X. The Position of Durable Goods in the Investment Structure

CHAPTER X THE POSITION OF DURABLE GOODS IN THE INVESTMENT STRUCTURE In the last chapter the emphasis was entirely on goods in process, that is, on the accumulation of capital due to the actual duration lof the process of· production. The Importance of This must not be taken to mean that this durable goods form of capital accumulation is the more important one. On the contrary, there can be little doubt that under modern conditions the much more im portant role is played by durable goods. The reason for our procedure was merely that certain relationships can be shown more clearly and easily for the case of a time consuming process where the input function has a simple and obvious meaning. In the ideal case of this sort (the "continuous input - point output" case) there is a definite moment when all the results of investment belonging to the process mature, and it is therefore possible to say at once for how long each additional unit of input is invested. The input function, describing the range of investment periods for the different units of input, lends itself particularly well to description by the three-dimensional figure which we have just used.

Turning now to durable goods, we shall again first consider "ideal" durable goods, that is, the "point input - continuous output" case. This means that we "Idea)" durable assume, firstly, that the time it takes to goods assumed make a durable good is so short that it can be disregarded, and, secondly, that the durable good, once it has been produced, will render direct services to th~ consumer without any further ~ co-operation from current pure input. In other words, we disregard the . 126 CH. x Durable Good8 and Investment Structure 127 time it takes to make the durable good (and the time it may take for the products produced with the help of the durable good to reach the consumer) as well as the fact that further input may have to be applied to utilise the durable good once it exists. As we have already seen, in the case of durable goods the input function which we have used in connection with goods in process is not directly known. Even in the case of an ideal durable good we shall be Llmltallons to UIfl 01 able to state on technological grounds Input tuncllon merely how long we have to wait for the various units of its services, but not how long we have to wait for the products of particular units of input invested. In other words, all that is initially given as a technological " datum" is the output function, the range of periods during which we have to wait for the different units of output. We have already seen (see pp. 111-112 above) that there is no constant or invariable connection between these two magnitudes, and that the one cannot be unequi vocally converted into the other. It would no doubt be possible to make the output function the basis of the construction analogous to that used in the last chapter, but this would not avoid the real difficulty. For the moment it will be better to neglect the difficulty of attributing particular units of output (that is, of the services of the durable good) to definite quantities of input invested in the production of durable goods. We shall assume provisionally that this problem is solved.

On this assumption, that is, provided we know how long the various units of input remain invested in the durable good, it is easy to show how durable goods can be fitted into the schematic representation of the complete process. It will be for later chapters to show how far this pro visional assumption is justified. In considering how far durable goods can be fitted into the schematic picture of the continuous process given in the last chapter we shall refer once more to the three128 Investment in a Simple Economy PT. II dimensional figure used there and ask what meaning we can attach to its various parts when they are interpreted to refer to a stock of durable goods. There is no special difficulty about the interpretation of the curvilinear triangle in the base plane of our figure. It represents, in the already familiar manner, the flow Shape 01 the (COD-of services (in terms of such units as are structed) Input curve the product of units of input) which we may expect to accrue from the existing stock of durable goods.

The only point which needs further explanation is why, in this case too, we should expect the input curve to be concave. If we had to deal only with one kind of durable good which gave a constant stream of services throughout its lifetime, we should expect the rate at which services from the existing stock of these goods would accrue to fall off at an approximately 1 constant rate as the existing goods successively wore out. If goods of all ages, from those which had only just been completed to those which were on the point of wearing out, existed simultaneously, as would be the case under stationary conditions, the number of goods (from the initial moment's stock) which were still in existence, and consequently the amount of services which they rendered, would decrease at a con stant rate at every successive moment. The input curve would be a straight line. There are, however, two reasons why in fact, and for the economic system as a whole, this is not likely to be the case. The first and less important reason is that most durable goods will yield, during their lifetime, not a constant stroom of services but a decreasing one. In consequence, even if the number of goods surviving suc cessive dates decreases at a constant rate, the amount of services rendered by them will fall off only at a decreas ing rate. The second and more important reason, how ever, is that the· different durable goods existing in an economic system will be of very different degrees of dur1 I.e. neglecting interest.

OK. x Durable Goods and Investment Structure 129 ability. Thus even if within each group of durable goods of anyone kind the individual items wear out at a con stant rate, the aggregate effect must be that the total stock of durable goods of all kinds will be worn out only at a decreasing rate; this is because parts of the total stock will wear out at a faster rate and others at a much slower rate than the average. The best way of showing this is to conceive of the streams of services accruing from the different groups of goods of given durability as being represented by separate triangles of different heights, and then to imagine that they are combined in a single figure. The broken line which we thus obtain in place of the hypotenuse of the combined triangular figure will tend to become a continuous curve as the number of different goods increases. The question of continuity, to which we have referred a moment ago, raises a further problem. When we were dealing with goods in process, the assumption of complete continuity, although not entirely realistic, DlsoonUnulty of .. was at least not so far from reality as to placement seem unreasonable. But in the case of durable goods the assumption of continuity would mean that, at every moment, one piece of every kind of durable good was completed and put into service to replace one which was just being worn out. Where we have to deal with goods of comparatively small durability and of which a con siderable number are simultaneously in existence, this assumption may still not be too far from reality. But where goods of very great durability and of which com paratively few are in existence (e.g. railway engines or even bridges) are concerned, this assumption obviously becomer absurd. It is undeniable that for suoh goods production and replacement will inevitably be discon tinuous, and that in consequence the composition of the stock of such goods in existence will undergo periodic changes. In practice the effect will be that, if the quantity of capital is to be maintained intact, at certain times 10 130 Investment in a Simple Economy PT. II there will be a large number of goods of small durability to be replaced and at other times a smaller number of goods of greater durability. This means that the shape of the input curve itself will undergo periodic changes. It could also be shown, by a further slight modification' of our diagram, that it is possible for this to take place in a way which will preserve a certain kind of continuity such that the stock of durable goods as a whole will be replaced and maintained constantly. But it would take too long to go into these complications here. It must suffice to point out their existence, and to proceed with the ex position on the assumption of that perfect continuity which is implicit in the drawing of the diagram.

We turn now to the interpretation of the. vertical planes in the three-dimensional diagram (Fig. 6) applying to durable goods. When they referred to goods in process, The stock of durable these planes represented the stock of such goods -., goods existing at any moment of time, and this interpretation still applies to durable goods. The only difference relates to the concept of stages. The goods in process could be regarded as advancing bodily from stage to stage, so that at every successive moment the same material units would have moved forward to later stages. With durable goods the situation is that the services which will mature at different dates are all em bodied in the same material unit. Every such good has thus to be regarded as consisting of units of future ser vices which will mature at different dates and therefore belong to different "stages". Perhaps the situation can again best be explained by having recourse to the non-' cumulative representation of the time distribution of the services derived from the good. We may conceive of the stream of services which a good is expected to render as being represented by a vertical strip, of which the width indicates the rate at which the services will accrue and the length the period during which they will accrue. In Fig. 7a the durability of the good is indicated by subCR. X Durable Goods and Investment Structure 131 dividing the strip into sections corresponding to the number of unit-periods, say months or years, for which the good will last. In this way we can depict the whole collection of goods of different ages, but of the same kind, which exist at anyone moment. Let us assume that the good of the type in question lasts for five unit-periods, and that during each such unit-period one such good is worn out and one is produced to replace it. Then at the beginning of each period we shall have the position shown in the diagram. We shall have one good which has just been completed and still represents five unit-periods of t t o r o r a b FIG. 7 service, one which has already served for one unit-period and represents only four unit-periods more, and so on until we· come to the oldest good of the kind still in exist ence which represents services for only one more period.

It is evident that as the number of goods simultaneously in existence increases, and the intervals at which new ones are put into service become correspondingly smaller, the shape of the figure will tend to approach more and more closely to that of a simple triangle. As the number of goods approaches infinity and the share of the total services represented by a single good becomes infinitely small, the " stepped " line will tend to become a straight line. (We thus arrive back, of course, at the cumulative representation of the time distribution of services. For the amount of services which are still unexhausted in a 132 Investment in a Simple Economy PT. II good at a particular moment of its life will,under our assumptions, necessarily be equal to the total amount of services which are being rendered at that same moment by all the goods which still remain from among those which existed at the time the good in question was first put into service.) The main difference between this triangle and the similar triangles which we used in connection with goods in process relates to the concept of stages. In the former Tb t r ta case the different "stages ", which were e concep 0 s ,es In Ibe case of durable obtained by dividing the triangle into horigoods zontal sections, corresponded to different goods. In the present case the triangle has to be divided into vertical strips in order to obtain the share of the output that will be contributed by individual goods, and all such goods (except of course those which are on the point of being worn out) wiH belong to a number of different stages.

The triangular figures which we have just obtained are, of course, identical with the vertical planes in the three-dimensional diagram. One of the points they help to explain is what is meant by saying that one and the same good may at anyone time belong to several or even many stages. l We shall see that this is far from being a useless or artificial concept, and that it is really essential for the understanding of the factors affecting the prices of such goods. What we want to do now, however, is to show how the supply of services which accrues from these durable goods at any moment of time can be linked up with the investments which are necessary to produce these goods. 1 Cf. A. Marshall, Principle8 of Economic8, 1st ed., p. 109, note: "Of course, a good may belong to several orders at the same time. For instance, a railway train may be carrying people on a pleasure excursion, and so far it is a good of the first order; if it happens to be carrying at the same time some tins of biscuits, some milling machinery and some machinery that is used for making milling machinery, it is at the same time a good of the second, third, and fourth order."

OH.X Durable Goods and Investment Structure 133 l!'or this purpose we shall once more make use of the input function in its inverted form, i.e. as shown by the slanting planes in the three-dimensional diagram. The services rendered at any moment of time by· the total stock of durable goods will be rendered partly by goods which are almost used up and which were produced a long time ago, partly by goods which have only just been completed and will consequently last for a long time to come, and partly by goods in all stages intermediate between these two extremes. If we represent the services which will accrue at any given moment from all the goods in existence by the horizontal line TaRa at the base of the slanting triangle SaTaRaPa in Fig. 6, then the curve PaRa (which takes the place of the hypotenuse of a straight line triangle) will give us the dates at which the various investments have been made to which the respective fractions of the services of the durable goods in existence at '1'3 are due.

We have already mentioned the a priori ground on which it appears probable that in the case of durable goods too this input curve is likely to be concave. It is ex ceedingly difficult to get much empirical Distribution of ex evidence for its actual shape. But what-pected useful life of • I!. b h durable goods ever m.lOrmatlOn we possess a out t e actual length of life of durable goods used in the present world tends to confirm this conclusion. The most complete figures of this kind which are available refer to the output of business capital goods in the United States in one year (1929).1 From our point of view these figures suffer from the defect that they exclude durable consumers' goods and that of course the services rendered by the durable producers' goods may still be many stages re moved from consumption. But as these data are based on depreciation rates (the assumed length of life is simply the reciprocal of depreciation rate), they correspond roughly to our input function (i.e. they show the part of 1 Fabricant, 1938. p. 181.

134 Investment in a Simple Economy PT. II the original investment which is assumed to be returned year by year). And since our purpose is merely to illus trate a general point, it may be worth while to construct from the available figures a hypotheticai description of the stock of durable producers' goods that would be in existence at any moment if the annual production were repeated continuously year after year at the same rate at which Years 76 ...-75 I \ \ 60 26 10 2 26 60 76 100 Per cent of annual output FIG. 8 such goods were produced in the year to which our figures refer. The result of this calculation, represented in the same way as in the schematic diagrams just used, is shown in the accompanying Fig. 8. The conspicuous irregu larities are clearly due to a preference for round figures (10, 15, 20, 40 years) as a basis for depreciation. But even so it will be clear that the" input curve" for durable goods which we obtain if we smooth out the original data (as has been roughly done in the figure) is strongly concave. 1 1 Another point of general interest arising out of Dr. Fabricant's figures is that they show an essentially continuous distribution and no predominance of any particular figure for the expected length of life Cll. x Durable Goods and Investment Structure 135 The use of the inverted input form in this connection offers an opportunity to say a few words about a problem which we have so far neglected. Up to this point durable goods have been treated as if their produc-The period of gesta tion did not take any time, i.e. they were lion of durable goods treated as clear instances of the ideal" point input continuous output" case. This is of course even less true than the supposition that a time-consuming process of production will ever exactly correspond to the" continuous input - point output" case. It will always take time to make a durable good, and in consequence the investments to which the flow of services from the good is due will always extend over a certain period of time before the good actually begins to yield its services.

It was to illustrate this point that Jevons originally introduced his investment figure. He used a double for durable goods in general. This is, of course, very much in con· formity with our general attitude of stressing the essential continuity of the distribution of investment periods over a long range. And it flatly contradicts the assumption of the predominant frequency of a particular duration (especially ten years) which ever since 'Karl Marx has been made, on the slenderest evidence, the basis of generalisation, particularly in the theory of the trade cycle. A good instance of this is the statement by Professor Pigou that "there is reason to believe that many different sorts of machinery enjoy the same sort of length of life. Ten years seems to be not merely the average, but also the markedly predominant length. This at all events is the view of the Director of the British Census of Production." (I wIustrial Fluctuations, 2nd ed., 1929, pp. 229.230; see also Economic8 oj Welfare, 4th ed., 1932, p. 38). When one turns, however, to the pages of the Final Report on the Fir8t Census oj Production of the United Kingdom (1907) (London, 1922, pp. 35 and 36) to which Professor Pigou refers, his RBsertion is hardly borne out. All that the Director of the Census says is that" In determining the amount probably necessary for depreciation allowance on industrial capital, it may be remembered that it is commonly held by cautious manufacturers that provision should be made in business accounts for the renewal of buildings [sic] and plants in ten years .. and" The consideration that part of the capital does not require renewal in so short a period as ten years may be set off, not only against the fact that more speedy renewal is required in other cases, but also against the fact that the provision which is the subject of the present estimate is required to cover current repairs as well as renewal of outworn plant".

136 Investment in a Simple Economy PT. n triangle,! of which (in the form in which it is reproduced here) the lower part represents the gradual investment of input in the good while it is being made, and the upper Jevons' investment part represents the gradual disinvestment ftgure as it yields its services. But although this is a more realistic way of describing the life history of an individual good, it does not easily lend itself to a repre t T T' lJ-----~ 1 o r sentation of the complete process of using and maintaining a given stock of durable goods. The only way in which we can give a schematic repre sentation of this process is by concentrating either on all the output which is due to . the investment of services at, one moment (the original form of the input function), or on all the investment to which the out put of one moment is due (the inverted form of the input function). Both of these methods are, of course, artificial in the sense that they do not include the complete life history of any indi vidual good, but only either the results of the invest ments made at one moment in different durable goods in Dlmcultles of com-different stages of completion, or the in blnlng the period of vestments. to which the services derived gestation and the period of use in one at any one moment from all the durable FIG. 9 diagram goods then in existence are attributable.

In either case this means that we split up, as it were, the natural unit which a durable good represents, and treat as belonging to one process either such parts of the differ ent goods composing a given stock as were made at 1 W. S. Jevons, Theory of Political Econom.y, 1st ed. (1871), p. 223, 4th ed. (1911), p. 231. The figure has here been turned by 90 degrees as compared with the original, in order to make it correspond with the other diagrams used in the present work. Jevons' technique has been used and developed in the excellent discussion of the problems connected with durable instruments by R. F. Fowler, 1934.

CH.X Durable Goods and Investment Structure 137 one moment, or such parts as give their services at one moment. All this becomes relevant immediately we try to show the combined effect. of the time it takes to make a durable good and the time it takes to use it up. The actual process by which the durable good is produced The representation of could, of course, be directly shown, as in the combined process Jevons' diagram, by the inverted input function, but the result of using the good would again appear as a stream of services stretching over a further period of time .. Instead of this we want a description of the range of periods for which we have to wait for the products of all the input which matures at a particular moment of time. The in put which matures at any moment will have been invested in different goods and at different times. We shall have to assume that every investment made at any stage of the production of a durable good makes some contribu tion to the services which that good will yield at every moment of its existence. We have therefore to wait for the result of every investment, first for a period until the durable good is completed, and then for a further range of periods corresponding to the life of the good and the rate at which it yields its services at different periods of its life. (Incidentally this means that not only the durable good itself, but also the input which is invested in the durable good, has to be regarded as being .at one and the same time in a number of different "stages".) While it would not be impossible to represent this situation by a specially constructed diagram in three dimensions, it is hardly worth while to devote much more space to this point. 1 1 If the reader wishes, he can easily con~truct in imagination the appropriate diagram by first conceiving the range of periods for which different quantities of input are invested in the production of a durable good represented by a solid of which the input function with its co ordinates would give the elevation, while its base would be a square.

The further range of periods for which every unit of input invested in the durable good remains invested in that good after it has ,been com138 Investment in a Simple Economy PT. n, CH. x Compared with the real world, of course, even this case of a durable good which is made without the help of other durable goods (i.e. from pure input only) and which then serves consumption directly without further co-operation from other current input, is still very much simplified. Actually all the services maturing at anyone moment, as well as the results of all the investments of input made at anyone moment, will as a rule be the outcome of a long chain of alternating uses of durable goods and time consuming processes which will together form a very complicated pattern. But it is not necessary here to follow up these complications in all their details. It is quite sufficient to have elucidated the principle according to which even the most complicated patterns of this sort can be described by one input function.

pleted could then be shown by erecting on the upward-sloping surface of the solid so obtained, and at right angles to the first input function, a further solid consisting of a family of inverted input functions describing the durability of the good. The various vertical distances between the base and the top surface of the complete solid would then show the total range of complete investment periods, from the moment input is invested in the production of a durable good till the moment when the services of the durable good mature, and all the possible ways in which this total investment period can be divided between invest ment during the production of the durable good and investment during its life: for some parts of the total input both these periods and there. fore the total investment period will be zero, for some other parts the total investment period will be equal to the sum of the total duration of the process of manufacturing the durable good plus its total lifetime, while most of the input will be invested for some other combination of intermediate periods.