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

88 The Life-Cycle Hypothesis
long as the amount dD is not large in relation to the stock of capital (and the flow
of saving), the loss in the future stream of output will be adequately approximated
by r*(dD), where r* denotes the marginal productivity of capital. Now if
the government borrows in a competitive market, bidding against other seekers
of capital, then the (long-term) interest rate r at which it borrows will also be a
reasonable approximation to r*. Hence the annual interest charges r(dD) will also
be a good approximation to the true social yearly loss, or opportunity cost,
r(dD) 11 —provided we can also establish that the initial reduction in the stock of
capital will not be recouped as long as the debt is not repaid.
One can, however, think of many reasons why the interest bill might not even
provide a good measure of the true loss. To begin with, if the government operation
is of sizeable proportions it may significantly drive up interest rates, say
from r 0 to r 1 , since the reduction in private capital will tend to increase its marginal
product. In this case the interest on the debt will overstate the true burden,
which will lie somewhere between r 0 (dD) and r 1 (dD). More serious are the problems
arising from various kinds of imperfections in the commodities as well as
in the capital markets. In particular, the government may succeed in borrowing
at rates well below r* by forcing banks and other intermediaries to acquire and
hold bonds with yields below the market, or, as in war-time, by effectively eliminating
the competition of private borrowers. In the first-mentioned case, e.g., we
should add to the interest bill the lost income accruing to the bank depositors (or
at least to the bank’s stockholders). There is also the rather nasty problem that,
because of uncertainty, the rate of interest may not be a good measure of the productivity
of physical capital. To put it very roughly, r is at best a measure of return
net of a risk premium, and the actual return on capital is better thought of as a
random variable whose average value is, in general, rather higher than r. 12
Besides the relation of r to r* there is another problem that needs to be recognised.
In our discussion so far, and in our table, we have assumed that consumption,
and hence private saving, were unaffected because taxes were
unchanged. But once we recognise that the borrowing may increase the interest
rate, we must also recognise that it may, through this route, affect consumption
even with unchanged taxes. This problem might well be quickly dismissed under
the principle of “de minimis.” For, though economists may still argue as to
whether an increase in interest rates will increase or decrease saving, they generally
agree that the effect, if any, will be negligible. 13 But even if the rate of
saving were to rise from, say, S 0 to S 0 + e and the level of capital formation were
accordingly reduced only by dD - e, one could still argue that r*dD and not r*(dD
- e) is the relevant measure of the true loss to society. This is because, as suggested
by Bowen et al., 14 the income generated by the extra capital formation e
may be quite appropriately regarded as just necessary to offset the extra sacrifice
of current consumption undertaken by those who responded to the change in r.