L.S.E. Essays on Cost

2

Remarks upon certain aspects of the theory of costs

by LIONEL ROBBINS

The theory of costs is not one of those parts of economic analysis which can properly be said to have been unduly neglected. It has always occupied a more or less central position, and in recent years it has been the subject of a quite formidable body of new work. There is, indeed, no part of his subject about which the contemporary economist may legitimately feel more gratified, either as regards the quality of the work which has been done or as regards the temper in which it has been undertaken. Yet, in spite of this, the present state of affairs in this field is not altogether satisfactory. The various problems involved have been tackled by different sets of people; and the conclusions which have been reached in one part of the field have sometimes a rather disquieting appearance of incompatibility with conclusions which have been reached elsewhere. No doubt some of this apparent incompatibility is real. It is not to be expected that here—any more than elsewhere—economists should have reached finality. But some of it is probably illusory; and if in discussing these matters we were to state more decisively the problems which we are attempting to solve, and the assumptions on which we proceed, it seems likely that not only should we be able to clear up our outstanding real points of difference more quickly, but that, in the course of doing so, we should also discover that many of them depended essentially upon subtle differences of object and assumption, hitherto insufficiently stated. At any rate, it is in the belief that this would be so that these very tentative remarks are put forward.

The paper falls into four parts. In the first I discuss the fundamental nature of costs; in the second the relation between this
conception and the Marshallian supply curve; in the third the relation between costs and technical productivity. I conclude with some notes on cost variation through time.

I

I start, then, with fundamentals. The conception of costs in modern economic theory is a conception of displaced alternatives: the cost of obtaining anything is what must be surrendered in order to get it. The process of valuation is essentially a process of choice, and costs are the negative aspect of this process. In the theory of exchange, therefore, costs reflect the value of the things surrendered. In the theory of production they reflect also the value of alternative uses of productive factors—that is, of products which do not come into existence because existing products are preferred.
*10 Such is the conception of costs first systematically developed by Wieser
*11 and made familiar in English-speaking areas by Green, Wicksteed, Davenport, Knight and Henderson.
*12 Following the usage of Pantaleoni
*13 and many others, we may refer to it for short as Wieser’s Law.

It is probably true to say that at the present day the broad outlines of this conception are generally acceptable.
*14 The work of
Wieser’s successors in this field—in particular the various writings of Professor Mayer—have brought home to us all its central importance as a unifying principle in the structure of modern analysis. And, in the sphere of applied economics, it becomes more and more clear that many of the most urgent problems of the day can be understood only in the light of the knowledge that it furnishes.
*15

But there is one matter on which there is not yet full agreement. It relates to the precise
mode in which the displaced alternatives are to be conceived. Wieser’s usage is clear. They are to be conceived in terms of
values—in terms of the values of the goods of the first order displaced. ‘The cost of production of one thing’, said Wicksteed, ‘is the marginal value of another thing.’
*16 This is the sense in which it has usually been understood. In recent years, however, it has been suggested in some quarters that they should be conceived in terms of technical
quantities-in terms of the quantities (as distinct from the values) of the goods of the first order which might have been produced. This is the procedure suggested by Professor Knight in his ‘Suggestion for Simplifying the Statement of the General Theory of Price’.
*17 He invokes Adam Smith’s parable of the beaver and the deer and concludes: ‘In sum, the cost of beaver is deer and the cost of deer is beaver, and that is the only objective and scientific content of the cost notion.’ The same procedure is adopted by Dr Haberler in his recent article on the theory of comparative cost.
*18

Now there can be no doubt that there is much that can be said for this suggestion. The conception of costs as technical displacement has an objectivity and precision which is in itself an advantage. It has none of that elusiveness which seems to inhere in concepts involving subjective valuation. Moreover it is true that in equilibrium the values of goods produced with common factors of production and variability of technical coefficients are necessarily in harmony with their displacement-cost ratios. It has been well known since the time of the classical economists that this was the case with the products of simple unskilled labour. This is, of course, the moral of the parable of the beaver and the deer. It is the achievement of Professor Knight and Dr Haberler to have shown that the same generalization can be extended to cover the
case of production with more than one factor of production. If the amount of a commodity produced by a combination of factors of production is not the same as can be procured by devoting the same combination to the production of something else and procuring the first commodity by way of exchange, then clearly, if the conditions of production are technically variable, there will be evoked movements which tend to bring about this harmony.

So far so good. The argument seems overwhelmingly convincing. But on closer inspection certain difficulties present themselves. In the first place it is important to recognize that there are wide areas where the conception of costs as technical displacements clearly has no application. This is the case if the productive process involves fixed technical coefficients. The imputation problem (and hence the cost problem) here can only be solved in value terms. Costs of production in value terms can and will change with changes in demand.
*19 But the idea of changes in technical displacements in this instance has no meaning. The same is true where we are considering commodities produced with different factors of production. If A and B are produced with
n and
m and C and D with
p and
q, there will exist exchange ratios
between members of the first group and members of the second, but it is impossible to conceive of technical displacement cost ratios save
within them. There may be an exchange ratio between A and D, but when A is produced there is no technical quantity of D sacrificed. Yet there will certainly exist costs of production in the value sense.

Moreover—and this is even more important—it is the central requirement of any theory of cost that it shall explain the
actual resistances which production in any line of industry encounters;
that it shall explain to us the influences determining the elements of which account is taken by those responsible for production. Now there can be no doubt that these influences are of the nature of valuations. The isolated producer thinks of the sacrifice he is making by not producing something else. The entrepreneur in the exchange economy thinks of the prices he has to pay for the factors of production. In each case, although—as with all valuations—there may be in the background a technical condition, yet the final determinant is not merely technical. The isolated producer thinks not merely of the quantity of goods he gives up, but of their place on the relative scale, compared with the place on the relative scale of the goods he acquires. The price which the entrepreneur pays for the factors of production he uses is determined not by the
number of products which they can produce elsewhere, but by the value of such products. Indeed it is most highly improbable that he knows at all the number of products which can be produced elsewhere. All that he knows are values of the factors of production, which are, of course, reflections of the value of other products. If we reflect upon the way in which equilibrium is established, it is surely obvious that it is only through regard for cost in the value sense that any harmony between technical displacements and prices can be conceived to come about. It is only in equilibrium that such a harmony exists. In a state of disequilibrium, prices, costs and displacement ratios may all be different. If we do not keep these things conceptually discrete, we cannot understand the actual process of equilibration. This is not merely true of the Austrian approach. The condition that prices shall be equal to cost of production in the value sense is as essential a condition of equilibrium in the Walrasian system as the condition that marginal products shall be proportionate to factor prices.

For both these reasons, therefore, because there are whole areas where technical displacements are not conceivable, and because it does not focus attention on the actual process of price formation, I conclude that the conception of costs as quantities of goods forgone is not acceptable. No doubt the technical conditions of production play an important part in determining the conditions
of equilibrium. But to make the cost concept purely technical is to deprive it of important analytical functions and to run the risk of misunderstanding. We shall see that a very similar procedure underlies some of the deficiencies of particular equilibrium analysis.

II

But if this is so, what are we to say of the constructions, so familiar in the Marshallian system of what is sometimes called—in my opinion not very helpfully-‘partial equilibrium analysis’: the supply curve parallel to the
x axis, and the supply curve with a negative inclination? At first sight we seem to be faced with a complete contradiction. Here are constructions which, if
they are valid, seem to point to a definite rejection of our fundamental
conception, while if
it is valid, seem themselves to be doomed to be rejected. Nor are we in any way reassured when, turning to post Marshallian criticism, we find it stated on high authority that, for the analysis of competitive conditions—and of course it is competitive conditions which are in question—constant cost is to be regarded as the normal and increasing cost as the quite exceptional condition.
*20 We seem to have discovered a major inconsistency in the very centre of the corpus of pure economics.

Now in circumstances of this kind, before concluding that it is necessary to make a complete break with one or other of the apparently conflicting usages, it is always advisable to inquire more closely into the implicit assumptions on which they proceed. Again and again in the history of economic thought the apparent contradiction between different usages has come to be seen to rest not upon deficiencies of logic on the one side or the other, but upon differences of assumption concerning the problem to be solved. This was notoriously so in the case of the historic disputes regarding the theory of rent.
*21 A similar difference can, I think, be shown to underlie part at least of this apparent contradiction in the theory of costs.

For if we look more closely at the constructions in question, it becomes fairly clear that they are appropriate to the investigation of fundamentally separate problems. The general propositions regarding costs which spring from Wieser’s Law are essentially a description of the conditions of equilibrium. They answer the question, what would happen to costs if, from a position of equilibrium-
other things remaining equal-it were attempted to increase or diminish production in any particular line of industry. The constructions which we associate with particular equilibrium analysis, on the other hand, deal with what would happen if
other things were varied; i.e. if production were to be increased in
response to an increase in demand. That is to say, that they are essentially germane to a theory of variations. They relate not to forces which maintain equilibrium once it is established, but rather to the differences between one equilibrium position and another.

If what I have been urging is correct, it seems clear that we cannot regard the Marshallian supply curves as serving the exact purposes of any causal explanation. They are rather to be regarded as providing schemata of certain possibilities of price variation.
If the demand varies in this way and
if the cost varies in this way, then it is implicit in these assumptions that the price will change in this way. They provide, as it were, a convenient shorthand note of different ways in which particular changes may be regarded. According to Edgeworth, ‘movement along a supply and demand curve of international trade should be regarded as attended with rearrangements of internal trade: as the move
ments of the hand of a clock corresponds to considerable unseen movements of the machinery’.
*22 It is the implication of what I have already said, that this too must be the way in which we should view the supply curves of the theory of domestic values, if our usage is not to be out of harmony with the more precise implications of general-equilibrium analysis. They are notes of the implications of given changes of the general conditions of demand
and supply, even though one curve is not shifted.

If this is true, it follows that the construction in question must have a very limited validity for the analysis of the ultimate conditions of equilibrium. Its essential function is to facilitate the examination of what happens when certain conditions are varied. The assumption which underlies its use in descriptions of final equilibrium, that all possible variations outside the particular industry or market under consideration may be neglected, is essentially incompatible with the assumptions upon which any exhaustive description of such conditions must necessarily be based. This, indeed, is only another way of putting the point which has already been made. The assumption that the factors of production have an infinitely elastic supply leads to a concentration on the purely technical features of the situation which
necessarily misleads when the conditions of final equilibrium have to be determined. The objection made earlier to the Knight-Haberler method of treating technical displacements as equivalent to value costs applies much more strongly to a treatment of value costs which proceeds as if only technical determinants were relevant. It is quite true that, in a condition of competitive equilibrium, the prices of factors common to different industries are the same for the different industries concerned. But this is one of the
results of the equilibrating process. It cannot be assumed to be a
condition which would necessarily persist, were the other
relations in the equilibrium disturbed. Yet this, of course, is the implication of a ‘constant cost’ supply curve which is prolonged on either side of the point of equilibrium intersection.

But such uses have their limitations. It is clear that they may be very definitely misleading when it is a question of deciding the significance for the economic system as a whole of one equilibrium position as compared with another. As I have argued elsewhere,
*23 I am of the view that most investigations of this sort beg other, more fundamental, methodological questions. But, putting this on one side, it is surely clear that constructions which depend on the assumption that other things elsewhere remain unchanged, must necessarily lead to false conclusions when it is a question of estimating the total significance of changes which, by definition,
cannot be unaccompanied by changes elsewhere.

A simple example will make this clear. In the analysis of monopoly, for certain purposes the apparatus of intersecting demand-and-supply curves provides first approximations which are acceptable. But in any attempt to discover the significance for the economic system as a whole of monopoly in any line of industry it is open to very grave objections. For the assumption on which it proceeds—the assumption that other things remain equal—is incompatible with the most obvious implication of monopolistic restrictions; namely, the assumption that, since the number of factors employed in the monopolized industry is different from what would otherwise have been the case, their productivity in price terms
must necessarily be different. It is illegitimate to argue that this change is of the second order of smalls. It may be of the second order of smalls for the monopolist’s price policy. It may be
of the second order of smalls in each of the other branches of industry affected; but for all the other branches of industry taken collectively it must be of a magnitude comparable in the universe of discourse—the ‘social’ effect of the policy—with the magnitude of the primary variation. The objection, it will be noted, is almost exactly symmetrical with the fundamental objection to the use of the concept of consumers’ surplus.

The case I have chosen is, of course, a very simple one. I should be very sorry to be understood as suggesting that those who use the apparatus I am discussing more frequently than I would care to do are likely to be unaware of the proposition it exemplifies. But experience of the controversies of the last twenty years does, I think, suggest that the use of supply curves, rather than the apparatus of general-equilibrium analysis, in discussing questions of this sort, carries with it dangers which may entrap even the subtlest and acutest intellects. There is a passage in the late Professor Young’s critique of Professor Pigou’s former position with regard to diminishing return industries
*24 which has always seemed to me to be especially significant in this respect although, curiously enough, it has not attracted as much attention as other parts of the article. ‘The problem as a whole, it seems to me,’ he says, ‘is one to which the general theory of the diminishing productivity of individual factors is appropriate rather than the curve of marginal supply prices.’
*25 A fallacy which ensnared both Edgeworth and Professor Pigou is one which must necessarily be regarded as peculiarly deceptive. But I doubt very much whether they would have been thus ensnared if, instead of approaching the problem from the point of view of the intersecting curves of particular-equilibrium analysis, they had started from the marginal-productivity theorems—the example
par excellence of the general-equilibrium approach.

III

We have seen already that if demand for a particular commodity increases, it may be accompanied by changes in demand elsewhere such as to cheapen the factors of production in the line of production in question. This is a possibility which emerges from general-equilibrium theory, but it is not the
possibility with which I wish to concern myself in this connection. What I want to do rather is to concentrate upon the possibility of cost reductions which are due to the operation of technical factors.

But to solve the question in this way is only to find ourselves confronted with another. We have explained the possibility of
diminshing costs in this sense by invoking the existence of indivisibility in the methods of production. But the assumption of competition seems to preclude the existence of indivisible factors; in a fully competitive situation the factors of production must be capable of infinite division—or, in practical terms, of such degree of divisibility as to preclude the existence of any increasing return combination, using the term in its technical sense. How then, as the market enlarge with a general increase of factors of production, can we assume indivisibility to be exploited?

The example I have given is one which can be supposed to
occur under conditions which, to all intents and purposes, may be regarded as a capitalistic—that is, a condition in which production has not yet become, in important senses, roundabout: conditions in which there is little vertical division of labour. But, of course, it is under more fully developed capitalistic conditions that the phenomena which it typifies become important. As capital accumulates, and demand increases, it pays to combine original factors of production, hitherto used in other ways, to produce technically indivisible means of production—machines, means of transport, and so on, which hitherto, because of their indivisibility, have not figured in the realized system of productive combinations at all. (If we think of the way in which capital accumulation has made possible the utilization of indivisible transport systems, we can see how important considerations of this sort must be in any theory of localization.) It is clear that the advantages of roundabout production are essentially the advantages of this vertical division of labour and that another way of describing them is to say that they consist in the progressive exploitation of potential methods of production excluded in less expanded systems by their technical indivisibility.

It is in this sense, I take it, that we are to interpret the theory of increasing returns developed by the late Professor Allyn Young in his presidential address to the British Association.
*26 And it is worth noting, as he showed, how the phenomena in question escape the apparatus of particular-equilibrium analysis and, indeed, involve changes which are quite incompatible with its assumptions. Granted the assumption of the Youngian analysis, we can see how diminishing costs can be regarded as
implicit in a situation which is actually competitive. But we see, too, that such developments are to be regarded as being much more probably the function of the development of many industries than of one of them. We see too—and this is perhaps the more important point—that the diminution of costs here contemplated is essentially the product of vertical division of labour—that is, of the disintegration
of industries. Neither of these things is compatible with the implications of the supply curve. This seems to constitute a presumption that the use of this instrument in the analysis of variation may well involve a concentration on the insignificant exception to the neglect of what, both from the point of view of theory and practice, must be regarded as the typical and significant cases.

IV

So far in this paper the propositions I have discussed have for the most part dealt with variations of costs in terms of what has been well called comparative statics. That is to say, they consist essentially of a comparison of two states of equilibrium, and an investigation of the causes of difference. The demand for a group of products increases so that in the new equilibrium position factor prices and costs of production are different, and so on. They do little to elucidate the actual process of change—the path followed through time between one equilibrium position and the other.
*27 This is notoriously the field of theoretical economics in which least has been done and in which most remains still to do. In concluding this survey, therefore, it seems appropriate to add certain remarks on this matter.

It is not necessary in this connection to expatiate on the significance of the Austrian contribution to this theory. It is clear that, in the characteristically Austrian constructions, we have a technique which is pre-eminently suited to the explanation of the phenomena of movement. On the demand side, the conception of the dependent use (
abhängige Nutzen); on the supply side, the conception of the displaced alternative—here we are dealing with
elements which are the actual focus of attention of the economic subjects through whom changes come about. No one who has followed Wicksteed’s exposition of the continuous relevance of Wieser’s Law to the explanation of change
*28 can doubt that the main instrument of explanation in this field has already been devised.
*29

These things are well known. Rather than linger in this neighbourhood, it is more profitable to turn once more to the Marshallian system. For here we have theories in which propositions which are true and helpful are not altogether disentangled from ways of expression which sometimes give rise to misapprehension.

The Marshallian doctrine of short and long period price is essentially an attempt to provide a theory of price change in terms of the length of time which is taken to overcome various technical obstacles on the supply side. The relative specificity—to use Wieser’s term—of productive factors means that the immediate response to a change in the conditions of demand or supply is not necessarily a response to an ultimate equilibrium position. To take Marshall’s own example: in the short period, a change in the demand for fish will be met by an increased output from existing fishermen and a more intensive use of fishing gear already in existence. In the long period, however—I use Marshall’s own words—’the normal supply price… is governed by a different set of causes, and with different results’.
*30 Capital and labour come into the industry or leave it; the fixed equipment involved is augmented or depleted. In the sphere of cost theory this leads to the distinction between prime and supplementary expenses; in the sphere of distribution theory, to the distinction between quasi-rents and interest.

Secondly—and this criticism is more substantial—here too, as in other Marshallian constructions which we have examined, it may be objected that the emphasis tends to have too technical a
complexion. No doubt the technical obstacles to change, the resistances through time, are fundamental. But it should be clear that, given the range of technical obstacles, the obstacles that will actually be encountered in any process of adaptation depend essentially upon
estimates of the permanence of the change to which the adaptation is a response. The change which is expected to last for a short period invokes responses essentially different from the responses which are evoked by the change which is expected to be permanent. What are prime and what are supplementary expenses depend essentially upon the length of time over which a change of output is expected to be operative. Thus, if by long period we understand a period long enough for final equilibrium to be reached, we can say that the length of the period is not only a function of the magnitude of the technical obstacles but also of the expectations entertained by the producers. The time it takes for an industry to become adapted to a permanent shrinkage of demand depends in part upon the rate of physical depreciation. But it depends, too, upon the length of time taken by producers to become convinced that the chnage is permanent.

It seems therefore that in a complete theory of costs the part played by the estimates of the future of the various producers concerned will play a larger part than it plays in the original Marshallian doctrine. But, if this is so, then a further change is probable, which will necessarily bring this part of cost theory into more intimate relations with the other parts of the theory of change. There are certain cases of changes in data where different degrees of foresight on the part of producers have little effect save on the rate of adaptation. A single-line change of demand for consumer’s goods in a system otherwise in even balance may be a case of this sort. Here perhaps the old single-line methods of cost analysis may be sufficient to explain the total movement. But there are other cases where the different estimates on the part of producers will themselves bring about further changes in the general situation: a simultaneous falling off of demand for the products of a large group of industries, as at the turn of a trade cycle, is an instance. Here not merely the immediate policy of the producers concerned but the future course of the general oscillation
will be, in part at any rate, determined by expectations of the kind here discussed. And here single-line analysis is patently inadequate. If the cost problem here is to be handled properly, it must be dealt with in conjunction with the theory of economic fluctuations. It is probable that the extraordinary sterility of much contemporary thought on the problems of overhead costs and surplus capacity is due to the fact that this junction has not yet been satisfactorily effected.