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buying and selling, or borrowing and lending, must « clear the market. » Of the other three determining conditions the most important is that the rate of interest must be equal not only to the marginal rates of impatience but also to the « marginal rates of return on sacrifice ». This, though a fundamental and distinctive feature in my theory of interest cannot adequately be presented in this short sketch. It is fully elaborated in the « Rate of Interest». It is there shown that this principle — that rates of return on sacrifice harmonize with the rate of interest — may also be stated in the following form: of all the optional uses to which a man may put his capital he will choose that one which at the market rate of interest maximizes the present value of his capital — the discounted value of the uses chosen.
The remaining two conditions are the very obvious ones; (1) that what is borrowed at any time by some persons, equals what is loaned at that time by other persons and (2) that what any person borrows at one time must be repaid by that person at another time with interest at the market rate.
These six determining conditions are all essential. If any one of them is omitted we shall find ourselves trying to determine the unknown quantity, the rate of interest, by means of other unknown quantities — rates of impatience, rates of return on sacrifice, amount of loans and incomes — without providing adequate means for determining these other unknown quantities also. This is the difficulty with most theories of interest, the attempt to explain ignotum per ignotius. There is no objection to explaining one unknown in terms of others provided only we furnish enough determining conditions for all. It is a fundamental law of algebra that in order to determine fully each one of the unknowns we must have an exactly equal number of independent equations. As is shown in « The Rate of Interest », the six sets of determining conditions above mentioned provide exactly the number of equations needful to determine all the unknown quantities involved in them including the rate of interest itself.
We have now completed our study of the causes determining the rate of interest. If they are correct, we should find that the rate of interest is low (1) if in general the people are by nature thrifty, far-sighted, self-controlled, and love their children, or (2) if they have large or descending income