THE THEORY OF INTEREST

pected income program but of many possible such pro-grams each with its own series of probabilities, and thoseprobabilities are too vague even to be specifically ex-pressed or even pictured by the person concerned. Thatis, the average person is merely aware that he is willing,say, to pay five per cent for a $1000 loan because hethinks his future prospects will justify it. He vaguelyexpects that his present $10,000 income will probably riseto $20,000 within a few years, possibly to $30,000—andpossibly not rise at all. He could think of innumerablepossibilities and these would imply many other variablesthan those above cited. Much might depend on the in-come of others besides himself and on the future size ofhis family, the state of their health, and other conditionswithout end. His own future income is the importantmatter, but that itself is dependent on all sorts of vari-ables on which he will reckon summarily in a rule ofthumb fashion.

We could, formally, rewrite for the third approximationthe above equation so as to read:

f = FO

merely refusing to attempt any enumeration of theinnumerable variables inside the parentheses—amongthem being, perhaps, all the variables included in all theequations in the second approximation, including ratesof interest as well as numberless other variables such asprobabilities not there included. In so far as the latter,or new, variables enter, each of them requires a newequation in order to make the problem determinate.Such new equations would be merely empirical. Amongthe equations which would be needed, would be thoseexpressing the y’s and x’s in terms of real income—that

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