Front Page Titles (by Subject) 11: G.F. Thirlby, Economists' cost rules and equilibrium theory - L.S.E. Essays on Cost
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11: G.F. Thirlby, Economists’ cost rules and equilibrium theory - James M. Buchanan, L.S.E. Essays on Cost 
The L.S.E. Essays on Cost, ed. J.M. Buchanan and G.F. Thirlby (New York University Press, 1981).
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Economists’ cost rules and equilibrium theory
First published in Economica (May 1960).
This is an article about rules, devised and advocated by certain economists, for the control of business and other undertakings: rules, such as the one which says that marginal cost ought to be equal to price, which prescribe what are claimed to be correct relationships between an undertaking's cost and revenue. I have attacked the rules before in a paper1 which has received some notice.2 The following observations on four crucial and interconnected issues succeed a re–scrutiny of some of the fundamental theoretical literature3 which must have guided me in the preparation of that article and one which immediately preceded it.4 While I am still following the same line of attack, seeking to expose the non–objectivity and non–implementability of the rules, I am this time offering a little more than a hint that the rules ought to fall away with the ground on which they were built, that is to say, with the notion of perfect competition or competitive equilibrium. This notion requires, I believe, to be replaced by a different notion of equilibrium which was, I feel, implicitly recognized in the earlier of my two articles to which I have just referred.
conflicting notions of rationality
In economics the human being is supposed to pursue ends, valued and chosen by himself, with the use of means of some kind.5 This behaviour, including the choice, is spoken of as rational behaviour. But the content of the conception of rationality varies. Sometimes it is adjusted to admit the behaviour of the ordinary, sane, human being who is limited in his knowledge,6 and can make mistakes in the processes whereby he selects and pursues his ends. Sometimes it is something less fallible than this, in that it includes knowledge that the behaving subject does not possess, or objective data of which the behaving subject may be unaware.7 At the extreme it is something which is omniscient and infallible: something which has, or is, perfect foresight.8 It was, I believe, because of an attitude which tacitly assumed that the behaving subject was possessed of a rationality which transcended his actual state9 that it became possible to put forward the rules as implementable controls. The appropriate assumption is the other one: that the human being is limited and fallible.
The act of choice, which is part of the rational behaviour, involves the rejection of a course of action to achieve a value which is called ‘cost’, and the selection of a course of action to achieve another value which, in the context of the rules, is often caled ‘revenue’. These two values, ‘cost’ and ‘revenue’, are the subject of the rules.
confusion on the meaning of ‘cost’
In the consideration of the behaviour of isolated man in the non–market environment (Robinson Crusoe), it is admitted that the two values compared (the ‘cost’ and the other one) are values of alternative end products that might be achieved by the use of the same resources. The full application of the same doctrine to the entrepreneur in the exchange economy would require the cost to be regarded as the entrepreneur's own valuation of the outcome of a course of action that he rejects. And because, as a first approximation, money revenue is regarded as the entrepreneur's single aim, this outcome would be an alternative money revenue.10 But the doctrine is not always fully applied in this way. The rejected course of action with its outcome of money revenue tends to be ignored, and to be replaced (as the ‘cost’ element to be compared with the ‘revenue’ element) by the entrepreneur's resources themselves (these being assumed to consist of money) or, what amounts to the same thing, by the ‘prices’ of the factors to be bought and used in the accepted course of action.11 At this point, ‘cost’, defined as money resource input, or outlay, relinquishes its connection with the end value of the use of the entrepreneur's resources in an alternative course of action, and consequently with the entrepreneur's act of choice.
But this is not all. The subtle change in the meaning of cost, from the valuation of his own displaced end product to the money input required for the selected course of action, is a change leading to still another conception, which carries with it the suspicion that it is to be regarded as a social cost. It resembles the first meaning of cost, in that it is supposed to be an alternative value displaced, but differs from it in that it is not the entrepreneur's own valuation of his own displaced end product, but other people's (consumers’) valuations of products which might have been produced by other entrepreneurs had they not been displaced. This further conception aries in this way. The money–resource input (or ‘factor prices’) of the first entrepreneur is now supposed to ‘reflect’ these other people's valuations. It reflects these valuations because any one of the factor prices is supposed to be the limit (it should strictly be regarded as being above the limit) that the excluded bidder (another entrepreneur) would be willing to pay for the factor in order to produce a product himself, and accordingly to reflect its contribution to the value of that product to consumers.12
So now it appears that the meaning of cost, in an instruction to an entrepreneur to observe a certain relationship between cost and revenue, could be any one of these three. The very doubt about which meaning to apply would impede the proper implementation of the rule, for clearly both controller and controlled would in this respect have to be at one. However, this obstacle to the control is supplemented, so as to reduce the idea to absurdity, by the realities that are obscured by the manner of discussion of the conditions of equilibrium.
neglect of time and uncertainty in equilibrium analysis
The presentation of the conditions of equilibrium13 proceeds in such manner as to suggest that the act of choice and the complete implementation of it occurred simultaneously. There is no apparent gap in time either between the selection of a course of action with its advance reckoning of cost and revenue, or between the beginning of the actual expenditure of resources and the termination of the achievement of the valued outcomes of the course of action taken. The rational choice which plans the achievement of a ‘revenue’, by the disposition of resources, at a ‘cost’ in some sense, virtually disappears from view, or becomes merged in the actual disposition of resources and the actual achievement of the actual ‘revenue’. The termination of the achievement of the valued outcomes (‘revenue’), which in reality may occur only at the end of a long means–ends chain of events (purchases, conversions into outputs, sales and the like) occurring over a long period of time, appears to be simultaneous with a single–resource input. This procedure of telescoping time out of existence tends to obscure two things, which, brought into light, are devastating to any supposition that the rule under criticism could be implemented.
First it obscures the fact that any cost in the sense of a displaced alternative value or revenue (the imagined outcome of a course of action which is not taken) will never have an actual, realized, counterpart, observed as achieved results, to compare with the imagined outcome. This absence of an actual counterpart is a necessary condition of the situation, whether we are referring to the entrepreneur's own cost, or whether we are referring to the ‘social’ cost14 (both of which I have explained in section II above), and is a condition which would obviously prevent the rule from being implemented in a manner which required results to be looked at to see whether the rule had been observed.
The second thing that is obscured and has to be brought to light is something which stands in the way of implementation of the rule, not at time of the checking of results, but at the earlier time of the generation of the rational choice in the mind of the maker of it, that is to say, at the time when the controller would, presumably, want to know whether the planned course of action was in accordance with the rule. This is the uncertainty, or limited rationality,15 of the entrepreneur or anybody who tries to supersede or control him. When it is understood that a reckoning of cost, according to any one of the three concepts16 referred to in section II, depends upon the forecasting of events and outcomes of the future, and when it is understood that any individual is uniquely situated in relation to past events on which such forecasts are based, it becomes clear that the result of the reckoning is dependent for what it is upon the unique knowledge and attitude (towards uncertainty or risk) of the unique and uniquely situated individual who calculates it, and that the validity, correctness or authoritativeness of an overriding calculation by somebody else would often be dubious in the extreme. The cost (as well as the revenue) calculation, or residual elements in it, is ultimately a matter of subjective opinion, and, where one person is trying to control the other, is likely to be a matter of differences of opinion. To the extent that this conflict arises and remains, the substitution of one opinion (the controller's) for another (the controlled's) as the authoritative one can be regarded as effecting also a transfer of the responsibility for the calculation. The prevailing opinion itself then escapes control, and it, instead of the other one, has to be taken on trust.
I have related these obscurities to the timelessness that appears in the statement of the conditions of equilibrium. This notion of equilibrium was attacked, and a different notion substituted, by F. A. Hayek in 1937.17 His attack was directed largely against the assumption of perfect knowledge (or what I have referred to as the omniscent type of rationality),18 and against the use of the propositions of the pure logic of choice (which were supposed to relate to the choice of equilibrium of the single individual) for the purpose of describing an equilibrium (or social choice) of many people working competitively.19 Thus his attack supports my attitude in this section, and casts doubt on the validity of the use, as the cost concept, of the value to consumers of displaced products that might have been produced by entrepreneurs other than the one having to make the cost calculation–the third concept in section II. His restatement substituted time20 for timelessness, and recognized a distinction between the individual's plan (or what I have called rational choice) and the subsequent execution of it. The individual's actions, taken in execution of his plan, were to be regarded as being in equilibrium relationships with one another so long as his actual actions agreed with his planned actions–which21 means, approximately, so long as the emerging events of the external world, including the actions of other individuals in execution of their own plans, permitted this agreement, or, in other words, so long as the relevant forecasts expressed or implied in his plan proved adequately correct. Similarly for society, or individuals, at large, equilibrium and its continuance depended upon an adequate compatibility of one another's plans22 and adequately correct forecasting of emerging objective data.23
neglect of discontinuity of knowledge within ‘the firm’
I referred in section II to the apparent conversion of the individual cost/revenue relationship into a social cost/revenue relationship and in section III to (what amounts to much the same thing) the conversion of the individual choice or equilibrium into a competitive social equilibrium. An objection to the latter conversion, and hence to the former, is that in this competitive social situation there is discontinuity of knowledge, as between the different individuals who, each on the basis of his own particular knowledge, make the forecasts on which in turn their own individual actions are based. Hayek, in raising this objection with regard to the competitive situation in particular, was pointing24 to the lack of theories relating generally to the communication of knowledge. Regrettably, although many of his general observations were relevant, his interest did not lie specifically in the similar discontinuity of knowledge inside large business organizations. Consequently he was not led to criticize the practice, in the theory of the firm, of drawing no distinction between the one–man firm and the multi–man firm–a practice which ignores the possibility that in the business organization there might be any number of planning individuals ranging from two to as many as would be found in the competitive situation.
The discontinuity of knowledge inside the organization is significant, in the context of economic and administrative theory, for at least two reasons. First it raises the question whether the conversion of the idea of an individual cost/revenue relationship into the idea of an overall, or organizational, cost/revenue relationship is worthy of the same scepticism as is the conversion of the idea of an individual cost/revenue relationship into the idea of a social cost/revenue relationship. Secondly it relates to the question whether an internal rule relating to the cost/revenue relationship is non–implementable in the same way as is an externally imposed rule. On this second question, I do not propose to say much more than that what applies to a rule supposed to be imposed by an external controller upon the entrepreneur applies in much the same way to a rule supposed to be imposed by a superior (coordinating) administrator upon a subordinate administrator in the organization. I want to deal briefly with the first question, because I do not wish to leave the impression that if the social relationship goes, the organizational relationship goes with it. Before I do that, it will be well to look at what is left of the cost/revenue relationship after my treatment of it in sections I to III.
It will be seen that, after rejecting the other notions of cost, I am left with the view that cost is the entrepreneur's own second–best outcome–value (second–best ‘revenue’) reckoned by him according to his own uncertain, highly subjective, calculations, and rejected by him in favour of his own, similarly calculated, best–outcome value (best ‘revenue’) from the use of the same resources. I am left, too, with the view that, with the multi–product and output–variation ideas introduced, this best outcome–value differs from the second–best outcome value only by a net marginal variation. I say ‘net’ because the marginal variation in the planned course of action, upon which the change in value is dependent, can be conceived of as having a minus (‘marginal cost’) effect and a plus (‘marginal revenue’) effect upon the value–e.g. when the variation in the course of action consists in ideationally reducing the output of one product (and so its revenue) a little, and increasing the output of another product (and so its revenue) a little.25
This view can now be reduced to the simple statement that the entrepreneur's total cost is approximately equal to his total revenue,26 and his marginal cost is approximately equal to his marginal revenue,27 but it is a view which allows the planned revenue, related to the planned resource input (money or mixed) of the selected course of action, to be of any magnitude.28 And, to reiterate, it is a view which sees the costs and revenues as subjective data–unrealized planning data belonging to the decisional process preceding action.29
Now it appears to me that a rule, based on this theoretical statement of the final situation in the entrepreneur's decisional process, would be not only non–implementable, but also about as instructive and guiding as–and possibly much less intelligible than–an injunction of the order of ‘seize your best opportunities!’ The statement is not intended to be the basis of a rule to instruct or control the behaving subject: it is rather a theoretical, hypothetical, statement offered as a description of the behaviour of the behaving subject.
I shall now assume that this statement, understood as I have explained it, is as applicable to the organization as to the individual, and that the multi–person organization replaces the one–man entrepreneur as the behaving subject.30 And I turn to the question whether this conversion is as worthy of criticism as is the conversion of the individual cost/revenue relationship into the competitive social cost/revenue relationship. On this issue, and in support of the idea of the organization cost/revenue relationship, I can do little more here than point to two significant differences between the competitive situation and the organization:
There is now little more that can be done in the space available than to stress that this assumption that the individual declares his plan for the purpose of coordination does not imply that the coordinator perceives and comprehends it with the same exhaustiveness as does the individual who submits it, or that the individual perceives and comprehends the other plans, with which his own have to be coordinated, with the same exhaustiveness as do the other individuals who have to prepare them. In the organization there is discontinuity of knowledge between people of limited rationality, gaps that are filled by reciprocal–(mutual) authority relationships which replace some of the single–minded coordinations which occur when the individual operates alone in a narrower sphere. The individual's plan, though it clearly must disclose the elements which are required to be known for the purpose of coordination,34 is, as communicated, an authoritative statement whose acceptance is of necessity one which is to a greater or less extent accepted on trust as a communication possessing the potentiality of reasoned elaboration.35 To say this is not to say either that the reasoned elaboration is never requested, or that the plan can never be ‘faked’–any more than that these same assertions would be made of authoritative communications in other spheres. But acceptance on trust has to enter. And within what is so accepted will often be much revealed and unrevealed cost–and–revenue calculation.
‘The Ruler’, reprinted here pages 163–98.
Latterly in J. Wiseman, ‘The Theory of Public Utility Price: An Empty Box’, reprinted here, pages 245–71.
Particularly Lionel Robbins, The Nature and Significance of Economic Science, 2nd ed (1935); Lionel Robbins, ‘Remarks upon Certain Aspects of the Theory of Costs’ reprinted here, pages 19–41; F. A. Hayek, ‘Economics and Knowledge’ reprinted here, pages 43–68 F. A. Hayek, ‘Scientism and the Study of Society’, Economica (August 1942, February 1943 and February 1944).
‘The Subjective Theory of Value and Accounting “Cost”’, reprinted here, pages 135–61.
Cf. Lionel Robbins, The Nature and Significance of Economic Science, p. 18.
It is so adjusted in the following statement, ‘It may be irrational to be completely consistent as between commodities ... just because the time and attention which such exact comparisons require are (in the opinion of the economic subject concerned) better spent in other ways. In other words, there may be an opportunity cost of “internal arbitrage” which, beyond a certain point, outweighs the gain’ (Robbins, The Nature and Significance of Economic Science, p. 92). This opportunity cost of ‘internal arbitage’, which is introduced to limit the pursuit of maximization, is referred to alternatively as ‘the marginal utility of not bothering about marginal utility’.
Robbins appears to switch to this view of rationality in giving an instance of inconsistency which can be shown up by economics: the inconsistency of wishing to satisfy consumers’ demands fully and at the same time wishing to impede the import of foreign goods by tariffs, (Robbins, The Nature and Significance of Economic Science, p. 92.) He refers to this as irrationality. It would seem to be open to an advocate for the person having these inconsistent wishes to plead that the person had not the knowledge to show that the wishes were inconsistent, that he preferred (to the marginal utility of the extra knowledge) the marginal utility of not bothering about it, and that consequently he was rational according to Robbins's earlier view. (See note 6 above.) At least we may say that if in this instance the behaving subject is irrational through ignorance, rationality implies knowledge greater than the behaving subject possesses, and consequently we are able to call a man rational or irrational according to which of Robbins's conceptions we use.
The fact is of course that the assumption of perfect rationality in the sense of complete consistency is simply one of a number of assumptions of a psychological nature which are introduced into economic analysis at various stages of approximation to reality. The perfect foresight, which it is sometimes convenient to postulate, is an assumption of a similar nature; and ‘Rationality in choice is nothing more and nothing less than choice with complete awareness of the alternatives rejected’. (Robbins, The Nature and Significance of Economic Science, pp. 93–4, and p. 152 respectively.)
And possibly, confused the rationality of the behaving subject with the rationality of an observing economist, who was assumed to be omniscient. See Hayek's discussion of the confusion about the data, or facts, of the demand schedules, where he raises ‘the question whether the facts referred to are supposed to be given to the observing economist, or to the persons whose actions he wants to explain, and if the latter, whether it is assumed that the same facts are known to all the different persons in the system, or whether the “data” for the different persons may be different’ (F. A. Hayek, ‘Economics and Knowledge’, p. 52).
Which, if 1) the entrepreneur were allowed to be considering the production of a second product, besides the alternative of disposing of his resources in the resource markets, and 2) cost were regarded as being the best of the rejected alternatives, could be the contemplated revenue from one of the products. Further, if the calculations were marginal calculations (which might incidentally lead to the selection and subsequent production of some of each product, so that the entrepreneur became a ‘multi–product’ entrepreneur), marginal cost could be the contemplated (extra–) marginal revenue from one of the products.
Space does not permit me to enlarge either upon how this replacement might be permissible as a conceivable limiting case, or upon the necessity for rejecting the money input concept on the ground that money is not the entrepreneur's only resource.
My account of the transition from 1) the isolated producer's end–product value, regarded as cost, to 2) the entrepreneur's money input or factor prices, regarded as cost, and regarded also as something which reflects the value of excluded products, is offered as a fair statement of what occurs in Robbins's ‘Remarks upon Certain Aspects of the Theory of Costs’, section 1, pp. 22–7. I cannot accuse him of actually calling the value of the excluded products a social cost, but the suggestion seems to be there, particularly, perhaps, in his insistence that the excluded products themselves, as distinct from their values, are not to be regarded as cost. For doubt cast upon the validity of the method of transition from the individual situation to the social situation, see Hayek's discussion in which he stated he had ‘long felt that the concept of equilibrium itself and the methods which we employ in pure analysis have a clear meaning only when confined to the analysis of the action of a single person, and that we are really passing into a different sphere and silently introducing a new element of altogether different character when we apply it to the explanation of the interaction of a number of different individuals’, and in which he stated that ‘the data which formed the starting point for the tautological transformations of the Pure Logic of Choice ... meant ... only the facts ... which were present in the mind of the acting person ... But in the transition from the analysis of the action of an individual to the analysis of the situation in a society the concept [of “datum”] has undergone an insidious change of meaning’ (Hayek, ‘Economics and Knowledge’, pages 47 and 51 respectively.)
My comments in this paragraph are supposed to reflect fairly upon Robbins's discussion of the conditions of equilibrium in the ‘Remarks upon Certain Aspects of the Theory of Costs’, but are not supposed to suggest that he is oblivious of time and uncertainty, either elsewhere in that paper, or in The Nature and Significance of Economic Science. In The Nature and Significance uncertainty appears, e.g. in references to the theory of profit. In the ‘Remarks . . .’, it appears to belong to references to disequilibrium and equilibration (and to criticisms of Marshall), rather than to the discussion of the theory of costs in its competitive–equilibrium setting. (And it was surely competitive equilibrium that set the standard for the special rules about the cost/revenue relationship.)
And, where the cost referred to in the rule is a marginal cost, whether we are referring to either of these or to the money input concept. Cf. ‘The Ruler’, page 191.
The significance of it will not be fully realized unless it is seen that the period of time between the rational choice and the achievement of the outcome of the accepted course of action may be, not just a minute or less, but anything between a minute or less and ten years or more. The degree of uncertainty will often be extremely high.
It should be clear that this obstacle to implementation would remain if the meaning of cost were money (or other) resource input. However short the period of time between the cost calculation and the occurrence of the events which were the subject of it, the cost calculation would be uncertain and a matter of subjective opinion. While, in pure equilibrium analysis, ‘it is simply assumed that the subjective data coincide with the objective facts’ (Hayek, ‘Economics and Knowledge’ page 56.
Ibid. And see also his, in many ways, supporting series of articles, ‘Scientism and the Study of Society’.
It is significant that in his criticism of the pure equilibrium analysis, Hayek remarks: ‘It seems that that skeleton in our cupboard, the “economic man”, whom we have exorcised with prayer and fasting, has returned through the back door in the form of a quasi–omniscient individual’ (Hayek, ‘Economics and Knowledge’, page, 58). In his restatement he said: ‘It is important to remember that the so–called “data” from which we set out in this sort of analysis are (apart from his tastes) all facts given to the person in question, the things as they are known to (or believed by) him to exist, and not in any sense objective facts’ (page 48). The ‘data’, distinguished from ‘the objective real facts’ as supposed to be known by the omniscient economist (page 52), are to be conceived of ‘in the subjective sense, as things known to the persons whose behaviours we try to explain’ (page 52). ‘Subjective data’ and ‘individual plans’ can be used interchangeably (note 11. page 56.)
Cf. note 12 above.
‘Since equilibrium is a relationship between actions, and since the actions of one person must necessarily take place successively in time, it is obvious that the passage of time is essential to give the concept any meaning’ (‘Economics and Knowledge’, page 49).
‘The equilibrium relationship comprises only his actions during the period during which his anticipations prove correct’. (‘Economics and Knowledge’, page 49).
For a society then we can speak of a state of equilibrium at a point of time–but it means only that compatibility exists between the different plans which the individuals composing it have made for action in time’, ‘Economics and Knowledge’, page 53).
‘It [equilibrium] will continue ... so long as the external data [the objective real facts] correspond to the common expectations of all the members of society’, (‘Economics and Knowledge’, page 53).
In both ‘Economics and Knowledge’, and ‘Scientism and the Study of Society’.
I hope to attempt in a subsequent paper a reconciliation of this restatement. and some other aspects of my paper, with certain modern administrative theory.
That total cost (in some sense) should be equal to total revenue is one of the rules (or part of one).
There is a rule (or part of one) that where marginal revenues differ from price, output should be extended to that point at which marginal cost (in some sense) is equal to price. This rule, I believe, falls away with the ‘perfect competition’ which is the ground on which it is based. However, with cost defined as I have defined it, it appears to fall away for another reason too. With cost so defined, marginal cost is always displaced alternative marginal revenue, and, consequently, from the point of view of the rule advocates, open to the same stricture as is the selected marginal revenue itself: to get a marginal cost which was independent of autonomous pricing, we should be driven back on to marginal money input.
i.e. there is no ‘cost’/revenue equality in this sense.
The statements in this paragraph and the preceding one represent the principles behind the model (in which, however, the entrepreneur is converted into an organization) in my ‘The Subjective Theory of Value and Accounting “Cost”’. See note 30 below.
This is the conversion that I effected in ‘The Subjective Theory of Value and Accounting “Cost” ‘. See note 29 above.
It seems to me that common–goal orientation is silently–and perhaps unconsciously–assumed in the economists’ practice of using the same cost/revenue diagrammatic apparatus to represent the behaviour of ‘the firm’ regardless of whether the firm is a one–man or a multi–man set–up.
Hayek, condemning ‘an illegitimate use of anthropomorphic concepts’, adds in a footnote, ‘What is said in the text does of course not preclude the possibility that our study of the way in which individual minds interact may reveal to us a structure which operates in some respects similarly to the individual mind’ (Hayek, ‘Scientism and the Study of Society’ part II, p. 45 and footnote).
The process is illustrated in my ‘The Subjective Theory of Value and Accounting “Costs” ‘.
For an illustration of what elements would have to be disclosed, see, again, the model in my ‘The Subjective Theory of Value and Accounting “Cost” ‘.
For this expression, see Carl J. Friedrich, ‘Authority, Reason, and Discretion’, in Authority, ed. Carl J. Friedrich, (1958).