§11. Market Principle B (n Equations)

The equations for Market Principle B express the equivalence of loans and repayments, or, more generally, the fact that for each individual the present value of the total additions (amount borrowed, or lent) to his income stream, algebraically considered, will equal zero. Thus, for Individual 1, the addition the first or present year is x1', the present value of which is also x1', the addition the second year is x1'', the present value of which is

The addition the third year is x1''', the present value of which is

This is obtained by two successive steps, namely, discounting x1''' one year by dividing it by 1 + i'', thereby Edition: current; Page: [297] obtaining its value not in the present or first year but in the second year, and then discounting this value so obtained by dividing it in turn by 1 + i1''. The next item xIV is converted into present value, through three such successive steps, and so on. Adding together all the present values we obtain as resulting equations for Individuals 1,2,... n:

Similar equations will hold for each of the other individuals, namely:

making in all n equations.