The nature of capital and income

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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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APPENDIX TO CHAPTER XIII 383 tant from the present instant by the intervals #, ,, #;, ete., which may be equal or unequal, whole or fractional, or even positive or negative according as the income is in the future or in the past. Let 7 represent the rate of interest. The present value of such an income stream will be,— i a ay ag P= A+)" = (1+) =+ (A+) +5 ete. Or, in briefer notation, a V=2 Thi where 3 is taken in its usual sense of the summation of the series of terms of the type of that following it. §12 (ro Cm. XIII, § 8) Diagram and Formula for deriving Capital-value from a given Continuous Income Stream For any ineome stream flowing continuously, and represented in Figure 43 by the area below MN, the capital-value will be represented by the curve NO. The ordinate of the income stream at any point, as RS, represents the rate of its flow at that point, and any area, as RSS" R", represents its total flow through the period RR". The ordinates of the curve NO will repre- sent the capital-value of this income stream. NO is con- structed from N backward as follows: the curve begins at N on the income stream and is generated by a point moving in such a manner that at any position O its direction of motion is the resultant of two tendencies. To represent these two tendencies we draw through O the discount curve OP. Tangent to this curve we draw OH so as to meet the line QH drawn vertically and distant to the left one unit from OA. OH represents one of the two tendencies mentioned, that due to discounting the future. OK drawn vertically up from and equal to RS, the rate of income at that time, represents the other tendency. The resultant, OQ, drawn according to the principle of the parallelogram of forces, will represent the actual direction in which the curve will be moving at the point O. In other words, a point moving under the influ- ence of two forces, OK and OH, will generate the required curve NO.

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