Quarterly Journal of Austrian Economics
The Place of Economic Calculation in the Economic Theory of Ludwig von Mises
ABSTRACT: In exalting the subjectivity of value, the marginalist revolution posed a fundamental problem for economic theory. Each person chooses how to allocate his means and thereby, economize his actions by rank ordering the value of alternatives. Being interpersonally incomparable, ordinal ranks cannot serve directly to economize means within a division of labor. Neoclassical economists solved this problem by foregoing an explanation of the division of labor grounded in the reality of human persons and instead, constructed formal, mathematical models. F.A. Hayek’s subjectivist response to the neoclassical project was to augment formal, mathematical models with select characteristics of human persons. In contrast, Ludwig von Mises grounded economic theory in the reality of human persons. He demonstrated how voluntary exchange of goods for and against money generate cardinal numbers from ordinal ranks. Actual money prices emerging from actual human choices constitute the necessary condition for economizing resources across the division of labor. Unlike subjective valuations, which cannot be compared interpersonally, and barter exchange ratios which are incommensurate, money prices can be compared. Economic calculations of net income and net worth, furthermore, are a phenomenon of the market economy alone. Mises’s approach not only solved the problem of economizing resources in a division of labor, but provides a robust framework for economic research.
KEYWORDS: economic calculation, subjectivism, economizing, general equilibrium, socialism
JEL CLASSIFICATION: B13, B14, B24, B25, P11, P21, P51
Jeffrey Herbener (firstname.lastname@example.org) is chair of the Department of Economics and Sociology at Grove City College.
Quarterly Journal of Austrian Economics 21, no. 3 (Fall 2018) full issue, click here.
It is probably no exaggeration to say that every important advance in economic theory during the last hundred years was a further step in the consistent application of subjectivism (Hayek, 1955, p. 52).
F.A. Hayek (1955, pp. 52–53) appended the following footnote to his famous maxim concerning subjectivism quoted above:
This is a development which has probably been carried out most consistently by Ludwig von Mises, and I believe that most peculiarities of his view which at first strike many readers as strange and unacceptable trace to the fact that in the consistent development of the subjectivist approach he has for a long time moved ahead of his contemporaries. Probably all the characteristic features of his theories—from his theory of money (so much ahead of the time in 1912) to what he calls his a priorism—his views about mathematical economics in general and the measurement of economic phenomena in particular, and his criticism of planning all follow directly (although, perhaps, not all with the same necessity) from this central position. See particularly his Grundprobleme der Nationalökonomie (1933) and Human Action (1949).
One achievement of the Salerno camp in the second calculation debate was to demonstrate that Hayek, at least, leaves the wrong impression of the relationship between Mises’s work and his own. By referring to “the subjectivist approach,” Hayek seems to imply that his approach and that of Mises are fundamentally the same. Although Hayek admits to some differences in particulars, since Mises’s views, as he puts it, “all follow directly (although, perhaps, not all with the same necessity) from this central position.”
Mises, however, did not accept the subjectivist approach of Friedrich von Wieser, on which Hayek patterned his own framework, but instead worked within the causal-realist approach of Carl Menger and Eugen von Böhm-Bawerk.1 In discussing the two traditions in Austrian economics, Joseph Salerno (1999, p. 37) wrote:
It is important to note that even at this early stage, the Austrian school was deeply divided on a crucial issue of basic theory. On the one hand, Böhm-Bawerk fully absorbed Menger’s causal-realist approach to price theory and endeavored to develop it further and apply it to new areas. Wieser, on the other hand, seized narrowly on Menger’s “subjectivism” as embodied in the principle of marginal utility and, while usefully elaborating some of the implications of this principle, completely ignored the structure of reality-based price theory that Menger had labored to build upon it. Wieser’s purpose was to construct his own peculiar ideal of social welfare based on a state of general equilibrium that he called “natural value,” and to link it through the concept of marginal utility to foundations in human psychology.
With his acceptance of general equilibrium and emphasis on human psychology, Hayek belongs to the Wieserian wing of the Austrian school. Hayek attempted to graft onto the neoclassical general equilibrium conception his own insights into human learning, knowledge, and other “subjectivist” elements. In discussing the main contributions to modern price theory for an entry in The New Palgrave: A Dictionary of Economics in the early 1980s, which remained unpublished at the time, he wrote (Hayek, 1992, pp. 53–54):
Equally important is what may well be regarded as the final formulation of the marginal utility analysis by J.R. Hicks of the marginal utility analysis of value in the concept of the marginal rate of substitution, based on the indifference curve technique introduced by Irving Fisher and F. Y. Edgeworth. This conception of varying rates of substitution or equivalence, wholly independent of any conception of measurable utility, may well be regarded as the ultimate statement of more than half a century’s discussion in the tradition of the Austrian school….
Arguably, Hayek’s claim about Mises leading the advance of subjectivism may not be mistaken per se, however, Mises’s approach to grounding economic theory on a proper subjectivist foundation differed dramatically from that of Wieser and his followers.
ECONOMIC CALCULATION AND SUBJECTIVISM IN HUMAN ACTION
In his magnum opus, Human Action, Mises subsumes subjectivist aspects of catallactics within the concept of economic calculation. The book is organized into seven parts containing 39 chapters. He devotes one entire part of the book, part 3, to economic calculation. It contains three chapters. In one of those chapters, Valuation without Calculation, we find Mises’s discussion of the subjectivity of value. He did not offer insights about how the advance of the concept of subjectivity can make the general equilibrium framework more suitable to economic theorizing. Instead Mises focused on two fundamental principles concerning the subjectivity of value.
First, he juxtaposed the ordinal ranking inherent in valuation with cardinal numbers in which the goods being ranked are measured. He did this to demonstrate a principle of economic calculation. He wrote (Mises, 1998, p. 201):
The immediate goal of acting is frequently the acquisition of countable and measurable supplies of tangible things. Then acting man has to choose between countable quantities; he prefers, for example, 15 r to 7 p; but if he had to choose between 15 r and 8 p, he might prefer 8 p…. This is tantamount to the statement that he prefers a to b and b to c…. It certainly does not render reckoning with cardinal numbers possible. It does not open a field for economic calculation and the mental operations based upon such calculation.
Second, he referenced the principle he (Mises, 1998, p. 699) would call in his critique of socialist schemes to provide a method of economic calculation, “the fundamental theorem of modern economics,” namely diminishing marginal utility. His purpose was, again, to make a fundamental point about economic calculation. Mises (1998, p. 206) wrote:
There is no method available to construct a unit of value. Let us remember that two units of a homogeneous supply are necessarily valued differently. The value attached to the nth unit is lower than that attached to the (n–1)th unit.
Mises (1998, p. 206) concluded this line of argument with the following words:
It is a fictitious assumption that an isolated self-sufficient individuals or the general manager of a socialist system, i.e., a system in which there is no market for the means of production, could calculate. There is no way which could lead one from the monetary computation of a market economy to any kind of computation in a nonmarket system.
In the subsection that closes out this section of the book, which Mises titled, “The Theory of Value and Socialism,” Mises (1998, p. 207) wrote the following about subjectivism:
The illusion that a rational order of economic management is possible in a society based on public ownership of the means of production owed its origin to the value theory of the classical economists and its tenacity to the failure of many modern economists to think through consistently to its ultimate conclusion the fundamental theorem of the subjectivist theory.
ECONOMIC CALCULATION AND THE PROBLEM OF ECONOMIZING
As noted above, Mises considered the “fundamental theorem of modern economics” diminishing marginal utility, which can be deduced from a person economizing with homogeneous units of a good. Although diminishing marginal utility is accepted by all modern economists, Mises was the first to perceive the implication of its reasoning for making economizing decisions about the use of resources in society and its application to this problem in socialism. Concerning the proposal of mathematical economists to solve the problem of economizing in socialism, Mises (1978, p. 112) wrote:
They failed to see the very first challenge: How can economic action that always consists of preferring and setting aside; that is, of making unequal valuations, be transformed into equal valuations, and the use of equations? Thus the socialist came up with the absurd recommendation of substituting equations of mathematical catallactics, depicting an image from which human action is eliminated for the monetary calculation in the market economy.2
The deficiency in economic theory that needed correcting, according to Mises, was a fallacy economists held concerning economic calculation. Mises (1998, p. 202) wrote:
The elaboration of economic theory is heuristically dependent on the logical processes of reckoning to such an extent that the economists failed to realize the fundamental problem involved in the methods of economic calculation…. They misconstrued economic calculation. They took it for a category of all human action and ignored the fact that it is only a category inherent in acting under special conditions…. But they did not comprehend that money prices are the only vehicle of economic calculation. Thus most of their studies are of little use. Even the writings of the most eminent economists are vitiated to some extent by the fallacies implied in their ideas about economic calculation.
Contrary to Hayek, who thought that general equilibrium theory could be corrected by grafting subjectivist insights onto it, Mises perceived that the deficiency of the general equilibrium construct stemmed from its fallacious treatment of money. He identified two mistakes. First, the general equilibrium construct conceived of a market economy with only direct exchange and concomitantly asserted the neutrality of money. He wrote (Mises, 1998, pp. 203–204):
A serious blunder that owes its origin and its tenacity to a misinterpretation of this imaginary construction [a market with direct exchange] was the assumption that the medium of exchange is a neutral factor only…. This is, of course, what the fable of money’s neutrality implies. The whole theory of catallactics, it was held, can be elaborated under the assumption that there is direct trade only. If this is once achieved, the only thing to be added is the “simple” insertion of money terms into the complex of theorems concerning direct exchange. However, this final completion of the catallactic system was considered of minor importance only. It was not believe that it could alter anything essential in the structure of economic teachings. The main task of economics was the study of indirect exchange.
Only later economists realized that some of the most important and most intricate problems of catallactics are to be found in the field of indirect exchange and that an economic theory which does not pay full regard to them is lamentably defective.
Second, Mises noted a more momentous error drawn from the imaginary construct of a fictitious barter world, namely, that value is objective and can be measured by money.3 He wrote (Mises, 1998, p. 205):
Even Friedrich von Wieser and Irving Fisher took it for granted that there must be something like measurement of value and that economics must be able to indicate and to explain the method by which such measurement is effected. Most of the lesser economists simply maintained that money serves as “a measure of values.”
Mises’s corrective of the deficiencies of general equilibrium theory was based on his integration of money into subjective-value theory. He demonstrated (Mises, 1953) in 1912 how ordinal ranks are transformed into cardinal numbers suitable for economic calculation in a market economy. Buyers and sellers have preferences for a good they intend to exchange relative to money. They exchange to acquire the mutual benefit latent in the reverse ordering of their preferences. Competitive bidding by the buyers and competitive offering by the sellers results in a market-clearing price. As Rothbard (1991, p. 65) recounts it:
In the course of that notable integration of monetary theory and “micro” marginal utility theory, Mises was one of the very first to realize that subjective valuations of the consumer (and of laborers) on the market are purely ordinal, and are in no way measurable. But market prices are cardinal and measurable in terms of money, and market prices bring goods into cardinal comparability and calculation (e.g., a $10 hat is “worth” five times as much as a $2 loaf of bread).
Mises did not fully work out this integration and its implications until the German-language predecessor of his magnum opus, Human Action.4 In that work, he demonstrated that the market economy is the only solution to transforming rank orders of value into cardinal numbers suitable for making economizing decisions in a division of labor. Only three alternatives to the market solution of monetary prices exist, according to Mises.
One is inter-personal value comparisons among the participants in the division of labor. Yet, modern economists all agree that inter-personal comparisons of value are impossible and therefore, this alternative is not entertained by modern economists as a solution to the economizing problem. A second alternative is imputation of value across the division of labor by a single person. Valuation, Mises argued, can be applied only to a self-sufficient economy, i.e., an economy in which a person is the producer of everything he consumes.5 In this case, a single mind can integrate the use of its resources across the entire array of producer goods with which it acts. It does this by imputing the value of lower-order goods to those of higher order. According to Mises, however, a single mind cannot decompose the value of the end achieved into the value of each factor’s contribution. He wrote (Mises, 1998, p. 332):
Valuation as it can be practiced by an isolated actor (Robinson Crusoe or a socialist board of production management) can never result in a determination of such a thing as quotas of value…. It is permissible to declare that, due allowance being made for time preference, the value attached to a product is equal to the value of the total complex of complementary factors of production. But it would be nonsensical to assert that the value attached to a product is equal to the “sum” of the values attached to the various complementary factors of production. One cannot add up values or valuations. One can add up prices expressed in terms of money, but not scales of preference…. The process of value imputation does not result in derivation of the value of the single productive agents from the value of their joint product. It does not bring about results which could serve as elements of economic calculation.
Mises insisted that in making economizing decisions about the use of resources in an extended division of labor, it is necessary to disentangle the contribution of each complementary factor of production used in producing each good. The necessity arises because factors of production are neither perfectly specific to each good nor perfectly non-specific among all goods. Absent either of those extreme conditions, economic calculation cannot be done by knowing only the value of goods of first order and the technical conditions of production of these goods. Which raises the third alternative: using the cardinal numbers of production possibilities as the basis for economic calculation. Although technical consideration allow the decomposition of the physical contribution to output made by each factor, these numbers have no connection to value of the ends attained. Mises wrote (1998, p. 208):
[The fact that] the various means allow for various uses, set man the tasks of allocating them to those employments in which they can render the best service. Here the computation in kind as applied by technology is of no avail. Technology operates with countable and measurable quantities of external things and effects; it knows causal relations between them, but it is foreign to their relevance for human wants and desires…. [Technology] ignores the economic problem: to employ the available means in such a way that no want more urgently felt should remain unsatisfied because the means suitable for its attainment were employed—wasted—for the attainment of a want less urgently felt.
In an extended division of labor, individual factors of production can be shifted from one line of production to another and configured in various combinations with other complementary factors of production in each production process. Therefore, to know whether or not a particular configuration of complementary factors of production will be more economizing for society than another configuration, prices of individual factors of production must exist. Mises (1998, pp. 209–210) wrote:
[The practical man] must know whether what he wants to achieve will be an improvement when compared with the present state of affairs and with the realizable projects which cannot be put into execution if the project he has in mind absorbs the available means. Such comparisons can only be made by the use of money prices…. Where there are no money prices, there are no such things as economic quantities. There are only various quantitative relations between various causes and effects in the external world. There is no means for man to find out what kind of action would best serve his endeavors to remove uneasiness as far as possible.
Mises concluded this line of inquiry by returning to the starting point in Robinson Crusoe, i.e., production in self-sufficiency instead of a division of labor. Crusoe could compare the value of output with the value of the complementary factors used because the possible combinations he can exploit are simple enough for him to impute value adequately for economizing.6 He wrote (Mises, 1998, p. 210):
There is no need to dwell upon the primitive conditions of the household economy of self-sufficient farmers. These people performed only very simple processes of production. For them no calculation was needed, as they could directly compare input and output. If they wanted shirts, they grew hemp, they spun, wove, and sewed. They could, without any calculation, easily make up their minds whether or not the toil and trouble expended were compensated by the product. But for civilized mankind a return to such a life is out of the question.
ECONOMIC CALCULATION AND THE SCHEMES OF SOCIALISM
With his theory of economic calculation in hand, Mises critiqued the schemes of socialists to rationally allocate resources in chapter 26 in Human Action. Both the title of the chapter, “The Impossibility of Economics Calculation under Socialism,” and the summary list of schemes indicate Mises’s emphasis on economic calculation. He wrote (Mises, 1998, pp. 699–700):
The various schemes proposed can be classified in the following way:
1. Calculation in kind is to be substituted for calculation in terms of money....
2. Starting from the ideas of the labor theory of value the labor-hour is recommended as the unit of calculation….
3. The unit is to be a “quantity” of utility….
4. Calculation is to be made possible by the establishment of an artificial quasi-market….
5. Calculation is to be made with the aid of the differential equations of mathematical catallactics….
6. Calculation is to be made superfluous by resorting to the method of trial and error….
All of these socialist schemes, except number 6, are attempts to have economic calculation under socialism. And Mises’s critique of the socialist director using the method of trial and error to make economizing production and investment decisions relies on his views of economic calculation. He argued (Mises, 1998, p. 700) that economizing decisions fall into a category of trial and error in which “the only mark of the correct solution is that it has been reached by the application of a method considered appropriate for the solution of the problem.” His example is solving a multiplication problem. He wrote (Mises, 1998, p. 700):
One may try to guess the correct result by trial and error. But here the method of trial and error is no substitute for the arithmetical process. It would be quite futile if the arithmetical process did not provide a yardstick for discriminating what is incorrect from what is correct.
In the case of economizing decisions, the only way to discover if trial and error has succeeded is by a computation of profit and loss. Mises wrote (1998, p. 701):
The problem of socialist economic calculation is precisely this: that in the absence of market prices for the factors of production, a computation of profit and loss is not feasible.
We may assume that in the socialist commonwealth there is a market for consumers’ goods and that money prices for consumers’ goods are determined on this market…. But the characteristic mark of the socialist system is that the producers’ goods are controlled by one agency only in whose name the director acts, that they are neither bought nor sold, and that there are no prices for them. Thus there cannot be any question of comparing input and output by the methods of arithmetic.
Concerning the socialist scheme for a quasi-market, Mises noted that it represents the triumph of his approach to economics. He wrote (Mises, 1998, p. 702):
It is therefore nothing short of a full acknowledgement of the correctness and irrefutability of the economists’ analysis and devastating critique of the socialists’ plans that the intellectual leaders of socialism are now busy designing schemes for a socialist system in which the market, market prices for the factors of production, and catallactic competition are to be preserved. The overwhelmingly rapid triumph of the demonstration that no economic calculation is possible under a socialist system is without precedent in the history of human thought. The socialist cannot help but admitting their crushing final defeat.
Finally, Mises made it perfectly clear that the defeat of socialism owed nothing to the mathematical economics of general equilibrium. The problem of directing the use of resources in an economizing manner must start with existing conditions, which are not those of equilibrium but have been brought about by both successes and failures of the past. Even if the final equilibrium configuration of resource allocation is known, the economizing problem remains: how to move step-by-step from existing conditions to those of final equilibrium. For the solution to this problem, the mathematical expression of the state of final equilibrium is of no use. Mises wrote (1998, p. 709):
Even if, for the sake of argument, we assume that a miraculous inspiration has enabled the director without economic calculation to solve all problems concerning the most advantageous arrangement of all production activities and that the precise image of the final goal he must aim at is present to his mind, there remain essential problems which cannot be dealt with without economic calculation. For the director’s task is not to begin from the very bottom of civilization and to start economic history from scratch. The elements with the aid of which he must operate are not only natural resources untouched by previous utilization. There are also the capital goods produced in the past and not convertible or not perfectly convertible for new projects. It is precisely in these artifacts... that our wealth is embodied. Their structure, quality, quantity, and location is of primary importance in the choice of all further economic operations…. [The director] must try to take advantage of every piece of the already available capital goods in the best possible way.
Mises’s integration of money into the subjective theory of value did more than put monetary theory on solid ground. It set the entire body of economic theory on the causal-realist foundation laid by Carl Menger. Doing so required a reconstruction of price and production theory. Not merely grafting subjectivist elements onto general equilibrium theory, but rebuilding this theory from the bottom up. No better evidence of the soundness of this approach exists than Mises’s demonstration that central planners cannot allocate resources in an economizing manner in socialism for lack of economic calculation.
Since the second calculation debate made apparent Mises’s achievement in providing a truly general theory of economics, the causal-realist approach has been advancing on several fronts. To mention just a few: business cycle theory has been refined (Salerno, 2012); the theory of entrepreneurship and organizational theory has been developed (Klein, 2010); the theory of cost has been reconsidered (McCaffrey, 2018); the theory of interest has been further considered (Herbener, 2011); and Mises’s concept of entrepreneurial appraisement has been extended (Herbener and Rapp, 2016).
- 1. On Wieser’s approach, see Bostaph (2003).
- 2. Quoted in Salerno (1999, p. 58).
- 3. Mises (1998, pp. 697–699) repeats his indictment of the general-equilibrium framework in chapter 26 in which he criticizes mathematical economists for perpetuating the fallacy that economic calculation was possible in socialism.
- 4. See Rothbard (1991, p. 65) and Salerno (1999, p. 56).
- 5. As Mises (1998, p. 210) concedes, valuation is adequate to economizing resources within a family economy or that of a small tribe as well as a single person.
- 6. All of the combinations of factors of production can be valued by Crusoe through his own experience. Such cannot be done by a single person in a division of labor, especially the extended division of labor in a modern, capitalist economy.
Note: The views expressed on Mises.org are not necessarily those of the Mises Institute.
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Cite This Article
Herbener, Jeffery M., "The Place of Economic Calculation in the Economic Theory of Ludwig von Mises," Quarterly Journa of Austrian Economics 21, no. 3 (Fall 2019): 263-276.