276 ECONOMIC PRINCIPLES

special tax levies may be needed for purposes of non-recurring
 expenditure, and the distribution of the burden of such
levies may properly take accumulated wealth into consideration,
 as affording a measure for justice in its allocation.
Does the distribution of tax burdens in proportion to the
incomes of tax-payers realise equality of sacrifice? In one
point the general answer has been in the negative. The
poorest class of the community may, by such a sacrifice, be
made to seriously trench on the necessaries for efficiency, or
even for existence itself, while the rich sacrifice at most some
part of the funds which would have procured additional
luxuries, not reducing in any perceptible degree their
productive efficiency. Further, if the society have any such
institution as that of relief of the indigent poor from public
funds, to impose burdens by taxation may do little more
than create the need for assistance from such public funds,
so far as members of the poorest class are concerned. Other
questions of public policy, as well as considerations of
justice, therefore, require some modification of the rule of
proportionality of taxation to revenue. The minimum
necessaries for existence, if not for efficiency, should be
untouched by taxation. This modification gives the
practical test of equity in the form that the tax burden
ought to be proportional to revenue, but that, where
revenues are below a certain minimum, there should be
exemption from taxation. This rule, however, introduces
obvious inequity at the margin where exemption ends and
taxation begins. Moreover, if it be only an excess of
revenue over what suffices to provide for the necessaries of
life which indicates an ability to bear taxation, should not
that excess, rather than the whole revenue. be the measure
of the just tax burden?
The further suggestion has recently been made that, in
place of a single minimum of exempted revenue, there are,
properly speaking, corresponding amounts of revenue for
various grades of society. In the case of the smaller
incomes, the necessaries, the provision for which is the basis
of claim for, and the measure of, exemption from taxation,
are necessaries of physical existence almost exclusively : as