IN TERMS OF FORMULAS

sive years. These are to be applied to the original incomeitems (the y’s), deductions being included by assigningnegative numerical values. The income stream, as finallydetermined, will therefore be expressed by the successiveitems,

Vi + xS, yi " + * 1 ", V r + x/", ...., yi (m) +

§2. Impatience Principle A. ( n(m — 1) Equations )

Impatience Principle A states that the individual ratesof preference are functions of the income streams, andgives the following equations:

U = Fi (Vi' + */, yi " + x/', ..... Vi m) + * 1 (m) ),

U = F*' (y/ + x 2 ', y" + x 2 ", ...., y 2 (m) !+

U - F n ' {y: + x n ', y” + x", ...., y„ (m) + x B (m) ).

But these equations express the various individuals’rates of impatience only for the first year’s income com-pared with the next. (They are the slopes of the Will-ingness lines.) To express their impatience for thesecond year’s income compared with the third, there willbe another set of equations, namely:

/i" = F" ( yi " + x/', yr + x/",W — F " {y" + x 2 ", y”' + x 2 "',

y 1 (m, +x 1 «),

V2 im) +X2 (m) ),

fn" = F„" (y n " + x„", yr + xr, . , y n {m) +

For the third year, as compared with its successor,there would be another similar set, with in place of", and so on to the (m — 1) year as compared with thelast, or m year. Since each of these (m — 1) groups of

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