Time-Preference and Productivity: A Reconsideration

[This article was originally published in Economica, February 1945.]

The question I wish here to reconsider is in the first instance the purely theoretical one of the relative importance, in determining the marginal productivity of investment, of the productivity  schedule on the one hand and the so-called time-preference factor on the other. It will be remembered that on the whole the ” Austrians “, that is Boehm-Bawerk and his followers like I. Fisher, F. A. Fetter, and particularly L. v. Mises, emphasised the ” time preference” factor, while Wicksell and F. H. Knight tended to stress almost exclusively the productivity factor. In my Pure Theory of Capital I sided with the latter group, largely persuaded by Professor Knight’s arguments. I believe now that in this I have been partly mistaken. Professor Knight’s argument, although it seems to me still to prove its point so long as we confine ourselves to the consideration of an evenly progressing economy, does not necessarily apply to one in which the capital structure is not in full equilibrium. Though I had thought that I had made every effort to escape the ” static” approach which has had such an unfortunate effect on the theory of capital, in this particular respect I seem still to have been misled by it-and that in spite of the fact that already earlier I had seen and described part of the phenomenon I am about to discuss.

While the problem would at first appear to possess only theoretical interest, it seems that the answer I am about to suggest may be of some importance for clearing up certain problems raised by the historical course of the rate of interest. The fact that over a long period the rate of interest has fluctuated above a fairly constant basic level gives a certain plausibility to the contention that these fluctuations are connected solely with the monetary factors affecting it and not determined by any similar fluctuations in the underlying real phenomena-except via the changes in the money income, through which the marginal productivity of investment is adjusted to changes in the rate of interest. In particular, the rise of the rate of interest towards the end of a boom would appear, on that view, as determined solely by monetary factors, while the violent fluctuations of the volume of investment, on the other hand, appear to have been taken as prima facie evidence of the rapidity with which the marginal productivity of investment is reduced by any spurt of investment activity. The investment demand curve was thus conceived as being fairly steep, and the fact that the rate of return on investments never fell below a fairly constant minimum was regarded, not as showing that the productivity curve was fairly flat, but as evidence that below that minimum people were unwilling to invest; or, to put the point differently, the reason why the rate of interest did not fall below that minimum was sought not on the side of the demand for investible funds, but among the factors determining the supply of such funds. If the theoretical point I am going to make is correct, it would appear that these phenomena are capable of a different interpretation.

Before I proceed to state the correction I shall briefly restate the argument in favour of the predominant influence of productivity. The best way is to regard the problem as a special case of the general rule we must apply in deciding whether in a particular situation the relative value of two commodities depends mainly on their relative utilities or on their relative costs. ” Time preference,” of course, in this connection is no more than an abbreviated and rather misleading way of describing the relative strength of the demands for present and future goods respectively. I call it rather misleading because the true ” time preference” of individuals is, of course, only one of the factors determining this demand position, the other being the size and distribution of individual incomes. But, for the purposes of a brief exposition of the principle, there is a certain advantage in talking in terms of a single individual and his ” time preference” rather than in terms of demand on a market. It enables us to use the simple combination of a family of indifference curves and a transformationc urve; and there is no difficulty in then applying the argument to a market economy.

In the following diagram the transformation curve TT’ represents the productivity of investment, i.e. the terms at which parts of the income of the present period (measured along the y-axis) can be converted into increments of income in all future periods (measured along the x-axis)-or the rate at which the supply of future goods can be increased at the expense of present goods. “Time preference” is shown by a family of indifference curves of which only one, the fully drawn curve II’, touching the transformation curve at the point P, is shown. The argument in favour of the predominant influence of productivity on the marginal productivity of investment rests on the probability that the indifference curve will be very much more curved than the transformation curve, and that in consequence, whatever happens to ” time preference “, the marginal productivity of investment is likely to adapt itself to the comparatively constant productivity.

This argument, more fully set out in The Pure Theory of Capital, appears to me to be correct so long as we consider merely movements downwards and to the right along the transformation curve, i.e. so long as we assume a continuous and gradual accumulation of capital at a rate which at least comes up to expectations.  But it does not apply to a movement in the opposite direction, i.e. to the case where the supply of capital decreases or (what for the present purposes comes to the same thing) falls short of the amount in the expectation of which previous investments have been made. In such a situation it must probably be assumed that for such a backward movement the transformation curve will have a strong ” kink” at the point P where we find ourselves at any moment, and that in consequence, so far as such a movement backward is concerned, the transformation curve will be much more curved than the indifference curves, and “time preference” will therefore become the decisive factor.

The argument which leads to this conclusion is really the same as that which I employed in the article already referred to. In terms of the above diagram it can be restated as follows: The productivity of investment shown by the slope of the transformation curve at the point P, at which we find ourselves at any moment, will always refer to the expected productivity when completed of the investments now in the process of construction. Or, in other words, it will be based on the assumption of a certain rate of investment continuing for some time in the future. Only investments in excess of those required to complete those already under way will bring us to a point on the transformation curve to the right and below P, while continued investments over a certain period and at a decreasing rate are required even
to keep us at the point P which had already been reached. Should investments fall below the amount required to carry on with the processes already commenced, this would shift us to a point above and to the left of P. But the position into which such an unexpected decline of the rate of investment would place us would not be the same as that in which we would find ourselves had we never expected investments to be larger than they now turn out to be. The expectation of a larger supply of investible funds (or of a lower rate of interest) has had the effect that the investments commenced have been given a form different from what would otherwise have been the case; and although the marginal percentage returns on the larger amount of capital which was expected to be invested would have been smaller than those on
investments requiring a smaller total amount, the fact that the former have already been commenced means that the whole return to be expected from them depends now on the further investments required to complete them, and can, if necessary, be attributed to those completing investments.  In other words, the existence of ” uncompleted investments” (i.e. investments which can be made to produce their full output of consumers’ goods only if further investments are made) creates a specially urgent demand for capital, and will tend to raise the marginal productivity of investment much above the level at which it would have been if the supply of capital had never been expected to be higher.

The point P in the diagram then stands for a position at which TB of the potential current income (which otherwise might have been permanently maintained at the magnitude TO) was being invested and further investments sufficient to complete those under way were expected to take place. The marginal productivity of investment, represented by the coincident slopes of the two curves at P, would be the expected productivity of the completed investments. Had investments never been expected to be at the rate of TB per period, but only at the rate of TA, we should instead be at point P’, where the slope of the transformation curve is little smaller than at P. But if, after we had already moved to P, the rate of investment were unexpectedly reduce to TA, we could not move back to P’ along the given transformation curve. The situation would have been altered by the investments already made in the expectation of larger future investments, and the capital actually available, instead of being sufficient to enable us to start further new investments
at a slightly lower rate of return,i s now not even sufficient to complete those already started. The transformation curve along which we could then alone move would be something like the dotted curve PT”. If the supply of capital fell to TA, the marginal productivity of investment would therefore rise to a figure indicated by the slope of the tangent at P”.

We cannot assume, however, that with such a change in the marginal productivity of investment the supply of capital will fall as much as it would have done if the marginal productivity had remained constant. Indeed, we are not entitled in this context to think of the supply of capital as a fixed magnitude but ought to represent the change in the willingness to save as a shift of the indifference curves. Let us assume, therefore, that what has happened is that the indifference curves have shifted so that instead of the fully drawn curve In the dotted curve I12′ is now tangential to the original transformation curve at the new point P’. But as we can move backwards only along PT”, the ” kink ” at P will mean that even after a very considerable shift in the position of the indifference curves, tangency between the new transformation curve and one of the indifference curves (I, If ) will still occur at the point P. In other words, within the limits determined by the angle of the transformation curve at the “‘kink “, the marginal productivity of investment will be determined exclusively by the slope of the indifferencec urve, or by ” time preference”; and even above P the transformation curve is likely to be so strongly curved that the indifference curve may be comparatively flatter and therefore determine the marginal productivity of investment.

The conclusion we must draw, therefore, would seem to be that so long as we consider solely an evenly progressing economy, the marginal productivity of investment will depend almost exclusively on the investment demand schedule with the supply of capital adapting itself to the newly constant rate of productivity. But as soon as this even progress is held up, and the supply of capital turns out to be less than had been expected, ” time preference” takes charge-or, since ” the fall in the supply of capital ” is merely another form in which we refer to a rise in ” time preference” , so long as time preference remains constant or falls, the productivity element will be dominant; but whenever” time preference” rises, it takes control and we may get as a result sudden and violent increases in the marginal productivity of investment, and, in consequence, of the rate of interest.

To translate all this from the language of ” time preference” and rates of transformation in to that of demand and supply of future consumers goods on a market presents no real difficulty, but would occupy more space than we can give to it at the present moment.