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

94 The Life-Cycle Hypothesis
will be smaller relative to its income, and hence its rate of saving will be larger,
or its rate of dissaving smaller, than it would have been in the absence of the tax.
On the other hand, over the same interval, the income consumption and saving
of households who have entered the scene after t 1 will be basically unaffected by
the operation. Hence, in the L years following t 1 there will arise some positive
saving which will gradually die down as the taxed generation disappears. The
precise path of aggregate saving will depend on the way the taxed generation
chooses to distribute the reduction of consumption over its life. But, in any event,
the cumulated net saving over the entire interval t 1 to t 1 + L must come to precisely
s(dG), representing the required reduction of consumption relative to
income of the taxed generation. 24 This cumulated saving is just sufficient to make
up for the initial fall in the stock of s(dG), so that by t 1 + L the stock of capital
(as well as W) has returned to the original level, as shown in figure 3.2 (b), and
we are back in the original stationary state.
The above framework can be readily applied to analyse the effects of deficit
or surplus generated under different conditions, e.g., by varying taxes, expenditure
constant. Figure 3.1 (c), for instance, depicts the outcome of an increase in
taxes in the interval t 0 to t 1 , utilised to retire the debt D outstanding at t 0 . Here
again the entire burden of the retirement falls on the taxed generation—although
it is spread between t 0 and t 1 + L—and the gain accrues to those living after t 1 in
the form of an increase in the stock of capital by an amount which eventually
approaches the amount of debt retired and reflects the elimination of the wedge
between W and K.
It is also easy to verify that our results remain valid for a growing economy,
the only difference being that the dashed line AA would turn into an upwardsloping
curve. With debt financing the graph of K would, from t 1 on, run at a distance
dG below this line, while with tax financing the graph of K = W would
initially fall below it by s(dG), but would tend to return to it at t 1 + L.
In summary, then, under unit oac the cost of an expenditure financed by debt,
whether internal or external, tends to fall entirely on those living beyond the time
of expenditure, as asserted by the classical-burden position, though it is best measured
by r*dD rather than by the incremental tax bill rdD. This burden may be
eliminated at a later date by retiring the debt through a budget surplus, but thereby
the full cost of the original expenditure is shifted to the later tax-payer, who
financed the surplus. On the other hand, the cost of a tax-financed expenditure
will tend to be borne by society as a whole, partly at the time and partly for some
finite period thereafter. But the burden beyond t 1 still falls primarily on those who
initially paid the tax and reflects the spreading of the burden over their lifetime. 25
In the analysis so far we have concentrated on examining who bears the cost
of the expenditure. To complete the picture we must, of course, also reckon the