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

Long-Run Implications of Alternative Fiscal Policies 93
on aggregate private net worth W, and on the net stock of privately owned capital
K. The horizontal dashed line AA represents the behaviour of net worth in the
absence of dG. It is constant by our assumption of a stationary economy, implying
zero net saving, or gross saving and gross investment just sufficient to offset
the wear and tear of the capital stock. If we make the further convenient assumption
that there is initially no government debt (and ignore non-reproducible tangible
wealth), then W coincides also with K. The incremental expenditure dG is
supposed to occur in the interval t 0 to t 1 at the constant rate dG/(t 1 - t 0 ), and is
financed by tapping a portion of the gross saving otherwise devoted to capital
maintenance. As a result, between t 0 and t 1 K falls, as shown by the solid curve.
But the net worth W remains at the same initial level as the fall in K is offset in
the consumers’ balance sheet by the government debt of dG. By t 1 the gap
between W and K amounts to precisely dG, and thereafter the curves remain
unchanged until and unless some further disturbance occurs. The final outcome
is that the debt-financed expenditure, by generating a permanent wedge dG = dD
between W and K, 21 causes the entire cost of the expenditure to be borne by those
living beyond t 1 in the form of a reduction in the stock of private capital by dG
and in disposable income by r* (dG). 22 If, in addition, r* = r, then before-tax
income will be unaffected and the fall in disposable income will equal the tax
collected to pay the interest, as claimed by the classical-burden doctrine. 23
Consider now the effect of full tax financing of dG, illustrated in figure 3.1 (b).
The line AA has the same meaning as before. The impact effect of the tax-financed
expenditure—i.e., the effect within the interval t 0 t 1 —is to reduce consumption by
cdG and saving and private capital formation by sdG. Hence, as shown by the
solid line, by t 1 both W and K have fallen by sdG. As we had already concluded,
this fall in K partly shifts the effect of the expenditure to those living beyond t 1 .
However, by following up the delayed effect of the tax, we can now show that
in this case: (a) the shift of the burden is only temporary, as W, and hence K, will
tend to return gradually to the original pre-expenditure level, and (b) the burden
transferred to the period following t 1 is borne, at least to a first approximation,
entirely by those who were taxed between t 0 and t 1 .
To establish this result we need only observe that since those taxed have suffered
a loss of over-life (disposable) income amounting to dG as a result of the
tax, they must make a commensurate reduction in over-life consumption. If the
consumption is cut initially only by c(dG) the balance of the tax, or s(dG), is
financed out of a reduction in accumulation—including possibly borrowing from
other households—which at first reduces the net worth at time t 1 by s(dG), but
eventually must be matched by a corresponding reduction of consumption over
the balance of the life span. Let L denote the length of time until the taxed generations
die out. In the interval t 1 to t 1 + L, then, the consumption of this group