§13. How an Individual Adjusts his Income Position to the Market

Under these assumptions it is clear that Individual 1 will borrow $100 at precisely 10 per cent, and that Individual 2 will lend $100 at precisely 10 per cent, the market rate. Their individuality will find conscious play only in determining how far they will make use of the market. Let us now see how far beyond $100 each will borrow or lend at this fixed 10 per cent rate.

To do this we need merely compare Willingness lines with the Market line. Will Individual 1, who has shifted from P1 to M'1 along the 10 per cent Market line with a $100 loan, again shift from M'1 for an additional $100 loan, along this same 10 per cent Market line? He will do so only if he is still willing to pay more than the market rate.

Whether this is true can be tested by precisely the same process as before, namely by drawing from this new income position on the Market line a new Willingness line and ascertaining whether or not it is steeper than the Market line. And so, step by step, $100 by $100, as he shifts along the Market line, we can always test whether he will shift still further. Any individual has but one Willingness line, cutting through any one income position, but when he sets out from any P, he is going to shift along the Market line and, at each shift, he encounters a new Willingness line.

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On Chart 34 are represented a number of W lines which are assumed to depict Individual 1's varying degree of impatience at different income positions. A study of the chart will show how Individual 1, in income position P1, will borrow, because his degree of impatience exceeds 10 per cent, the market rate of interest. His borrowing will continue, of course, until his degree of impatience is Edition: current; Page: [255] reduced to 10 per cent, at which point he no longer secures a net gain from borrowing. This point is located at Q1 where the M line is tangent to Individual 1's W line through that point. There at last he reaches a position where the next $100 shift on the Market line is no longer less steep than his Willingness line but exactly as steep.

The same principles apply to Individual 2. The only differences are: first, that he shifts upward from P to his Q instead of downward—that is, he adds to next year's income at the expense of this year's income; and, secondly, that he acts in reference to a different family of Willingness lines entirely his own. Such a picture implies the utmost sensitiveness or fluidity of inducements and responses. There would be a continual readjustment of loans and borrowings, back and forth; practically every person would be either a borrower or a lender; the extent of his borrowings or loans would be very finely graduated, and constantly changing.

We have not yet pictured geometrically the whole problem of the rate of interest; but we have pictured the solution of the problem of how any one individual will adjust, under the ideal conditions assumed, his lending or borrowing to the market rate of interest. This simplified solution consists, we have seen, in finding Q at the point where the M line at a given rate of interest is tangent to one of the given family of W lines.

Having solved this individual problem, we now proceed to the market problem.