XI. The Productivity of Investment

CHAPTER XI 'l'HE PRODUCTIVITY OF INVESTMENT THE mere description of any given investment structure by means of the input (or output) function is only a pre liminary, even though a very necessary preliminary, to the central problem with which we have to deal. Up to this point we have not considered the reasons why any particular structure of production should have been chosen in preference to all the other possible organisations of the available resources. That is to say, we have neglected all consideration of the different productivity of different forms of investment and their influence on the choice of a par ticular investment structure. .In the last two chapters in particular, the exposition was based entirely on the concept of the input function which, by definition, excludes any consideration of possible variations in the size of the total output derived from a given input. It would have made little difference in this respect if we had used for this pur pose of mere description of the structure of production the output function instead of the input function. Even in this case we should not have been able to investigate the relation between the way in which input is invested and the size of the output. This can only be done if we know the exact connection between particular input functions and particular output functions, and this connection is closely connected with, and in part dependent on, the rate of interest.

The rate ofinterest depends, however, on a relationship which we have not yet considered, namely, that between variations in the investment structure and changes in the size of the output. This relationship is not the same as the connection, within any given investment structure, 139 140 Investment in a Simple Economy PT. n between the value of the various units of input and the value of the corresponding units of output, and it is im portant that these two things should not be confused. In Elfeel of changes In this latter case we have to deal with a Ihe Investment olruo-growth of value in time at a given rate of tore on the size of the ' product interest, in the course of a given process of production. And this growth of value will be represented by the difference between a given input function and the corresponding output function. In the case we want to consider now, however, the subject of investigation is the connection between changes in the shape of the input function and changes in the shape of the output function.

The question we have to answer is how the productivity of investment reacts to changes in the range of investment periods. Now we can plainly see why it is that the theory of interest can only be correctly formulated after we have obtained an adequate understanding of the nature of the The ranges of Invest-investment structure. In the past certain ment periods cannot oversimplified conceptions have led to an usefully be reduced to One single time approach to the interest problem which is Interval of little use in explaining the phenomena of the real world. These concepts found their way into the analysis when it was clearly recognised for the first time that there was a definite relationship between the need for capital and the time elapsing between invest ment and the maturing of the product, and when this relationship was first explicitly made the basis of theo retical analysis. It was assumed, by Jevons and B6hm Bawerk, and even, though with some misgivings, by Wicksell, that the variety of different waiting periods with which we have to deal could in some way be reduced to a single time interval, and that this average or aggregate investment period of society, which was regarded as a technical datum, could be unequivocally linked up with the quantity of capital. On this assumption of a unique correlation between "the supply of capital" and some CR. XI The Productivity of Investment 141 single time dimension of investment which could be determined on purely technological grounds, it seemed possible to represent the prodllctivity of investment as a simple function of" the" period of investment, or, what was regarded as equivalent, the quantity of capital. It was assumed that the size of the total product would increase at a decreasing rate with successive increases in this investment period (or in the quantity of capital), and that the ratio between the marginal increase of the pro duct (due to the last extension of the average investment period) and the total product determined the rate of interest.

This approach suffers from two fundamental defects, which not only make the conclusions inapplicable to any real phenomena, but even deprive it of value as an initial simplification. For the unrealistic assump tions which it makes do not merely refer to incidental circumstances; they touch the very core of the problem and conse quently make it impossible to proceed from them to more realistic cases. The first of Neltber ibe ran" of waiting periods" em bodied In a pvea Inve.tment Itructure nor ibe supply of " waltln," are on ... dimensIonal magnI tudes these two defects is the assumption that the variety of waiting periods which are involved in any given structure of production can be combined on a technological basis, and described in terms of a single aggregate which has an unequivocal meaning. The second defect is the assump tion that the extent to which we are in a position to wait for part of the product of the existing resources, without reducing consumption below the level at which it can be permanently maintained, can similarly be expressed in terms of a single " amount of waiting", a kind of product of the volume of commodities for which we have to wait and the time we have to wait for them. These two points are so important that it is necessary to deal with them separately in considerable detail.

All attempts to reduce the complex structure of waiting periods, which is described by the input functions and 142 Investment in a Simple Economy PT. II the output functions, to a single aggregate or average 1 investment period, which could be generally substituted for these functions in the discussion of the productivity CondUions under of investment, are bound to fail, because which descrlpllon In the different waiting periods cannot be !erm. of a .Ingle time Interval would be reduced to a common denominator in valid purely technical terms. This would only be possible provided we had to deal with only one homo geneous kind of input,2 and provided the value of the product were always directly proportional to the amount of this input that was used. Of course neither of these assumptions is true in reality. But it is such ideas as these, dating back to the real cost theories of value, which have until quite recent times disfigured and invalidated much of the theory of capital.

Actually we have to deal with a situation where first there are a great number of different kinds of input, and The two main polnls where, secondly, what is more important, In which the tradl-the value of the product due to different tlona1 assumpllons are contrary to reallty units of input is variable and can be deliberately varied by using more or less of the particular 1 In the traditional discussions of these problems only the concept of the average period of investment or of production has been used, but it is of course uniquely related to the idea of an aggregate or a sum of all the investment periods. And to make it clear that our objections are not merely directed against the process of averaging, but against the whole idea that the investment structure can be adequately described by a process of summing up the individual investment periods, the expression "aggregate or average" will be used throughout the text. In terms of the diagram, the concept of an aggregate of all investment periods is represented by the area enclosed under the input curve. It is always equal to the base line of the curvilinear triangle multiplied by its average height (representing the average investment period). The important point is that triangles with the same area but bounded by input curves of different shapes cannot be regarded as representing equal quantities of capital because the shape of the input curve possesses a special significance which must not be neglected.

• This would imply also that the intermediate products resulting from the investment of this input could not be used for a,ny other purpose than that for which they were originally intended, and would not therefore have to be counted as separate resources.

OR. XI The Productivity of Investment 143 kind of input in combination with given other kindE! of input. The first of these two circnmstances means that in all cases where different kinds of input are applied in the different stages of anyone process of production, the relative amounts of waiting involved in different processes will depend on the relative values of the different kinds of input. In order to arrive at an aggregate figure of the amount of waiting involved in each process we have to assign definite weights to the different units of input, and these weights must necessarily be expressed in terms of value. But the relative values of the different kinds of input will inevitably depend on the rate of interest, so that such an aggregate cannot be regarded as something that is independect of, or as a datum determining, the rate of interest. Still more serious is the second difficulty. This is directly connected with the fact already noted that in some cases only the input function (i.e. the range of periods for which we have to wait for the produc+js of different units of input) and in other cases only the output function (i.e. the range of periods for which we have to wait for the different units of output) is directly given and that the one can only be converted into the other on the assumption that the rate of interest is given. This means that in many cases (in all cases where durable goods are concerned) we cannot say in any general way, and on purely technical grounds, how long the different parts of the total amount of input invested will remain invested.

But this is not all. The fact that the value of any invest ment grows gradually (at compound interest) into the varying value of its product means that larger and larger quantities have to be regarded as being invested at each successive period for which the given investment is con tinued. If, e.g., the product of one year's investment of a given quantity of input is reinvested for another year, the amount that is reinvested includes the interest 144 Investment in a Simple Economy PT. II accrued on the original investment during the first year. And the result of investing a given quantity of input, at a given rate of interest, for two years will be larger than the result of investing twice the quantity of input for one year. The effect of this is that the amount of waiting in volved in a particular investment is not simply propor tional to the length of the investment period and the value of the input invested, but is dependent ~~e.:'~:o:o~':~~:!~ also on the rate of interest. 1 In conse proportional '0 ,he quence, when we compare two different Inves'ment period investment structures, it will not always be possible even to say, on purely technical grounds, which of them involves the greater amount of waiting.

At one set of relative values for the different kinds of input and at one rate of interest, the one structure, and at a different set of values or a different rate of interest, the other structure, will represent the greater amount of waiting, or will be "longer" in the sense in which this term has commonly been used. If, e.g., we take two investment structures of processes of production in which labour and raw materials are used in different proportions but where at one set of relative prices of labour and the 1 Cf. Wicksell, Lectures, vol. i, p. 184: "It should perhaps be pointed out here that the assumption that the average period of investment is independent of the rate of interest (i.e. of simple interest) only applies, strictly speaking, where several different capital invest ments relate to one and the same future act of consUmption (-as in Bohm-Bawerk's example). In the opposite case, where one (or more) factors of production are' invested in a single capital good or durable conSumption good, it may easily be seen that the average investment period will be dependent on the rate of interest, even with simple interest.

" On the whole the theory of the coincidence of the rate of interest and the 'marginal productivity of· waiting' is only applicable as an exact mathematical formula on certain abstract assumptions. This is quite natural, for waiting on the part of society as a whole - and frequently also on the part of the individual-is not a simple quantity, but is, as we have just pointed out, a complex; 'average waiting' as a rule exists only as a mathematical concept, without direct physical or psychic significance."

OK. XI The Productivity of Investment 145 raw material the average investment period for the whole input is the same, a rise in the price of labour relatively to that of raw material will make the average period of the one of the two processes longer than that of the other, and a fall in the price of labour relatively to that of the raw material will have the opposite effect.1 In short, there is no way in which the variety of tech nical periods during which we have to wait, either for the products of different kinds of input or for particular units of the product, can be combined into an Wblch 01 two Invllt aggregate or average which can be regarded mInt luuctlll'H II • as a technical datum. No matter what procedure we were to adopt, the same technical combination of different inputs wbole Involves more w&1tlnl eannot be de cided on purely teeb nolo".&1 grouna would, under different conditions, appear to correspond to different aggregate or average periods, and from among the different combinations sometimes one and sometimes another would appear to be the "longer". But as the size of the product will clearly depend on the technical combination of the different kinds of input, it obviously cannot be represented as a function of any such aggregate or average period of investment. All that we can say is that it depends on the combination of the different invest ment periods or waiting periods which are incommensur able in purely technical terms, and that· ceteris paribus a change in anyone of these periods will cause some definite change in the size of the product. We must therefore base the following analysis on the multiplicity of data provided by our description of the investment structure, without trying to combine them into a single productivity function of waiting or of capital.

The difficulty associated with the idea that the pro ductivity of capital is unequivocally dependent on the length of a definite aggregate or average investment period has its counterpart in a similar difficulty connected with 1 For further discussion of the points provisionally raised in the last two paragraphs see below, Chapter XV, pp. 199·201. II 146 Investment in a Simple Economy PT. II the concept of a definite supply of capital which is supposed to make it possible to " wait" for a determinate aggregate or average period. Sometimes it is assumed The corresponding that a given" quantity" of capital is avail dlmculty In the conable in a "free" form. In this context cept 01 a given supply 01 waiting the vague concept of "free capital" can hardly mean anything else but a stock of ready consumers' goods, which, if consumed at a given rate, will enable us to wait for a definite period for the product of current pro ductive activity. But although this is not an impossible assumption, it is not a useful one. In the first place, the supply of capital is never given in the form of consumers' goods to the extent of more than a small fraction of its total. And in the second place, the problems which would arise if it were given in this form would be very different from the problems which actually arise under the conditions that current consumption is supplied out of current output and is at least partially due to current (mixed) input. 1 In place of this unrealistic concept of an actual stock of consumers' goods, B6hm-Bawerk introduced 2 the more refined concept of the subsistence fund, which consists, Btihm-Bawerk's sub-not of ready consumers' goods, but of slstence lund quantities of prospective or inchoate con sumers' goods which are as yet only represented by inter mediate products. This stock of intermediate products, however, would correspond to one definite quantity of consumers' goods, and therefore determine a'single possible waiting period, only if all of the intermediate goods were completely specific in the sense that each of them could only be turned into a fixed quantity of consumers' goods maturing at a particular date. In fact it is only in excep tional cases that the goods of which the stock of capital consists are specific in this sense. As a rule the quantity of consumers' goods that is obtainable from a given inter mediate product, and the date or dates when this quantity 1 Cf. Chapter VII, p. 88, footnote.

2 Cf., however, the passage from N. W. Senior quoted above, p. 85.

CR. XI The Productivity of Investment 147 will become available, will depend, just as in the case of pure input, on how the good is used, i.e. with what kinds and quantities of other capital goods it is combined. A given stock of capital goods does not represent one single stream of potential output of definite size and time shape ; it represents a great number of alternatively possible streams of different time shapes and magnitudes. In fact what is meant by the " supply of capital", in so far as this term refers to things of the outside world and not simply to a psychical attitude (that is to a prefer ence for income streams of particular time Meaning 01 the shapes), can be more exactly described only .. supply 01 capital It in terms of the alternative ways in which the existing stock of nonpermanent resources can be used to provide contributions to income at different dates. Each of the constituent parts of this stock can be used in various ways, and in various combinations with other permanent and nonpermanent resources, to provide temporary income streams while we wait for the return from other resources which have been invested in processes which will not yield their product until a later date. What we sacrifice in order to obtain an income stream of a particular shape is always the parts of the potential income streams of other time shapes which we might have had instead. The datum usually called the "supply of capital " can thus be adequately described only in terms of the totality of all the alternative income streams be tween which the existence of a certain stock of non permanent resources (together with the expected flow of input) enables us to choose.

This brings us back to our starting point and the correct formulation of our main problem. Our task is to determine the principlJs on which a given stock of nonpermanent resources (including, of course, any supply The data 01 the prob .. of consumers' goods not needed for current lem consumption) can be most effectively combined with the expected flow of input in order to give that income stream 148 Investment in a Simple Economy PT. n which is preferred to all other possible income streams. The initial datum from which we must start is a full description of the results which are known to be obtain able from various combinations of the existing stock of nonpermanent resources with the expected flow of pure input. This means that the data on the technical side which we require are not simply the quantity of some homogeneous substance, some given "fund" of capital, but a complete enumeration of all the different income streams which can be obtained from given resources, and of the ways in which these income streams are affected by varying the use that is made of particular resources. 1 In other words, the only technical data are the quantities of a great variety of different resources, with full information as to how they can be used, the quantities of the product which can be derived from different ways of using them, and the dates at which the product will be obtained. 2 In addition to this we shall, of course, require definite information about the psychical attitude of the individual or individuals concerned, their preferences as between The problem orUme income streams of different time shapes, preference postponed or their willingness to undergo a temporary by assumpllon that constant Income reduction in consumption in order to be .tream Is desired able to consume more later on, or vice versa.

To facilitate the exposition, however, we shall divide our discussion of the problem into two parts. First w.e shall confine our attention to the effects of the productivity of investment, on the assumption that the object is to obtain an income stream which under all circumstances remains constant in time. Then, after having analysed the effects of productivity in this comparatively simple case, we shall proceed to study the effect of the possible willingness of the people concerned to let the size of the income stream vary in time. The exact meaning of this 1 Of. Irving Fisher, The Nature of Oapital and Income, 1906. I Cf. last section of Cha.pter XIV below.

CU. XI The Productivity of Investment 149 assumption that people aim at a constant income stream ,will be explained at the beginning of the next chapter in connection with certain other simplificatory assump tions, which we shall have to employ in our first approach towards a solution of the problem. In the remainder of the present chapter we shall merely try to sum up the problems which have arisen out of this first survey of the productivity of investment, and shall restate them in a form in which they will be more useful in the subsequent stages of the analysis. It will be remembered that in the first diagram which we used,the curvilinear triangle, whose area represented the part of the future output stream which already existed in the form of nonpermanent Th raJ I" e pn. Ie a"on resources, was drawn on the assumption between the 1118 01 h . ul hod f . h the ontput and tile t at a partIC ar met . 0 usmg t ese ranp 01 Investment resources, a particular structure of pro-periods duction, had been decided upon. Many other ways of combining these resources with the expected stream of input would be possible, and each of these would give an output stream which would have to be represented by a triangle of different shape. We have seen that it is impossible to represent the size or shape of this output stream as being dependent on some single time interval applying to the investment of all the different kinds of input (some single aggregate or average period of invest ment), and that we have to start by analysing the effects of variations in those individual investment or waiting periods which can be isolated.

This means that all that we can say in practice is that if the use made of all other input is already determined, changes in the investment periods of particular units or groups of input will lead to certain known changes in the size of the product. And in all cases where the lengthen ing of any such individual investment period needs to be taken into account as a real alternative, its effect will be to increase the product obtained from the input concerned.

150 Investment in a Simple Economy PT. II But the size of the increase in the product which will be brought about by any particular extension of an indi vidual investment period will depend on the use that is made of the whole of the rest of the input. The size of the return cannot therefore be regarded merely as a function of this particular investment period: it must be regarded as a function of all the individual investment periods of the different units of input. This is perhaps the place where it should be expressly pointed out that while so far we have assumed that the physical product of every individu3.1 unit of input can be Only eII •• 1s 01 mar-determined, this assumption is not essen glnalchange. nood be tial for our further analysis All we need to known for purpooes of . further analysis know for the purposes of what follows are the effects of marginal changes 1 and particularly the relations between the changes in the investment periods of those particular units of input which it may be advisable to use differently in the given position and the changes in the total quantity of capital. Strictly speaking it would for this purpose not even be necessary to know the total length of these investment periods. It would be quite sufficient if we knew the amount by which a particular investment period is lengthened or shortened, that is, the interval of time between the· moment when (in conse quence of the change in question) the output stream is decreased, and the moment when some additional output, which is substituted for it, will mature. According as the date of the new output is later or earlier than that of the output which has been sacrificed to obtain the former, the investment period would have been lengthened or shortened, and we need in this connection not refer back to the date when the input is invested. Since, however> 1 cr. Wicksell, Lectures, vol. i, p. 260: "Fundamentally it is just as absurd to ask how much labour is invested in either one or the other annual use as to try to find out what part of a pasture goes into wool and what part into mutton. It is only at the margin of production that these quantities can be differentiated and have a concrete signific ance assigned to them."

CR. XI The Productivity of Investment 151 we shall as a rule know which units of input we have used differently in order to bring about an increase of output at one date and a decrease at another, we shall normally have no more difficulty in ascertaining the total length of the investment period of a particular unit of resources than in finding the marginal change in that period. It is, however, undeniably true that the technically given structure of investment is rarely if ever so simple in character that particular units of input can always be unequivocally ascribed to particular quan-It is not always pos tities of input .• The popularity which the sible to connect IndIvidual units of Input examples of the growing of trees or the wIth IndividUal units maturing of wine have enjoyed with 01 output writers on this subject is due to the fact that these examples correspond pretty closely to this simplest of cases, the " point input - point output" case. But to assume that all cases of investment can be treated on these lines is to evade the main problems. As we have seen, the relation ship between the product and the input used will as a rule be in the nature of a joint demand for resources to be used at different moments to produce the output of a given moment, or of a joint supply of products spread over a period of time and due to the input invested at one moment, or it will be a combination of both. Sometimes we shall be able to say only that a particular quantity of output is due to aU the input invested over a period of time, without being able to decide on a technical basis what part of the output is due to the quantities of input in vested at particular dates. At other times the only thing which can be regarded as a technical datum will be the fact that the input invested at a particular date brings forth a stream of output extending over a period of time, and we shall not be in a position to state in general terms what part of this stream is to be attributed to particular· units of this input. And even more frequently the only technical link which we shall be able to establish will be the connection between a stream of input stretching over 152 Investment in a Simple Economy FT. II a period of time and a stream of output stretching over another period of time.

In a great many cases, though not in all, the fact that the connection between these aggregates of input and aggregates of output is not absolutely rigid makes it Useoftheprlnclpleo! possible to analyse the connection further. variation Whenever the amounts of input, which are invested at particular stages of the process, can (at least within certain limits) be continuously varied, it will be possible to observe the effects of marginal variations of input on the quantity of output at particular dates. Where we have to deal with time-consuming processes of production it will as a rule be possible to invest some of the units of input at an earlier stage, i.e. for a longer period, or to invest more units for a given period, and to observe the effect of this variation on the magnitude of the product maturing at a given date. And in this sense it will be possible to state how the product will vary, ceteris paribus, with variations in the investment period of this factor. Similarly, where we have to deal with durable goods, it will often be possible to observe that changes in the amounts of particular kinds of input invested in them will bring about definite increments or decrements to the services rendered by these goods at definite dates. And then it will be possible here, too, to say that, ceteris paribus, the investment of an increasing proportion of the total supply of the factor in question for longer periods will bring about increases in output at a definite rate.

But even where there is this continuous variability of the investment structure which makes it possible to estab lish the contributions to output due to changes in the investment periods of particular factors, we have still to face the difficulty that this functional dependence of the size of the product on the investment period of the unit of input concerned is only true for a particular arrangement of all other input, and will be different for any other arrangement. And the effects of variations in the investCH. XI The Productivity of Investment 153 ment periods of different units of input cannot, as we have seen, be set out in any unequivocal way according to the length of the periods so that one complex investment structure can always be said to be longer than another, or so that the total size of the product can be described as being dependent on the length of the investment structure.

Finally there is the difficulty, to which we have so far only alluded by implication, that in many cases there will be whole blocks or ranges of input and similar blocks or ranges of output between the individual units of which it is impossible to establish any connection by the principle of marginal variation, because the rate at which input has to be invested at different times and Sometimes we cannot establish any physical relationship beyond tbat between agere-· gates of input and aggregates of output the rate at which output matures are not capable of variation but are rigidly fixed for a particular process. In these cases, as we shall see, all that we have to go upon is the variation in the value of the product concerned relative to the variation in the total quantity of input devoted to its production. Such, then, is the variety of possible variations in the investment structure which we shall have to take into account .in our search for the principles on which any stock of nonpermanent resources can be combined with the expected flow of input in the most advantag~ous manner.