APPENDIX I. Time Preference and Productivity

On the first point there is now fairly general agreement among economists, and at any rate nothing has been said ~ere which is not already contained in the most modern exposition of the views of the Time Preference School, Professor Irving Fisher's Theory of Intere8t. On the second point also the difference between the preceding exposition and that given in the work just mentioned is probably but largely verbal. Since, however, the terms employed by Professor Irving Fisher, particularly the term "impatience", still carry with them some of the flavour of the earlier less defensible views, it 413 414 Appendix I is perhaps necessary to supplement what has already been said by a more explicit refutation of the confusions contained in the earlier· theories. On the third point, finally, the views expressed definitely diverge from those still commonly (t,hough not universally) held, and although all that is really essential is already contained in Chapters XVII and XVIII, a few further remarks on the general nature of the problem involved may not be out of place. The two sections which follow will accordingly be devoted to a more explicit discussion of the views defended here on the two latter points in comparison with other widely held views on these problems.

(1) The way in which Bohm-Bawerk formulated the prob lem of interest has gained considerable support. Particularly in the form in which Professor Schumpeter 1 has quite con sistently developed the Bohm-Bawerkian approach, it has led to the assertion that the existence of interest is incompatible with stationary conditions, a view which is now widely held. The whole approach, therefore, needs more explicit examina tion than was possible to give in Chapters XVII and XVIII. We shall try to demonstrate here that in the form in which Bohm-Bawerk put the central question it is meaningless and is merely one of those pseudo-problems which arose out of the idea of utility as an absolute magnitude. The starting point of the Bohm-Bawerkian analysis was the question why people did not avail themselves of the opportunity of increasing by investment the product obtain able from given resources to such a point that the utility of the future product would fall to a level corresponding to that of the alternative current product which might have been obtained from the same resources. This is what one would expect from the general rule that all resources will be distributed among their different uses in such a way that the marginal utility of a product of a unit of resources will be everywhere the same, and hence also equal to the (derived) marginal utility of the factors used. If one started from the idea that, unless ~astes change, the marginal utility in an absolute sense of equal quantities of commodities should be the same at different dates, the only possible explanation why people did not in fact act in accordance with this rule seemed 1 In particular his Theory of Economic Development, chap. i.

Time Preference and Productivity 415 to be that they did not attach this true utility to future pro ducts but attached a lower valuation to them which decreased in proportion with their time-distance from consumption. This would mean that people would stop investing for the future before the true future utility of the (greater) future product had fallen to the level of that of the (smaller) alter native present product. This would account for the existence of the "gap" between the utility of the factors and the utility of the product, which, according to Bohm-Bawerk, is the true source of interest. If, however, one denied, along with Professor Schumpeter, the existence of any such psychical discount, the same assump tions would necessarily lead to the conclusion that saving must continue so long as additional investments brought a greater produce than could be obtained from the use of the same resources for the current satisfaction of wants and that, in consequence, a stationary state could be reached only after interest had disappeared. At anyone moment, it is true, the amount which it would be advantageous to invest would be limited by the fact that the marginal utility of given additions to the output at any future moment would fall, and that, in consequence, even if the future product obtainable from fUrther doses of investment was greater in quantity than the alternative present output, it might have a smaller utility than the latter. But this would only limit the rate of saving, it would not alter the fact that some saving would continue so long as the physical return from any factor could be increased by investing it for a longer period. Only the complete exhaustion of all opportunities for increasing output from any factor in this way could put a stop to further saving. And since a stationary state implies the absence of new saving, such a state could exist only if the productivity of capital, and therefore interest, had disappeared.

It will be seen that this proposition is nothing more than the logical outcome of the assumptions originally made by Bohm-Bawerk, provided the initial assumption about the identical shape of the utility curves at successive moments is not subsequently modified by the introduction of psychical discount. This argument, as has already been pointed out, depends for its validity entirely on the older, absolute, concept of 416 Appendix I utility. It is therefore necessary to state more explicitly the difference between this older view and the modern view, and to indicate the special relevance of this difference to inter temporal comparisons. With the utility of a commodity conceived as an absolute magnitude, it was natural to define constant tastes as implying that at all successive moments the marginal utility of equal quantities of a commodity available at successive dates must be the same. It makes little difference for our purpose whether this assumption is stated in the simpler and even more objectionable form U z = f(x) , implying that the marginal utility of x depends on the quantity available of that com modity only, or whether it is stated in the slightly more meaningful form U z = f(x, y, z, " .), implying that the marginal utility of x depends on the quantities of all the commodities available. Whichever of these alternatives we adopt, the essential point remains the same. In either case it is assumed that the marginal utility of any commodity at a particular moment depends only on the quantities of commodities avail able at that moment, that it is independent of the quantities provided for other moments, and that this statement about the absolute utilities at different moments allows us to make deductions about the relative utility of quantities available at different moments. It does not matter whether the assump tion made is that the supply of all other commodities is constant, or whether this is treated as being irrelevant. The result is in either case that the utility of different quantities is regarded as adequately represented by independent utility curves which, if tastes are assumed to be constant, must be of identical shape. l It is no longer questionable that absolute utility functions have a definite meaning only in so far as they can be trans lated into a statement as to what quantities of the· com modities in question will have the same utility under the given conditions, or be perfect substitutes for each other.

The utility curve for any commodity would thus express the decreasing quantity of some other commodity (the total supply 1 In an attempt which I made a number of years ago to clear some of the difficulties connected with this approach, I myself used this approach without being aware of the illegitimate assumptions which it involves. (Cf. Hayek, 1927, pp. 517.532, especially p. 523.) Time Preferen.ce and Productivity 417 of which was assumed to be constant) which under otherwise unchanged conditions would just be equal to the utility of successive marginal additions to the supply of the first com modity. The meaning of the assumption that the two utility curves for the same commodity at two different moments will be identical, is slightly more complicated. It can, however, also be expressed in the form of a statement about the relative quantities of the commodities available at the two moments which will give the same utility. As a little reflection shows, this assumption must mean that if the total quantities of the commodity available at each of the two dates are the same, equal quantities will have the same value, and that if the total quantities available at the two moments are different, a small addition to the smaller total will be as useful as a larger addition to the larger total.

This, however, would be merely a statement about the attitude of the person concerned at the earlier of the two dates in question, since it is only at this date that he could actually choose between two such quantities. It would not state whether his attitude was the same at the two dates or different. In order to be able to make this latter kind of statement, we should have to know how he would decide if he were in a similar position at the second date. Of course, if the assumption of constant utility curves refers not merely to the two dates considered, but to all other possible dates as well, this implies that his decision would be the same at the second date. But it becomes at once obvious that this might just as well be the case if the utility curves for the different moments were not the same in an absolute sense. In order that my choice between to-day and to-morrow may be the same as to morrow's choice between then and the day after, it is by no means necessary that on each occasion the quantities of to day's goods and to-morrow's goods respectively, which I regard as equally useful, should be identical quantities. All that is necessary is that the proportion between the quantity of to-day's goods and the quantity of to-morrow's goods, which I regard as equally useful, should be the same on both occasions.

The fact is that the assumption of identical utility curves at all successive moments does not merely state the general postulate that the choice between present and future will be made in the 8arne way at different moments. It implies in 28 418 Appendix I addition that the choice will be made in a particular way. Instead of being merely a formal assumption that the attitude of a person will be the same at successive points of time, it is a very definite assumption about the particular attitude he will take at each moment. We have seen to what extent this particular assumption has any merit which would justify us in regarding it as a particularly significant case, or as repre senting in any sense the normal case. At this point we are interested only in showing why it seemed to follow directly from the assumption of constant tastes necessary for static analysis, so· long as utility was conceived as an absolute magnitude which could be described as a function of one variable, the quantity of the commodity in question.

But while the modern " substitution" or "indifference" approach makes it easy to see that any attitude as between present and future is compatible with the assumption of con stant tastes, it is also not difficult to understand why the older approach led Bohm-Bawerk and his followers to introduce the idea of a" perspective undervaluation of future wants". The special case which they regarded as the case of constant tastes would indeed require that people should save and invest until the value of the present factors had become equal to the future utility of their product, i.e. until interest had disappeared. In fact, however, by adopting this procedure, they did no more than overcome a difficulty of their own making. It waH only because they had assumed that constant tastes implied that equal quantities of a commodity at two dates ought to have the same marginal utility to a person at a particular moment that they had to introduce a special explanation as to why this was in fact not the case. In the particular form in which they gave it, their explanation has little meaning.

It implies a comparison between the present (absolute) utility of a future commodity and its future (absolute) utility which is regarded as its true utility. Such a comparison does not arise in any act of choice, since by the nature of things it is im possible to contemplate anything at one and the same time both from the standpoint of the present and from the stand point of the future. All comparisons of relative utilities are necessarily made at one moment of time, so that all that they express are relations between present utilities of present goods and present utilities of future goods. The utilities attached Time Preference and Productivity 419 to goods at different moments can only be compared by con trasting the relative utilities of one pair of commodities at the one moment with the relative utilities of a corresponding pair of physically similar commodities at the other moment.

The answer to Bohm-Bawerk's question as to why there is a difference between the value of the present factors and the value of their present product is that there is no such difference. If there is a rate of interest of 5 per cent, this means simply that 100 to-day is equal in value to 105 available a year hence. The contrary answer which Bohm-Bawerk gave was based on the assumption that if the present money value equivalent of the factors invested was 100 and the future value equivalent in money of the product was 105, this proved that there was a difference between the value of the product and the value of the factors. But this would follow only if he could maintain that 100 units of money to-day were equal in value to 100 units of money next year, which would be contrary to his own assumptions. The statement that there is a difference in value between the factors and their product, or (in an exchange economy) between the present goods and the quantity of future goods for which they are exchanged, is simply meaning less.

It would hardly have been justifiable to give so much space to the refutation of views which are now clearly obsolete if tbey had not left traces at least in the terms which are still commonly employed in this context. In particular there can be little doubt that, in the analysis of Professor Irving Fisher, although it is formally free from the confusion here discussed, the use of the term "impatience" still preserves something of the old idea of a " perspective undervaluation" of future needs. A person is " impatient" according to his terminology if, being assured of equal present and future incomes, he prefers some addition to his present income, even if only a very large onel to any permanent addition to his future income, even if only to a very small one.! That means that the term" impati ence" actually implies what it conveys in popular language, i.e. that a person is anxious to anticipate his future income in order to increase his present income beyond the level at which it can be permanently kept. This, however, is by no means 1 See I. Fisher, The 'l'heory of Interest, pp. 61 et seq.

420 Appendix I a necessary condition for the existence of interest in any society except a stationary one. All that is required in a progressive society for the existence of interest is that its members should feel some reluctance to postpone consumption of present income in order to increase future income beyond the present level at more than a lImited rate. l But to say that people do not save more than they actually do because they are impatient is not only a rather peculiar way of putting it; it is definitely misleading if it suggests, as it undoubtedly does to some people, that there is one definite rate of impatience which determines the rate of interest. (2) On the second question to be discussed here - the relative importance of time valuation and productivity in determining the rate of interest - there probably exists more disagreement among economists than on most other points connected with the theory of interest. The position taken here is as follows: Of the two branches of the Bohm-Bawerkian school, that which stressed the productivity element almost to the exclusion of time preference, the branch whose chief representative is K. Wicksell, was essentially right, as against the branch represented by Professors F. A. Fetter and I. Fisher, who stressed time preference as the exclusive factor and an at least equally important factor respectively. The weakness of Wicksell's case was that he never attempted expressly to justify his neglect of the time preference element. Professor Fisher; on the other hand, although he may claim to have furnished us with a formal apparatus which enables us to describe the interaction of all the relevant factors, even if he had attached no more than their equal importance to the two factors involved - and he certainly has been understood to regard the psychical element as the dominant one - would have given the psychical factor more than its due share. The most widely held view is probably that, as in Marshall's two blades of the scissors, the two factors are so inseparably bound up with each other, that it is impossible to say which has the greater and which the lesser influence.

Our problem here is indeed no more than a special case of 1 The same distinction apparently underlies the distinction made by Professor F. X. Weiss between underestimation of future needs and the non-underestimation of present needs. See Weiss, 1928, p. 1148, footnote.

:L'ime Preference and Productivity 421 the problem to which Marshall applied that famous simile, the problem of the relative influence of utility and cost on value. The time valuation in our case corresponds of course to his utility, while the technical rate of transformation is an expression of the relative costs of the commodities (or quan tities of income at the two moments of time). But Marshall himself has pointed out there are cases where it is legitimate to distinguish between the magnitude of the two influences. l The statement of our problem in terms of relative costs and relative utilities, which is more in conformity with the modern theory of value than Marshall's formulation, will indeed enable us to show that even in the more general case there may yet be more sense in the question of the relative importance of the two factors than Marshall was willing to admit. The applications of the conclusions derived from the consideration of the more general case to our particular case will probably be obvious.

We have first to define what we mean when we say that in a particular case either utility or cost determines value. We shall say that utility alone determines the relative values of two commodities, and that it is unaffected by relative costs, if it can be shown that a change in the cost conditions will not affect these relative values. And we shall say that value depends solely on cost and not on utility if it can be shown that changes in the relative utilities (as expressed by the indifference cur\7es) will not affect values. If these definitions are accepted it can easily be shown that in certain extreme cases either utility alone or costs alone will determine the relative values of two commodities, while in other cases which come near to one of the extremes it would be legitimate to say that the influence of one of the two factors is so predominant as to make the influence of the other negligible.

To begin with the case where the relative values of the two commodities depend on costs alone, we shall assume that the quantity produced of each commodity can be changed at 1 Principles, 8th ed., p. 349: "a person . . . may be excused for speaking [in cases of constant cost] of price as governed by cost of production - provided only he does not claim scientific accuracy for the wording of his doctrine, and explains the influence of demand in its right place".

422 Appendix I the expense of the quantity of the other at a constant cost, in terms of that other commodity. In diagrammatic terms this means that the displacement curve which shows the rate at which the one commodity can be produced in place of the other, is a straight line. It is then immediately evident that, whatever the shape of the indifference curves representing the relative utilities of the two commodities, their relative values will be uniquely determined by their relative costs. In Fig. 30 the two different utility relations are shown by the alternative y o T' FIG. 30 x indifference curves I and l' and the constant cost by the dis placement (or transformation) curve TT'. The equilibrium value of the commodity, expressed by the slope of the curves at the points of contact P and P', is of course the same in both cases. The opposite case, where the relative utilities are entirely independent of the relative quantities of the two commodities, is more difficult to conceive.l But we get practically the same result if we assume that the curvature of the indifference curve (representing the elasticity of substitution) is so small as to approach, at least over the relevant range, a straight line. If at the same time the displacement curve has a coni It would mean that the two commodities were perfect substitutes yet still different commodities because produced in a different way so that their costs might change differently.

Time Preference and Productivity 423 siderable curvature it is clear that the relative values of the two commodities will be practically unaffected by changes in relative costs (as represented by changes in the shape of the displacement curve) and that they will depend almost exclusively on the relative utilities. In Fig. 31 the two different y x FIG. 31 cost conditions are represented by the displacement curves T and T', and the relative utilities by the indifference curve I. It will be seen that the value expressed by the slope at the points of contact is very nearly the same at P as at P'. We need only substitute present and future income for the two different commodities in order to obtain the general results discussed in Chapter XVII.