THE THEORY OF INTEREST

U = F/ (c/ + x/, c/':+' x x ", ...., c x (m >x^),

U = F 2 ' (C/ + X 2 ', Ca " + X 2 ", . . . C 2 (m) 4- Xa^),

/»' = F n ' (c/ + x„', c„" 4- x„", ..... c n (m) +, x n (m) ).

These n. equations express the rates of time preferenceof different individuals (// of Individual 1, // of Indi-vidual 2, .... /,/ of Individual n) for the first year’s in-come compared with the next.

To express their preference for the second year’s in-come compared with the next there will be another groupof equations, namely:

W = F x " (c x " + x x " cr + x/", ..... c x « 4- X x (m) ),

U" = Fa" (Ca " + X 2 " C 2 '" + x/", ..... C 2 (m) '4- X 2 (m) ),

in' = F (c„" 4- X„" C n '" 4- X n "

Cn cm) ^<-0).

For the t/w'rd year there will be still another group,formed by inserting the superscript '" for ", and so onup to the year (m — 1), for the year (to — 1) is the lastone which has any exchange relations with the next,since that next is the last year, or year to. There willtherefore be (to — 1) groups each of n equations, like theabove group, making in all n (to — 1) equations in theentire set.

§9. Impatience Principle B (n(m — 1) Equations )

To express algebraically Impatience Principle B 6 weare compelled to recognize for each year a separate rate

'This principle here expressed in “marginal” terms has been alterna-tively stated in words in Chapter V and in geometric terms in Chapter

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