XXI. The Effect of the Accumulation of Capital on the Quantities Produced and on Relative Prices of Different Commodities

CHAPTER XXI THE EFFECT OF THE ACCUMULATION OF CAPITAL ON THE QUANTITIES PRODUOED AND ON RELATIVE PRICES OF DIFFERENT OOMMODITIES IT has been pointed out earlier in this Part that, in order to make the argument developed here applicable to the real world, where the investment structures are not necessarily capable of continuous variation, Capital aecumulatlen certain modifications have to be intro-may lead to the expansion of some lines duced. It is necessary to do this explicitly, of Industry at tbe particularly as certain real phenomena, expense of otbers which can undoubtedly be observed empirically, have led many economists to deny explicitly or implicitly the pro position that the accumulation of capital will as a rule lead to a change in the methods of production. These economists have suggested that all that really happens is a mere multiplication of the equipment of the kind already in existence. This may be true in two cases. One is where there are unemployed permanent resources avail able, the services of which can be used to produce addi tional output by exactly the same methods of production as have been used previously. The other is where the increase in the supply of capital leads for the most part to an expansion of some industries at the expense of others. The first case has been briefly touched upon in connection with the discussion of the effects of saving (Chapter XX above), and, since it is a phenomenon which is mainly due to monetary causes, and therefore falls outside the scope of this study, it need not be further con sidered here. The second case, however, is of immediate interest.

The phenomenon to be considered is closely connected 285 286 Capitalistic Prodnction nnder CmnpeIition PT. III with a distinction already mentioned which the Austrian School used to describe as the difference between a growth of capital taking the form of an extension of .. Deepening" and its time dimension and one taking the "widening" 01 the form of an extension of its "labour" structure of production dimension, and which Dr. Hawtrey has recently christened the" deepening" and the" widening" of capital respectively.1 More capital can clearly be used in a given industry or a given economic system either by equipping a greater number of workers (or combining a greater quantity of "pure input") with proportionate quantities of equipment of the type used before, or by pr.oviding an unchanged number of workmen with more (or more elaborate) equipment. For the economic system as a whole the first of these alternatives is possible only if there is a labour reserve available. But in any particular industry the required additional labour may be attraeted from another industry.

If, as we have assumed, the investment structure can in many or most lines of industry be changed only dis continuously, the sole effect of a change in the relative A lall in rate of in-demand for capital goods in terms of teres~ may. allect O~iY consumers' goods may be to change the reiatlve sIze of dIfferent industries relative size of the different lines of production without (to revert for once to the traditional terms) affecting the proportions between capital and labour in any of them singly. An increase in the relative amount of consumers' goods offered for capital goods, or a fall in the rate of interest, will cause an expansion of those industries which use more capital in proportion to labour than others do, while the inverse case will favour the industries using relatively little capital. More or less capital will be used in industry as a whole, not because the proportion between capital and labour (and con sequently the technique of production) has changed in anyone industry, but only because the relative size of 1 R. G. Hawtrey, 1937, p. 36 (cf. p. 270 above).

CR. XXI The Effect of Accumulation on Prices, etc. 287 the groups of industries using comparatively much and comparatively little capital respectively has changed. The technique of production may have changed in none of the industries. All the different products may still be produced in the same manner as before. And yet the investment periods of the individual units of input which have been transferred to the expanding industry will have increased. What has happened is simply that the industries whose costs of production have been reduced more than those of others by the fall in the rate of interest have expanded at the expense of the second group. This effect is, of course, merely an application to industry as a whole of the general proposition which was invoked a short while ago (Chapter XVI, p. 206). Wherever the coefficients in which the different factors A special case 01 the f d t · b b· d· . d· general rule for fixed o pro uc Ion can e cOm lne In In 1-coefficients 01 providual industries are relatively or absol-ductlon utely rigid, a change in the relative scarcity of the different factors can be met only by an expansion of the scale of output of those industries which use relatively less of the factors that have become more scarce, and a corresponding contraction on the part of those industries that use more of those factors. And what is true of that general case applies in this case also, namely, that unless the pro portions in which the factors can be combined are variable at least in some industries, any change in the relative supplies of the factors is likely to cause violent changes in their relative values and may even render some factors completely valueless.

The effects of changes in the relative demand for con sumers' goods and capital goods on the value of input in general can be shown without great difficulty. A problem which is at least as important but much Effects on relative more complicated is the problem of their values of different factors more complleffects on the relative values of different cated kinds of input. In particular it is almost impossible to explain the changes in the relative values of different 288 Oapitalistic Production under Oompetition PT. III types of capital goods without going back to the factors which determine the changes in the relative values of the different kinds of pure input. But any attempt to give an exhaustive analysis of the intricate relationships here involved would unduly expand the size of this study. All that can be attempted within its limited compass is to suggest the different considerations which have to be taken into account, without trying to show in detail how they combine to determine equilibrium.

These can best be shown by first assuming that there is only one sort of input: the homogeneous" labour" which in the traditional analysis is usually contrasted Effects on value and with capital. On this assumption, the distribution of a • 1 d·· (. f single kind of Input margina pro uctivity In terms 0 conrecapitulated sumers' goods) of successive quantities of " labour" applied in the different stages of the process of production can be represented by a series of curves as shown in the following diagram. We can assume these stages a, b, c, etc., to be separated by equal time intervals, and to be arranged in the diagram from left to right in ascending order of maturity, so that stage a would be twice as far from consumption as stage c (e being the Inoment when the process of production is actually completed), and so on. In each of these curves the ordinate shows the addition to the product which is due to the successive quantities of input applied to that stage, the quantities being measured along the abscissa.

As we know already, t.hese different productivity curves cannot be regarded as simultaneously and independently true. They show only how the product will vary if the amount of input invested in anyone of the stages is varied while the amount invested in all other stages remains fixed at a particular figure. There is, of course, no reason to assume that the shape of these curves will be the same in the different stages, though this has been assumed in the diagram in order to make the point which it is meant to illustrate come out more elearly.

CR. XXI The Effect of Accumulation on Prices, etc. 289 The marginal product shown by these curves is, of course, the undiscounted marginal product, the total addition to the product which is due to the investment of an additional unit of the factor in question at the relevant stage. The actual share of the product to be attributed to a unit of " labour" or the demand price which, entre preneurs will be willing to pay for a unit of " labour" if employed at that stage, will be equal to the value of the marginal product discounted at the current rate of interest over the relevant investment period. a b C FIG. 25 d e In the diagram the effect of this discounting can be shown by lowering the diHerent productivity curves (or, more exactly, all the individual points on these curves) by an amount corresponding to the discount appropriate to the periods for which the respective units of input are invested. Since the stages are supposed to be separated by equal time intervals, this can be shown graphically by means of a discount curve from which the individual productivity curves may be supposed to be suspended so that they will be moved upwards or downwards as the rate of interest decreases or increases. (Strictly speaking, we need a family of discount curves connecting each point of the curve on the extreme right with the corresponding points on all the other curves, so that with every change in the rate of interest not only the position, but also the shape, of the individual curves will be changed, since every point will be lowered or raised, not by the same absolute amount but in the same proportion.) 20 290 Capitalistic Production under Competition PT. III The following diagram shows two such discount curves along with the productivity curves in their corresponding position. The fully drawn set of curves corresponds to a lower rate of interest (it), and the dotted set to a higher rate (i2)' Since in equilibrium the discounted marginal product of the factor in question must be the same in all stages, the distribution of a given supply of the factor will evidently be determinate for any given rate of interest.

We may suppose that, e.g., at the higher rate of interest shown by the discount curve i2 the available supply of the factor will just be exhausted, and its discounted 111------t;:----.-_ -.-:-:-,""-~ + + a b c FIG. 26 d ......... 1, ..... ~ e marginal product will be everywhere the same, if it is distrib~ted among the stages in the proportions indicated by the segments of the line ending at Pt that are marked off by the corresponding productivity curves and their respective ordinates. Then if we a.ssume tha.t the rate of interest is lowered (represented by the discount curve it), the given supply of the factor in question will evidently have to be redistributed between the different stages so that more will go to the earlier and less to the later stages. The segments of the abscissa in the diagram that are marked by plus and minus signs show the changes in the quantities of input invested in the respective stages.

The discounted value of the marginal product of the factor (or its price in terms of consumers' goods), indicated by the distance from the base of the line ending at P 2, will necessarily be higher than it was before.

CR. XXI The Effect of Accumulation on Prices, etc. 291 So far this diagram is only a way of restating con clusions with which we are already familiar. But it can be used, although only with obvious limitations, to illus trate the factors that will determine how Eftects on relallv. much the price and the distribution of any value ot dlft.renl • c t '11 h' f sorts ot Input gIven lac or WI C ange m consequence 0 a given change in the rate of interest. So far it has been assumed that the shape of the productivity curve of the factor in question in the different stages is the same. But this is not at all likely in practice. And the actual effect of a change in the rate of interest on the price and the distribution of anyone factor will evidently depend on what we may call the relative elasticity of its productivity in the different stages. For a factor whose productivity curves in the early stages are relatively flat, a given fall in the rate of interest will cause a much greater transfer from the late to the early stages, and a much greater rise in price, than would be the case with a factor whose productivity curves are comparatively steep in the early stages. When we remember that only a few of the different factors (the perfectly versatile ones) will be demanded in all stages, and that the majority of them will be useful only in a limited number of stages (their elasticity of productivity in the other stages being zero), it becomes at once obvious how different the effect of a given change in the rate of interest on the prices of different factors must be.

We shall not follow up this point in detail. For the method adopted to give a general picture of the considera tions involved is really not adequate for an exhaustive analysis. The reason for this is, of course, Problems ot comple as in all other cases where productivity menlarlly Involved or demand curves for individual factors are regarded as given, that these curves cannot be regarded as simultaneously and independently valid. But to take account of the complicated relations of technological (and psychological) complementarity which are involved, re quires another technique which has been evolved quite 292 Capitalistic Production 't~nder Competition PT. III recently in closely related fields, and which will also have to be used in a more exhaustive investigation of our problems. Here all that we shall mention is that if we were to start from a complete statement of the substitu tion relationships between all the different resources con cerned, all kinds of peculiarities and apparent anomalies in the behaviour of individual factors would appear to be quite consistent with the general tendencies which can be deduced from the cruder type of analysis. It is, for instance, quite possible that while a fall in the rate of interest will create a tendency for the services of most of the permanent factors to be invested for longer periods and for their prices to rise, in the case of some individual factor the effect may well be that it will be invested for shorter periods, or that its price will be lowered, or both.

But all this belongs to the more complicated aspects of the subject which it is not proposed to treat here in extenso. After this admittedly sketchy outline of the factors that will affect the relative prices of the different kinds of input in the course of a change in the capitalistic structure of proauction, it is only necessary to return for a moment to one question which was raised previously but was left unanswered. How does a change in the rate of interest affect the relative prices of different capital goods which are produced and used before and after it takes place? The explanation just given of the difference between the changes in price of the different kinds of input also accounts for the change in the relative prices of the Effects on value of intermediate products at the successive dltIefent eapltal goods stages. At first it might seem as if, since in the long run the relative prices of the different inter mediate products must correspond to their respective costs, these prices could change permanently only to the relatively small extent to which the direct interest element in their cost changed. But to think of interest only as a direct cost factor is to overlook its main influence CR. XXI The Effect of Accumulation on Prices, etc. 293 on production. 1 What is much more important is its effect on prices through its effect on the demand for the intermediate products and for the factors froIn which they are produced. It is in consequence of these changes in demand, and the changes in relative costs which they bring about by raising. the prices of those factors which are in strong demand in the early stages relatively to the prices of those factors which are less demanded in those stages, that the prices of the intermediate products are adjusted.

The point, which in this connection is so frequently overlooked and which at the same time is so very important for the understanding of the effect of changes in the interest rates, is that the change in the price of a particular factor consequent upon a change in the rate of interest may stand in no direct relation to the changed value of the particular factor at the point where it is used. The change in its price may be many times greater than would be due merely to its particular marginal product being discounted at a different rate of interest. The cause of this is, of course, that the price of a particular factor will not depend solely on its productivity in the particular use in question and that the demand for it elsewhere may be affected much more strongly by the change in the rate of interest. The rise in the value of labour and the immediate fall in the cost of machinery in a particular industry consequent upon a fall in the rate of interest may be very small, yet the increase in the demand for labour elsewhere caused by the same fall in the rate of interest may drive up the price of labour to such an extent as to enforce an extensive substitution of machinery for labour.

We shall come back to this important point in Part IV of this book when we discuss the effect of changes in demand on the profitability of different kinds of invest ment (see Chapter XXVII below). 1 Cf. Machlup, 1935a.