XII. Planning for a Constant Output Stream

CHAPTER XII PLANNING FOR A CONSTANT OUTPUT STREAM WE must begin our discussion of the ways in which all resources must be organised to obtain the best result by stating more fully the assumptions on which we shall Assumptions on which proceed. Our starting point will be a the principles deter-community which is equipped from the mining the time structureofproductlonwlll ,outset with a stock of many kinds of non be Orst discussed: (a) The supply of re-permanent resources, and which expects sources to command a constant flow of pure input which can be combined with the capital assets in the manifold ways already described to provide output streams of different sizes and time shapes. Whatever provisional plan for the combination of these different kinds of resources we assume to be con templated, there will always be numerous possibilities of increasing the size of the product obtained from particular units of input or particular capital items by using them in such a way that the date at which they will yield their product is postponed. The range of these possibilities will be very wide. Investment periods which are already very long may be lengthened further as well as those which are comparatively short. And in some cases a relatively small extension of an investment period or of a range of investment periods may cause a relatively large increase of the product, while in other cases a very considerable extension of an investment period may result only in a small increase of the product.

The reason why only some of these possibilities of in creasing the product from particular units of input will be turned to account is, of course, that every postponement of the return from these units of input will cause, ceteris 154 CR. xn Planning for a Constant Output Stream 155 paribus, a gap in the expected income stream at some point, and this gap will have to be filled, if the output stream is to be constant, by investing other units of input for correspondingly shorter periods. So long as there is any limitation on the extent to which the members of our society are willing to restrict their consumption for the sake of increases in output which may be obtained by investing input for longer periods, there will always be the problem of deciding what part of the available input should be invested for relatively long periods and what part should be used to provide sustenance in the interval before the product of the input invested for the longer periods accrues.

The decision as to which of the alternatively possible combinations of the resources is the most advantageous, and the question of how to proceed in every individual case in order to arrive at this best total (b) The general value arrangement raises of course a value problemwlUbestudled " , . . for a .. simple oeoproblem of the most general nature. It is nomy" a value problem which would arise independently of any possibility of exchange between different persons, since even an isolated individual would have to take account of the same factor in making his dispositions. In cases of this kind it is always useful to commence by studying the problem in its most general form, i.e. in the case where a single person administers all the available resources in the service of a single system of ends. l This assumption allows us to investigate the influence of the technological data in their simplest form, without having to take account of the differences in aims of a multiplicity of persons and the effects of a different distribution of resources between them. It is only in a second and separate stage of the analysis that we shall link up the result obtained under this assumption with the explana tion of prices in an exchange economy.

1 Cf. the passage from Marshall quoted above, Chapter II, p. 27. footnote 1.

156 Investment in a Simple Economy PT. II But although we shall employ the idea of an economic system directed by a single will, we shall not go back to the case of a single individual, a Robinson Crusoe who -that I., for a 8Om-works in complete isolation. Such an indi munlst society - vidual would obviously be unable to make use of more than a very few of the advantages of time consuming processes, since most of them are applicable only where production is carried on on a fairly large scale and where there is scope for a good deal of specialisation or division of labour. It will be more helpful, therefore, to consider the case of a communist society in which all economic activity is directed by the will of a single dictator or general manager. I shall retain this assump tion for this and the next six chapters and shall post pone consideration of the problems of a market until Chapter XVIII.1 We shall assume that this communist society is equipped, at the moment when we begin to consider it, with a stock of nonpermanent resources of many different kinds. Some of these will be the result - which has previously been statlon-of the productive activity of the past and 81")'- others will be wasting natural resources of various kinds. The problem of our dictator will then be how to make the best use of this stock, i.e. how to derive from it the stream of income which is preferred to all the other streams that are also technically possible. We may assume that in the past the amount of these non-per manent resources, or of " capital ", which was used in each of the various industries and processes, was deter mined either arbitrarily or else in accordance with some traditional routine, but without any definite calculations 1 On the significance of this methodological procedure, cf. Friedrich Wieser, Theory of Social Economy, New York, 1927. It need scarcely be added tha.t such a discussion of how a communist dictator ought to act if he wanted to obtain an economic distribution of resources does in no way prejudice the question whether he could so act; we a.re, in other words, assuming an omniscient dictator without, of course, believing that such a dictator could ever exist.

CK. xu Planning for a Constant Output Stream 157 of profitability. We shall assume in particular that our dictator has disdained to take account of the interest factor in his calculations. But we may suppose that it has now become so evident that the traditional distribu tion of these resources between the different industries is wasteful that the dictator feels compelled to attempt a redistribution which will secure the use of the resources to the best advantage. On what principle will he have to act? We mentioned in the last chapter that, in discussing this problem, we should at first make a further simplifying assumption. We shall assume that what the dicta.tor aims at is to produce the greatest possible _ and now aim. al income stream which remains constant in prodQolDclalhefutun Ihe enaltt! pOllIIlI. size. This means -that for the present ualtaat laoome we shall exclude the possibility both of Itnam temporarily reducing the income stream in order to increase it by a larger amount at a later date, and of a temporary increase in consumption (even if advan tageous because it would not entail any considerable reduction in the income stream at later dates). This assumption that under all conditions the aim will be to secure a constant income stream is, of course, highly unrealistic,l and will be removed at a more advanced stage of the analysis. But for the time being, and until we expressly introduce more specific assumptions about the willingness of people to sacrifice part of their present income in order to obtain additions to future income, or vice versa, this assumption will help us in much the same way 80S the hypothesis of the stationary state helps us in general economic analysis.

1 This is particularly the case if we interpret our assumption in the strict sense of the dictator having to reach at once the maximum income stream which can be permanently maintained.. But if we want to exclude any consideration of the sacrifice he is willing to make in order to increase future income at the expense of present "income, we shall have to interpret our assumption in this strict form. and not allow him any time during which to approach this maximum rate of consumption - although output may increase more slowly if consumption in the meantime can be supplied from stocks.

158 I nvestment in a Simple Economy PT. II But it is first of all necessary to define the concept of a constant income stream more exactly. If it is taken too literally, to mean that the income must also be 'of Meanlngofaconstant constant composition, i.e. that it must con Income stream sist at every moment of the same combination of the various commodities, a great many of the possible improvements in the use of the available re sources will be excluded. Making better use of the existing resources will not only mean producing certain com modities in different ways; it will also mean extending the production of some of them at the expense of the produc tion of others. And even though we do assume that the level of total satisfaction has to be maintained constant throughout, our dictator will evidently have a much wider range of possibilities of improvement before him if he is allowed, in the course of reorganising or readapting the existing structure of production, to substitute additional quantities of some commodities at certain points for equivalent amounts of other commodities.

By admitting this possibility of changes in the com position of the income stream we are, of course, leaving the completely stationary conditions which have formed the subject of most of our discussion up to this point. Hence forth we shall deal with equilibrium conditions in the wider sense explained above in Chapter II, that is, we shall merely assume that the data given to our dictator at the beginning of the period remain unchanged; but these data include foreseen changes in circumstances which will make him plan from the beginning for all those successive changes in his allocation of resources, which the conditions of the moment will cause to appear appropriate. A constant income stream then has to be defined not simply in physical terms as such and such quantities of each of the commodities included, but in value terms. It need not be of The best way of describing it will, of course, constant composition be by the apparatus of indifference curves, or rather n-dimensional indifference surfaces. If we CR. XII Planning for a Constant Output Stream 159 assume that the preferences of our dictator at every successive moment are represented by an identical!

system of indifference curves, then an income stream of constant value will have to consist at every successive moment of a combination of goods which occupies a position on the same indifference surface. At successive points of time additional quantities of some commodities (or perhaps commodities which were known but not produced previously) can be substituted for some of the commodities available at earlier moments, but they must always be in such quantities that the additions just compensate for the deductions without making the total in any way more or less attractive. We have assumed that from the date at which the rearrangement of resources is made our dictator has to keep the income stream constant. His task, subject to this condition, is to maximise the income Every change In dls stream by making the best possible use of position of resources Involves two shifts In the available opportunities for increasing opposite directions output by investing some of his total input for longer periods and some for shorter periods. We have already seen that every attempt to improve upon the original arrangement of the resources, which also yielded a con stant income stream but not one of optimum size, neces sarily entails this double shifting of resources in opposite directions in time. The postponement of the date at which the return from any particular investment will become available will mean, ceteris paribus, that though the income stream will be swelled at this later date to a higher level than it would otherwise have reached, it will be reduced at some earlier date below that level. This 1 We have to postulate identity of tastes at successive moments in this sense in order to give the concept of a; constant income stream an objective meaning. The subjective views of the person in question as to what increment of income at one date just suffices to balance 8 decrement at another date belong to the phenomenon of time prefer ence which we want to reserve for later treatment. See Chapter XVII below, and Hayek, 1935b.

160 Investment in a Simple Economy PT. n gap will have to be filled by some reshuffling of resources. And if the whole transaction is to be advantageous it must be possible to shift some other resources from production for the later date to production for the earlier date at a cost which is smaller than the gain from the first operation. Let us first consider variations in the investment periods of individual units of input in a case where it is easy to follow the connection between changes in their invest The exteDllon of the ment periods and changes in the product, Investment periods of i e a case where the investment period of a Individual units of •• . Input single unit or a small group of units of input can be altered without at the same time altering the investment periods of other units. Under the conditions that we have assumed there will always be some instances where the profit to be obtained by lengthening the invest ment periods of individual units· of input will be particu larly conspicuous. A certain material, say a quantity of coal, which had originally been intended to heat a house during some period in the immediate future, might, if it could be made available for smelting iron ore, make possible the production of certain urgently needed tools which would at a later date make a very considerable contribution to the output stream.

But if advantage is to be taken of this opportunity and the total income stream is nevertheless to be kept constant from now onwards, two further adjustments in The compensator1 the disposition over the available input IhortenIng of the In-will be necessary First it will be necessary vestment periods of ., other Input to fill the gap created in the earlier segment of the income stream, at the expense of the later segment, so that the income will again be equally large at both dates but larger than it was before the rearrangement. In many instances the readjustment will have to take place in an indirect, roundabout way, involving changes in the use made of a great many different kinds of input. But to begin with a comparatively simple case, we shall assume that the change which just compensates for the CR. xli Planning for a Constant Output Stream 161 extension of the investment period of our quantity of coal consists in using for curren t consum ption certain input which under the old scheme would have gone to produce some commodity which would have matured at the time when the product of the coal is due to mature under the new scheme. Assume, for instance, that, at the time when the new increased product of the coal is due to mature, some durable consumer's good will wear out and would under the old arrangement have had to be replaced: but as it is decided not to replace this good, t~e input which between now and the date concerned would have been used for that purpose becomes available for current consumption.

But after this second rearrangement we shall still only have increased the income during two segments of the future income stream. And to make it constant all the time it will be necessary to make further Similar changes will h . f '·1 t . th have to be made in exc anges 0, a SImI ar na ure In e the use of input at all utilisation of input accruing at all future future dates dates. Tl).is means that not only the investment periods of one pair of present units of input, but also the invest ment periods of all the corresponding units of input accruing at later dates will have to be adjusted in like manner iQ. order to make the future income stream constant. Hence one effect of the change will be that, instead of the services of the durable good, we shall, from a cer tain date onwards, have the services of the new product of the coal., And since a corresponding The net effect of the t ·t f . I tl d d ·11 double change Is a quan 1 y 0 coa curren y pro uce WI new constant income be used in the same manner at all future stream dates, or since the labour and other input invested in this quantity of coal will in the future always be invested for t he longer period and will yield a correspondingly larger product, this change will mean a permanent addition to the future income stream. Against this we have to balance in the first place the temporary gap ca:used by 12 162 Investment in a Simple Economy PT. n investing the coal for a longer period. We shall assume for the purposes of the argument that the services which we can expect to obtain from the product of the coal will be just equal in value to the services which the durable consumer's good renders while it lasts. ~n the second place, we have to take account of the decrease in the product from the input which would have been used, under the old arrangement, to replace the durable good, and which is now used, under the new arrangement, to serve current consumption.

The net effect of these various changes on the size of the ipcome stream can be shown more easily by means of a simple diagram (Fig. 10). The two dotted lines marked Diagrammatic lllus-A and B in each of the two parts of the tration diagram represent the streams of input which, under the original arrangement, would have been currently used to reproduce the quantity of coal and to replaee the durable good respectively. This-original A~~.~.~ .. ~A~.~~.~ .... ). ~ - ----- - ---- -- ~ rei'" - - - - - - - - - - --~ ~-----------. ~-~-~~ rc;r-------~ L::l.. __ _____ .. r7T---- ---- -~ r-::I ~----------~ ~ B~~~~ [-E----'---------. ---------------~ B. f. .. t.1 .. t . .t. .. t .. .t. . .1 ... 1..> FIG. 10 arrangement is shown on the left-hand part of the diagram, and the right-hand part represents the situation after the change has been made. The blocks marked C ·and D show the stream of services to be obtained from the coal and the durable good respectively: the height of the blocks represents the rate at which the services will acorue and their length represents the period during CR. XII Planning for a Constant Output Stream 163 which they will accrue. The continuation of these blocks in dotted lines in the left-hand part of the diagram indicates the similar services which would be obtained if o and D were continually replaced. This replacement through the investment of input is indicated by arrows.

In the original position (shown on the left) the groups of input A and B would be continuously invested to repro duce goods similar to 0 (coal) and D (the durable con sumer's good). But under the new arrangement, where the product of the investment of A (i.e. the coal) is invested further in order to give later a larger product, 0', the flow of services B has to be used for direct con sumption as it becomes available, and accordingly gives a smaller product. This decreased return from B is shown by the narrow strip E at the bottom of the right-hand half of the diagram. Since the current use of a constant stream of input will obviously give us a constant stream of output, it is clear that, in order for the total income stream to be constant also, the rate at which services will be obtained from 0' will have to be exactly equal to the rate at which services will in the near future be obtained from D. In the preceding paragraph we assumed that this was so, and it will now be clear why this assumption was necessary.

This last conclusion, which may at first sound surpris ing, becomes plausible immediately we look at the situa tion in a slightly different way. It is really the existence of the stream of services embodied in the durable good (D) which makes it possible to wait (without temporarily reducing the income stream below its previous level) for the product of some other resources. In the initial situa tion it was the stream of input B which was invested (to reproduce goqds of the type of D). In the new situation another kind of input, i.e. the coal, which has for the . most part still to be produced by the investment of A, is invested instead and B is used for current consumption. Instead of a single good D, we might of course have taken 164 Investment in a Simple Economy PT. II any group or aggregate of nonpermanent resources which would have served the same purpose. In order to make the further investment of 0 possible in the case assumed, all that is necessary is to find some group of commodities which, in the interval before the product of 0 becomes available, will give services that are equal in quantity to those which 0 will produce later.

But what decides whether the whole transaction is advantageous or not? The part of the total income stream which consists first of the services of D, and then The conditions under of 0' and the goods that replace it, is just which the rearrange-equal in value to the part which was ment will give a net gain formerly obtained from D and which could have been continuously obtained by replacing D. The net change in the total size of the income stream will therefore depend on the relative magnitude of the return formerly obtained from the group of resources A (shown by the strip marked 0 on the top left-hand side of the diagram) and the return now obtained from the group of resources B (shown by the strip marked E at the bottom of the right-hand half of the diagram). If the latter is greater than the former the difference is clearly a net gain. If it were smaller the transaction would have resulted in a net decrease of the total income stream instead of an increase.

These income streams (0 and E) are the product of resources either of which could equally well have produced an income stream of the size of D or 0' if it had been invested to yield its product later by an interval corre sponding to the duration of D. But if the product (0) of A is invested further for this period, the final product of the magnitude of D will grow from a smaller magnitude than if B is used instead, i.e. the rate of increase obtained by extending the investment period of A will be greater than that obtained from the extension of the investment period of B. This means that we get a given part of the output stream, of the size of D, at a smaller sacrifice of other CR. XII Planning for a Oonstant Output Stream 165 output by investing A instead of B for the longer period and .. are therefore in a position to increase the size of the total output stream. It will now be evident that whenever the rate of in crease of the product which can be obtained by lengthen ing the investment periods of some units of input is greater than the rate of decrease of the The eondlUon for product caused by shortening the invest-maxlmlslng the Income stream Is equal ment periods of other units of input by the lsaUOD of all rates of same interval of time, it will be advantage-Inerease ous to make the corresponding changes. So long as there are differences in the rates of return that are obtained by investing different units of input for any given period, it will be possible to go on increasing the total size of the income stream in this way. Hence the condition for maximising the total income stream which we have been seeking is that this rate of increase of the product due to an extension of the investment period by a given interval shall be the same for all investments.

We shall, however, soon see that, in the form in which it has just been stated, this condition is a necessary but not a sufficient condition for fully determining the opti mum position. The rates of increase of Necessary qualillca the product which are due to the extension Uon of this statement of the investment period by any given interval must be the same for all units of input. But this says nothing about the relationship which has to prevail between the rates of increase due to investments for different intervals. As we shall see, it is only after this question has been considered that a complete solution to our problem can be formulated. But since a full discussion of this point will take considerable time, and since it is closely connected with several other points, it must be postponed to a later chapter. In the meantime it is necessary to add some further remarks on the concept of a "rate of increase of the product" and the terms in which it is measured.

166 Investment in a Simple Economy PT. n If we could assume that the relative values of the different commodities always remained the same, that is, if our constant income stream were also of constant The rates of Increase composition, then the concept of a uniform when the kind of out-rate of increase for all investments made at put chaDges • f'" d . t th one pomt 0 tIme an maturmg a ano er would present no difficulties. Whenever the sacrifice of a given quantity of one commodity at the earlier date led to the production of an increased quantity of the same commodity at the later date, the ratio between these quantities would have to be the same for all the com modities concerned. And in the probably more numerous cases where the sacrifice of a given quantity of one commodity at the earlier date led to the production of a quantity of another commodity at the later date, these two quantities would have to be such that their value equivalents in terms of any third commodity at the two dates would bear the same ratio to one another. There would then be a uniform rate of increase over the interval concerned which, in terms of no matter what commo dity we expressed it, would show the same numerical value.

We have already observed, however, that this sort of stationariness is not compatible with making the best use of the existing stock of nonpermanent resources. During Why the relative the initial rearrangement of the resources values oUhe dillerent certain substitutions of one kind of com commodities wlU usnally ohann during the modity for another at successive dates will process of adjustment be part of the plan. And the same will apply, although to a lesser and rapidly diminishing degree, ' to all later stages of the process of change. The reason is, of course, that we start out with an assortment of non permanent resources, which is the result of a particular historical development, and which will consist in large part of items which it is either impossible or else unprofit able to reproduce. Since the form in which these re sources exist at the beginning, and at every subsequent CR. XII Planning for a Constant Output Stream 167 stage, will exert an influence on the kind of resources by which they will be replaced, and since the resources existing at every moment are determined by past condi tions, we have to deal with a process of continuous change.

Even if we could assume that at the initial moment, when our dictator makes his new plan, he is in possession of complete knowledge of all future conditions, this plan would have to envisage an infinite series of changes. These changes would, it is true, rapidly decrease in mag nitude as time went on, and would after a while become insignificant, but in principle they would continue in some small degree for ever. This means that we shall have to deal with a stream of different goods whose relative values will be con stantly changing, at first, perhaps, quite considerably and even later to some extent. In such a The rates of Increase system the concept of a uniform rate of when the values oftoe dlllerent commodIties increase of all investments made from one change point of time to another point of time is much less simple, but it still has a quite definite meaning. We now have to take account of the possibility of a change in the value of every single commodity relatively to the values of other commodities. But it will still be true that, measured in terms of anyone commodity, the rate of increase will have to be the same for all commodities.

The actual numerical value of this rate of increase will, however, be different, according as one commodity or another is chosen as the standard of comparison or "numeraire ". This statement requires some elaboration. Let us consider two points of time of which the earlier one repre sents the date at which numerous investments are made and the later one the date when these investments mature. Let us assume further that the relative values of the different commodities are different at the two dates. If we now take anyone commodity (definec;l in technical terms) which is used at both dates and of which the 168 Investment in a Simple Economy PT. II quantity available at the later date can be increased at the expense of the quantity available at the earlier date, we shall have a definite quantitative rate of increase due to the "investment" of that commodity. For another commodity we. shall probably find a different rate of increase. Equilibrium (i.e. the most advantageous dis position over the resources) requires that these two rates of increase between the two dates shall stand in a definite relationship to the relative values of the two commodities at the two dates. If we take such quantities of the two commodities as are of equal value at the first date, and make them increase by investment at their different individual rates, the quantities of the two commodities obtained at the second date must again be of equal value.

This, of course, amounts to the same thing as the state ment made before, that in terms of anyone commodity (any "numeraire") the rate of increase must be equal for all commodities. Although the quantitative ratio between the physical amount invested at the earlier date and the physical amount obtained at the later date may be different for different commodities, the value equi valents in terms of the "numeraire" at the two dates must bear the same ratio to one another for all com modities. It is probably unnecessary to emphasise that there is no way in which this multitude of different" own rates of interest" (as Mr. Keynes has called these rates of increase No One rateoflncrea.e in terms of particular commodities) can can be regarded as be reduced to one single rate which has II the" rate of pro" duetlvlty 01 IDvest-a stronger claim than any other to be rement garded as the rate of productivity of invest ment. To distinguish, in any particular case, between the part which is due to circumstances affecting the value of the particular commodity and the part which is due to the productivity of investment is just as impossible as to divide the change in the relative value of two com modities into the part which is due to a change in the CH. XII Planning for a Oonstant Output Stream 169 value of the one, and the part which is due to a change in the value of the other. Although the search for this philosopher's stone is probably still being, pursued by some economists, nothing more need be said about it here, CHAPTER XIII COMPOUND INTEREST AND THE INSTANTANEOUS RATE OF INTEREST IN the last chapter we found one of the conditions which must be fulfilled if the maximum constant income stream is to be obtained from a given stock of nonpermanent A uniform rate of In c ..... for aU Invest menta between anJ two polnta of time 11 on\J one oondlllon of malllmum resources in collaboration with a constant flow of input. This is that the rate of increase of the product which is due to the investment of input from anyone poirit of time to any other point of time shall be the same for all units of input that are invested for this particular time interval. It will be remembered that when we speak of " the rate of increase being equal " we do not mean that the rates of increase in physical terms must necessarily be equal for all the different commodities, but only that the rates of increase in value terms must be equal.