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

Utility Analysis and the Consumption Function 39
which does not necessarily involve a constant planned rate of consumption over time. Finally this
conclusion also remains valid if we recognize the existence of a typical life pattern of income and
redefine a stationary household as one who expects its income not to be constant over time but rather
to follow the normal life pattern, and whose expectations are continuously fulfilled in the sense stated
in part (b) of the original definition in the text. Just what effects these two relaxations would have on
the relation between the proportion of income saved and age depends, of course, on the specific shape
of the pattern of allocation of resources to consumption over the life cycle and on the shape of the
life pattern of income. Note, however, that since the line of relation between saving and income for
each age group is supposed, in any event, to go through the origin, even if we fail to stratify by age,
the regression of consumption on income should tend to be linear (though not homoscedastic) and a
regression line fitted to the data should tend to go approximately through the origin.
e
e
dy
24. As we have seen, under the assumption y = y
Ê
and therefore = 1
ˆ
the individual marginal
Ë
propensity to consume is
dy ¯
N- t+1 ,
which reaches a maximum for t = 1, the maximum being
N
L .
25. Cf. M. Friedman and S. Kuznets, Income from Independent Professional Practice, pp. 325 ff.
26. Since the individual was in stationary equilibrium up to the end of period t - 1, we must have
a t = a(y t-1 , t) and, by assumption, y t-1 = y e t.
27. From the last equality in equation (II.2¢) and with y e t = y t-1 , we derive immediately
st
M NL ( - t)-M
yt
yt
= +
Ê -
y L LL Ë y
t
28. From equation (II.2¢), with y e t = y t-1 and since
( t-1)
M
at
= yt-1,
L
we derive,
st
M ( t-
) M yt
yt
= +
Ê -
y L LL Ë y
t
L t
1 -1
t
t
t
t
ˆ
.
¯
-1
ˆ
.
¯
It is easily verified that the right-hand side of this expression is necessarily smaller than the corresponding
expression given in the preceding note.
29. This conclusion fails to hold only if the elasticity of expectations is substantially greater than
unity.
30. More precisely, unless there is a very strong correlation between the current change in income,
y - y -1 , on the one hand, and the difference between the previous “accustomed” level and the
previous year income, y e -1 - y -1 , on the other.
31. See, for instance, G. Katona and J. Fisher, “Postwar Changes in the Income of Identical
Consumer Units,” Studies in Income and Wealth, Vol. XIII, pp. 62–122; G. Katona, “Effect of Income
Changes on the Rate of Saving,” The Review of Economics and Statistics, May, 1949, pp. 95–103;
W. W. Cochrane, “Family Budgets—a Moving Picture,” loc. cit., Aug., 1947, pp. 189–198; R. P.
Mack, “The Direction of Change in Income and the Consumption Function,” loc. cit., Nov., 1948,
pp. 239–258.
32. Katona and Fisher, ibid., especially Section D, pp. 97–101; and G. Katona, ibid.