Box 1. An algebraic approach to Harrod-Domar Model.
Savings (S) is a (s) proportion of national
income (Y): S = sY.
s can be seen as the Average Propensity to Save
(APS) also called savings ratio when expressed as S/Y.
Investment (I) is the change in capital stocks
(ΔK): I = ΔK.
Let k represents capital-output ratio: k = K/Y.
In the original Harrod-Domar Model, both Average
Propensity to Save (s) and capital-output ratio (k) are held
constant, that is they are determined by the structural of the
economy which does not change in the short run. Thus, we will
also assume that both s and k are constant.
If k is constant then ΔK/ΔY is
also constant, and more precisely k = ΔK/ΔY.
Thus, I = ΔK becomes I = k ΔY.
And for simplicity sake, let us assume that it is a close economy
and when equilibrium level of national income is achieved:
S = I
sY = k ΔY. (by replacing I with k ΔY)
s/k = ΔY/ Y (rearranging from above) or
ΔY/Y = s/k
that is the rate of economic (national income) growth is the
savings ratio (S/Y) over capital-output ratio (K/Y).
More growth if the economy
has higher saving rate or lower capital-output ratio, that is a
unit of output can be produced with less amount of capital. The
latter can be achieved by improvement in production technology.