Books / Digital Text
2. The Evenly Rotating Economy
Analysis of the activities of production in a monetary market economy is a highly complex matter. An explanation of these activities, in particular the determination of prices and therefore the return to factors, the allocation of factors, and the formation of capital, can be developed only if we use the mental construction of the evenly rotating economy.
This construction is developed as follows: We realize that the real world of action is one of continual change. Individual value scales, technological ideas, and the quantities of means available are always changing. These changes continually impel the economy in various directions. Value scales change, and consumer demand shifts from one good to another. Technological ideas change, and factors are used in different ways. Both types of change have differing effects on prices. Time preferences change, with certain effects on interest and capital formation. The crucial point is this: before the effects of any one change are completely worked out, other changes intervene. What we must consider, however, by the use of reasoning, is what would happen if no changes intervened. In other words, what would occur if value scales, technological ideas, and the given resources remained constant? What would then happen to prices and production and their relations? Given values, technology, and resources, whatever their concrete form, remain constant. In that case, the economy tends toward a state of affairs in which it is evenly rotating, i.e., in which the same activities tend to be repeated in the same pattern over and over again. Rates of production of each good remain constant, all prices remain constant, total population remains constant, etc. Thus, if values, technology, and resources remain constant, we have two successive states of affairs: (a) the period of transition to an unchanging, evenly rotating economy, and (b) the unchanging round of the evenly rotating economy itself. This latter stage is the state of final equilibrium. It is to be distinguished from the market equilibrium prices that are set each day by the interaction of supply and demand. The final equilibrium state is one which the economy is always tending to approach. If our data—values, technology, and resources—remained constant, the economy would move toward the final equilibrium position and remain there. In actual life, however, the data are always changing, and therefore, before arriving at a final equilibrium point, the economy must shift direction, towards some other final equilibrium position.
Hence, the final equilibrium position is always changing, and consequently no one such position is ever reached in practice. But even though it is never reached in practice, it has a very real importance. In the first place, it is like the mechanical rabbit being chased by the dog. It is never reached in practice and it is always changing, but it explains the direction in which the dog is moving. Secondly, the complexity of the market system is such that we cannot analyze factor prices and incomes in a world of continual change unless we first analyze their determination in an evenly rotating world where there is no change and where given conditions are allowed to work themselves out to the full.
Certainly at this stage of inquiry we are not interested in ethical evaluations of our knowledge. We are attaching no ethical merit to the equilibrium position. It is a concept for scientific explanation of human activity.
The reader might ask why such an “unrealistic” concept as final equilibrium is permissible, when we have already presented and will present grave strictures against the use of various unrealistic and antirealistic premises in economics. For example, as we shall see, the theory of “pure competition,” so prevalent among writers today, is based on impossible premises. The theory is then worked out along these lines and not only applied uncritically to the real world, but actually used as an ethical base from which to criticize the real “deviations” from this theory. The concepts of “indifference classes” and of infinitely small steps are other examples of false premises that are used as the basis of highly elaborate theoretical structures. The concept of the evenly rotating economy, however, when used with care, is not open to these criticisms. For this is an ever-present force, since it is the goal toward which the actual system is always moving, the final position of rest, at which, on the basis of the given, actually existing value scales, all individuals would have attained the highest positions on their value scales, given the technology and resources. This concept, then, is of legitimate and realistic importance.
We must always remember, however, that while a final equilibrium is the goal toward which the economy is moving at any particular time, changes in the data alter this position and therefore shift the direction of movement. Therefore, there is nothing in a dynamic world that is ethically better about a final equilibrium position. As a matter of fact, since wants are unsatisfied (otherwise there would be no action), such a position of no change would be most unfortunate, since it would imply that no further want-satisfaction would be possible. Furthermore, we must remember that a final equilibrium situation tends to be, though it can never actually be, the result of market activity, and not the condition of such activity. Far too many writers, for example, discerning that in the evenly rotating economy entrepreneurial profits and losses would all be zero, have somehow concluded that this must be the condition for any legitimate activity on the market. There could hardly be a greater misconception of the market or a greater abuse of the equilibrium concept.
Another danger in the use of this concept is that its purely static, essentially timeless, conditions are all too well suited for the use of mathematics. Mathematics rests on equations, which portray mutual relationships between two or more “functions.” Of themselves, of course, such mathematical procedures are unimportant, since they do not establish causal relationships. They are of the greatest importance in physics, for example, because that science deals with certain observed regularities of motion by particles of matter that we must regard as unmotivated. These particles move according to certain precisely observable, exact, quantitative laws. Mathematics is indispensable in formulating the laws among these variables and in formulating theoretical explanations for the observed phenomena. In human action, the situation is entirely different, if not diametrically opposite. Whereas in physics, causal relations can only be assumed hypothetically and later approximately verified by referring to precise observable regularities, in praxeology we know the causal force at work. This causal force is human action, motivated, purposeful behavior, directed at certain ends. The universal aspects of this behavior can be logically analyzed. We are not dealing with “functional,” quantitative relations among variables, but with human reason and will causing certain action, which is not “determinable” or reducible to outside forces. Furthermore, since the data of human action are always changing, there are no precise, quantitative relationships in human history. In physics, the quantitative relationships, or laws, are constant; they are considered to be valid for any point in human history, past, present, or future. In the field of human action, there are no such quantitative constants. There are no constant relationships valid for different periods in human history. The only “natural laws” (if we may use such an old-fashioned but perfectly legitimate label for such constant regularities) in human action are qualitative rather than quantitative. They are, for example, precisely the laws educed in praxeology and economics—the fact of action, the use of means to achieve ends, time preference, diminishing marginal utility, etc.1
Mathematical equations, then, are appropriate and useful where there are constant quantitative relations among unmotivated variables. They are singularly inappropriate in praxeology and economics. In the latter fields, verbal, logical analysis of action and its processes through time is the appropriate method. It is not surprising that the main efforts of the “mathematical economists” have been directed toward describing the final equilibrium state by means of equations. For in this state, since activities merely repeat themselves, there seems to be more scope for describing conditions by means of functional equations. These equations, at best, however, can do no more than describe this equilibrium state.
Aside from doing no more than verbal logic can do, and therefore violating the scientific principle of Occam's razor—that science should be as simple and clear as possible—such a use of mathematics contains grave errors and defects within itself. In the first place, it cannot describe the path by which the economy approaches the final equilibrium position. This task can be performed only by verbal, logical analysis of the causal action of human beings. It is evident that this task is the important one, since it is this analysis that is significant for human action. Action moves along a path and is not describable in an unchanging, evenly rotating world. The world is an uncertain one, and we shall see shortly that we cannot even pursue to its logical conclusion the analysis of a static, evenly rotating economy. The assumption of an evenly rotating economy is only an auxiliary tool in aiding us in the analysis of real action. Since mathematics is least badly accommodated to a static state, mathematical writers have tended to be preoccupied with this state, thus providing a particularly misleading picture of the world of action. Finally, the mathematical equations of the evenly rotating economy describe only a static situation, outside of time.2 They differ drastically from the mathematical equations of physics, which describe a process through time; it is precisely through this description of constant, quantitative relations in the motion of elements that mathematics renders its great service in natural science. How different is economics, where mathematics, at best, can only inadequately describe a timeless end result!3
The use of the mathematical concept of “function” is particularly inappropriate in a science of human action. On the one hand, action itself is not a function of anything, since “function” implies definite, unique, mechanical regularity and determination. On the other hand, the mathematics of simultaneous equations, dealing in physics with unmotivated motion, stresses mutual determination. In human action, however, the known causal force of action unilinearly determines the results. This gross misconception by mathematically inclined writers on the study of human action was exemplified during a running attack on Eugen Böhm-Bawerk, one of the greatest of all economists, by Professor George Stigler:
... yet the postulate of continuity of utility and demand functions (which is unrealistic only to a minor degree, and essential to analytic treatment) is never granted. A more important weakness is Böhm-Bawerk's failure to understand some of the most essential elements of modern economic theory, the concepts of mutual determination and equilibrium (developed by the use of the theory of simultaneous equations). Mutual determination is spurned for the older concept of cause and effect.4
The “weakness” displayed here is not that of Böhm-Bawerk, but of those, like Professor Stigler, who attempt vainly and fallaciously to construct economics on the model of mathematical physics, specifically, of classical mechanics.5
To return to the concept of the evenly rotating economy, the error of the mathematical economists is to treat it as a real and even ideal state of affairs, whereas it is simply a mental concept enabling us to analyze the market and human activities on the market. It is indispensable because it is the goal, though ever-shifting, of action and exchange; on the other hand, the data can never remain unchanged long enough for it to be brought into being. We cannot conceive in all consistency of a state of affairs without change or uncertainty, and therefore without action. The evenly rotating state, for example, would be incompatible with the existence of money, the very medium at the center of the entire exchange structure. For the money commodity is demanded and held only because it is more marketable than other commodities, i.e., because the holder is more sure of being able to exchange it. In a world where prices and demands remain perpetually the same, such demand for money would be unnecessary. Money is demanded and held only because it gives greater assurance of finding a market and because of the uncertainties of the person's demands in the near future. If everyone, for example, knew his spending precisely over his entire future—and this would be known under the evenly rotating system—there would be no point in his keeping a cash balance of money. It would be invested so that money would be returned
in precisely the needed amounts on the day of expenditure. But if no one wishes to hold money, there will be no money and no system of money prices. The entire monetary market would break down. Thus, the evenly rotating economy is unrealistic, for it cannot actually be established and we cannot even conceive consistently of its establishment. But the idea of the evenly rotating economy is indispensable in analyzing the real economy; through hypothesizing a world where all change has worked itself out, we can analyze the directions of actual change.
- 1. [PUBLISHER'S NOTE: Page numbers cited in parentheses within the text refer to the present edition.] Another difference is one we have already discussed: that mathematics, particularly the calculus, rests in large part on assumptions of infinitely small steps. Such assumptions may be perfectly legitimate in a field where behavior of unmotivated matter is under study. But human action disregards infinitely small steps precisely because they are infinitely small and therefore have no relevance to human beings. Hence, the action under study in economics must always occur in finite, discrete steps. It is therefore incorrect to say that such an assumption may just as well be made in the study of human action as in the study of physical particles. In human action, we may describe such assumptions as being not simply unrealistic, but antirealistic.
- 2. The mathematical economists, or “econometricians,” have been trying without success for years to analyze the path of equilibrium as well as the equilibrium conditions themselves. The econometrician F. Zeuthen recently admitted that such attempts cannot succeed. All that mathematics can describe is the final equilibrium point. See the remarks of F. Zeuthen at the 16th European meeting of the Econometric Society, in Econometrica, April, 1955, pp. 199–200.
- 3. For a brilliant critique of the use of mathematics in economics, see Mises, Human Action, pp. 251, 347–54, 697–99, 706–11. Also see Mises, “Comments about the Mathematical Treatment of Economic Problems,” Studium Generale VI, 2 (1953), (Springer Verlag: unpublished translation by Helena Ratzka); Niksa, “Role of Quantitative Thinking in Modern Economic Theory”; Ischboldin, “Critique of Econometrics”; Paul Painlevé, “The Place of Mathematical Reasoning in Economics” in Louise Sommer, ed., Essays in European Economic Thought (Princeton, N.J.: D. Van Nostrand, 1960), pp. 120–32; and Wieser, Social Economics, pp. 51 ff. For a discussion of the logical method of economics, see Mises, Human Action and the neglected work, J.E. Cairnes, The Character and Logical Method of Political Economy (2nd ed.; London: Macmillan & Co., 1888). Also see Marian Bowley, Nassau Senior and Classical Economics (New York: Augustus M. Kelley, 1949), pp. 55–65. If any mathematics has been used in this treatise, it has been only along the lines charted by Cairnes:
I have no desire to deny that it may be possible to employ geometrical diagrams or mathematical formulae for the purpose of exhibiting economic doctrines reached by other paths. ... What I venture to deny is the doctrine which Professor Jevons and others have advanced—that economic knowledge can be extended by such means; that Mathematics can be applied to the development of economic truth, as it has been applied to the development of mechanical and physical truth and unless it can be shown either that mental feelings admit of being expressed in precise quantitative forms, or, on the other hand, that economic phenomena do not depend on mental feelings, I am unable to see how this conclusion can be avoided. (Cairnes, Character and Logical Method of Political Economy, pp. iv–v)
- 4. George J. Stigler, Production and Distribution Theories (New York: Macmillan & Co., 1946), p. 181. For Carl Menger's attack on the concept of mutual determination and his critique of mathematical economics in general, see T.W. Hutchison, A Review of Economic Doctrines, 1870–1929 (Oxford: The Clarendon Press, 1953), pp. 147–48, and the interesting article by Emil Kauder, “Intellectual and Political Roots of the Older Austrian School,” Zeitschrift für Nationalökonomie XVII, 4 (1958), 412 ff. 5Stigler appends a footnote to the above paragraph which is meant as the coup de grace to Böhm-Bawerk: “Böhm-Bawerk
- 5. Stigler appends a footnote to the above paragraph which is meant as the coup de grace to Böhm-Bawerk: “Böhm-Bawerk was not trained in mathematics.” Stigler, Production and Distribution Theories. Mathematics, it must be realized, is only the servant of logic and reason, and not their master. “Training” in mathematics is no more necessary to the realization of its uselessness for and inapplicability to the sciences of human action than, for example, “training” in agricultural techniques is essential to knowing that they are not applicable on board an ocean liner. Indeed, training in mathematics, without adequate attention to the epistemology of the sciences of human action, is likely to yield unfortunate results when applied to the latter, as this example demonstrates. Böhm-Bawerk's greatness as an economist needs no defense at this date. For a sensitive tribute to Böhm-Bawerk, see Joseph A. Schumpeter, “Eugen von Böhm-Bawerk, 1851–1914” in Ten Great Economists (New York: Oxford University Press, 1951), pp. 143–90. For a purely assertive and unsupported depreciation of Böhm-Bawerk's stature as an economist, see Howard S. Ellis’ review of Schumpeter's book in the Journal of Political Economy, October, 1952, p. 434.