§8. Impatience Principle A (n(m - 1) Equations)

The equations expressing Impatience Principle A will now be in several groups, of which the first is:

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f1' = F1' (c1' + x1', c1'' + x1'',..., c1(m) + x1(m)),
f2' = F2' (c2' + x2', c2'' + x2'',..., c2(m) + x2(m)),
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fn' = Fn' (cn' + xn', cn'' + xn'',..., cn(m) + xn(m)).

These n equations express the rates of time preference of different individuals (f1' of Individual 1,f2' of Individual 2,... fn' of Individual n) for the first year's income compared with the next.

To express their preference for the second year's income compared with the next there will be another group of equations, namely:

f1'' = F1'' (c1'' + x1'', c1''' + x1''',..., c1(m) + x1(m)),
f2'' = F2'' (c2'' + x2'', c2''' + x2''',..., c2(m) + x2(m)),
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fn'' = Fn'' (cn'' + xn'', cn''' + xn''',..., cn(m) + xn(m)).

For the third year there will be still another group, formed by inserting the superscript ''' for '', and so on up to the year (m - 1), for the year (m - 1) is the last one which has any exchange relations with the next, since that next is the last year, or year m. There will therefore be (m - 1) groups each of n equations, like the above group, making in all n (m - 1) equations in the entire set.