OBJECTIONS CONSIDERED

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Under the hypothetical conditions so assumed, time pref-erence would cause interest without help from any rate ofreturn over cost. But such assumed conditions never door can exist in the real world.

Of course a constant rigid physical productivity, yield-ing unchanging physical income streams, is contrary tothe observed facts of life, just as unchanging time prefer-ence for each individual at all times and under all condi-tions is an absurdity. In real life men have the oppor-tunity of choosing among many optional income streams. fWhen such opportunities exist, time preference alonedoes not and cannot explain the emergence of interest. Asa mathematical problem, the rate of interest would underthe conditions of the second or third approximations beindeterminate without introducing the influence of the , / .

opportunity (or productivity! factor . 24 ’ i

( r <t Productivity, that is, the possibility of increasing the a, 1

jU'uJkji present value of the income stream, introduces newvariables which have to be determined as a part of theinterest problem and every new variable requires a newequation or condition.

It happens that, for lack of applying this mathematicalprinciple, writers have often thought themselves ingreater disagreement on the explanation of interest thanthey really were. Wordy warfare has been waged amongthe various productivity theorists and the capitalization

M As is always possible in solving simultaneous equations we can, if wewish, express certain of the variables, such as those relating to produc-tivity, or opportunity, namely the rates of return over cost, in terms ofthe other variables and thus seem to eliminate them. In my first bookI tried, for the most part, thus to present the rate of return over cost,or as I then called it, the rate of return on sacrifice as determinedthrough the rate of preference. But we can just as well in like mannereliminate time preference and present it in terms of rate of return.

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