THE THEORY OF INTEREST

above type. Since each such continuous equation is evi-dently made up of n constituent equations, there are inall n (m — 1) equations in the second set of equations.

§10. Market Principle A (m Equations)

The next set of equations, expressing Market Prin-ciple A, represents the clearing of the market. Theseequations are as follows:

Xi -f- x 2 ' :-f .... -f- = 0,

x/'+x/' x„" =o,

Zi (m) + x 2 (m> + X„ (m) = 0.

There are here m equations.

§11. Market Principle B (n Equations)

The equations for Market Principle B express theequivalence of loans and repayments, or, more generally,the fact that for each individual the present value of thetotal additions (amount borrowed, or lent) to his incomestream, algebraically considered, will equal zero. Thus,for Individual 1, the addition the first or present yearis Xi, the present value of which is also cc/, the additionthe second year is Xi', the present value of which is

1 i

The addition the third year is x"', the present value ofwhich is

(1 + i')(l -H")

This is obtained by two successive steps, namely, dis-counting Xi" one year by dividing it by 1 + i", thereby

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