L.S.E. Essays on Cost

Edited by: Buchanan, James M. and George F. Thirlby
(1919- )
CEE
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First Pub. Date
1934
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New York: New York University Press
Pub. Date
1981
Comments
Collected essays, various authors, 1934-1973. First published as a collection 1973 for the London School of Economics. Includes essays by Ronald H. Coase, Friedrich A. Hayek, Lionel Robbins, and more.
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9
Uncertainty, costs, and collectivist economic planning
by JACK WISEMAN

First published in Economica (May 1953).

I INTRODUCTION

9.1

The purpose of this paper is to consider the possibility, in conditions of uncertainty, of utilizing a marginal-cost 'rule' to distribute resources between uses in an economy in which there is consumers' sovereignty, with freedom of choice of goods and occupations, but in which factors of production cannot be privately owned and exploited.*28

9.2

It will be argued that in conditions of uncertainty (i.e. once the fact of time is admitted), the marginal-cost rule, as normally framed, gives no clear guidance to those responsible for the organization of production in such an economy. Attempts to reinterpret the rule in such a way as to take account of uncertainty preclude the possibility of a direct check on the efficiency of collectivist managers in obeying that rule. Any indirect, objective, check used as a supplement to the marginal rule will in fact supplant that rule as the directive for managerial effort, and in any case no completely objective check is possible. Further, whatever rule or check is adopted, imperfectly competitive behaviour is to be expected in the absence of detailed regulation to control it.

9.3

In these circumstances the most satisfactory distribution of resources seems likely to be obtained by an instruction to collectivist managers similar to the profit-maximization 'rule' of the market economy. Identification of the managerial and the public interest would then have to be sought through the detailed regulation of managerial behaviour, in much the way that the government in a market economy attempts to regulate imperfectly competitive behaviour by entrepeneurs.*29

II THE NATURE OF THE RULE

The competitive market economy

9.4

The 'rule' to be discussed derives from the classical model of the perfectly competitive market economy, and is best understood in relation to that model. It was elucidated in the course of controversy as to the possibility of distributing productive factors efficiently between uses in an economy in which such factors were owned collectively.*30

9.5

In this competitive market economy resources are privately owned and exploited. They are also, in the perfectly competitive model, perfectly divisible and perfectly mobile between uses. Producers are assumed to act in the light of known data; i.e. their task is the combination of factors of production with known prices in the production of products to be sold at known prices. The distribution of resources between uses is carried out by an administrative mechanism, the characteristics of which are profit maximization and a system of competitive markets in which buyers and sellers compete. With such a mechanism producers' decisions about the use of resources are determined by opportunity cost; i.e. the use of resources in the chosen way is the result of an assessment of the revenues to be obtained by their use in any other way, the greatest of these forgone alternative revenues being the opportunity cost.

9.6

With the conditions of the model the process described must result in an 'efficient' distribution of resources between uses in the sense that, with given consumer incomes, no reallocation of factors or products between uses could increase the satisfaction of any one consumer without reducing that of another. Since all relevant factor and product values are assumed known, there is no doubt about the production decisions to be taken by individual producers. The subjective (opportunity) costs have an objective counterpart in lists of known factor prices, which are in effect the sole content of the opportunity-cost decision. The producers' task is simply the pricing of money inputs (i.e. sums of known factor prices) and product outputs, in the case of some production plan, and the relating of this certain result to the money values of products forgone, the prices of these products also being known. Different individuals in similar circumstances should make identical assessments and reach identical decisions. That is, the opportunity-cost concept in such conditions is merely a reassertion of the fundamental economic problem of scarcity; it contains no element either of uncertainty or of judgement.

9.7

The competitive model as normally set out nevertheless contains an indirect check on efficiency in resource distribution, implicit in the mechanism of competitive profit maximization. It is a property of the ideally efficient situation that producers' total money revenues will equal their total money outlays (including payment for their own services). Inefficiency in production (and hence in resource distribution) results in a money loss which indicates a need to redistribute resources. That is, the final check on the efficiency of the individual firm would be the bankruptcy court. However, the idea that firms can be 'extra-marginal' (in this sense of money outlays exceeding money revenues) requires the introduction of time into the analysis in some form, since otherwise it is difficult to explain, in the light of the assumptions of the competitive model, how the resources came to be in that use or why there is not an instantaneous readjustment removing all extra-marginal production. This difficulty is usually circumvented, not by introducing a problem of judgement by relaxing the assumptions about knowledge, but by retaining the assumptions about knowledge and introducing time only as a modification of the assumptions about mobility. Only some of the productive factors are now fully free to move; losses can therefore be incurred as a result of the use of temporarily immobile factors, if the data on which the decisions were taken change after that use was decided upon.

9.8

A solution along these lines is uncomfortable in two important and related respects. The producer plans his productive activities in terms of factor and product prices of which it is assumed he has knowledge. It appears that he does not take possible future changes into account in reaching his decisions. If this is because the assumptions imply knowledge of future prices, and these are the prices which influence decisions whenever relevant, then how can the data change so as to create extra-marginality, since the change was foreseen? If, on the other hand, future conditions are not assumed known, then how can the producer plan in terms of known prices? Associated with this problem is the difficulty of establishing a precise relationship between mobility and time: the concept of the long period as a period in which all factors are free to move seems to make sense only if regarded as a planning period—i.e. a subjective notion about future activity sufficiently distant for all resource uses to be replanned. But such an interpretation appears to imply the need for foresight and judgement, which are ruled out by the perfect-competition assumptions.

The liberal collectivist economy

9.9

This then is the model from which the cost rule of the liberal collectivist economy derives. As has been said, a liberal collectivist economy is one in which resources cannot be privately owned and exploited. With this reservation the same freedom of choice of goods and occupations pertains as in a competitive market economy.*31

9.10

The administrative mechanism of profit maximization is replaced in the liberal collectivist economy by a 'marginal rule'. This rule has several formulations;*32 the most general one is the rule that managers of collectivist enterprises, working through a system of competitive markets similar to that of the market economy, should produce that output which makes marginal (money) cost equal to price. The origins of this rule are to be found in the model of the competitive market economy. It is a property of the 'efficient' situation in such an economy that marginal money cost (i.e. the sum of known prices of marginal factor inputs) of producing each product must be equal to the price for which the product can be sold. This equality is merely another way of expressing the fact that profit is being maximized, since in the conditions postulated a maximum profit (excess of revenues over outlays) is made when marginal cost is equal to price.

9.11

This is a property of the market economy model, an incidental result of the operation of the administrative mechanism of profit maximization in the rarified conditions of perfect competition. It is no one's purpose to make marginal cost equal to price. But in the liberal collectivist economy this incidental property becomes a principle of administration, by following which, it is argued*33 a liberal collectivist economy could not only effect an efficient distribution of resources, but could do so more quickly and accurately than a market economy, because a broader survey of the data relevant to his decisions could be made available to each collectivist manager.

III TIME AND UNCERTAINTY

9.12

Once we admit that the future is unknown, analysis of the behaviour of producers in terms of adaptation to known future conditions becomes irrelevant. It is therefore necessary to ask how the admission of time and uncertainty affects the administrative mechanism of the market economy and of the liberal collectivist economy. The task of the producer is now to decide, on the basis of his own estimates about likely future conditions, between the possible alternative courses of action open to him at any point in time. Present prices and conditions are relevant only in so far as they provide a basis for judgements about the future. There is now no reason to suppose that individuals in similar circumstances will make the same assessments and hence reach the same decisions.

9.13

The administrative mechanism of competitive profit maximization can still function in the market economy, but the 'efficient' distribution of resources between uses must now take account of the use of new resources and of the development of new products. An excess of money revenues over money outlays, once the element of judgement inevitable with uncertainty is admitted, is no longer necessary evidence of an inefficient distribution of resources; it may be due simply to exceptional skill in forecasting. But at the same time the fact of uncertainty makes the association of competitive behaviour and profit maximization, on which the market-economy model depends, less generally acceptable. The desire to reduce uncertainty by gaining control of the uncertain variables must be an important motive in attempts to eliminate competition. Uncertainty thus implies the need for positive government policy to ensure competitive behaviour in pursuit of profit maximization, since only such behaviour conduces to an efficient distribution of resources. The difficulty in framing such a policy lies in distinguishing those factors which are the inevitable accompaniment of ignorance and uncertainty and those which arise simply out of a desire to maximize net revenue in an environment characterized by these things.

9.14

It is no longer possible, once uncertainty is admitted, to interpret the opportunity-cost problem as one of scarcity alone, to be solved by a choice between alternative factor inputs and product outputs with all prices known. That is, opportunity cost is no longer a simple question of summation and comparison of known data. Prices and other variables have to be estimated: opportunity-cost decisions involve uncertainty (and therefore judgement) as well as scarcity. The cost problem now arises as a choice between alternative plans of action, i.e. a choice between a series of estimates of the outlays likely to be incurred and the revenues likely to be obtained as a result of the adoption of particular alternative courses of action. Costs are in fact incurred when decisions are made; to understand the use of resources over time it is necessary to go back to the decisions which decided that use, and to understand cost requires consideration of the estimated forgone alternative revenue associated with the decision when taken. These forgone alternatives (i.e. discarded plans) not then implemented may in fact never be implemented at all.*34 But in the circumstances of the market economy errors in the alternatives considered by any one producer do tend to be adjusted by the ability of others to take advantage of his oversight.

9.15

Since opportunity costs cannot be treated simply as known money costs, but must be considered as estimates of forgone alternative revenues, it is no longer very useful in conditions of uncertainty to speak of equality of marginal money cost and price as a property of an efficient resource distribution. This is unimportant in a market economy, since the equality comprises no part of its administrative mechanism. Uncertainty creates conditions in which it is to be expected that the mechanism of profit maximization in competitive markets will function imperfectly and will require positive government action to support it. But the final check on efficiency is still the bankruptcy court, and difficulties about the interpretation of the marginal-cost-price equation are unimportant to its functioning. In fact the admission of uncertainty disposes of those difficulties of the comptetitive market economy model which arise out of the association of time with resource mobility only. Once the assumptions about knowledge are dropped, 'extra-marginality' becomes reasonable; it is a function both of accuracy in forecasting and of speed of reaction to change (i.e. flexibility in coordination and the replanning of activities).

9.16

The problem is of greater importance in a liberal collectivist economy: it follows from the nature of the opportunity-cost problem that an instruction to equate marginal money cost and money price in conditions of uncertainty gives no clear guidance to collectivist managers as to their productive behaviour. Thus the rule requires reformulation. The most appropriate reformulation would appear to be in terms of anticipated objective outlays. The marginal cost of any decision must be the displaced alternative revenue which would have accrued from some alternative use of the resources concerned. To obtain this figure requires a comparison of alternative sets of ex ante budget calculations. Each set of calculations gives the expected revenues and outlays involved in the production of each of the two relevant outputs of some product. The budgeted marginal cost is the difference between the outlay and revenue calculations in the case of the best forgone alternative budget.*35

9.17

The question is whether the rule, thus reinterpreted, can provide an unambiguous guide for collectivist managers, and whether it enables a check to be made on the efficiency of the distribution of resources between uses similar to that provided by profit in the market economy.

IV THE RULE AS REFORMULATED

9.18

If no rule other than the marginal cost rule is used,*36 and that rule is interpreted as a relationship between budgeted marginal cost (as defined) and budgeted price, is there any check on the efficiency of the distribution of resources between uses?

9.19

A direct check on efficiency requires a check on decisions in relation to results. But only one of the budgeted outlays becomes a realized objective outlay, since only one plan can in fact be decided upon. Thus the 'marginal cost' with which we are concerned rests upon a judgement by the manager as to the accuracy of his estimates about the revenues which would have accrued had the forgone alternatives in fact been chosen. That is, estimation of marginal cost involves an inevitable element of personal judgement. There may in some cases be a check upon the 'reasonableness' of estimates. This is the more likely to be so the more the alternatives considered relate to the production of known things by known methods. The imponderables, and with them the difficulty of a direct check on efficiency, become the greater the more unique or novel are the matters with which decisions are concerned. All decisions about new and major investments of resources seem likely to involve important imponderables of this kind; it appears that those decisions likely to be most important to efficiency will be those upon which no adequate check can be made with the rule as now interpreted.

9.20

There is a further difficulty not yet considered. How is it to be decided whether the plans considered are the relevant ones? Suppose, for example, there is a difference of opinion about market prospects between the manager and the checking authority. If the checking authority can impose its views on the manager, then decisions about resource distribution (i.e. about costs) inhere in the checking authority; the decisions of that authority become the ones relevant to a check on efficiency, and the same questions have to be asked about them as about the decisions of the collectivist manager. The removal of investment decisions from managers robs them of their primary function from an economic viewpoint: the concentration of decisions in another authority shifts the relevance of the analysis towards that authority. It becomes appropriate to consider the joint decisions of the two bodies, in so far as any decisions are left with the manager at all. In effect, the vesting of such powers in the checking authority carries with it the need to abandon rules of the kind considered here, and to adopt some kind of centralist scheme*37 for the distribution of resources.

9.21

If the check is made at intervals, it must also be taken into account by the checking authority that estimates are subject to constant revision; skill and speed in revision must in effect be recognized as factors in efficient behaviour. But the existence of, and need for, such revision of plans is a further obstacle to a sensible check by an outside authority.

9.22

Thus, if the only criterion used is a marginal-cost-marginal-revenue relationship, as now defined, there can be no possibility of an unambiguous check on managerial efficiency through the use of these magnitudes. The most that can be done is to check efficiency, in the limited sense of correct forecasting, in the plan actually chosen. If both the manager's planned results and his realized results can be stated in unambiguously objective (empirical) terms, and if the plan is unambiguously his own, the comparison of planned and realized results provides (ex post) a check on forecasting efficiency in respect only of the plan actually chosen. But this provides only a very partial check, since it cannot explain whether that plan should have been chosen at all.

9.23

There seems little possibility of a direct check upon whether the marginal-cost rule has been obeyed: can the liberal collectivist economy then function without such a check? There are two possibilities: abandonment of any attempt to check obedience to the rule and the use of some other indirect check in the form of a relationship between total revenues and total outlays, ex post, arising out of the plan actually implemented.

V THE RULE WITHOUT A CHECK

9.24

The rule as reformulated does not carry with it any relationship between total revenues and total outlays. In the absence of some further instruction there seems no reason why a manager should not obey it whilst producing continuously at a loss.*38 The manager can check his own efficiency (i.e. the extent to which his activity conduces to an efficient distribution of resources, as defined), or can have it checked by someone else, only through the fulfilment or non-fulfilment of the plans he elects to implement. And even the meaning of the results of this limited check is not unambiguous: what degree of nonfulfilment should suggest to a manager (e.g.) that he should cease producing?

9.25

The manager is not told what things to take into account in drawing up budgets. As a result, it is to be expected that he will often base his policy partly upon judgements about the policy of his close rivals, since he considers this to be realistic budgeting, unless he is instructed to ignore such related policies when compiling his own. But how could such an instruction be formulated or enforced? Would it be conducive to efficiency in any case to attempt to make managers act on the basis of assumptions they believed to be unrealistic? But, in the absence of any guidance or control beyond the 'rule', it is a short step from this 'ogliopolistic competition' to attempts to make budgeting easier by reaching policy agreements with rivals—that is, to collusive, imperfectly competitive behaviour.

9.26

Knowledge of rivals' reactions gained in this way is not, of course, what is envisaged by those who suggest that a liberal collectivist economy could reach an equilibrium more quickly and efficiently because more data on which to base decisions could be placed at the disposal of each manager. Their argument is quite other: its basis is the idea that more information could be made available to all managers by the use of some kind of central information service. But there is a logical fallacy here. What each manager wants is knowledge of the firm plans of other managers, on which to base his own plans. But plainly not all managers can have such information unless either all plans are imposed from above (a possibility already rejected) or the plans are made jointly through some form of collusive (non-competitive) behaviour.

9.27

If there is to be no check on the efficiency of managers in attempting to obey the 'rule', the choice of the managers themselves becomes particularly important to efficiency. The market economy depends, for the correction of errors of judgement, upon the ability of any producer to take advantage of the oversights of others. From this point of view, any restriction of the field of choice of managers is a restriction upon possibly useful entrants and hence a curb upon efficiency. On the other hand, if anyone can be a collectivist manager, how are the managers of banking institutions to decide who is to have control over liquid resources, and how much?*39 Presumably they would have to try to judge whether the applicant was capable of equating marginal cost and marginal revenue, although, once the funds have been granted and used, those granting them become dependent upon the applicants' view as to whether this has been done or not.

9.28

It has sometimes been suggested, as an alternative, that managers should qualify by some kind of competitive examination.*40 Apart from the difficulty of formulating a suitable test, it still has to be decided what those who have qualified become entitled to. Can they all demand control over the same volume of liquid resources or does the volume controlled vary with seniority or is there some other means of deciding?

9.29

In the absence of a check on the outcome of managerial behaviour, then, managers will be uncertain as to the implications of the consequences of their own act, no other authority will be in a position to check the efficiency of those acts, oligopolistic and collusive behaviour is to be expected, and there is no clear criterion for the allocation of control over resources between managers. Therefore, while there can be no direct check on efficiency in resource distribution through the marginal relationship, an indirect objective check is plainy desirable; the problem is to discover one.

VI CHECKS THROUGH NET REVENUE

9.30

Since the marginal check is ineffective, the only possibility remaining lies in a check on efficiency depending upon the relationship between total money revenues and total money outlays. There are two possible relationships between total revenues and total outlays which might be accepted as a standard of efficiency: equality of total outlays and total revenues, and maximization of the excess of receipts over outlays.

9.31

The equality criterion is indicative of an efficient resource distribution only in the conditions of the perfectly competitive model. Uncertainty introduces the possibility of a difference between revenues and outlays due to exceptional ability in forecasting, and such a difference cannot be considered incompatible with efficiency. Thus to use such a check might entail the abandonment of plans which producers would expect to yield greater revenues for the same outlays. Since such plans would be implemented if the marginal rule were followed, a criterion of equality of total revenues and total outlays is incompatible with the marginal rule, as reformulated to take account of uncertainty. A check on the equality of total revenues and total outlays would not operate as a supplement, for the checking authority, to the marginal rule to be followed by managers, but would in fact replace that marginal rule as the directive to managerial effort.

9.32

The most likely result of the use of an equality criterion is secret budgeting for revenue surpluses on the part of managers. These surpluses can then be 'lost' if they seem likely to materialize, so that the required equality is always achieved. There is also an inducement to non-competitive behaviour. Oligopolistic situations arise for reasons already argued, and the realization of interdependence must lead to a realization that the equality of total revenues and total outlays is more easily budgeted for and achieved if some variables can be ruled out of account by collusive action.

9.33

The seeming objectivity of a check on the equality of total receipts and total outlays is in any case misleading. The check must by its nature be periodic, and to obtain the requisite receipt and outlay figures for any period it is necessary to place a valuation upon the physical resources of the organization at the beginning and end of the period concerned. This valuation rests upon a judgement about possibilities of future revenues from the use of the resources in question—a judgement incapable of complete check by another person or body.*41

9.34

An instruction to managers to maximize the excess of money receipts over money outlays raises fewer problems. It is compatible with the marginal rule, in that the latter would lead to the same choice of plan as does the instruction to maximize net revenues. But the marginal rule is no longer needed; once net revenue is accepted as the guide, the marginal rule is no more important to a check on efficiency than it is in the market economy. On grounds of convenience it is therefore better dispensed with. There is with this revenue rule some kind of check on efficiency, in the size of the net revenue, and some possibility of formulating a criterion for the allocation of resources between producers, probably in term of the size of past net revenues. The utility of the net-revenue rule does, however, depend upon two preconditions.*42 First there must be similar opportunity for individual producers to take advantage of the oversight of thers as was the case in the market economy, so that absence of net revenue is a clear indication of a need to redistribute resources and its persistence in the case of any one manager an indication of the inefficiency of that manager. Second, the behaviour of managers in maximizing net revenue must be conducive to efficiency, i.e. it must be competitive. But since in conditions of uncertainty the net-revenue rule provides the same kind of incentive to imperfectly competitive, collusive and monopolistic behaviour as in the market economy, the net-revenue rule could only hope to function reasonably efficiently given detailed government regulation of revenue maximizing behaviour of kinds incompatible with efficiency in the distribution of resources.

VII CONCLUSIONS

9.35

The most effective general rule for managers of enterprises in a liberal collectivist economy seems to be one similar in nature to the profit-maximization 'rule' of the market economy. This appears to be the only rule offering the possibility of any external check on managerial efficiency; the 'marginal' rule is of no value in this respect. The 'net-revenue' rule also makes possible the formulation of a criterion for the allocation of resources to producers in the future in terms of achieved past net revenues. The use of the 'net-revenue' rule (or, for that matter, any other of the rules examined) provides an incentive for non-competitive behaviour on the part of producers, which would need to be tackled by detailed regulation similar to that required in a market economy.*43

9.36

It may be that imperfectly competitive behaviour would be less of a problem in a liberal collectivist economy, because the link between personal income and net revenue is less direct and the desire to act in the public interest more important. But it must be borne in mind that in the case of joint-stock organization the link is also indirect, and also that it is implicit in the whole liberal collectivist pattern that the incentive to obey the rule (in this case to maximize net revenue), whatever that incentive might be, is such that producers treat it seriously.

9.37

If the preceding argument is sound, and the need for a net-revenue rule is accepted, then the only difference of economic importance between the two systems lies in this possibility of greater simplicity in the control of imperfectly competitive behaviour in the liberal collectivist economy, balanced against the loss of the 'unparalleled simplicity and force' of the motive of private profit in the market economy. It becomes relevant at least to consider whether a competitive market economy might not function more efficiently even while accepting such impairment of the force of the profit motive as resulted from policies of income redistribution satisfactory to collectivists.*44


Notes for this chapter


28.
Such an economy will be referred to hereafter as a 'liberal collectivist' economy.
29.
While the argument presented is related to the functioning of a liberal collectivist economy, it has a direct bearing on problems arising in a 'mixed' society such as our own. It is relevant, for example, to a consideration of the pricing policy of public utilities which is normally discussed in relation to similar rules. This is a question the writer hopes to take up in a later paper.
30.
Much of the early discussion has been brought together in two sets of reprints of relevant articles: Collectivist Economic Planning, ed. F. A. Hayek (which includes L. von Mises's pioneer article, 'Economic Calculus in the Socialist Commonwealth') and On the Economic Theory of Socialism, ed. Benjamin E. Lipincott (which includes reprints of articles by O. Lange and F. M. Taylor suggesting and elaborating the use of marginal criteria). A number of other papers on the subject were published in the Economic Journal and Review of Economic Studies during the 1930s, and a marginal 'rule' was elaborated by (inter alia) A. P. Lerner in Economics of Control (1944).
31.
An economy of this kind is discussed (e.g.) by A. P. Lerner, Economics of Control, and E. F. M. Durbin, Problems of Economic Planning.
32.
e.g. Lerner, Economics of Control, formulates five conditions relating marginal private and social benefit, cost, etc. Durbin, Problems of Economic Planning, (paper VIII), has suggested the use of marginal-value products. These differences do not affect the substance of the argument.
33.
e.g. Lange (in On the Economic Theory of Socialism pp. 89-90,) Durbin (Problems of Economic Planning, p. 50), P. M. Sweezy, Socialism, p. 231.
34.
A decision to build a particular type of bridge over a river, for example, is likely to mean that alternative plans concerned with other types of bridges, considered ex ante, will never be implemented.
35.
This formulation is based upon that used by G. F. Thirlby, 'The Ruler', reprinted here, pages 163-98.
36.
i.e. no relation between total revenues and total outlays is postulated (see section VI).
37.
Cf. H. D. Dickinson, 'Price Formation in a Socialist Economy', Economic Journal (December 1943), and The Economics of Socialism, pp. 104-5, and M. Dobb, Political Economy and Capitalism, chapter VIII. Dobb advocates such a scheme in preference to the competitive solution using a marginal rule; Dickinson merely suggests it as a possible practical alternative.
38.
i.e. if no plan considered is expected to yield a surplus of revenues over outlays.
39.
I leave aside the question of where these managers come from, and whether they can interpret the marginal rule, if they are expected to follow it.
40.
e.g. Durbin appears to envisage 'planning' of this kind being taken care of by extension of the Civil Service: Problems of Economic Planning, paper VI.
41.
A valuation problem similar to this arises, of course, in a market economy. In either economy there is more possibility of an approximate check than was the case with the marginal rule, since wide fluctuations in successive valuations of particular assets appear reasonably clearly and need to be explained.
42.
It also depends upon a reasonably satisfactory solution of the valuation problem, which is still relevant (see note 15 above).
43.
Where, in the nature of things, competition cannot function (e.g. for technological reasons), revenue maximization with detailed regulation may be unsatisfactory; a combination of regulation and some given net-revenue objective might operate more efficiently. This is the public utility pricing problem of the market economy.
44.
I am particularly indebted to the valuable suggestions and criticisms of Mr G. F. Thirlby, and to my colleagues who commented on the article in draft.

Essay 10, The theory of public utility price—an empty box

End of Notes


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