"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

The “Life-Cycle” Hypothesis of Saving 69
C
C
h – n
(C = Y )
h – r
a 3 S o
¢ ¢ (Y 1 , C 1 )
a 3 A o–1
(Y o , C o )
¢ Y 1
(Y 1 , C 1 )
C 1 (C = aY + a 3 A o )
Y 0 ¢
Y 1
Y
C o (C = aY + a 3 A o–1 )
Figure 2.2
Consumption income relations: long-run and short-run
Needless to say, these calculations are very crude and are given here primarily
to bring out certain interesting testable implications of the consumption function
discussed in this paper. Among these implications the long-run stability of
the ratio of net worth to income is particularly significant, for it paves the way
for an explanation of the historical stability of the capital-output ratio in terms of
the supply of capital, thereby challenging the prevailing notion that the behavior
of this ratio is explained by technological requirements [1] [2] [5] [29].
As for the cyclical implications of our model, we need only observe that at any
given point in time net worth A t-1 is a given initial condition. Hence, retaining
for the moment the assumption that Y e Y, (2.6) implies that the aggregate consumption
function for any given year is a straight line in the C-Y plane with slope
a and intercept a 3 A t-1 . It is shown in figure 2.2 for the year 0 as the line labeled
C¯ 0, and looks like the orthodox Keynesian version. Yet, it differs from the latter
in one essential respect, namely, that its intercept will change in time as a result
of the accumulation (or decumulation) of wealth through saving. As we have
shown in preceding paragraphs, so long as income keeps rising on its exponential
trend, the growth in net worth will shift the function in such a way that the
observed consumption-income points will trace out the long-run consumption
function (2.19) represented in our graph by the line C¯ through the origin. This
point is illustrated in figure 2.2 for two years, 0 and 1. However, suppose that a
cyclical disturbance caused income to fall short of Y 1 , say to the level Y¢ 1 . Then