Chapter XI

CHAPTER XI MrSES' THEORY. PROPOSED SOLUTIONS: MATHEMATICAL SOLUTIONS AND THE " EXPERIMENTAL METHOD" THE THREE previous chapters have been concerned with various factors which the central authority in the socialist society must include in its calculations and accounting if "the economic principle" is to be followed. These factors all had one thing in common; they were either difficult, or impossible, to determine without prices for the means of production. If it should be impossible in the socialist society to put prices on means of production, this will entail other and far more serious con sequences than that these factors can not be measured. Unless there are prices for the means of production the economic activity of any modern, industrialized community will be haphazard. Without such prices the central authority will lack the necessary data to· determine how and. in what combination the various means of production can be put to the optimum economic use. Nor will it be able to follow the fundamental law that should govern allecononUc activity, namely that the result varies according to the different combinations of production factors. 1 Without prices to indicate their scarcity, those means of production which exist only in limited numbers and quantity (in the society or place concerned) could be used for purposes that are without im portance in relation to the given end, with the result that more im portant aims could not be achieved. Without prices for means of production the central authority will have no data for determining whether the contribution and the sacrifice are greater or smaller than the result. Without them calculation is impossible, and without calculation there can be no rational conduct, nor any rational use of the community's resources. On the whole, all who have taken part in this discussion are agreed that prices for means of production are necessary IThis view may cause surprise, since the increasing and diminishing yields resultirig from such attempted combinations are, in theoretic discussion, generally measured in natura and expressed in units of quantity of one of the production factors or of the final product. Economic calculation, however, demands prices, prices that are commensurable and express the relative scarcity of the means of production in relation to its various possible uses and the different combinations.

See also Professor Ragnar Frisch's Inledning til produfe.sjonsteorien(Stencil), Oslo, 1937, and Professor George M. Peterson's DiminishingReturn and PlannedEcono",-v, New York, 1937.

130 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY for calculation and that calculation is a necessary prerequisite of rational economic activity. N ow Professor Mises' assertion is that it is impossible to arrive at prices for means of production in the socialist society. His argument is that in the socialist so'ciety the state, by definition, owns the means of production, hence there will be no markets or prices for them. From this follows, in Mises' opinion, that economic calculation will be impossible and socialism unfeasible. 1 The first statement follows from the definition, and as such is unassailable. The correctness of the second will depend on what is understood by markets, prices and calculation. We shall repeatedly revert to this question when discuss ing the solutions proposed by Mises' opponents. Mises' opponents naturally have this in common: they all agree that his point of view is false. The solutions they have put forward, however, differ greatly, and some have even raised strong and seriQus objections to the others' proposals.

The solutions proposed fall mainly into two groups: one insisting that prices can be put on means of production and agreeing to-and in certain cases assuming-the existence of free choice of goods and occupation, while the second and smaller group holds that this free choice cannot be sustained in the socialist society. The solutions of this latter group will be dealt with separately at the end. We still assume free choice of goods. and occupation or more specifically (I) consumers' free choice of goods and services, and (2) free choice of occupation and place of work. The solutions of the first group coincide to a certain extent. In many cases one and the same person has put forward several solu tions. As the assumptions on which they base their argument are not always indicated precisely, it is difficult to classify them exactly, but roughly they fall into the following groups: (I) Solutions that aim at a moneyless economy. (2) Those that are based on the original Marxian theory of value, and in which the input of labour is regarded as the only factor determining value. <3) "Mathematical solutions" and those which recommend the "experimental method". (4) Those that recom mend marginal costing, and (5) those that aim at introducing com petition. A relatively comprehensive survey of them all can be found in CollectivistEconomic Planning, in which special attention should be given to Professor Hayek's concluding chapter "The Present State of the Debate". Clare Tisch's contribution gives a good general picture of what had appeared in German up to that time.

We are not here concerned with those solutions that are based on a IFor references, see footnote on p. 82.

MISES' THEORY AND· SOME PROPOSED SOLUTIONS 13 I moneyless. economy or on the theory of labour-values, since it has already been demonstrated that econom:ic calculation cannot be made on that basis,! a view generally accepted by those now partaking in the discussion (with the exception of Drs. G. Dobbert and C. Landauer among others).2 . Most of the solutions proposed are allied to group 3, called "mathe matical solutions". That of Dr. Clare Tisch is mentioned first, because her solution is expressively put forward as a counter to Mises. She contests Mises' point that in the socialist community there will be no exchange between two contracting parties. There will, rightly enough, be no markets, but there will be a choice and that, in her opinion, is sufficient to create the exchange-relationship Mises de mands. Here she is in the strong position of being able to quote Mises himself as saying.that the economic transactions of the management of an isolated economy can "in one sense" be called exchange (Theoriedes Geldes,p. 10). Now, Mises added that not even the greatest genius can perceive "the importance" of one of innumerable goods of a higher order. To this Dr. Tisch rightly says that this is a practical and not a theoretical objection. But then, however, she seems to be under estimating the importance of the practi<;al difficulties when she writes: "Naturally an enormous statistical apparatus will be needed to deal with production and the technical coefficients, but this can all be worked out by subordinates and need not burden the 'mind' of the Director of Industry." 3 Besides, Dr. Tisch agrees with Mises that a monetary system is a prerequisite for calculation and that a moneyless economy leads nowhere. However, she maintains that the claims-to-consumption in a socialist community are money and that the existence of money makes it possible to price the means of production. Dr. Tisch builds up her solution on Professor Cassel's TheoretischeSozialiJ'konomieand maintains that mathematical economics have given us exact methods for deter. mining the equivalent prices of means of production without markets: "when only certain data are known to· one, and one takes into consideration the prerequisites of equilibrium (price and cost, supply and demand)." .

lSee Chapters IV and V. 2In "L'Economia Programmatica nella URSS" in L'Economia Programmatica by L. 13rocard, C. Landauer, I. A. Hobson, L. L. Lorwin, G. Dobbett and U. Spirito, Florence, 1933; and in "L'Economia Russa" in NU01JO Esperienze Economiche by E. v. Beckerath, G. D. H. Cole, L. L. Lorwin, G. Dobbert, J. B. Condliffe, S. Nagao and U. Spirito, Florence, 1935, according to Herbert Zassenhaus in Zeitschrift fur Nationalokonomie, 1936. See also p. 51. 30p. cit., pp. 66-67.

132 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY She refers us to statements by Walras, Pareto, Schumpeter and, especially, Barone, l but she herself builds on Cassel's simpler methods, that are built on those of Walras. Dr. Tisch thinks that Professor Cassel has shown that prices for the means of production can be determined merely by use of the principle of scarcity and costing. However, she does point out that Cassel has been guilty of an in admissible simplification in assuming the technical production coefficients as given. This, of course, they are not, as they vary with the price of the means of production (and, she might have added, with technical developments). She maintains, though, that by producing each of the production-coefficients in a concern as a function of the price of the means of production and by doing this for every existing concern, one will get "as many equations as unknowns".

Later we shall discuss these mathematical solutions on which Dr. Tisch also touches. It will suffice to say here that Professor Halm in his criticism of Dr. Tisch's solution (The Possibility of Adequate Cal culation)2 agrees that Professor Cassel, by saying that price-equations were all that was necessary, has given grounds for misunderstanding. But Professor Halm concedes that Cassel did not mean to explain actual price-processes, but merely to set up an ideal scheme for prices to which actual price-processes would have to be adjusted. And, instead of a factual explanation Cassel has given us rules and principles. 3 He does not help us, says Professor Halm "to understand the type of connection between cause and effect that is characteristic of the social economy", which Cassel himself has demanded. 4 The author of this treatise can confirm that Halm is right and that Professor Cassel never regarded his equations as a basis for an arithmetical or a mathematical computation of prices, but merely as an expression of principles that are generally applicable to an exchange economy.

H. D. Dickinson's treatise is rich in suggestions for solving the problem and will have to be discussed in different places. It is men tioned here, because Dickinson, too, has referred to Cassel's price equivalents, for which Dr. Lerner has taken him to task. 5 lRespectively, Element d'economiepolitrque pure, Lausanne, 1829; Cours d'Economie politique, II, Lausanne, 1897 (in which Pareto refers to Irving Fisher's Mathematical Investigations in the Theory of Value and Prices); Wesen und Hauptinhalt der theoretischen NationalOk,onomie, Leipzig, 1908; and "II ministro della produzione nello stato collectivista" in Giornale degliEcon. II, 1908. 21n Collectivist Economic Planning. sProfessor Alfred Amonn says in his review of Cassel's book in Archiv fur Sozialwissenschaft und Socialpolitik" 1923, that Cassel does not give a principle for arriving at such price-equations and that his presentation of the process of price formation is no explanation of that process, but only the prelude to an explanation.

4"Der Ausgangspunkt der TheoretischenNationalbkonomie" in Zeitschriftfur de gesamte Staatswissenschaft, Year 58, 1902, p. 592. 5"Economic Theory and Socialist Economy" in Review of Economic Studies, 1934-35, p. 52.

MISES' THEORY AND SOME PROPOSED SOLUTIONS 133 Dr. Herbert Zassenhaus has put forward another suggestion for a mathematical solution.! He first discusses the question on the assump tion that the members of the community do not have free choice of consumer goods, and then on the assumption that they do. The former will be discussed in Chapter .XIV together with the other solutions in this main group; the latter is built on Barone's system of equations. Zassenhaus says that Barone "reduces the task of the Minister of Production, for our case, to an exceptionally simple formula". 2 After a short survey of Barone's equations Zassenhaus arrives at the con clusion that the magnitudes required to solve the equations are (1) the quantity of means of production, (2) the function of demand, and (3) the function of the production-coefficient. Of (1) he says that is eo ipso given. However, it is not so evident as that. In the first place it is very difficult to determine what really are resources, what can be made to serve production and what not. In this connection one has to d~scuss the conditions for stimulating those who take the initiative in tne community in question, so as to make the maximum use of poteptial possibilities. This, however, introduces problems which, for v~rious reasons, we shall not go into here (see p. 189). In the second place the importance of production-factors does not only depend on the~r number, but also on existing possibilities for combining them. This r~ises questions of the geographic position of the means of production, t~e labourers' place of dwelling, cost of possible transport, and once again one is brought up against the old difficulty, that apriori there are no prices for means of production (and transport) in the socialist society. In the third place, the magnitude of a pro duction-factor like that of human labour will within certain limits vary with the size of its reward and will also depend on regulations govern ing working hours, child-labour, etc. This data can at any time be said to be given, but not the extent to which people are prepared to work for given wages. Let it be remembered that we are for the time being discussing under the assumption that there is a free choice of occupation.

Zassenhaus' attitude to (2), the function of demand, is rather sceptical and there is reason to be even more sceptical than he is (see Chapter VI). He says of (3) the function of the production-coefficients, that in any concern and· with a given amount of production they depend on the prices of the means of production. In this connection he, like Professor Halm, has a word of reproach for Professor Cassel for replacing this dependence in his system of equations by the adoption lccUber die okonomische Theorie der Planwirtschaft" in Zeitschrift fur National okonomie,Vienna, 1934. 20p. cit.

134 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY of constant coefficients "which is not quite correct". However, this reproach appears in rather a curious light, when one considers that Zassenhaus himself avoids this difficulty by assuming a static com munity. He goes on immediately to say: "And as we have assumed certain technical conditions, along with static conditions, we may conclude that the Ministry of Production knows them as well ".1 Elsewhere he puts this assumption of staticness more concisely: "Finally, everything so far pictured belongs to the static theory of planned economy (and we are confining ourselves to that); that means that we have assumed that the data of the system are known and do not alter during the period of observation, not even as a result of any movement of the system against equili brium. This later assumption could also be expressed as the assumption that the variable magnitudes of the system have an infinitely large speed of reaction." 2 The problem, however, is precisely how these data can be procured.

Zassenhaus' assumption of them as given reduces the value of his views, and the fact that he argues on completely unrealistic assump tions, destroys their practical value. However, he himself realizes that they only have a "mittelbare Anwendungsfaehigkeit". The group of solutions based on the trial and error methodis closely allied to the mathematical solutions. To save them from being entirely superficial, they assume some sort of computation based on various data. The greate~t exponent of this trial and error method is Professor Fred. M. Taylor, who thinks that the central authority, by taking account of the consumers' demand as expressed in surplus or shortage of consumer-goods (see Chapter VI, p. 80), will "ascertain with a sufficient degree of accuracy these effective importances or values of all the different kinds of primary factors, and that they will have embodied the results in arithmetic tables, which I shall usually designate factor-valuation tables."3 It is this reference to "arithmetic tables" and "factor-valuation tables" that makes it possible to put Professor Taylor's solution with the mathematical solutions. It has been rosily described by Dr. Oskar Lange as the only step forward made in the discussion since Barone's treatment of the problem, and he regrets that not only has Professor Hayek omitted to print Professor Taylor'S paper in CollectivistEconomic Planning, but also that he has called it a theoretic solution alongside lOp. cit., p. 52 9.

21bid., p. 515· 3 AmericanEconomicReview, 192 9, p. 4.

MISES' THEORY AND SOME PROPOSED SOLUTIONS 13 5 those of Barone, Dickinson, etc., "whereas Taylor indicates a solution by trial and errQr".1 Such eulogy is very surprising, as is the reproach against Professor Hayek. In the first place Professor Taylor's "method" had already been suggested by Barone, and Dr. Leichter has also mentioned it. In the second place, it is a very obvious method and the one which anyone with a little knowledge of the price economy would think of first. In fact,it is so far from. being sensationalthat it was not even mentioned during the discussion on Central Planning of Production in Soviet Russia held by the American Economic Association the day after Professor Taylor had discussed it in his paper op~ning the congress. 2 And, in the third place, the problem can by no means be said to have been solved by the suggestions put forward by Professor Taylor. Dr. Lange's own and much more thorough treatment of the question shows that not even he regards it as the last word on the subject.

Professor Taylor ended his paper by saying that he found himself inclined: "to affirm rather dogmatically' that, if the economic. authorities of a socialist state would recognize equality between cost of production on the one hand and the demand price of the buyer on the other as being the adequate and the .only proof that the commodity in question ought to be produced, they could, under all. ordinary conditions, perform their duties, as the persons who were immediately responsible for the guidance of production, with well-founded confidence that they would never make any other than the right use for the economic resources placed at their disposal." 3 ' One cannot accept Professor Taylor's assertion that he has solved the problem. The main objection is that he assumes that both cost of production and demand price of the buyer are given, whereas the real problem is to determine how a socialist community is to obtain these data. The reader is referred here to our objections given in Chapter VI, and we shall only add that Professor Taylor's solution clearly, though not expressly, presupposes that the community is static.

Dr. Lange's attempt to solve the problem deserves special attention, if forno other reason than that Dr. Lerner has called it "the most up to-date of what has been written so far on the subject ... these words 1"On the Economic Theory of Socialism" in Review ofEconomic Studies, October, 1936, p. )6. 2AmericanEconomic Review, 1929, Supp., pp. 90-130. 30p. cit., p. 8.

I; 6 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY (used) in a rather specialized sense".I Dr. Lange's most important contribution to the discussion is in his two papers "On the Economic Theory of Socialism" in Review oj Economic Studies of October, .1936, and February, 1937, in both of which he discusses the question of economic calculation. The papers are very different in character. The second is prefaced by a section "The Economist's Case for Socialism" and comprises arguments in defence of the socialist society that would seem unusually dogmatic for an economist to put forward as such, and which do not directly concern our discussion. In the first paper, however, Dr. Lange discusses the problem of calculation, assuming both that free choice of goods and occupation exists, and that it does not. We shall continue to assume that it does. The other alternative will be discussed in Chapter XIV.

Dr. Lange is one of the few to make a straightforward attack on Mises'view. He pays him, though ironically, the honour due to him for having got the socialists to discuss the problem of calculation systematically (see p. 4). But he says that Professor Mises' view is based on a "confusion concerning the nature of prices", and recalls that Professor Wicksteed pointed out that the term "price" has two meanings. It can either have its popular meaning of the exchange relationship between two goods on a market, or it can have the more general meaning of the "terms on which alternatives are offered". 2 He goes on to say that it is only prices in this generalized meaning of the word that are necessary to solve the problem of the distribution of resources. There is, however, no justification for accusing Mises of "confusion concerning the nature of prices", since he has expressly stated that it is prices in the sense of exchange-relationship and value-relationship that are needed. 3 It is also questionable whether Dr. Lange has not misunderstood Wicksteed when he uses his expression "terms on which alternatives are offered" in the way he does. The point Dr. Lange wants to make, and it is an important one for his point of view, is that the prices do not need to be market-prices. It is enough for him that they are parameters. Now, Dr. Lange says that by "terms on which alter natives are offered" he understands "the functions of production" and "the technical possibilities determining the transformation of goods". 4 Professor Wicksteed, however, uses the term in quite another sense.

As he himself says in the first two lines of his introduction, his whole ISee "A Note on Socialist Economics" in Review of Economic Studies, October, 1936, p. 76. 2Dr. Lange refers to The Common Sense of PoliticalEconomy, 2nd Edn., London, 1933, p. 28. 8See Socialism,p. 120. ·Op. cit., p. 55.

MISES' THEORY AND SOME PROPOSED SOLUTIONS 137 work is "intended primarily as a popular but systematic exposition of the 'marginal' theory of economics". The "terms on which alternatives are offered" that he has in view, are the subjective balancings and value-judgments made by the individual person. Far from indicating non-market prices, Wicksteed tries to show that the principles that held good in a market are those more or less consciously used by the individual when making his choice. '(Whatever the nature of the alternatives before us, the question of the terms on which they are offered is always relevant. If we secure this, how much of that must we pay for it, or what shall we sacrifice to it? And is it worth it? What alternatives shall we forgo? And what would be their value to us? In the market this problem presents itself in terms of money prices."! And then he gives an example of the individual's thoughts when weighing up advantages and sacrifices. What Wicksteed wishes to emphasize is the individual's often irrational and unconscious, but ever subjective, weighing-up of "terms", of stronger or lesser need, of desire and dislike.

In the author's opinion Wicksteed's treatment of the "terms on which alternatives are offered" does not in any way permit the in ferences made by Dr. Lange. However, they give rise to another question of importance for his alternative solution, but which Dr. Lange has evidently overlooked .. Is it possible for a third person, e.g., the central authority, to draw up a scale of preference giving asatis factory picture of the heterogeneous and constandyshifting needs of the members of a community? As we shall see Dr. Lange seems also to have overlooked the fact that the chapter in Professor Wicksteed's book to which he refers us, in another respect too constitutes an argument against his own.point of view. Dr. Lange says that. the economic problem is a problem of choice between different alternatives and maintains that for that reason three data are necessary to solve it: (I) a scale of preferences to guide people in making their choice, (2.) knowledge of "the terms on which alter natives are offered", and (3) knowledge of the extent of existing resources. With these the problem of choice is solved. Dr. Lange maintains that (I) and (3) are given, at least to the same extent as they are in capitalist society, and that the only thing on which there may be some doubt is whether the data for (2.) are available. He mentions that Mises denies that they are, but says that a careful study of the theory of price and production shows convincingly that once the data for (1) and (3) are given, so, too, the terms on which alternatives are lThe CommonSenseof Politica/Economy,London, 1910, p. 21.

J 138 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY offered are, in the last resort, settled by the technical possibilities of transforming one good into another, that is to say, by the functions of production. The leaders of the socialist society will have exactly the same information, or lack of information, concerning the functions of production, as has the capitalist producer, he says. He then goes on to repeat that Professor Mises has confused the two forms of prices and concludes by saying that Mises' denial of the possibility of economic calculation in the socialist society must be dismissed. Neither of these assertions can be considered tenable. In the first place, it is highly doubtful whether the economic leaders of a socialist society would agree that they had solved the problem (rational distribution of thousands of individual means of production), even if they were handed these three data. They will rather be inclined to agree with the assertion that there are just as many equations as unknown quantities. Dr. Lange ought, in any case, to have said that his alleged solution was not of practical value.

In the second place the data for (I) and (3) are not given to the same extent in the socialist society, as they are in the capitalist one. To get his "scale of preferences to guide people in making their choice" Dr. Lange falls back on Professor Taylor's solution. He says: "A'!)' price differencefrom the equilibriumprice would show at the end ~f the accountingperiod as a surplus or a shortage of the commodity in question."! Since Dr. Lange has brought up this side of the question, it must be asked to what extent a surplus or shortage of consumer goods can be considered satisfactory data for evaluating consumers' preferences in a socialist society. As we attempted to show in Chapter VI, this cannot be said to be the case except under certain, very unlikely, assumptions. As to (2) ("the terms on which alternatives are offered") Dr. Lange obviously means by that the functions of production, and to this one can only say that the functions of production do not depend only on the technical possibilities. If only technical coefficients are to be taken into consideration, one will run the risk of molybdenum being used for the manufacture of toy swords' and microscope lenses for schoolboys' magnifying glasses. The'use of technical coefficients must depend, too, on the values (prices) of the means of production and these are not determined only by quantities. As far as information on the extent of resources (3) is concerned, we have already pointed out that accurate data are not. easy to obtain. In addition comes the fact that the possibilities of production also depend on existing possibilities for combination.

lOp. cit., p. 164. Dr. Lange's italics.

MISES' THEORY AND SOME PROPOSED SOLUTIONS 139 Dr. N. Kaldor's review of Dr. Carl Landauer's Planwirtscbaftund Verkehrwirtschaftin the EconomicJournal of June, 1932, contains some valuable comments on the method of trial and error, that are worth quoting: " ... in order to find out anything at all in this way, the different factors must be moved simultaneously, and not alternatively ... So long as 'factor movements' are carried out alternatively (i.e. under not simultaneously valid conditions) the results disclose little about the tru.e situation; while· if all factors are moved simultaneously, any attempt to deduce factor-prices from the existing price-relationships of consumption goods becomes impossible; even if the above objections did not hold, such a process of trial and error would prove to .be absurdly un economical, as all factors would have to be tried in all employ ments; and carrying factors from one employment into another involves a special cost-even in a Socialist State."!

It must be added, that Dr. Lange, like Professor Taylor, obviously assumes that the community is static. In a dynamic community technical development, among other things,.would make Dr. Lange's coefficLentschange continually. Dr. Lerner, too, for all his apprecia tion, has to call Dr. Lange's solution "reactionary and static". 2 Another solution based on the trial and error method is that of W. Crosby Roper Jr. He, too, says that lack of a consumer good is a clear indication that the central authority must revise its prices for its means of production, until "a sort of equilibrium" is found. At the same time he expresses strong doubt as to the practicability of the method.' He realizes that a mistake will entail changes in the whole system (see the quotation on p. 8I), and also that equilibrium can only be achieved in this way in a static community, which cannot exist. In his short essay Crosby Roper, while expressing his strong sym pathy for socialism, is obviously of the opinion that the best that can be achieved is a system approaching that used in the capitalist society.

He writes: "Our socialist state would be justified in claiming success, if it could point to a productive structure based on a pricing mechanism as near exactness 'as that of present economy. Economically it is perfectly conceivable." But he adds later that: "The great obstacle is in the limitation of human abilities. The IP.280. 20p. cit., p. 75.

140 ECONOMIC CALCULATION IN THE SOCIALIST SOCIETY complexities of a national pricing structure would be far beyond those of any present system of accounting. Added to the generally recognized difficulties of managing a· centralized state's produc tive apparatus, these problems would almost certainly prove in surmountable obstacles to successful administration. It seems safe to say that the pricing apparatus necessary for an efficient centralized collectivism, is, at best, only a remote possibility." He ends by saying: "It (his argument) indicates that the best chance for success of a socialist society lies in a decentralized organization which retains, so far as possible, the strong features of capitalism."l Professor Hayek has said of these mathematical solutions that the apparatus by which theoretical economics explains the formation of prices and the direction of production in a competitive system may determine the value and quantity of the various goods that are to be produced, provided there is complete knowledge of all relevant data.

It is not an impossibility in the sense of being logically contradictory, says Hayek, but that is only one side of the question. To argue that because it is logically conceivable to determine prices by such a pro cedure, it in any way invalidates the contention that it is not possible, only shows ignorance of the real nature of the problem. It is only necessary to try to visualize what the application of that would imply in order to reject it as "humanly impracticable and impossible". 2 If the central authority is to reach the same degree of economy as in a competitive society, it will in its calculations have to treat the means of production as being of about as many different types of goods as there are individual units. Two technically similar goods in different places, differently packed and of different age, says Hayek, cannot possibly be considered similar as regards utility and serviceability, if even a minimum of effective use is to be secured. Since the manager of a factory in a centrally directed community will have no powers to substitute one good for another as he wishes, all the innumerable different units will have to appear separately in the calculations of the central authority. This would be a greater statistical task than anyone has ever dared to attempt.

But as Professor Hayek says, this is not all. The information the central authority will need must also include a comprehensive descrip tion of all relevant technical characteristics of each single good, including the cost of transport to each and every other place where they might conceivably be employed to greater advantage, costs of possible repairs, ,alterations, etc., etc. lOp. cit.) pp. 60-62. 'JOp. cit., pp. 2.07-2.08.

MISES' THEORY AND SO~rE PROPOSED SOLUTIONS 141 Professor Hayek points outthat this choice of suitable uses is only possible if all this information is taken into consideration in the calculation, which in practice would mean that it was concentrated with one or two people who could formulate the necessary equations, and this is patently absurd even if one assumes that the information "exists" at a given moment. In reality this knowledge consists of the ability to take quick decisions in respect of a given set of circumstances. With regard to the data concerning consumer goods Professor Hayek points out that previous experience is of no value, since tastes are constantly changing, so that the list would have to be constantly revised, while hundreds of thousands of comparisons will be needed to fulfil the task, and that is beyond man's capacity. Professor Lionel Robbins has the same objection, only he says that the central authority will have to solve millions of equations. 1 He has also discussed the question in his Economic Planning and International Order,where he says: "In a world economy, with hundreds of thousands of types of commodities and hundreds of thousands of ways of producing them, the attainment of one solution, let' alone the continuous change of solution which changing conditions will involve, would b~ completely out of the question." 2 To this Dr. I.ange has objected that consumers also solve equations without taking an examination in higher mathematics; that Professor Hayek and Professor Robbins themselves "solve" hundreds of equa tions every day when buying a paper or deciding to eat in a restaurant.

Dr. Lange's objection, however, does not hold. Quite apart from the fact that the equations the central authority would have to solve are of quite a different nature to those of the private individual, the latter tend to solve themselves automatically, which Dr. Lange must admit the former do not. However, the best argument against this objection is to be found in the chapter of Professor Wicksteed's book to which Dr. Lange has himself appealed, where Wicksteed says: "Weare not obliged to be constantly considering alternatives, because in a fairly well regulated mind the suggestion of any particular item of expenditure does not as a rule arise until it is approximately in its proper turn and place for gratification."3 It may be as well, in conclusion, to draw attention to what is not devoid. of significance in our appraisal of these mathematical solutions; that those who first suggested them, Vilfredo Pareto and Enrico IThe Great Depression, London, 1933, p. 151.

2P. 201. SOp. cit.) p. 35.

142 ECONOMIC CALCULA 'fION IN 'rHE SOCIALIS'f SOCIE'fY Barone, themselves stated that their systems of equations were not capable of being put into practice. Pareto wrote: "Remarquons, d' ailleurs, que cette determination (de l'equilibre economique)' n' a nullement pour but d' arriver a un calcul numerique des prix. Faisons l'hypothese la plus favorable a un tel calcul; supposons que nous ayons triomphe de toutes les difficultes pour arriver a connaitre les donnees du probleme, et que nous connaissions les ophelimites de toutes les marchandises pour chaque individu, toutes les circonstances de la production des marchandises, etc. C'est la deja une hypothese absurde, et pourtant elle ne nous donne pas encore la possibilite pratique de resoudre ce probleme. Nous avons vu que dans Ie cas de 100 individus et de 700 marchandises il y aurait 70699 conditions (en realite un grand nombre de circonstances, que no~s avons lusqu'ici negligees, augmenteraient encore ce nombre); nous aurons donc a resoudre un systeme de 70699 equations. Cela depasse pratiquement la puissance de l'analyse algebrique, et cela la depasserait encore davantage si l'on prenait en consideration Ie nombre fabuleux d'equations que donnerait une population de quarante millions d'individus, et quelques milliers de marchan dises. Dans ce cas les roles seraient changes: et ce ne seraient plus les mathematiques qui viendraient en aide a l'economie politique, mais l'economie politique qui viendrait en aide aux .mathe matiques. En d'autres termes, si on pouvait vraiment connaitre toutes ces equations, Ie seul moyen accessible aux forces humaines pour les resoudre, ce serait d' observer la solution pratique que donne Ie marche." 1 Enrico Barone wrote: "Many of the writers who have critized collectivism have hesitated to use as evidence the practical difficulties in establishing on paper the various equivalents; but it seems they have not perceived what really are the difficulties-or more frankly, the impossibility-of solving such equations a priori." 2 The following is the first of his conclusions: "From what we have seen and demonstrated hitherto, it is obvious how fantastic those doctrines are which imagine that production in a collectivist regime would be ordered in a manner substantially different from that of 'anarchist' production." 3 IManueld'economiepolitique,Paris, 1909, pp. 233 and 234.

20p. cit., p. 287. 30p. cit.) p. 28 9.

MISES' THEORY AND SOME PROPOSED SOLUTIONS 143 It is amazing that the many who have proposed a mathematical solution of the problem, basing it on Pareto's and Barone's systems of equivalents, have not been aware of these reservations. When, in addition, it is realized that the data which are a prerequisite of such math~matical solutions are partly difficult and partly impossible to obtain in a socialist society, and that equivalents of this kind, more or less explicite, assume a static community, one is entitled to conclude that the mathematical suggestions do not solve the problem.