esi

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3

304 NATURE OF CAPITAL AND INCOME [Cuar. XVII

curves; so that the total capital-value at the time C is
represented by the altitude BC.
But this separate representation for capital and for income
 respectively need not be adhered to, because the
capital curve AB alone contains in its vertical teeth all
that is necessary to indicate the installments of income; and
in the present chapter the main propositions relating to

a al a' a

 

 

 

C A
Fie. 13.
capital and income will be restated with the aid of geometrical
 representations of which this capital curve AB
is the type.
§2
First of all, such a curve exhibits the fact that the value
of any capital is the discounted value of the expected income.
 In Figure 14 the several discount curves used in
previous diagrams are all continued to meet CB. The
parts into which CB is thus divided, b, b', b”, b""', will
represent respectively the present values of the income
items a, a’, o//, a'"’. This may readily be proved from
the nature of the discount curves.