate of growth of per worker income is zero, no
matter what the rate of population growth. But at lower rates of population
growth, the long run standard of living will be higher. A fall in the population
growth rate after a nation is in a "Steady State" would allow
living standards to begin growing again until it reached the new "steady
State". |
 |