The creation and accumulation of capital depends on the ability of
a nation to give up current consumption of Final Goods (goods used for
direct consumption) to make resources available for the accumulation
of this capital. Deferring consumption (known as savings)
depends on the ability of that nation to first meet the basic needs
of its citizens with existing production technology and resource availability.
A country that exists on the frontier of subsistence could make resources
available for the creation of capital only at the expense of feeding
a given proportion of its population. In this case, capital accumulation
comes with the price of starvation.
In every economy, a tradeoff always exists between using resources
for the production of Intermediate (capital)
Goods or Final (consumption)
Goods although the consequences of this tradeoff may differ among nations. This
trade-off is modeled in the diagram to the left (use your mouse to drag on
the "Allocation of Resources" button)
One way to understand the relationship between current production, savings
activity and the accumulation of capital is
via the Solow Growth model
which defines the conditions for the tendency of different nations to approach an
equilibrium (steady-state) level of the capital stock.
We begin by using an economy-wide production function in
Cobb-Douglas form with constant returns to scale:
Y* = f(L,K) = ALαK
As a first step, we modify this expression to put it
into a form that represents the standard of living
(simply the ratio of output to labor input):
y* = Y*/L = f(1,K/L) = A(K/L)1-α
The term 'k' represents the
capital/labor ratio better understood as the amount of
capital available per unit of labor input. We would
expect that greater amounts of capital per labor-unit would make that labor
more productive and thus raise the living standards within a particular nation.
Capital is unique in that over time it wears out. This factor input is
subject to the effects of friction, obsolescence and climate such that
at some future date it ceases to make a useful contribution to the production
process. This is known as depreciation. The reciprocal of the life-span
of a unit of capital is then defined as the rate
of depreciation 'δ'. The
implication of this is that without replacement (via investment expenditure)
the capital-labor ratio would naturally decline over time. In order
to maintain this ratio, the required level of investment 'Irequired'
(a flow variable) must be equal to the depreciation in the capital stock:
Irequired = δK
It must be noted that with greater amounts of capital
greater levels of investment are required to maintain a
particular capital-labor ratio (i.e., the more capital that exists, the more capital
there is to wear out in a given time period).
With growth in the size of the labor force (due to
population growth and increasing labor-force
participation rates), additional investment is also
necessary to maintain the capital-labor ratio (K/L) at a
particular level. Thus, the level of investment must
exceed rate of depreciation by an amount equal to the
growth-rate 'n' in the labor-force:
or if we divide both sides by 'L'
Irequired = (n + δ)K
= (n + δ)k
Investment is possible only if a
given country makes resources available for this
accumulation of capital. These resources, known as
savings, represent those goods produced in the current
time period not devoted to final private or public
consumption. In a closed economy, we could write the
Savings: S = Y* - C - G
S = sY*
where 's' represents the proportion of
output not devoted to private consumption 'C' or public (Government)
consumption 'G'. With efficient financial and capital markets, these
savings could then be made available for investment in new capital:
Savings = Irequired
or in per-capita terms:
A "steady-state" level of capital is defined as the above equality and is modeled
by the intersection of 'sy*' (per-capita savings as a proportion of
per-capita income) and '(d+n)k' in the diagram below:
sy* = (n+δ)k
According to this model, an increase in the rate of savings
leads to growth in the capital stock and therefore a higher
Standard of Living.
Reductions in population growth rates 'n' may accomplish the same result.
It is important to note that even though an economy may be in a "steady-state"
condition, this does not imply that there is no growth in factor inputs or output. If
k is constant, this implies that the %ΔK =
%ΔL. In addition, given that y* is also constant in the
steady state, %ΔY* = %ΔL. Thus we
If we observe an economy with a growth rate that exceeds the rate of population
growth, we can conclude that this economy is currently below its steady state level
of capital per unit or labor or to exogenous changes in technology (i.e.,
the %ΔAt > 0).