The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 102659555X

URN:: urn:nbn:de:zbw-retromon-82920

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541

Title:: The nature of capital and income

Place of publication:: New York

Publisher:: The Macmillan Company

Year of publication:: 1923

Scope:: XXI, 427 Seiten

Digitisation:: 2019

Collection:: Economics Books

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386 NATURE OF CAPITAL AND INCOME the composition of forces or motions is very evident. Availing ourselves of this analogy, we may say that in the case of dis- continuous income, the point O traces the capital curve (back- ward) by obeying alternately two tendencies, — one, to follow the discount curve at times when no income occurs, and the other, to rise vertically whenever income occurs. In the case of continuous income these motions occur simultaneously instead of alternately, and the resultant is a smooth curve instead of a series of teeth. The same principles apply when part of the income curve is below the horizontal axis, representing negative income. If Fic. 45. at the beginning the prospective cost just counterbalances the prospective income, the capital-value will at that instant be zero, and will from that point rise and fall again to zero at the end, as indicated in Figure 44. The formula for capital-value in the case of a continuous income stream will be,— da =Ja+wy in which da may be said to represent the infinitesimal income which flows in the infinitesimal increment of time df. In other words, da represents an infinitesimal element of the area ABC (Fig. 45), of which element the base or breadth represents the in- finitesimal time dt. For the purpose of integration we may sub- stitute for da the expression f(f)dt, where f (f) represents CB, or the ordinate of the income stream taken as a function of time 2. If the special form of the function f (¢) is known, it is evidently possible to integrate the expression and obtain its value for any given limits,

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