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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APPENDIX TO CHAPTER XVI 403 of his income. Such a system would secure justice in the taxa- tion of income. It is practically what has usually been called the system of taxing « consumption,” APPENDIX TO CHAPTER XVI § 1 (ro Cr. XVI, § 6) Mathematical Coefficients of Probability, Caution, and Risk Let us call the riskless value V, the mathematical value Vv, the commercial value V", the coefficient of probability P, the coefficient of caution C, and the entire coefficient of risk R. “We have, — Cal EL ral V 4 2) Whence it follows that BR = PC. That is, the total effect of risk on value is twofold: first, through mere probability, which gives mathematical value; and secondly, through caution, which gives commercial value. Practically, it'is usually impossible to separate P and C. The object of this analysis is not so much to introduce the caution factor explicitly, as to make the general distinction between R and P, and to point out that the actual market value of secu- rities is not their actuarial or simple “ mathematical ” value; that, in other words, R is not the same thing as P. § 2 (ro Cu. XVI, § 7) Formula for Mathematical Value of Risky Bond Let us denote by p, the probability of receiving the first installment, a,, of income due in one year, and by p. the prob- ability of receiving the second installment of income, yy pro- vided the first year’s is received, and again by p, the probability of receiving a, in three years, provided the previous two have been received, and so on for p, . . . p,, where n is the number of years to the last payment. The chance of receiving the first Payment is p,; hence the “mathematical value” of the first payment, when due, is a;p,, the present value of which is a. But the chance of receiving the second payment is +3 —————— i ee... TR A LU Sas EE ne

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