Sec. 6] EARNINGS AND INCOME 239

ing. Yet even popular usage seldom or never deducts this
depreciation from the pension to obtain the “true” income;
 and the reason we instinctively include (as we
ought) the whole of such a pension in income, is that
the depreciation is not actually offset. In ordinary business,
 on the other hand, we are accustomed to deduct
depreciation, because this is usually offset by actual payments
 into a depreciation fund. Even in this case the
depreciation is not itself an expense; but there is a concomitant
 expense approximately equal to it, in the form of
payments into the depreciation fund. It thus makes all
the difference in the world whether the depreciation fund is
actually maintained, or merely reckoned. If a depreciation
 fund isactually maintained, the expense of maintaining
 it serves to reduce realized income so as to make it
coincide with earned income. In such a case, therefore, the
ideal earned income becomes realized in actual fact.
Assuming a fixed rate of interest, the depreciation fund
may be defined as a fund formed by accumulating that
part of income which must be turned back into capital in
order to maintain the value of capital at a fixed level. A
depreciation fund is thus made from annual contributions
equal to the excess of realized income above earned income.
 If, instead of an excess, there is a deficiency, the
contributions to the depreciation fund become negative,
that is, instead of a certain quantity of income being converted
 into capital, a certain quantity of capital must be
converted into income.
Geometrically, a depreciation fund is very simply represented.
 In Figure 7 let the income consist of the items
a, a, a’, a", av, ete. The capitalized value of this income
 stream is AB. The interest on AB is represented by

the height AC,so that the standard income would be

represented by a series of annual lines of the height of the

dotted line CD. The excess of the lines a, @’, a’, etc.,
above the dotted line CD therefore represents the contri-