Review of Austrian Economics

Calculation and the Question of Arithmetic

Jeffrey M. Herbener

The view that Ludwig von Mises had more in mind in his calculation critique of socialism than the Hayekian knowledge problem has recently been attacked by Leland Yeager.1 This article addresses Yeager’s central claim that,

I cannot believe Mises was merely saying that if the socialist planners possessed in some remarkable way all the information normally conveyed by genuine market prices, they still would be stymied by inability to perform calculations in the narrow arithmetical sense, an inability that advances in supercomputers might conceivably overcome.2

Yeager then asserts that Joseph Salerno, Murray Rothbard, and I (SRH) claim that this is what Mises meant. If Yeager means by this assertion that we believe that this is Mises’s entire calculation argument, then Salerno is correct in responding that, “it is wholly beside the point, because it rests on a gross misinterpretation of the meaning explicitly attached to the term ‘calculation problem’ by SRH.”3 In response to Yeager, Salerno says,

it does not follow that, for SRH, the calculation problem as Mises conceived it refers narrowly to the mathematical techniques employed for manipulating the given quantitative data; it refers, instead, to the origination and meaningfulness of the data themselves. It is, in short, a problem of “appraisement” and not of “arithmetic.”4

From this beginning point, he proceeds to cogently rebut Yeager’s claim by demonstrating that entrepreneurial appraisal is not subsumed under market information.

Yet Yeager seems to imply something else in his claim that by its nature goes untouched by Salerno’s rebuttal. Yeager seems to imply that the arithmetic facet of Mises’s calculation argument is trivial. This claim is not only false but is odd coming from a student of Mises’s work; for Mises made several true and nontrivial arguments based solely on arithmetic or mathematics and statistics, more generally: the impossibility of interpersonal utility comparisons (lack of a unit of subjective value), the impossibility of economic calculation (inability of comparing heterogeneous units of factors of production), the impossibility of mathematical equations in economic theorizing (lack of constants in human action), and the impossibility of statistical analysis in economic theory (lack of a probability density function for the data of human action).5 Acceptance of these merely arithmetic, mathematic, and statistical points destroys several major branches of orthodox economic theory: utility and welfare, socialist, mathematical, macroeconomics, and econometrics. Together these constitute a significant portion of what passes for economic thought today.

While it is true that Mises’s calculation argument is not merely arithmetic; it is also true that it is not merely appraisement. Mises argued that economic calculation is a problem of both arithmetic and appraisement.6 More precisely, Mises’s calculation argument has two dimensions: the impossibility of central planners performing the arithmetic of profit and loss computation in pure socialism which, in turn, makes it impossible for them to engage in entrepreneurial appraisals necessary to give meaning to profit and loss, and, thus, rationally allocate factors of production.7 Although information enters into the latter, it cannot enter into the former.8

The arithmetic facet of Mises’s argument deals with the existence, or lack thereof, of a format in which information can be put and appraisals can be made. A format is necessary because the “raw data” required to answer relevant economic questions posed by the operation of a social process of exchange and division of labor are denominated in incommensurate units. Unless these units can be converted into a common standard, they cannot be compared; unless they can be compared the economic questions cannot be answered. As Mises said of one socialist scheme of economic calculation, “Calculation in kind is to be substituted for calculation in terms of money. This method is worthless. One cannot add or subtract numbers of different kinds (heterogeneous quantities).”9 The impossibility of comparing the number of apples to the number of oranges is an arithmetic problem; and a fundamental, not trivial, problem of arithmetic. Without its solution, no arithmetic operations can be conducted at all.

The profit and loss calculation solves the arithmetic problem inherent in answering both economic questions posed by the operation of a social process of exchange and division of labor: what consumer goods should be produced and which combination of factors of production should be used to produce each consumer good. The arithmetic problem of the first question is the incommensurability of the subjective values of different individuals who participate in the social process of exchange and division of labor. There are two dimensions to the impossibility of making interpersonal comparisons of utility: no unit can be defined for preferences since they are subjective and even if units of subjective value existed for each person, they would not be comparable from one person to another.10

The solution to the problem of the incommensurability of the subjective values of individuals and the answer to the question of what consumer goods should be produced to satisfy them lies in the possibility of market prices denominated in money. Consumers demonstrate their preferences for some goods relative to others by purchasing and refusing to purchase. Since all preferences are demonstrated using the same standard, viz. money, the effects of action based on these preferences, viz. money prices, are commensurate, and, therefore, formatted for meaningful economic calculation.

Entrepreneurs then impute market value to each factor of production according to its marginal value product via their demand for the factors. Factors prices are then determined by the intensity of entrepreneurial demand relative to the opportunity cost placed on them by their owners. These prices make the different units of the factors commensurate and therefore, permit entrepreneurs to efficiently allocate factors across the production of consumer goods.11

As a student of Mises’s work, Yeager is surely familiar with his account of the relationship between the subjective values of consumers and market prices as well as the impossibility of interpersonal utility comparisons. Even for those economists, few in number and among whom one should not expect to find Yeager, who disagree with the latter claim, it would seem strange for them to characterize the problem of interpersonal utility comparisons as anything but an arithmetic problem. You can only add or subtract items of like units. This fact is both arithmetic and non-trivial. An entire branch of economics (welfare economics) crashed to the ground on this point and another branch (utility economics) was completely revamped because of it.12 The arithmetic dimension of Mises’s calculation argument is based on the same arithmetic truth that makes interpersonal utility comparisons impossible; and recognition of this fact helps clarify and strengthen instead of, “caricature and trivialize,” Mises’s argument as Yeager claims.13

Mises understood that the question of what consumer goods should be produced can be answered by the central planners and therefore, is not a barrier to the establishment of a centrally-planned economy.14 The planners can do this by simply substituting their preferences for the unknowable and incomparable preferences of consumers. They produce, or attempt to produce, the goods they themselves value. This solution, however, is arbitrary with reference to the preferences of consumers. These, the central planners cannot know and even if they did they could not make the relevant comparisons to determine what subset of valuable goods should be produced to the exclusion of other goods consumers find valuable. Central planners with perfect information of consumer preferences still could not calculate what to produce to satisfy such preferences because they are ordinal rankings and therefore, cannot be compared. Even if central planners had perfect information of the subjective values of each individual denominated in units, they could not perform economic calculation because it is impossible to compare any items that are denominated in dissimilar units. Only if the central planners knew how to convert the subjective units of each individual into a common standard would they be able to perform this part of economic calculation.

The central arithmetic facet of Mises’s calculation critique is the incommensurability of the different factors of production that could be combined in different ways to produce each consumer good. Hours of labor cannot be compared to acres of land nor can these units be compared to units of each capital good. As Mises, discussing his example of central planners contemplating building a railroad, wrote in 1920, “Where one cannot express hours of labor, iron, coal, all kinds of building material, machines and other things necessary for the construction and upkeep of the railroad in a common unit it is not possible to make calculations at all. The drawing up of bills on an economic basis is only possible where all the goods concerned can be referred back to money.”15 Nearly thirty years later, he wrote,

The director wants to build a house. Now, there are many methods that can be resorted to. . . . Which method should the director choose? He cannot reduce to a common denominator the items of various materials and various kinds of labor to be expended. Therefore he cannot compare them. . . . In short, he cannot, in comparing costs to be expended and gains to be earned, resort to any arithmetical operation.16

Concerning the pricing process of the market by which economic calculation solves the problem of incommensurability, Mises concluded that socialism cannot reduce the value of the means of production to “the uniform expression of a money price.” In a market economy, “all prices can be referred back to a common expression in terms of money.”17

If there were no arithmetic facet of this “common expression in terms of money,” (contrary to Mises’s explicit statement that there is) then the problem of economic calculation would not exist since the planners could discover the value of each factor in each use by withdrawing it.

Mises summed up the problem of calculation in socialism by saying, “In the main, socialist production might only appear rationally realizable, if it provided an objectively recognizable unit of value, which would permit of economic calculation in an economy where neither money nor exchange were present.”18 If this problem has no merely arithmetic facet, then why did socialists struggle to employ the labor theory of value to solve it? Mises finished the quote above by saying, “And only labor can conceivably be considered as such.” But, why not perform economic calculation in all factors of production at once claiming each of them to have intrinsic value and thereby dispense with the search for a “socially necessary” amount of labor, i.e., a common unit of labor in which all factors can be rendered? The existence of cardinal units is not sufficient for economic calculation to be performed. One cannot add together factors denominated in incomparable cardinal units, nor compare the efficiencies stated in cardinal numbers, e.g., the average product of labor with the average product of capital, of different factors of production. The task of economic calculation requires, in addition to cardinal units, a method by which the different units can be transformed into a common cardinal unit.19 If it is not necessary to have a common objective unit in which all factors can be meaningfully compared, then a large part of the debate about the labor theory of value was so much spilled ink.

Yeager’s contention about the arithmetic facet of Mises’s argument makes it neither erroneous nor trivial. To the contrary, it is both correct and devastating to naive socialists who believe that the economic problem of factor usage can be solved by central planners in the absence of profit and loss calculation based on monetary prices, i.e., in pure socialism, including those who think the problem could be solved by “advances in super-computers.”

It is only to defeat those socialists who wish to enter the debate on economic theory that Mises moves to more complex dimensions of his calculation argument.20 To the assertion that socialism can overcome the incommensurability of different factors by having central planners set monetary prices for all goods and factors, Mises responds that the problem is calculation of objective value, not objective units per se. Such a procedure would not solve the allocation problem since it leads to a “solution” that is arbitrary even from the viewpoint of the central planners, let alone that of consumers. The problem of factor usage cannot be solved by having the central planners assign a monetary wage to be multiplied by labor hours, and so on for each factor, so that the monetary costs of different combinations of factors capable of producing a given consumer good can be compared and the least cost method selected. Such cost calculations have no relationship to the preferences placed on the consumer goods and therefore, are useless for economic calculation. Only the market process can connect the value of factors to the value of consumer goods in a meaningful way.

Mises demonstrates this point by allowing that a socialist state could have a medium of exchange, limited in its scope to trading in some consumer goods. But, as he said,

where the means of production are state controlled . . . because no production good will ever become the object of exchange, it will be impossible to determine its money value. Money could never fill in a socialist state the role it fills in a competitive society in determining the value of production goods. Calculation in terms of money will here be impossible.21

To the assertion that the central planners can overcome the arbitrary nature of prices set by their own decree by having the managers of state-operated production facilities act as if they were entrepreneurs engaged in trade, Mises argues that one cannot “play” market.22 For entrepreneurial competition to perform the function of factor evaluation, the possibility of bearing the opportunity costs of different factor allocations must be real. Only with private property can entrepreneurs and capitalists risk their own wealth in the process of social production and therefore be in a position to make accurate appraisals of factor values.23, 24 To argue that play acting could mimic the results of the market was to confuse the functions of management with those of entrepreneurship.

One cannot play speculation and investment. The speculators and investors expose their own wealth, their own destiny. This fact makes them responsible to the consumers. . . . If one relieves them of this responsibility one deprives them of their very character. They are no longer businessmen, but just the group of men to whom the director has handed over his main task, the supreme direction of the conduct of affairs. Then they—and not the nominal director—become the true directors and have to face the same problem the nominal director could not solve: the problem of economic calculation.25

To the assertion that the central planners can overcome the “game-playing” nature of market socialism by using the pre-existing market set of prices, i.e., those prices existing in the capitalist system just prior to socialization, Mises argues that the transition from capitalism to socialism is too fundamental for the old prices to bridge the gap and that pricing must be “dynamic” since underlying economic phenomena are constantly changing. By destroying the differences in wealth in the existing market economy when expropriating private property, socialism disconnects the prices that correspond to those inequalities with the different conditions now prevailing for which calculations must be made. Moreover, any changes in conditions that underlie the economic allocation of factors makes the existing set of prices obsolete, and all the more so the greater the extent of such changes.26

Furthermore, as Salerno pointed out, Mises understood that answering the economic questions of what and how to produce requires entrepreneurs to correctly project appraisals of goods and factors into the future.27 Since the data are continually changing, static modeling cannot be substituted for entrepreneurs to perform economic calculation. Comparative statics serves no better since it cannot determine how human action moves the solution from one point to another.28

Moreover, general equilibrium is irrelevant to the actual problem that economic calculation must solve and that can be done so only by entrepreneurial activity. Neither the actual prices, both present and future, nor the preferences necessary for factor allocations to be made have any relationship to those of equilibrium. As Mises said, “what impels a man toward change and innovation is not the vision of equilibrium prices, but the anticipation of the height of the prices of a limited number of articles as they will prevail on the market on the date at which he plans to sell.”29

General equilibrium equations are formed by knowing the constants of those equations, under the assumption that no further change in the data is permissible. Without the assumption of no further changes, no constants exist and no equations can be formed. Yet, the economic system cannot achieve, or move toward, the equilibrium without changes from the existing set of data. The equations are, thus, useless for the task of allocating factors of production toward their general equilibrium uses. As Mises said, “What acting man needs to know is not the state of affairs under equilibrium, but information about the most appropriate method of transforming, by successive steps, [the total supply of produced factors allocated as they are today] into [the total supply of produced factors allocated as they need to be in equilibrium], With regard to this task the equations are useless.”30

Even if the central planners had full knowledge of the state of general equilibrium and could see how to move production from original factors to the final equilibrium state, this would not suffice to circumvent the problem that only economic calculation can solve. The existing state of production does not correspond to any state of this perfect-knowledge production process. Existing capital goods embody past allocation errors relative to their perfect knowledge uses. Since these capital goods can neither be freely transferred into other uses nor transferred efficiently without taking account of their existing characteristics, central planners with perfect knowledge would still need to resort to economic calculation to properly allocate them. Mises concludes his discussion of economic calculation at this step where no recourse is made to the arithmetic facet of the argument when viewed in its entirety.31

Instead of realizing the logical construction of Mises’s argument—beginning with its arithmetic facet and then in turn allowing, for the sake of argument, that the central planners can overcome progressively more difficult aspects of the calculation problem—Yeager implies that SRH assume that Mises was conceding that the central planners could solve these problems. Yeager says,

The necessary preparations for the vast central calculation, let alone the calculation itself, could not be accomplished; they are, to use Mises’s word, “impossible.” It seems perverse, then, to interpret Mises as nevertheless conceding the possibility of all those preparations and of balking only at the possibility of the calculation itself.32

But Mises did not concede that a “preparation” or “information” problem could be solved by the central planners in the actual operation of socialism. He conceded the solution to these problems, for the sake of argument, for the very purpose of demonstrating that his calculation argument proved the impossibility of economic calculation, even if these problems were solved. The fact that he chose this method of argumentation is proof that his calculation argument has more to it than just the lack of information available to central planners.

In fact, Mises “concedes” much more than the solution to the “information” problem, in the final step of his argument. If Yeager has this perfect-information scenario in mind in his quote at the beginning of this article, then he misstates Mises’s hypothetical conditions (under which there is no arithmetic facet of the argument). Mises is not, here, assuming that the central planner has perfect information and therefore, can perform economic calculation, as Yeager implies in his quote. Mises is assuming that the central planner has “miraculously” solved the problems of economic calculation—not just information but calculation itself—and could therefore construct a perfect production structure over time, starting without any capital goods, to achieve some final equilibrium state. Even if the central planners had perfect information and the ability to calculate with that information, however, they still could not calculate how to effectively operate any actual existing economy they are attempting to control.

If Yeager means what he seems to say—that Mises could not have meant that a central planner with perfect information about preferences and factor conditions could not perform the arithmetic operations necessary to calculate—then he is wrong; for this is precisely the first step of Mises’s argument demonstrating the impossibility of economic calculation in the socialist commonwealth.33

On the importance of the arithmetic aspect of the economic calculation, Mises said,

every action can make use of ordinal numbers. For the application of cardinal numbers and for the arithmetical computation based on them special conditions are required. These conditions emerged in the historical evolution of the contractual society. Thus the way was opened for computation and calculation in the planning of future action and in establishing the effects achieved by past action. Cardinal numbers and their use in arithmetical operations are also eternal and immutable categories of the human mind. But their applicability to premeditation and the recording of action depends on certain conditions which were not given in the early state of human affairs, which appeared only later, and which could possibly disappear again . . .

Modern civilization is above all characterized by the fact that it has elaborated a method which makes the use of arithmetic possible in a broad field of activities. This is what people have in mind when attributing to it the—not very expedient and often misleading—epithet of rationality.34

Jeffrey M. Herbener is associate professor of economics at Washington and Jefferson College and wishes to thank the anonymous referees for their helpful comments.

The Review of Austrian Economics Vol. 9, No. 1 (1996): 151–62

ISSN: 0889–3047

Because Rothbard fails to mention the arithmetic facet of calculation but does mention information in discussing the debate between Mises and Lange, Yeager attempts to construe Rothbard as once holding the Yeager position and then shifting to the SRH view. See Yeager, “Mises and Hayek,” p. 106. But Rothbard had no more reason to mention the arithmetic facet of calculation in this context than did Mises. Moreover, neither Mises, nor Salerno, nor Rothbard, nor I claim that the central planners do not face an information problem. The SRH claim is that Mises’s calculation argument has more to it than the information problem. Yeager’s claim that it does not is not proven by noting that Mises and SRH recognize information as a problem.

• 1Historical Statistics of the United States, part 1 (Washington, D.C.: 1975), series D-86 for unemployment rates and series F-32 for gross national product. Throughout this article, the standard data series for unemployment rates are used, with recognition that there has been a challenge to the validity of those data during the Great Depression years. See Michael R. Darby, “Three-and-a-Half Million U.S. Employees Have been Mislaid: Or An Explanation of Unemployment, 1934–1941,” Journal of Political Economy 84, 1976.
• 2A.C. Pigou, Industrial Fluctuations, 1st ed. (London: Macmillan, 1927), p. 176.
• 3A.C. Pigou, Theory of Unemployment (London: Macmillan, 1933), p. 252. Pigou makes his arguments in a variety of other places. For example, see his “Real and Money Wage Rates in Relation to Unemployment,” Economic Journal 47, 1937, and “Money Wages in Relation to Unemployment,” Economic Journal 48, 1938.
• 4It is perhaps something of an exaggeration to ascribe this position entirely to Pigou. A number of other economists espoused similar views. Recognizing that the list is incomplete, we cite a few, beginning with Jacob Viner, Balanced Deflation, Inflation, or more Depression (Minneapolis, Minn.: University of Minnesota Press, 1933), especially pp. 12–13. See also W.H. Beveridge, Causes and Cures of Unemployment (London: Longmans, Green and Co., 1931), p. 25, and Unemployment, A Problem of Industry (London: Longmans, Green and Co., 1930), chapter 16; Wilford I. King, The Causes of Economic Fluctuations (New York: Ronald Press Co., 1938), chapter 8; and Lionel Robbins, The Great Depression (New York: Macmillan, 1934).
• 5John A. Hobson, The Economics of Unemployment (New York: Macmillan, 1923), p. 84.
• 6W.T. Foster and W. Catchings, Profits (Boston: Houghton Mifflin, 1925) and Business Without a Buyer (Boston: Houghton Mifflin, 1927); and C.H. Douglas, Credit-Power and Democracy (London: C. Palmer, 1920) and Warning Democracy (London: C.M. Grieve, 1931). A more recent interpretation of the Great Depression with underconsumptionist overtones in John Kenneth Galbraith, The Great Crash, 1929 (Boston: Houghton Mifflin, 1976).
• 7Murray N. Rothbard, America’s Great Depression (Princeton, N.J.: Van Nostrand, 1963), p. 45.
• 8Henry Ford, The New York Times, November 22, 1929, p. 2.
• 9The New York Times, November 22, 1929, p. 1. It is interesting to note that Hoover’s inclinations toward underconsumptionism were recognized and, of course, approved, by trade unionists. Witness a statement by the AFL’s John P. Frey in 1929 relating to a public works scheme of Hoover’s. In effect, Frey argued that the president was in agreement with the AFL’s position that depressions were the result of underconsumption and low wages. See Joseph Dorfman, The Economic Mind in American Civilization (New York: Viking Press, 1959), vol. 4, pp. 349–50. See also Ronald Radosh, “The Development of the Corporate Ideology of American Labor Leaders, 1914–1933” (doctoral dissertation in history, University of Wisconsin, 1967).
• 10Rothbard, America’s Great Depression, chapter 8. Not to be ignored is the fact that ideas such as those that enamored Hoover were not as unorthodox among professional economists as sometimes claimed. See J. Ronnie Davis, The New Economists and the Old Economists (Ames, Iowa: Iowa State University Press, 1971). Davis presents an interesting array of statements by economists and other academics relating to the issue of the impact of wage reductions on the economy (pp. 94–99).
• 11John M. Keynes, The General Theory of Employment, Interest and Money (London: Macmillan, 1936).
• 12Abba P. Lerner, “Mr. Keynes’ ‘General Theory of Employment, Interest and Money,’” International Labor Review 34, 1936. See also W.B. Reddaway, “The General Theory of Employment, Interest and Money,” Economic Record 12, 1936. A systematic description of the thought of this time is contained in Lawrence R. Klein, The Keynesian Revolution (New York: Macmillan, 1947). For a taxonomic description of the various views of the aggregate demand schedule for labor, see Sidney Weintraub, “A Macroeconomic Approach to the Theory of Wages,” American Economic Review 46, 1956.
• 13Paul M. Sweezy, personal letter to John B. Shelley, dated February 11, 1977, cited in Dana C. Hewins and John B. Shelley, “Sweezy’s Kink: Macro Foundations of a Micro Theory,” Economic Inquiry 17, 1979.
• 14For a description of the various dimensions of the Keynesian critique of classical economics, see Alvin H. Hansen, A Guide to Keynes (New York: McGraw-Hill, 1953). More recent appraisals and restatements of the total thrust of Keynesianism are Abba P. Lerner, “From ‘The Treatise on Money’ to ‘The General Theory,’” Journal of Economic Literature 12, 1974; and Hyman P. Minsky, John Maynard Keynes (New York: Columbia University Press, 1975).
• 15Peter Temin, Did Monetary Forces Cause the Great Depression? (New York: Norton, 1976), p. 140. Temin also attempts to demonstrate that the Great Depression was brought on by an autonomous shift in the consumption function. That view has been challenged (successfully, we think) by Thomas Mayer, “Consumption in the Great Depression,” Journal of Political Economy 86, 1978.
• 16Keynes, The General Theory. In chapter 2, Keynes is very explicit. In reference to the principle that real wages and employment are systematically related, he says, “I am not disputing this vital fact which the classical economists have (rightly) asserted as indefeasible.”
• 17Ludwig von Mises, The Theory of Money and Credit (New Haven, Conn.: Yale University Press, 1953). Permission granted by Mrs. Margit von Mises. Quotes from 1981 Liberty Classics, Indianapolis, edition.
• 18Milton Friedman, “The Role of Monetary Policy,” American Economic Review 58, 1968.
• 19In particular, see Jerome Stein, Monetarist, Keynesian, and New Classical Economics (Cambridge, United Kingdom: B. Blackwell, 1982).
• 20The key assumptions are constant returns to scale and neutral disembodied technical progress.
• 21The underlying statistical models are moderately complex. They are described briefly in the statistical appendix. The logic and structure of the models are more fully developed in Lowell Gallaway and Richard Vedder, The “Natural” Rate of Unemployment, staff study, Subcommittee on Monetary and Fiscal Policy, Joint Economic Committee, Congress of the United States (Washington, D.C.: 1982).
• 22Federal Reserve Bulletin, various issues.
• 23Historical Statistics, series D-86.
• 24The productivity-adjusted real wage rate on a quarterly basis is calculated by dividing the manufacturing wage bill by the product of Federal Reserve Board (not the wage bill) and the index of average labor productivity (not total output) should be used. However, converting the wage bill and the index of industrial production to wage rate and productivity measures involves dividing both of them by the same quantity of labor (L). Since L appears in both the numerator and denominator of the expression for the adjusted real wage rate, it cancels out and can be ignored.
• 25As calculated from Historical Statistics, series D-688.
• 26Ibid,, series D-683 and D-688.
• 27Ibid., series D-724 and Paul A. David and Peter Solar, “A Bicentenary Contribution to the History of the Cost of Living in America” in Paul Uselding, ed., Research in Economic History, vol. 2 (Greenwich, Conn.: JAI Press, 1977), pp. 59–60.
• 28Broadus Mitchell, Depression Decade, vol. 9, The Economic History of the United States (New York: Rinehart, 1947), p. 84; and Arthur Schlesinger, Jr., The Age of Roosevelt: The Crisis of the Old Order, 1919–1933 (Boston: Houghton Mifflin, 1957), p. 249. Interestingly, though, some observers of the period disagree with this assessment. For example, Leo Wolman, Wages in Relation to Economic Recovery (Chicago: 1931) notes, “[I]t is indeed impossible to recall any past depression of similar intensity and duration in which the wages of prosperity were maintained as long as they have been during the depression of 1930–1931.” Similarly, Don Lescohier, “Working Conditions,” vol. 3, History of Labor in the United States, 1896–1932, John R. Commons and Associates, eds. (New York: Macmillan, 1935) states:
• 29Historic Statistics, series D-802, D-813, D-818, and D-824, respectively.
• 30Robbins, The Great Depression, p. 224.
• 31Geoffrey H. Moore, ed., Business Cycle Indicators, vol. 2, Basic Data on Cyclical Indicators (Princeton: Princeton University Press, 1961), p. 129.
• 32Benjamin M. Anderson, Economics and the Public Welfare (New York: Van Nostrand, 1949), p. 72.
• 33Historical Statistics, series D-839.
• 34Anderson, Economics, p. 220.