An Oversight in the Dominant Theory of Interest

Harry Gunnison Brown

[Reprinted from the American Journal of Economics and Sociology,
Vol. 21, No. 2 (April, 1962), pp. 203-207]

IN A RECENTLY PUBLISHED ARTICLE,[1] Professor Paul A. Samuelson expressed the belief that "Bohm and Fisher have given us the essential insights into the pure theory of interest."

Writing in Econometrica in 1948, the late Professor Joseph Schumpeter of Harvard University characterized Fisher's book on The Theory of Interest as "a wonderful performance, the peak of achievement, so far as perfection within its own frame is concerned, of the literature of interest." And Schumpeter went on to say of Fisher's study that it is "an almost complete theory of the capitalist process as a whole, with all the interdependences displayed that exist between the rate of interest and all the other elements of the economic system. And yet this interplay of innumerable factors is powerfully marshalled around two pillars of explanation: Impatience (time discount) and Investment Opportunity (marginal return over cost)."[2] Schumpeter adds, in a footnote, that "Keynes himself also accepted the time-discount factor, i.e., the whole of Fisher's theory."

On the basis of such comments as these, it is perhaps not unreasonable to conclude that Fisher's theory of interest is presently the dominant one.

Certainly Irving Fisher must be ranked among those who have contributed greatly to the theory of interest. And certainly he worked out more fully than Bohm-Bawerk had done, the explanation of how the preference for present income over future income affects the net (i.e., in excess of allowance for depreciation) marginal productivity of capital, and how the productivity of capital affects individual rates of preference for present income over future income.

Nevertheless, there is an aspect of Fisher's analysis which seems to me and has long seemed to me to be incorrect.

I

FISHER CORRECTLY CONCLUDES that a high per cent net productivity of capital -- in his phraseology, a high "rate of return over cost" -- will operate to produce a high rate of interest. He correctly concludes that this high productivity will tend to bring about a high rate of preference for present income over future, i.e., a high rate of "impatience." He insists, however, that the high net productivity of capital does not have a direct effect in raising the interest rate, but only an indirect effect. It raises the rate of interest only by or through raising men's rates of impatience"-- of preference for present income over future income.

In order that the reader may form his own judgment regarding the Fisher viewpoint, I shall quote several passages. In the first of these, discussing critically a passage in Bohm-Bawerk's Positive Theory of Capital, Fisher says[3] that "the only[4] way in which the existence of long processes of production acts on interest is by overendowing the future and under- endowing the present, thus creating a 'scarcity value' of present goods."

In a second passage,[5] commenting on the gains that may be secured from "a newly discovered method of exploiting capital," he says: "The effect in raising interest comes merely6 from the shifting forward of the income stream, which leaves the immediate income smaller than before, but compensates for this by a still greater increase afterwards."

In a third passage, replying to a reference by H. J. Davenport to equipment loans (loans to persons or corporations that are borrowing for the purpose of securing equipment -- capital instruments --to aid in production), Fisher contends that[7] such loans "are made for the purpose of securing large incomes in the future, and larger incomes mean larger consumption. Production loans then are made only in contemplation of future consumption. Hence, though loans for the acquisition of intermediate goods do greatly preponderate in the loan market, these loans have power to affect the interest rate only by[8] changing the relative amount of future incomes compared to present incomes."

If I have correctly interpreted these passages in Fisher, the views expressed can be stated in five propositions, as follows:

1. A high net marginal productivity of capital-"marginal rate of return over cost" -- encourages investment in capital in order to realize this gain.
2. Such investment in capital for the sake of larger future income involves sacrifice of present income.
3. This sacrifice of present income strengthens the desire for present income which has thus become scarce and weakens, relatively, the desire for future income which now promises to be larger --thereby raising the rate of preference for present income over future, the "rate of impatience."
4. Because of this higher "rate of impatience," the rate of interest rises.
5. The effect of the productivity of capital on interest is brought about only via these successive steps.

However much of truth there is in the passages I have quoted, they do not contain the whole truth. They leave out, in fact, an important part of the truth. A high marginal productivity of capital-a high "rate of return over cost" -- has a direct effect on the interest rate, apart from any indirect effect it produces on interest by first changing the rate of preference for present income over future.

II

LET US SUPPOSE the net marginal productivity of capital (the yield above depreciation) to be or to become 8 per cent a year. And let us use the simplest, the least complicated, illustration we can. John Deckleburg, a fisherman, is able to catch 1,000 fish a year, with which, as best he can, he provides for himself and his family. If he should be able to build a boat, he could thereafter catch enough more fish per year to cover depreciation of the boat (i.e., repay the cost of the boat during its life) and, in addition, get 80 more fish -- 8 per cent return above cost -- per year. He can build such a boat during a year-thus its cost of production is the 1,000 fish he could otherwise catch during the year -- if he can borrow 1,000 fish during the year to live on. For then he will not have to spend the year catching fish and can devote the year to building the boat. And because the boat will yield -- or earn -- 8 per cent on its cost of production, it will pay him to borrow at any interest rate below 8 per cent. It will pay him to borrow at 3 per cent, 5 per cent, 7 per cent or 7.9 per cent. The fact that there is an 8 per cent gain from using capital, i.e., from round-about production, makes him willing to offer interest to a lender. It gives him a motive to bid against other potential borrowers.

Does not this 8 per cent net marginal productivity -- an 8 per cent "rate of return over cost"-motivate him directly? Surely we have here a preference for more against less. And surely this preference for more rather than less does not arise because preference for present income over future has risen. The preference for more rather than less is an influence in its own right and can act directly. It is not an influence which can make itself felt only via first setting into motion the other influence of "impatience."

It is, in my opinion, correct and more realistic to recognize that our fisherman, John Deckleburg, could have his living from day to day without borrowing; that he does not borrow in order to be able to enjoy appreciably more fish-or other present income -- this week or this year; that, on the contrary, he borrows in order to be able to build the boat instead of having to spend his time catching present fish for present needs; that he borrows in order to be able to carry on roundabout production; that, in short, he borrows chiefly, if not solely, because he prefers more to less and not because he prefers present income to future income or earlier income to later income. This is the emphasis that the Fisher analysis- like the analysis of Bohm-Bawerk earlier[9] -- seems to lack.

It is the same if we consider the case of a potential lender. He also can be motivated directly by a preference for more as against less, just as certainly or as much as by a preference for present income over future income. Suppose that he is able to produce more than he and his family need to consume, and thus is able to save. Then this excess producing, and saving, can take the form of productive capital from which he can hope to enjoy a return. If he is unwilling to lend to another for 5 per cent or 7 per cent, this may be because, by using his savings himself in the form of productive capital, he believes he will be able to gain 8 per cent. In that case, the reason he does not appear on the supply side of the borrowing and lending market is clearly that he prefers more to less. His reason for not lending does not have to be that he prefers present income to future income by 8 per cent. It can well be that he is influenced far more by his opportunity to use his savings profitably himself than by any desire to enjoy more present income at the expense of having less future income.

Then how can it be said that the productivity -- or the anticipated productivity -- of capital affects his interest offer only by and through first making his present income comparatively small and thus increasing his preference for present income over future income?

A potential lender may be influenced by a preference for more as against less, or by a preference for present income as against future income, or by both. Preference for present income as against future may affect the amount of saving, thus the amount of capital and thereby the marginal productivity of capital. The productivity of capital may affect the amount of saving and may thereby affect the distribution of the saver's income between present and future and, hence, the degree of his preference for present goods. But that preference for more as against less can have no effect on the loan market and the interest rate except through its effect on preference for present income over future income is simply not true.

Yet Fisher's study presents so carefully and thoroughly the various interrelations involved in the matter of the interest rate, the "impatience" rate and the net marginal productivity of capital, that one is tempted to assume he realized clearly the direct effect of capital productivity on the interest rate. It is his insistence, in the passages quoted, that the net productivity of capital has only an indirect effect, and the thought that students of Fisher's analysis will-and presumably do-so interpret him and themselves accept this view, that are the justification for these comments. marginal productivity of capital. The productivity of capital may affect the amount of saving and may thereby affect the distribution of the saver's income between present and future and, hence, the degree of his prefer- ence for present goods. But that preference for more as against less can have no effect on the loan market and the interest rate except through its effect on preference for present income over future income is simply not true. Yet Fisher's study presents so carefully and thoroughly the various interrelations involved in the matter of the interest rate, the "impatience" rate and the net marginal productivity of capital, that one is tempted to assume he realized clearly the direct effect of capital productivity on the interest rate. It is his insistence, in the passages quoted, that the net productivity of capital has only an indirect effect, and the thought that students of Fisher's analysis will-and presumably do-so interpret him and them- selves accept this view, that are the justification for these comments.

FOOTNOTES AND REFERENCES

1. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, 66 (December, 1958), p. 467.
2. "Irving Fisher's Econometrics," Econometrica, 16 (July, 1948), pp. 225-6.
3. The Rate of Interest, New York, Macmillan, 1907, p. 72.
4. Italics are mine.
5. Ibid, p. 199.
6. Italics are mine.
7. The Theory of Interest, New York, Macmillan, 1930, pp. 433-54.
8. Italics are mine.
9. See my paper, "An Off-Line Switch in the Theory of Value and Distribution," Am. J. Econ. Sociol., Vol. 3, No. 4; also reprinted in Some Disturbing Inhibitions and Fallacies in Current Academic Economics, New York, Robert Schalkenbach Foundation, 1950, Chapter 4. See also my Basic Principles of Economics, 3rd ed., Columbia, Mo., Lucas Brothers, 1955, Chapter XIII, especially pp. 326-55. This chapter grew out of an article published in the Quarterly Journal of Economics, August, 1913, entitled "The Marginal Productivity versus the Impatience Theory of Interest."