.^<^. ":j>^ ■O' ■y .\^' A -^A ^v .^' "-^. LAWS OF WAGES THE MACMILLAN COMPANY NEW YORK • BOSTON • CHICAGO SAN FRANCISCO MACMILLAN & CO., Limited LONDON • BOMBAY • CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, Ltd. TORONTO LAWS OF WAGES AN ESSAY IN STATISTICAL ECONOMICS BY HENRY LUDWELL MOORE PROFESSOR OF POLITICAL ECONOMY IN COLUMBIA UNIVERSITY ' ' II progresso dell' Economia politica dipenderk. pel futuro in gran parte dalla ricerca di leggi em- piriche, ricavate dalla statistica, e che si parago- neranno poi colle leggi teoriche note, o che ne faranno conoscere di nuove." Pareto. THE MACMILLAN COMPANY 1911 AU rights reserved V ,^" o^ COPTEIGIIT, 1911, By the M ACM ill an CO. Set up and electrotyped. Published December, 1911. Nortoooli ^t£ss J. S. Gushing Co. — Berwick & Smith Co. Norwood, Mass., U.S.A. ©C1A303503 TO JOHN BATES CLAEK IN ADMIRATION AND AFFECTION I DEDICATE THIS ESSAY CONTENTS PAGE Introduction 1 CHAPTER I STATISTICAL LAWS A Scatter Diagram 11 Definition of Terms . .15 Cliaracteristics of Statistical Laws 21 CHAPTER II "WAGES, MEANS OF SUBSISTENCE, AND THE STANDARD OF LIFE Description of Data , 26 Wages and the Means of Subsistence 29 Wages and the Standard of Life 33 Wages of Skilled and of Unskilled Laborers . . . .39 CHAPTER III WAGES AND THE PRODUCTIVITY OF LABOR Description of Data . , . .45 Fluctuations in the Rate of Wages and in the Value of the Product 46 Fluctuations in the Laborer's Relative Share of the Product and in the Ratio of Capital to Labor 55 The General Trend of Wages 61 vii viii Contents CHAPTER IV WAGES AND ABILITY An Hypothesis as to the Distribution of Ability . Grounds for the Hypothesis . The Expression of the Gaussian Law in a Form that will facili- tate the Testing of the Differential Theory of Wages . The Standard Population The Application of the Theory of the Standard Population Remark upon the Preceding Demonstration PAGE 74 76 78 82 85 93 CHAPTER V WAGES AND STRIKES Outcome of Strikes as affected by the Strength of Trades-Unions 105 Outcome of Strikes as limited by Economic Law . . . 121 Summary 134 CHAPTER VI WAGES AND THE CONCENTRATION OF INDUSTRY Wages as affected by the Concentration of Industry . • . 140 Amount of Employment 153 Continuity of Employment 156 Length of the Working Day 161 CHAPTER VII CONCLUSIONS Statistical Economics and Industrial Legislation . . . 169 Practical Aspects of the Results of Preceding Chapters . . 174 Statistical Economics and Synthetic Economics .... 196 LAWS OF WAGES LAWS OF WAGES INTRODUCTION Theke are five circumstances tlie coexistence of which at the present time will probably determine in the near future the direction and character of such economic investigations as shall have for their object the discovery of general facts and laws : — (1) The pure theory of economic statics has reached a definite, mathematically symbolic form; it supplies a general view of the economic field, and indicates the desiderata for further theoretical inquiries. The utility of economic theory is to be measured by the degree in which it solves its triple task of definition and analysis of concepts, the discovery of appropriate methods for handling mutually dependent social phenomena, and the presentation of a general view of the economic field. Clearness and precision of definition are absolutely indispensable to any form of quantitative work. So long as economic terms were employed with the vagueness illustrated by Jevons when he showed that in the use of the word " value " three distinct meanings were habitually ■ confused, it " was not to be expected that we could profitably discuss such matters as economic doc- 2 Laws of Wages trines." ^ The net result of the subtle discrimination and criticism of concepts which has characterized a great portion of contemporary work is that, for the first time, the inductive worker has a choice of groups of terms that are precise and clear. In a similar manner, in quite recent years, the idea of the relations of economic phenomena has widened, and methods have been discovered that enable us to visualize these interrelations in their complexity. Economic events are not arrayed in linear connection, the one event following the other in direct series, as was frequently assumed by the classical economists. It was an idle controversy that Malthus and Ricardo conducted upon the question whether the abundance of food increases the popula- tion or the multitude of consumers increases the supply of food. Social phenomena are interrelated, are mutually dependent, and the appropriate method of treating such a form of interdependence is the use of a system of simultaneous equations in which the equations are equal in number to the unknown quan- tities in the problem. There are hints of this con- ception in the works of the earlier economists; for exan.ple, in Cournot's RecliercJies sur les princiijes mathematiques de la theorie des richesses, but it was missed by Jevons, as was shown by Professor Marshall in his Academy review of Jevons's TJieory of Political Economy. Walras introduced it in an important special case in his earlier treatise. It has received ^ W. S. Jevons : The Theory of Political Economy, 3d edition, p. 81. Introduction 3 its complete development in Professor Marshall's Principles of Economics and Professor Pareto's Cours d' economic politique. The third part of the task of the economic theory — the presentation of a general view of the economic field — was achieved in the perfection of the method of simultaneous equations which has just been de- scribed. In a non-symbolic form, the general survey was made in the original treatise of Professor J. B. Clark. (2) Marxian socialists have distinguished between the constructive and the destructive elements of their prophet's teachings, and are seeking to extend the theory of socialism through the development of the constructive idea in the light of concrete data. The real beginning of a "scientific socialism" was in Bernstein's confession : " Die Fortentwicklung und Ausbildung der marxistischen Lehre muss mit ihrer Kritik beginnen. Heute steht es so, dass man aus Marx und Engels alles beweisen kann."-^ It was a considerable step toward "industrial emancipation" for leading socialists like Bernstein and Sorel to recognize the vagueness, inconsistency, and inade- quacy of Marx's teachings ; it was a greater stride in the same direction to face the necessity of attack- ing anew the old problems and to decide to conduct further inquiries upon the basis of concrete facts. The newer " scientific socialism " will rest upon ^ Ed. Bernstein: Die Voraussetzungen des Sozialismus und die Auf- gaben der Sozialdemokratie, p. 19. 4 Laws of Wages formulae derived from experience : " Je propose de nommer economie concrete la science moderne qui se fonde, a la fois sur I'observation directe des faits et sur la connaissance des theories abstraites qui lui permettent de comprendre I'emploi que Ton pent faire des concepts."^ The aim of modern theoretical so- cialism thus described by Sorel is the aim of modern economics. (3) The growth of social democracy has led to measures of industrial reform whose administration requires the periodic collection of varied statistics upon a large scale. Reforms in measures of taxation, where the reforms are genuine, now, for the first time, give a definite idea as to the amount of the wealth of nations and its yield of earned and un- earned incomes. Reforms in the character of indus- trial insurance and in government reports as to the condition of labor now give detailed information as to the distribution of wages, the cost of living among laborers, the causes and seasons of unemployment, the relative frequencies and causes of industrial dis- putes, the prevalence of diseases among workers, and the disabilities of old age. The material for the concrete treatment of economic questions is being supplied yearly in increasing abundance. (4) The problems of natural science have required the invention of a calculus of mass phenomena that will probably yield its best results when applied to the material of the social sciences. The wealth of ^ Georges Sorel : Introduction a Vdconomie moderne, p. 28. Introduction 5 the statistical material relating to economic questions is itself a source of embarrassment. To utilize it for scientific purposes, it must be described in brief, summary formul£e, and these formulae must be arranged upon a plan of increasing complexity so that it will be possible to pass from accurate descrip- tions of mass aggregates to the relations between the aggregates themselves. Now, concurrently with the development of economic and socialistic theory and the increasing supply of statistical data, the mathematical instrument for rendering the statistical data available for scientific purposes has been per- fected. The calculus of mass phenomena, like the infinitesimal calculus, owes its development to many workers, but, in recent years, its efficiency has been increased by the labors of Professor Pearson and Professor Edgeworth far more than during the whole period intervening since the days of Laplace and Gauss. There is reason for believing that, as the science of statistics had its origin in the treatment of social questions, so likewise the newer statistical methods will yield their most important results when applied to social data. (5) The perfection of mechanical devices for per- forming mathematical computations has rendered it possible for individual scientists to elaborate the new data supplied by government bureaus. When a science is in its early stages, individual scientists must do work of many kinds. For some years to come all essays in the direction of connecting economic 6 Laws of Wages theory with economic practice must be tentative, for the investigator must at the same time master the theory, collect the facts, and take from them their content by means of new and difficult methods. With the mass of data before him, the task would be impossible without mechanical aids to computa- tion. These aids are being supplied in increasing numbers and value in the form of mathematical tables, mechanical tabulators, and arithmometers. In the following chapters I have endeavored to use the newer statistical methods and the more recent economic theory to extract, from data re- lating to wages, either new truth or else truth in such new form as will admit of its being brought into fruitful relation with the generalizations of economic science. The first chapter contains a description of the meaning of the terms representative fact, hypothesis, statistical law, which are the principal categories by means of which scientific results are classified. In order to secure a wise expenditure of capital and energy, it is necessary in economic science as in economic affairs to make, from time to time, an inventory of one's possessions, and to this end it is all important that there should be no ambiguity about the table of values by means of which the inventory is effected. In particular, we economists should recognize the truth that, throughout a very Introduction 7 long period of its history, our science has been con- cerned with hypotheses while it has pretended to the discovery of laws. Having defined our terms and illustrated our method, we pass to the consideration of economic theories of wages in the light of existing data relat- ing to the income of laborers. The persistence in economic speculation of the doctrines of wages that are associated with the names, respectively, of Turgot and Ricardo requires that the statistical economist should measure, if he can, the degree of truth con- stained in each theory. Data are now available, per- haps for the first time, upon which to base an inductive investigation. This material is utilized to measure the degree of relation between wages and the cost of the means of subsistence, and between wages and the standard of life of the laborer. The theory according to which, under perfect com- petition, the laborer tends to receive as wages the value of his specific product is one phase of a general theory of distribution that owes its development to contemporary economists. It will not be denied, I think, that one's attitude toward theoretical eco- nomics and industrial reform should be greatly affected by the outcome of an inductive test applied to this doctrine. The theory contains two principal parts : (1) as to the trend of the share of the product that goes to the whole class of laborers in the form of general wages, and (2) as to the law of the distri- bution of general wages among the subgroups form- 8 Laws of Wages ing the laboring class. These two parts of the productivity theory of wages I have subjected to statistical treatment. Owing to the fact that the productivity theory was developed by economists who employed the device of a static state to facilitate the working of their isolated hypotheses, it has been assumed by sympathetic critics that its validity is limited to a hypothetical static state. This criticism must be withdrawn if it can be shown that the theory sup- plies the clue to the explanation of a concrete, highly dynamic phenomenon of the first importance. What light can the productivity theory of wages throw upon the scientific problem of the economic laws of strikes and their outcome ? To answer this ques- tion the first obvious desideratum is the proof that strikes and their outcome are subject to law ; it will then be time to inquire whether the observed regu- larities are explicable by means of the productivity hypothesis. Of at least equal importance with the question of the relation of strikes to wages is the consideration of the effects upon the condition of the laborers of the concentration of industry in large establishments. It will be shown, for example, that the mean rate of wages in the textile industries tends to increase with the size of the establishment. But what shall be the interpretation of this result ? Shall the infer- ence be that the more highly organized technical equipment of the larger establishments results in a Introduction 9 higher effective productivity of the laborer, which finds its expression in a larger wage? Or may it not be that the great industrial machines select the ablest laborers at the age when they are most pro- ductive, and then, after the very best of their lives has been exploited, throw them out of the industry to find their support elsewhere? The law of the variation of wages with age, in the general industry and in the large establishments, will give light upon this problem. The high mean wages of large estab- lishments may be spurious averages due to the differ- ent ages of the populations in large and in small establishments. The real social gain or loss resulting from the concentration of industry can be measured only after the consequences have been apprehended of the selective process that concentration entails. In a concluding chapter, the general results of the essay are summarized with the purpose of consider- ing their bearing upon the problem of the organiza- tion of industry. It is hoped that, supported as they are by economic theory and inductive verification, they may, in their degree, add to the positive knowl- edge that shall be utilized in the control of the eco- nomic changes that follow upon our increasing wealth and population. CHAPTER I STATISTICAL LAWS " En general, une theorie scientifique quelconque, imaginee pour relier un certain nombre de faits trouves par I'observation, peut etre assimile'e k la courbe que Ton trace d'apres une ddfinition mathe'ma- tique, en s'imposant la condition de la faire passer par un certain nombre de points donnds d'avance. Le jugenient que la raison porte sur la valeur intrinseque de cette the'orie est un jugenient probable, dont la probabilite tient d'une part a la simplicite de la formula th^orique, d'autre part au nombre des faits ou des groupes de faits qu'elle relie." _ Cournot. The statistical economist is concerned with eco- nomic facts, hypotheses, and laws. He begins his investigations with the assembling of facts, and seeks through the mediation of hypotheses to arrive at laws. As economist, his aim is to throw the great- est possible light upon the relation of the economic facts before him, and, as scientist, he expects to achieve this end by summarizhig the descriptions of the relations of facts in the simplest and most gen- eral formulae possible. Equipped with new and powerful instruments of research, he approaches his task in a precise, systematic way that yields results in a much more definite and usable form than the inspiring generalizations of the early masters of the science. What, precisely, was the meaning of Adam Smith in 10 Statistical Laws 11 his eniimeration of the following circumstances in con- nection with the discussion of the inequalities in wages ? " First, the agreeableness or disagreeableness of the employments themselves; secondly, the easiness and cheapness, or the difficulty and expense of learning them ; thirdly, the constancy or inconstancy of employ- ment in them ; fourthly, the small or great trust which must be reposed in those who exercise them ; and fifthly, the probability or improbability of success in them." Did he mean that these factors are always present as causes of inequalities in wages, that they are of equal im- portance, and that wages vary in either direct or inverse ratio with their several variations? Or, was not his meaning, rather, that the enumerated factors are so many possible hypotheses, one or more of which, in particular cases, may give the clue to the observed inequality in wages ? Before it would be allowable to speak of a law of wages, in any particular case, it would be necessary to show not only that wages vary with the assumed factor, but to derive the formula of the variation and to meas- ure the degree of association between the phenomena. It will contribute to the better understanding of the nature of the results in subsequent chapters to consider here the meaning of the terms : general or representative fact, hypothesis, statistical law. In the accompanying Figure 1 the details of a " scatter diagram " ^ are depicted. A scatter diagram is a graphic description of the quantitative relation 1 A term due to Professor Pearson. 12 Laws of Wages Statistical Laws 13 < g CO '^ ■35 2 CO CO o iq ■ i-H 1—1 1—1 o H CS o r* 1—1 1—1 (^^ lO GC 00 ^ oo c^ ^ r» o ^ lO 110 1— I o w « t- o o "^ 1—1 T— 1 (M lO (4 t- IS T-\ C^J CO co o •* 1^ » "«< lO "7 I— 1 1—1 Ol O) PS •J 50 ro O M (M a '^ 1—1 CO r^^ CO ■N 03 •A rsx i-O c^ CO CO iq CO CD O S Tfi kC a: 1-1 © CO CO 1—1 CO o tH o CO H ^H * Ij © C5 O] T-H (M HO iri CO ira OS T-H CO 1—1 o o ' in each case is the supposition as to the nature of the relation of the representative facts. The law of the facts and of the points is the supposition that satisfies best the accepted standard of simplicity and ex- cellence of lit of the facts to the hypothesis. Before any theory is accepted as the appropriate explana- tion of the phenomena, proof nnist be submitted that the facts which it purports to describe are representative facts and that it satisfies the approved Statistical Lavjs 21 test of nirnplicity and excellence of fit to the general facts. But added to the common idea in the general use of these terms, th(3re are special characteristics in case of statistical laws that must be discriminated. The inductive laws that are established by means of statistical methods in the social sciences are — (1) Laws of mass phenomena. In order to arrive at the conception of statis- tical law that has been described in this chapter, we summarized the characteristics of groups of phenomena by means of repre- sentative facts, and then proceeded to test the hypothesis as to the relation of the general facts by means of a conventional standard of simplicity and excellence of fit. As the test is applied with reference to the general facts, the law is, in reality, the law of the general facts : its validity is limited to the general facts and need not apply to the particular instances. For example, a knowledge of the law of mortality will not enable one to predict that X, aged forty years, will die in a given year. The law, however, does yield the necessary information for predicting the average proportion of those now living who will die in successive years. (2) Laws the strict validity of which is limited to a particular time and place. 22 Laws of Wages A statistical social law is a summary descrip- tion of the resultant of many independent factors whose combination varies in time and place. The statistical law of the varia- tions of price with the supply of a com- modity has one form in a highly competitive center and quite a different form in an agri- cultural community. y< (3) Laws the strict validity of which does not ex- s< tend beyond the limits of observation. A statistical law of inheritance derived from the investigation of a population varying between the normal limits should not be assumed to apply to dwarfs and giants. (4) Laws the generality of which ranges from an empirical summary of the quantitative rela- tion between series of facts of a particular time and place to an inductive verification of a general theorem of a jyTiori science. It would be easy to establish that, in a partic- ular country, at a given time, the average wage of laborers varies in direct relation with the density of the population. But such a law of association is simply an em- pirical law. If we extended our investiga- tion to different times and places, we should expect to find a great variation in the de- grees of association of the two phenomena. But suppose that the productivity theory of wages should receive inductive verification Statistical Laws 23 in a particular instance. In that case the confidence in the generality and the stability of the results would be far greater because of the added weight of the a priori demon- stration. It has been frequently assumed, even by econo- mists, that pure economics, concerned as it is with general theories, can have but scant relation to the varying succession of particular instances of concrete life. And, indeed, it is sometimes regarded as futile to attempt to bring the two into factual relation. But there can be little doubt that the despairing note is due to our ignorance of the empirical laws that bind together the whole social organism. A definite conception of the character and strength of these binding ties must lead to a perception of the direct connection between pure theory and concrete life. Statistical economics, in which the following chapters are essays, proposes this twofold object: (1) to bring to the test of representative facts the hypotheses and theorems of pure economics ; (2) to supply data, in the form of general facts and empiri- cal laws, for the elaboration of dynamic economics. CHAPTER II WAGES, MEANS OF SUBSISTENCE AND THE STAND- ARD OF LIFE " The natural price of labour, therefore, depends on the price of the food, necessaries, and conveniences required for the support of the labourer and his family." " It is not to be u.nderstood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. It varies at different times in the same country, and very materially differs in different countries." — RiCARDO. Three aspects of the remuneration of labor have each, at different times, so engaged the attention of economists as to lead to three different theories of wages : the theory of the dependence of wages upon the means of subsistence; the theory of their dependence upon the standard of life ; and the theory of their dependence upon the laborer's economic pro- ductivity. The special conditions of the times in which these hypotheses had their origin were doubt- less responsible for the distorted perspective exhibited in the various attempts to state a scientific theory of the laborer's income. In recent years there has been a disposition to recognize that each of the partial sketches contains an element of truth, but the degree of truth in each has not been measured, and consequently it has not been possible to weave into a satisfactory whole the elements supplied by the several theories. 24 Means of Subsistence and the Standard of Life 25 " The general tendency of wages since the intro- duction of power machinery and the employment of women and children in its operation has been upward, but it will be difficult to decide positively whether such increase is due absolutely to the use of machinery or to a higher standard of living, or to the increased productivity of labor supplemented by machinery, or to all these causes combined, or to other causes. . . . This phase of the subject there- fore involves too much speculation for a thoroughly statistical presentation ; the method can be only suggestive of the arguments which might be used for or against the use of machinery because of its effect on wages." -^ To accept this view of the problem of wages and of the limitations of the statistical method would be to abandon the hope of solving one of the most important problems of industrial life. Indeed, if the power of the statistical calculus does not suffice to analyze this problem into its constituent elements, then all effort in the direction of a concrete science of economics is vain ; for all the fundamental prob- lems of the science present similar degrees of com- plexity. Instead of seeking a unique solution of the wages question in an a priori way, we shall approach the concrete problem by attempting to find statistical answers to several important questions related to 1 Thirteenth Annual Report of the Commissioner of Labor, for the United States, 1898, Vol. 1, p. 5. 26 Laws of Wages the subject of this chapter. In the following chap- ters other aspects of the problem will be investigated. Do wages vary with the cost of the means of subsistence, and, if so, what is the law of the vari- ation and what is the measure of the correlation in the variation ? Do wages vary with the standard of life, and, if so, what is the law of the variation and the degree of the correlation ? Are wages more directly affected by the cost of the means of sub- sistence than by the standard of life ? Do the answers to these questions differ according as the waojes of skilled or of unskilled labor are under investigation ? Is there any relation between the variation of the wages of skilled labor and the wages of unskilled labor ? If there is such a relation, how does the degree of correlation compare with the correlation of wages with the cost of the means of subsistence and with the standard of life ? These are some of the very critical questions affecting the theory of wages that need to be treated in an induc- tive way. Description of Data. Table I, in the Appendix to this chapter, embodies a valuable collection of material relating to the means of subsistence, the standard of life and wages. It is drawn from the monumental report on Salaires et diiree du travail dans V Industrie frangaise which was published, in 1893-1897, by the French Office du Travail. It has the advantage of having been col- Means of Subsistence and the Standard of Life 27 lected and compiled by a single authority and of covering 87 separate departements, thus insuring, through the method and simultaneity of the collection of data, an unusual comparability of results, and, through the scope of the investigation, an adequacy of material for scientific generalization. In column I, the 87 departemients of France are enumerated. In columns II and III, the mean wages respectively of unskilled and of skilled laborers are given. The raw material upon which the means are based was obtained from the conseils de prud'hommes, in 1896. The means given for wianceuvres, or unskilled laborers, are derived from the wages of journaliers and terrassiers, and the means for skilled laborers (I'ouvrier de 7netier ordinaire) are the averages for the following trades : compositeur d' imprimerie, cordonnier, tailleurs d' habits, charron, marechal /errant, plombier, magon} In column IV is tabulated for each dejmrtement a " coejjicient de depense en objets d' alimentation et de chauff age, "which will be referred to, in the argument later on, as the cost of the means of subsistence. The figure given, in case of each departement, represents the cost in that departement of definite quantities of selected commodities that are regarded as sufficient to sustain, for one year, a family of six members three of whom, on the average, are at work. The prices that enter into the estimate of the costs are wholesale prices that were paid in the respective dep)artements, in 1 Salaires et dure'e du travail dans Vindustrie franqaise, Vol. IV, pp. 225, 239, 240. 28 Laws of Wages 1893, by representative institutions, such as schools and hospitals. The kinds of commodities making up the laborer's budget were selected by the Office du Travail after having examined the series of index numbers previously used in other investigations in France. An actual record of expenditures by 14 families of weavers, composed of six members three of whom, on the average, were at work, formed the basis for the estimate as to the portions in which the several commodities should enter into the index number. It is to these weaver budgets that reference is made in the French report as to the principles that were followed in composing the standard : " nous pren- drons simplement pour base de la depense, en ohjets d' alimentation, des quantites exprimees en chiffres ronds, de telle maniere: (1) que ces quantites soient effectivement capahles d' assurer r existence de 6 persoimes, par exam- ple ; (2) que la repartition de la depense qui en resulte ne secarte pas trop de celle rapportee ci-dessus" ^ The figures in column IV represent, therefore, the relative costs in the several departements of fixed means of subsistence.^ ^ Salaires et dure'e du travail dans V Industrie fran<;aise, Vol. IV, p. 251. 2 The kinds and quantities of the commodities are tabulated in Vol. IV, p. 252. In criticism of this standard budget, it may, of course, be objected that retail, instead of wholesale, prices should have been used. But the Office du Travail resorted to the use of wholesale figures only after the failure of the attempt to secure satisfactory retail prices. Besides, the wholesale figures were regarded by the Office du Travail as being fairly representative of the local variations of retail prices in France. It is to be regretted that an error of unknown magnitude was in- troduced in the effort to compensate for the relatively low wholesale Means of Subsistence and the Standard of Life 29 Column V contains for each dejMrtement, the daily ^^ prix ordinaire de pension pay e par Vouvrier isolej^our le logeTnejit et lanourriture." In the subsequent argu- ment, this column will be referred to as being repre- sentative of the cost of the standard of life.^ Column V differs from column IV in that the prix de pension is representative of a standard that varies in kind and quantity, as v^ell as in prices, from departement to departement, v^hile column IV simply records the de- partmental prices of a fixed mode of subsistence. The figures were obtained, in 1896, from the conseils de prudliommes? With this description of our data, w^e may now enter upon an investigation of the interdependence of the several factors that have been described. Wages and the Means of Subsistence. In its crassest form the doctrine that wages are de- termined by the means of subsistence of the laborer was formulated by Turgot. " En tout genre de travail prices by increasing the quantities of commodities. " Comme les prix qui servent de base aux calculs ci-apres sont desprixde gros,nous avons ades- sein plutot force les qunntites a multiplier par ces prix, de telle fa(; on que les produits representent, aussi approximativement que possible, la depense ordinaire d'une famille ouvriere, du type observe, qui ach'ete au detail les objets ne'cessaires a l' alimentation et au chauffage." — Vol. IV, pp. 252-253. ^ I think I am aware of the criticisms that may be urged against the assumption that the varying prix de pension is representative of the varying standard of life. My study is intended as a first approxi- mation, and I hope that judgment will be suspended until the argu- ment of the chapter is completed. ^Ibid., Vol. IV, pp. 244-245, 257-258. 30 Laws of Wages il doit arriver et il arrive en effet que le salaire de Vouvrier se home a ce qui lui est necessaire pour lui procurer sa subsistance."^ If this doctrine has any relevancy to the conditions of France to-day, one would say, a 2^riori, that the wages of unskilled laborers must be in close associa- tion with the cost of the means of subsistence. If the relation between the two is one of cause and effect, that is to say, if the wages of unskilled laborers are determined by the means of subsistence, then the de- gree of association must approach unity. These corol- laries of the Turgot doctrine may be tested by means of columns II and IV of Table I. Turgot's doctrine relates to real wages. Column IV, as we have seen, is the cost in the different de- par tements of a fixed mode of life that approaches the necessary means of subsistence of a laborer's family. If the relation between means of subsistence and the wages of unskilled laborers is a relation of cause and effect, then the money wages of unskilled laborers in the several departements should be closely correlated with the corresponding prices of the means of subsist- ence in the departements. How close is the association actually found to be ? The graph showing the relation between the variation in the cost of subsistence and the wages of unskilled laborers is given in Figure 2. The law of the asso- ciated variation of wages with the cost of subsistence is the equation to the straight line, namely, ?/= .864 ^ Turgot : Re'Jlexioyis sur la formation et la distribution ties richesses. Means of Subsistence and the Standard of Life 31 ■o ^ o> <0 <») ^ «<5 ^ ^ CV £-j9JO(7e/ pa///Majn JO ^a^Pyif 32 Laws of Wages + .0014 X. The coefficient of correlation is r=.306. If we agree to regard values of r less than .25 as indicating low correlation ; between .25 — .50, as fair correlation; .50 — .75, as high correlation; and .75— 1.00, as very high correlation, then, we may say that the correlation between the wages of unskilled laborers and the means of subsistence, as tested by the official data for France, is only fair. We do not overlook the facts that the computation of column IV presented very great difficulties, and that if rent, properly estimated, had been included and the re- maining figures had been more accurately determined, a closer relation might have been discovered. The hypothesis of the causal relation between the means of subsistence and the wages of unskilled laborers may be tested. If the relation between the two were a relation of cause and effect, then ?' should approach unity. ^ It is found, however, that the actual value of r is .306 ±.066. When the probable error of r is considered, it is seen that, if the means of subsistence and the wages of unskilled laborers were in' causal relation, such a deviation of r from unity as ^306 would be practically impossible. So far as the data under investigation represent the conditions of France to-day, it may be said — (1) that the wages of unskilled laborers vary in the same direction as the cost of the means of subsistence ; ^ Pearson : Grammar of Science, 2d edit., p. 397. Means of Subsistence and the Standard of Life 33 (2) that the law of the association of the wages of unskilled laborers and the means of sub- sistence is linear ; (3) that the value of the coefficient of correlation is r= .306. ±.066, (4) that there is no relation of cause and effect between the two. These conclusions are based upon the data for all of the 87 departements of France, excepting the Seine and Rliin (Ilaut). For the latter, no record is avail- able in case of column lY. The Seine, being the departement of Paris, presents anomalous conditions. Wages and the Standard of Life. Despite Lassalle's intrepretation of Ricardo, the classic theory of the relation of wages to the standard of life is found in Ricardo's chapter, " On Wages." " The natural price of labour . . . depends on the price of the food, necessaries and conveniences required for the support of the labourer and his family." " It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely constant. It varies at different times in the same country and very materially differs in different countries." ^ The thesis is that the standard of life varies in time and in place and that the wages of laborers vary pari passu. The phases of the doctrine relating to local variations will be subjected to a test. ^ Ricardo : Principles of Political Economy and Taxation. McCulloch's edition, pp. 50, 52. 34 Laivs of Wages Do the wages of unskilled laborers in France vary with the local variations in the standard of life ? If a concomitant variation does exist, what is the meas- ure of the degree of association between the variables ? An approximate answer to these questions may be ob- tained from the data of Table I. In column II of that Table are recorded the average wages of unskilled laborers in the several dejKirtements. In column V, the local values are tabulated of our representative of the standard of life — the prix ordinaire de ])ensio7i paye par Vouvrier isole pour le logement et la nourriture. From these data we find — (1) that the money wages of unskilled laborers vary in the same direction as the cost of the stand- ard of life ; (2) that the law of the association of the money wages of unskilled laborers and the cost of the standard of life is linear ; (3) that the money wages of unskilled laborers are much more closely related to the cost of the standard of life than to the cost of the means of subsistence. In the former case r=. 667; in the latter, r= .306. The graph representing the relation of the two variables is given in Figure 3. In making the com- putations, all of the departements for which records ex- ist were considered except Gironde and Maine-et- Lolre. Figure 3 exhibits the law of the variation of wages Means of Subsistence and the Standard of Life 35 36 Laws of Wages of unskilled laborers as the prix de pension varies from departement to departement. If the prix de p)ension were taken as a function of the wages of unskilled laborers we should have, as the equation of the rela- tion between the two variables, ?/=.5786 a; +.2537, where x is put for the wages of unskilled laborers. From this equation it is clear that, for an increase of one franc in the wages of unskilled laborers, there is on the average an increase of about 58 centimes in the p)rix de pension. There is a subtle difficulty to be overcome before our investigation can be brought into closer relation with the Ricardian doctrine. The preceding results are conclusions as to the relation between money wages and the prix de pension. But the Ricardian doctrine, postulating an invariable money unit, is a theory as to the relation of wages and the concrete things composing the standard of life. Would it be possible to close the gap between our results and the Ricardian theory ? The statistical calculus supplies the tool for connect- ing the empirical conclusions with the a priori doctrine. Thus far it has been shown that the money wages of unskilled laborers are correlated with the p)rix de p>ension and also with the coefficient de depense en oh- jets d' alimentation et de chauffage. Let us represent the coefficient measuring the correlation in the first case by rjo, and in the second case by r^^. The coeffi- cient de depense, we know, is the money value of the same kinds and quantities of things in the different de- Means of Subsistence and the Standard of Life 37 partements, while the prix de pension is the price of a standard that varies from departement to departement. As the former represents the variation in the purchas- ing power of money in the different regions of France, we should infer that the prix de pension would be correlated with the coefficient de depense. Let the measure of correlation in this case be r.^^. In order to connect our results with the Ricardian theory it is necessary to eliminate from the empirical conclusion as to the relation of the money wages of unskilled laborers to the price of the standard of life the factor due to the local variation in the purchasing power of money. According to the theory of the partial coefficient of correlation/ if three variables are so interrelated that their gross coefficients of association are respec- tively ri2, ^13, ^237 then the partial or net coefficient of correlation between the variables 1 and 2 is measured by /)i2 = ^^ ^^ ^'^ Using this method of Vl - 7*13^ Vl - nj treating our problem, we find that the net correla- tion between the wages of unskilled laborers and their standard of life is pi2 = -628, where the r sym- bols in the above formula for ^^2 have the meanings described in the preceding paragraph. The actual values of these coefficients are ri2= .6667 (the coeffi- cient of correlation between money wages of un- skilled laborers and the prix de pension) ; r^g = .3064 ^ See G. Udny Yule : " On The Theory of Correlation." Journal of the Royal Statistical Society, December, 1897. 38 Laws of Wages (the coefficient of correlation between the money wages of unskilled laborers and the coefficient de depense en ohjets d' alimentation et de chauff'age) ; 7'23=.3405 (the coefficient of correlation between the prix de pension and the coefficient de depense en ohjets d' alimentation et de cliaujfage)} From this result it follows that, so far as the data upon which the investigation rests may be assumed to be representative of the true values of the factors in the problem, the degree of association between the wages of unskilled laborers and their standard of life ^ is measured by pi2 = .628. 1 In computing the value of rgg, all of the records were used ex- cept that for Lozere. 2 I have been unable to find in the French report any precise def- inition of the term I'ouvrier isole as it appears in the investigation concerning /)nx de pension pai/e par Vouvrier isole j^our le logement et la nourriture. Does it refer to the single unskilled laborer, or to the single skilled laborer, or was it impossible to measure the difference between the prix de pension of the two classes of laborers? The last interpretation would seejii most probable; for the attempt, in Vol. IV, p. 260, to compare the wages of skilled and of unskilled laborers with the prix de pension pniji par I'ouvrier isole assumes a common prix de pension for the two classes of laborers. It may be noted incidentally that the present chapter contains a solution of the problem that is abandoned in the French report. " A vrai dire, la relation qui pent exister entre le salaire et la depense pour le logement et la nourriture ne semhle ni directe, 7ii simple." — p. 260. The relation is both direct and simple and the coefficient measuring the degree of the net relation is p = .628. The justness of taking the prix de pension as the representative of the standard of life of unskilled laborers is reenforced by the consid- eration that the mean value of t\\e prix de pension d'lm ouvrier isole is 76 per cent of the mean value of the wages of unskilled laborers. It therefore represents with a high degree of accuracy the effort of the unskilled laborer to maintain a standard that varies from de'partement to departement. Means of Subsistence and the Standard of Life 39 ' Wages of Skilled and of Unskilled Laborers. Table I supplies data for measuring a relation that has great importance for the theory of Chapter IV, and for the appreciation of practical schemes that have for their aim the raising of the level of general wages. What is the relation between the variation in the wages of skilled and of unskilled laborers ? The results that are about to be given are based upon a consideration of all of the 87 departements of France, except three, — Seine, Seine- et-Marne, Seine-et-Oise, which are unduly affected by the pecul- iar conditions of wage receiving in Paris. We find — (1) that the wages of skilled and of unskilled la- borers vary in the same direction ; (2) that the law of the relation is linear ; (3) that the coefficient of correlation is r = .775, which is hio;her than the coefficient measur- ing the correlation between the wages of unskilled laborers and the cost of the stand- ard of life. The graph representing the relation is given in the accompanying Figure 4. The equation to the straight line is ?/ = 1.24 + .9142 x, where x = the wages of unskilled laborers. Inasmuch as both classes of wages are affected by the local variations in the purchasing power of money, the net relation between the two variables 40 Laws of Wages ,j \ 1 { \ \ \ \ \ \\ \ k \ \ ^ \ \ \ \ \ V ^ !^ ^ IQ ^ ^ ^ IQ Vl^ ^ '^^ c*i oi ^ OS c\i £-ua.joqf&/ yoa///^£- JO sdJi5ipyiy Means of Subsistence and the Standard of Life 41 can be found only after the money factor is elimi- nated. If, as in a previous case, we represent the correlation between the wages of skilled laborers and the wages of unskilled laborers by r^g ; the correla- tion between the wages of skilled laborers and the coefficient de depense en ohjets d' alimentation et de chauffage by i\2, 5 ^^^^ "t^^^ correlation between the wages of unskilled laborers and the coefficient de de- pense by r2z', then, the net correlation between the wages of skilled laborers and the wages of unskilled laborers is /)i2= •'''S^- We have now definite quantitative solutions to the problems we set out to examine. The wages of un- skilled laborers vary, from place to place in the same country, directly (1) with the cost of the means of subsistence, (2) with the standard of life, the close- ness of the relation being measured, respectively, by r=.306, /)=.628. The wages of skilled laborers vary directly with the wages of unskilled laborers, the degree of the association being measured by /) = .757. The very high correlation between the wages of skilled laborers and the wages of unskilled laborers suggests the wisdom of further investigation as to the mechanism of their relation. This investigation is supplied in Chapter IV, on " Wages and Ability." 42 Laws of Wages M >; ►J b O O o o p •^ c« w Pi PU o <5 05 -i CO CI OOiOOOOOOOmiQiOOO OO'-HOOOOiOOOOICOCjOOOD ■^c6cococOTt5-^-^cO':jHcocoeoco 00 OI (M (M oot^eoosot-^ocjiOrH oj c^ CO (>i ci (M CO ci oj CO • O 5-^ r^ (D ■QJ .g rj Cfi ^ •^ >^ ^ f-, ro r3 w TO t-o y^ vA/ w .^ U -01 9[ Jnod 9I0SI .i9iJAnoj -red 9ABJ noisna j 9p ojreuipao xuj iracOt^OOOlOi— i o "^ WO 1— ICICO-^lOC01>.C300iO^HCICO-+t Means of Subsistence and the Standard of Life 43 lO lO lO >0 O lO CO T— I (>j T-H >-; t>; oi c4 (^i oi c^ T-i lO lO O lO (M to lO CO oi oi oi oi oireiooooioooiooLoo Ol>-00iOOOC0i-it--«5C0C0i0 (>j>-Hoioicoc6c4c^'-5rHc^ji-i.-i O(M00i— I COCOOOIOJIOO'^IOOWCO-^T— IC0t^CO^COt--IO(M CO T^I CO (M >— I (M >0 (M CO rtH r-i (M OJ CO ^ OJ (M Ol (M O] (M TtlCO00COCOCO-*-*-^COCOCO-*-*t^-^-^CDC0COCOCOTtlCO-*COCO-^Tt(. OOiOOOOOiOOirjiOiOOOOlOiOOOOOO^OiOOOOiO OiOt^COT-^COOt>;'*cqt>;l>7000COC>ICOiOCCi-^OOOQ01>.iOiCiiOt-- c6{^ic^(^^(^^<^^oicicoc^c^<^^c6c6uic6eoc6(^^(^i(^^(^^(^^(^^o^(^^(^icac^ « aj oj Qj M ij) SD SD siJ N_ '^ a fl ~ - N^ vqj) sq;) Ch :=! a W OJ ^( !> i-H o) a; 03 i 0) o) 35 ci a a s ■" ■;= OT S CO . . , , r- ^ - ,w -^ n ►- .^ .„ .r-l .r^ .r-l 'Ji J^ ^ P Z^}^^X2 7Z ^ 1^ =^ i^ tS a> oj ^iD o .--.">--.--.- ^ ■ OOpHPHPHP-lf^PqWcCC«C/3COCOMCOC»C/5CCC/3HE-iJ>!>t>r» ;.;:;.;; > s O 'T3 S C ^ C^ C^ C^ C^ ID tm 0) .2 S § oiOi— i(Mco-^i-racDt--coo50i— i(Mco-riH>-ocot^ooc»Oi— lo-jco-^iomt^ lOCDQDCOCOOCDCD'SaOCDt^lr-t^t^t^t^t^t^t^t-OOCOCOCOCOCOCOOO loioooioioioiooioiomoioooooooooooo T-H(>30iooqcqcocoOi--icooqi>;i>--*ooiLOOOioiocooo ,-^(^^r-^,--^rHc4o^o^(^^l-^o^'--^l-^oo(^^(^^(^i(^^(^jcar-^c^o^(^^ (MlOOOOCOi— It^OiCOOii— It^lOC-li-CiCDCOCDOJCISCOCOrHOSCOGOi— (t^OlCO t^lOCXJClT— (i— lOl-^OICOOO-^Oit^-^COCJOSCOt^COtMCOOOiOt^i— II--050 CM C>J CM r- 1 xtH LO CO T— I (M (M ^1 CO Ol ■* 1— I -* CO (M CO CO T— 1 CM CO ■* ■* O-l ■* (M Oa CO lOOOOif^OOiOiOOOOO'OOOOi-OOOOOiraOiOOiOOOO l:^ooosco>OlOGqcoOT-^oc^^^>;OlOo5(^^lOo^— iiocoot^oooooio c^-'d^'^cococo-^oicocoTjHTj^-^coco-^coeo-^-^cocoTjHTjHcococo-^co-^ OOlOlCiOiOOOiCiraiOlOOiOlOOOiOiOiOi-OiOOOOtOiOiOOiO ^ "^ '~; "^ '^J '^I "^ "-5 '^ '^? °9 •^ '-? "^J ^ "^ '^ '^ 1^ "^ "^ "^1 '^ "^ "^ '^J t^ '"J '9 "^J (^j c^j CO (>i (^^ o5 CO (M c^i CM oi oj CO CO r-H CO (M r-i CO CO cj oi CO ^^ f V V \ ^ \\ \ ^ \ 1 \ < \ ^ \ \^ \, \* ~> \ " soasjy Wages and the Productivity of Labor 51 ity of labor is accompanied with a variation of wages in the same direction. That is to say, as an average result, an increase or decrease in the productivity of labor is accompanied with an increase or decrease in wages. This proposition, therefore, is a thesis affect- ing the fluctuations about the general trend, and con- sequently, in order to bring the two series to a comparable basis, their differences due to their differ- ence in general trend must be eliminated. Our first problem, then, is to find the equation to the general trend of the figures in each series. If the type of equation for each series be taken as of the geometric order y = AB^, and the constants A, B be evaluated by the method of moments, the equation to the general trend for the wage series is y= 2.1063(1.015)% and, for the series of the values of the product, ?/ = 5.1115(1.012)% the origin, in both cases, being at 1847. The two equations are repre- sented upon Figure 5 by the smooth curves passing through the two series of numbers. The knowledge of the equations to the curves of general trend makes possible the next step in the problem, which is the computation of the relative deviations of the actual figures from the general trend. The actual figures, as we know, are recorded by the zigzag line. The absolute deviations of the actual figures for the successive years are obtained by sub- tracting from the actual figure for each year the value of the general trend for the same date. For example, the absolute deviation for 1900, in case of 52 Laws of Wages ^ — — - -^ ■ — ■ — -^ =s. "N~ __^ 1? y ^ > 5 L^ ■^ /^ -^ -^ Si ^ ~> s ^§ ^ y >- ^ 4 5>" r ^ -= — —J -< ^ — s> ^ fc==^ ^ -^ 3 ^ -— . t % sc/cu/eM^ &6eutj»x/ac^ Wages and the Productivity of Labor 53 the daily product, was 10.78 — 9.43 = 1.35, because the mean value of the daily product per laborer, in 1900, was 10.78 francs, and the value of the general trend for the same year was 2/= 5.1115 (1.012)^' = 9.43 francs. The relative deviation of the actual figures for each year is the ratio of the absolute devi- ation to the corresponding value of the general trend. 1 35 In 1900, the relative deviation was — — = 14.3 per 9.43 ^ cent. It is desirable to deal with the relative, in- stead of the absolute, deviations because the two series of figures move about axes with different absolute values and with different rates of change. After the relative deviations of the two series of figures have been computed, it is possible to treat their correlation. On Fiarure 6 the relative devia- tions of the two series are plotted about a horizontal line. It is quite evident from the general concurrent flow of the curves that the two series of percentage deviations are closely associated. What is the meas- ure of the degree of their correlation ? The computation of the coefficient of correlation by the usual method gives r = .843. Figure 7 shows the regression of the percentage deviation in the mean daily wage upon the percentage devi- ation in the mean value of the daily product per laborer. We conclude, therefore, from this part of the in- vestigation, that, in case of the great industry of coal mining in France, — 54 Laws of Wages ^1 5> s. ,| ss ir £36eAi /f^/epueacu o/ sc/a/G/AS/o ai^jaaojaf^ Wages and the Productivity of Labor 55 (1) the fluctuation in the mean daily rate of wages varies directly with the fluctuation in the mean value of the daily product of the laborer ; (2) the coefhcient measuring the degree of associa- tion between the percentage variation in the rate of wages and the percentage variation in the mean value of the daily product per laborer has the very high value of r = .843. Fluctuations in the Laborer's Relative Share of the Product and in the Ratio of Capital to Labor. The second essential proposition in the productivity theory of wages is that the fluctuation in the laborer's relative share in the value of the product varies di- rectly with the fluctuation in the amount of machine power per laborer employed in the industry. The establishment of this proposition in a rigid form would give to the productivity theory in its most important aspect the sanction of inductive proof. For the pure theory of the distribution of income is a theory as to the apportionment of the product of industry between the agents cooperating in its pro- duction and is, therefore, concerned with relative shares of the product and not with their absolute magnitudes. Our first proposition concerning the relation of wages to the value of the product is a proposition affecting the absolute value of wages and not the laborer's relative share of the product of in- dustry. The proposition that we are about to ex- 56 Laws of Wages amine is concerned with the latter, more fundamental aspect of the wages question. Table II in the Appendix exhibits the material upon which the investigation rests. Column II of that table gives, throughout a period of 53 years, the ratio of a day's wages to the value of a day's product per laborer. The two items from which the ratios are derived may be obtained from Table I. Column III, which gives the amount of machine-power per 100 laborers employed in mining, is derived from two items that are taken from M. Simiand's work ^ : (1) the total horse-power of the machinery employed in the mines, and (2) the number of laborers so em- ployed. The figures in column III are the ratios of these two items expressed as the number of horse- power per 100 laborers. The problem that will be investigated is tlie relation of the variations of the figures in column II to the variations in column III. It would have been desirable to investigate directly the relation of the variation of the laborer's share of the product to the variation of the amount of capital associated with labor in production. But the figures for the capital employed, at successive years, were not accessible to me. The proposition in the form in which it will be tested is of first importance in itself, and if it is permitted to make the reasonable assumption that the machine-power employed in mines is directly related to the amount of capital employed, then the 1 Simiand : Le Salaire, p. 49. Wages and the Productivity of Labor 57 establishment of the proposition in its present form renders practically certain the doctrine of pure eco- nomics that the laborer's relative share of the product varies directly with the relative amount of capital with which he works. A moment ago reference was made to the exploita- tive implication in Von Thiinen's treatment of the productivity principle. To affirm that the marginal product of labor decreases with an increase in the labor force and that the general rate of wages falls with the decrease of the marginal product, leaves room for the inference that the earlier laborers are exploited of a part of their product when, in conse- quence of the growth of the labor force, the marginal product of labor decreases. Professor Clark, as we know, has shown why such an inference is unwar- ranted. The explanatory facts are that the increase of the labor force implies a reduction in the average amount of capital with which the laborer works, and that the fall of the general rate of wages is due to a lessened specific productivity of labor following the per capita reduction of the amount of capital employed. Has this theory relevancy only to the hypothetical static state that forms the groundwork of theoretical speculation, or does it have a bearing upon the highly dynamic conditions of actual industry ? The investi- gation that we are about to enter upon will answer the question. Our present query has this form : Does the fluctua- tion in the laborer's relative share of the product of 58 Laws of Wages ^ ^ -^ Jl —' \ S ^ u ==: -__ I 1 ■~^ ^ ^ . r" <« -< -^ ^-" ^ s. ^ ? % c N ^ ^ ""^ -.— — ~-^ ^ -^ - — ■ — — •C ^^ ^ N ^ >e J . — ■^ ^ 1 — - "^1 -;;^ -^ ~^ • ^ :~^ "£ • ^ , , — - -*- .__ -- ~' s> ~* ^ 13 ■2 ^ a -^ o -^ 2 o OS c* 0) ^ szxtu&/isfl affe/u9JK/9^ Wages and the Productivity of Labor 59 industry vary directly with the fluctuation in the relative amount of machine-power with which he works, and if so, how closely are the concomitant variations related ? The method of investigation is the same as the one we have already employed. If the quantities in col- umns II and III of Table II are plotted, the graphs will take a generally ascending zigzag course. The equa- tion to the general trend, in case of the ratio of wages to the value of the product, is ?/ = 40.756(1.0039f, and, in case of the ratio of machine-power to men, 2/ = 28.758(1.025)% the origin in both cases being 1847. On Figure 8 the percentage deviations are traced about a horizontal line, and on Figure 9 the regression of the percentage deviation of the first series upon the percentage deviation of the second series is shown, that is to say, the regression of the percentage deviations, in case of the ratio of wages to the value of the product, upon the percentage deviations in case of the ratio of machine-power to men. The coefficient of correlation is r = .599. We conclude, so far as the industry of coal mining in France is concerned, — (1) that the fluctuation in the laborer's relative share of the product of industry varies directly with the fluctuation in the relative amount of machine-power with which he works ; (2) that the coefficient of correlation is /■= .599. (3) that if it is permitted to assume that the 60 Laws of Wages ^ d >>3 »- fl ♦ ♦l-l-H- lllllll Wages and the Productivity of Labor 61 amount of machine-power varies directly with the amount of capital employed, then the fluctuation in the laborer's relative share of the product of industry varies directly with the fluctuation in the relative amount of capital employed. 17ie General Trend of Wages. The third essential proposition in the productivity theory of wages is that, other conditions remaining the same, the general trend of the laborer's relative share of the product is dependent upon the ratio in which capital and labor are combined in production. Up to this point we have been concerned with fluctua- tions about the general trend of wages ; we now enter upon the question of the general trend itself. This corollary of the productivity theory is a proposition in dynamic economics ; it concerns the reward of the laborer in a society in which conditions and methods of production are changing, and consequently it has a very direct bearing upon concrete industry. Because of the lack of data to treat this proposition fully, we shall be compelled to approach the problem by investigating, in a particular instance, a corollary of the proposition before us. We observe, then, that if it be true that the general trend of the laborer's relative share of the product of industry increases with the relative amount of capital with which he works, it would follow that, in the same industry, in 62 LaiDs of Wages neighboring places, with similar methods of produc- tion, the general trend of the laborer's share would increase most rapidly where the general trend of the relative amount of capital per laborer employed in- creased most rapidly. Or, to put the corollary in a form in which it Avill admit of treatment by means of available statistics, we may say that in case of the same industry, in neighboring places, other con- ditions remaining the same, the general trend of the laborer's relative share of the product will increase most rapidly where the general trend of machine power per laborer increases most rapidly. Table III in the Appendix exhibits the data used in the investigation. Column II gives the ratio, per hundred laborers, of the machine-power employed in the direct exploitation of the coal mines in the Bassin de Nord. Column III gives, for the same basin and the same period, the ratio of daily wages per laborer to the value of the daily product per laborer. Columns IV and V give the corresponding data for the neigh- boring Bassin de Pas-de-Ccdais. All of the figures have been taken from M. Simiand's work.^ The record for the period 1880-1902 is used because the figures for the years before 1880 are not comparable with those for the later period. M. Simiand gives figures for only three basins — Loire, Nord, and Pas- de-Calais. The methods of exploitation and the gen- eral conditions of production in case of the neighboring basins Nord and Pas-de-Calais are regarded by M. 1 Simiand: Le Salaire, p. 112. Wages and the Productivity of Labor 63 Simiand as being so much alike as to justify his class- ing them together ^ and treating them in sharp con- trast to the southerly Bassin de Loire. It is quite clear, therefore, that the Bassin de Nord, and the Bassin de Pas-de- Calais, because of their be- ing in neighboring departements, because of the simi- lar methods of exploitation and the similar general conditions of production, and because of the exist- ence of statistical material covering a long period, offer a favorable case for testing the corollary that has just been formulated. Our immediate problem is to find, for the two coal basins, the general trend of the increase, first of the ratio of the machine-power per hundred laborers, and secondly, of the ratio of wages to the value of the product. In case of the data as to the ratio of machine-power to the number of men, we find, by us- ing the same method that has already been employed in this chapter, that the equation to the general trend for the Bassin de Word is ?/ = 46.815(1.0504)-«, and for the Bassin de Fas-de- Calais, 7/ = 61.793(1.0344)% the origin in both cases being at 1880. As both of 1 Simiand: Le Salaire, pp. 110-111. "II suffit a uotre dessein de consid6rer les bassins dont Timportance domine et regie revolution globale et d'atteindre les cas d'6volutioii 6conomique les plus diver- gents que nous puissious rencontrer. Or, il se trouve qu'a tons les moments de notre experience, Loire, Nord et Pas-de-Calais fournissent a eux seuls la plus grosse part de la production franpaise totale (d'abord sensiblement plus de la moiti^, ensuite jusqu'a 70% et plus). Puis une etude anterieure nous a indiqu6 que le bassin de la Loire d'une part, les bassins du Nord et du Pas-de-Calais de I'autre, semblaient s'opposer le plus nettement au point de vue de la conduite 6conomique." 64 Lairs of Wages 1 1 i ^ \ 1 \ 1* \ \ \ \ \ !J \ H ^ \ 1 \ \ \ V S \ ' \ \ \ '^ \ \ \ S \ \ \ \ > ^ \ \ \ * \ \ \ , 1 \ \ \ J, \ 1 \ > 1 \ \ 5^ \ \ 1 \ 1 \ ^ \ \ \ v ^ \ \ \ \ ^ \ \ \ \ k \ 1 % \ \ I \ \\ % \ ^ ^ \\ % M ^ I \ ^ ^ b O eS a > a ^ I) is 03 >> ^ -3 > O Is 1 o _ U .n cu ^ b rt 01 ^ o ■^ a aj "^ x> § § Wages and the Productivity of Labor 65 these equations are of the geometric form, it follows that the ratio of annual increase in the ratio of machine-power per hundred men, for the Bassin de Nord is 1.0504, and for the Bassin de Pas-de-Calais is 1.0344. Hence, as the Bassin de Nord offers the greater ratio of increase, we should expect to find, according to the principle of the productivity theory, that the ratio of the laborer's relative share in the product increased more rapidly in the Bassin de Nord than in the Bassin de Pas-de- Calais. Before passing to the question of wages, we should note that, if the equations to the general trend for the relative machine power in the two cases be put in the form, respec- tively, of 2/= 100(1.0504)% and ?/= 100(1.0344)% the upper part of Figure 10 will represent the relative ratios of increase for the two basins. In case of the data as to the ratio of wages to the value of the product, we find that the equation to the general trend for the Bassin de Nord is 2/ = 49.139(1.0035)% and for the Bassin de Pas-de- Calais, 2/ = 44.697 (1.0013)% the origin in both cases being at 1880. The ratio of the annual increase in the former case is 1.0035 and in the latter case it is 1.0013. If the two equations be put in the form of ?/= 100 (1.0035)" and ?/ = 100 (1.0013)% respectively, the lower part of Figure 10 will represent, for the two basins, the ratios of increase of the laborer's relative share of the product. i 1 In order to make visible the ratios of growth in the two cases, the upper and the lower parts of Figure 10 are drawn to different perpen- dicular scales. 66 Laws of Wages We find, accordingly, that, true to the principle of the productivity theory, — (1) the general trend of the laborer's share of the product is upward where the general trend of machine-power per laborer is upward ; (2) the ratio of increase in the general trend of wages is greater, the greater the ratio of in- crease in the relative amount of machine- power with which the laborer works. If it is reasonable to assume that the amount of machine-power employed in coal mining varies directly with the amount of capital employed, the preceding investigation justifies the conclusion that the increase in the general trend of the laborer's share of the prod- uct is greater, the greater the increase in the general trend of the ratio of capital to labor employed in pro- duction. The conclusions of this chapter have, for the most part, been expressed in general form, while the ma- terial upon which the investigation rests has been drawn from the history of one industry in one country. This has been done with no intention of exaggerating the scope of the inductive inferences nor in ignorance of the narrow statistical basis upon which the last proposition rests. The purpose of the investigation was to make the connection between certain general conclusions of pure economics and the concrete facts of some one great industry. The general character of Wages and the Productivity of Labor 67 the propositions is due to their a priori origin ; the investigation has established that, far from being without relevancy to actual industry, these general propositions are the accurate description of the eco- nomic laws of wages in the one great industry that has been subjected to inductive treatment. 68 Laws of Wages APPENDIX TABLE I. — Daily Wages and Mean Value of Daily Product PER Laborer Mean Value Mean Value Year Mean Daily Wages of the Daily Product per Laborer Year Mean Daily Wages of the Daily Product per Laborer I II III I II III 1847 2.07 5.13 1875 3.58 8.41 1848 2.14 4.76 1870 1849 2.16 5.09 1877 1850 2.14 5.27 1878 1851 2.07 4.75 1879 1852 2.04 4.81 1880 1853 2.20 5.32 1881 1854 2.32 5.40 1882 3.71 7.91 1855 2.35 5.95 1883 3.84 8.06 • 1856 2.51 6.32 1884 3.83 8.06 1857 2.48 5.93 1885 3.72 8.05 1858 2.55 5.97 1886 3.71 7.71 1859 1887 3.72 7.65 1860 2.50 5.73 1888 3.71 7.60 1861 2.57 5.94 1889 3.87 7.88 1862 2.52 5.89 1890 4.16 8.84 1863 2.69 5.83 1891 4.17 9.09 1864 2.60 5.69 1892 4.24 8.46 1865 2.69 6.02 1893 4.14 8.03 1866 2.76 6.31 1894 4.14 8.01 1867 2.89 6.52 1895 4.10 7.93 1868 2.96 6.45 1896 4.10 7.86 1869 2.99 6.58 1897 4.14 8.08 1870 3.04 6.55 1898 4.23 8.41 1871 3.08 6.88 1899 4.38 9.21 1872 3.35 7.91 1900 4.66 10.78 1873 3.45 9.30 1901 4.82 10.68 1874 3.56 8.93 1902 4.57 9.75 Wages and the Productivity of Labor 69 TABLE II. — Ratio of Daily Wages to the Value of a Day's Product per Laborer and Ratio of Machine-Power to One Hundred Laborers Katio of Ratio of Daily Wages Eatio of Daily Wages Ratio of Tear to the Value Machine-Power Year to the Value Machine-Power of a Day's to 100 of a Day's to 100 Product per Laborers Product per Laborers Laborer Laborer I II III I II III 1847 40.4 32 1874 39.9 43 1848 45.0 37 1875 42.6 45 1849 42.5 36 1876 43.1 51 1850 40.7 34 1877 45.0 54 1851 43.6 36 1878 45.5 59 1852 42.5 36 1879 45.7 61 1853 41.4 32 1880 45.2 64 1854 43.0 34 1881 45.6 65 1855 39.5 34 1882 46.9 68 1856 39.7 36 1883 47.7 67 1857 41.8 39 1884 47.5 72 1858 42.7 44 1885 46.2 77 1859 — 1886 48.1 82 1860 43.7 44 1887 48.6 81 1861 43.3 42 1888 48.8 82 1862 42.8 . 41 1889 49.1 79 1863 46.2 39 1890 47.0 85 1864 45.7 38 1891 45.8 87 1865 44.7 40 1892 50.2 92 1866 43.8 44 1893 51.7 100 1867 44.3 44 1894 51.7 108 1868 45.9 45 1895 51.7 105 1869 45.5 47 1896 52.1 108 1870 46.4 49 1897 51.3 111 1871 44.8 48 1898 50.3 111 1872 42.3 44 1899 47.6 110 1873 37.1 41 70 Laws of Wages TABLE III. — Ratio of Machine-Power to One Hundred Laborers and Ratio of Daily Wages to the Value of a Day's Product per Laborer Bassi> DE NORD BaSSIN DE Pas-de-Calais Tear Ratio of Machine-Power to 100 Laborers Ratio of Daily Wages to tlie Value of a Day's Product per Laborer Ratio of Machine-Power to 100 Laborers Ratio of Daily Wages to the Value of a Day's Product per Laborer I II III IV V 1880 45 48.7 64 40.2 1881 46 49.3 63 42.3 1882 48 49.0 71 45.0 1883 50 49.9 72 45.2 1884 58 51.5 70 45.7 1885 68 50.1 70 44.1 1886 69 50.6 85 45.8 1887 71 49.9 82 46.6 1888 77 49.9 83 46.5 1889 77 48.8 79 47.4 1890 82 47.4 75 44.3 1891 79 45.5 78 40.9 1892 85 50.0 83 47.5 1893 90 54.8 94 49.5 1894 91 56.7 115 48.4 1895 90 57.9 104 49.0 1896 95 56.8 101 49.8 1897 93 55.3 110 49.2 1898 92 53.7 109 49.0 1899 107 51.6 97 44.5 1900 137 45.8 125 39.8 1901 153 50.5 149 42.2 1902 156 52.7 146 42.1 CHAPTER IV WAGES AND ABILITY " Le capitalisme . . . tend a produire vine certaine ^galisation du travail entre les diverses parties de I'usine ; mais comme il a besoin d'un nombre considerable d'hommes particulierement actifs, attentifs ou experiment's, il s'ing6nie a donner des supplements de salaire aux hommes qui lui rendent ainsi plus de services ; ce n'est point par des considerations de justice qu'il se regie dans ce calcul, mais par la seule recherche empirique d'un equilibre r^gie par les prix. Le capitalisme arrive done a r'soudre un probleme qui semblait insolu- ble, tant qu'il avait 6t6 etudie par les utopistes ; il r'sout la ques- tion de regalite des travailleurs, tout en tenant compte des inegalites naturelles ou acquises qui se traduisent par des inegalites dans le travail." — Georges Sorel. In the preceding chapter we examined statistically the most important aspects of the first of the two in- quiries that are faced in a complete theory of wages, namely, the question as to the law and cause of the variation in the share of the product of industry con- stituting general wages. In the present chapter we shall be concerned with the second of these funda- mental inquiries, namely, with the law and cause of the distribution of general wages among the members of the labor group. Our point of departure is Pro- fessor Marshall's treatment of the topic. " We may then regard competition, or, to speak more exactly, economic freedom and enterprise, as tending to make time-earnings in occupations of 71 72 Laws of Wages equal difficulty and in neighbouring places not equal, but proportionate to the efficiency of the workers." ^ The sense in which Professor Marshall uses the word " efficiency " is to be inferred from the context. He defines " efficiency-ivages " as " earnings measured, not as time-earnings are with reference to the time spent in earning them ; and not as piece-work earn- ings are with reference to the amount of output re- sulting from the work by which they are earned ; but with reference to the exertion of ability and effi- ciency required of the worker." ^ In the fourth book of the Principles of Economics, Chapter V opens with this sentence : " We have next to consider the con- ditions on which depend health and strength, physical, mental and moral. They are the basis of industrial efficiency, on which the production of material wealth depends." Elsewhere,^ Professor Marshall asserts " that what makes one occupation higher than an- other, what makes the workers of one town or coun- try more efficient than those of another, is chiefly a superiority in general sagacity and energy which is not specialized to any one trade." From these refer- ences it may be inferred that the term " efficiency " when applied in the theory of wages in a subjective sense ^ means a balance of physical, mental, and moral 1 Principles of Economics. 4th edit., p. 6-30. ^Ibid., pp. 630-631. ^ Ibid., p. 286. *The word "efficiency" is one of a large group of terms — such as belief, truth, probability — in which there is ambiguity due to their having both a subjective and an objective connotation. The two meanings of " efficiency " in the theory of wages should be carefully discriminated. Wages and Ability 73 qualities, which is fehcitously summarized in the phrase "general sagacity and energy." Is there any ground for believing that this general theory has any relation whatever to the conditions of wage receiving in actual industry? Suppose the relevancy of the theory were- denied, — as indeed it is denied frequently and vehemently, — how could one proceed to *fortify it otherwise than by reverting to remote hypothetical premises and repeating the long chain of logical deductions ? If the theory is to be accepted as a law, using the word law in the sense of our first chapter, it must rest upon the concrete facts of industry. A similar position is to be assumed in approaching the explanation of wages from the inductive side. The conclusion upon this topic of the French Office du Travail, in its voluminous report on wages for 1893-1897, is summarized in these words : " On voit entre quelles limites etendues varie la valeur relative du salaire dans les diverges professions. Cette valeur relative depend essentiellement de la rarete des aptitudes intellectuelles et physiques necessaires a I'ouvrier, du degre de developpement de ces m^mes aptitudes qu'exigent les diverses pro- fessions." ^ It is entirely true that one does see from the statis- tical schedules that there is a wide variation in rel- ative wao;es, but in the whole of the four volumes of the report there is not a word to show a quanti- 1 Salaires et duree du travail dans l' Industrie franf:aise. Vol. I, p. 512. 74 Laws of Wages tative relation between the amount of wages and " la rarete des aptitudes intellectuelles et physiques " of the laborer. So far as the use of words is con- cerned, administrative inquiry and pure theory take common ground. Would it be possible through the discovery of an economic law to bring the two to- gether so that the theory might organize the data and the data support the theory ? An Hypothesis as to the Distribution of Ability. Before we can establish a quantitative relation be- tween wages and ability we must have an hypothesis as to the distribution of ability among a representa- tive class of laborers. The particular hypothesis that is put forward in this chapter is that industrial ability — general sagacity and energy — is distrib- uted according to the normal or Gaussian law. The normal, or Gaussian, law is represented graph- ically in Figure 11 by either of the two curves AMB, amb. If from a homogeneous group of men a large number of measurements of any physical character are made, for exanjple of stature, it will be found that the measurements may be arranged in such a way that the relative frequencies of the deviations from the average measurement will, when plotted, produce a curve approximating this type. A deviation in excess of the average stature is measured to the right of point 0, on the line ox, and the corresponding frequency of the deviation is then plotted perpendicularly at the end of the Wages and Ability 75 I £ 76 Laws of Wages deviation. Similarly, deviations below the average are measured to the left of point 0. The two sides of the curve are symmetrically disposed about the maximum ordinate, and the scatter of the meas- urements about this ordinate varies with the stand- ard deviation of the measurements. The standard deviation of the curve amh is twice that of the curve AMB. Grounds for the Hypothesis. In justification of the hypothesis that has just been described the following considerations are offered : — (1) The accumulation of a great number of meas- urements of physical characters, w^hich was begun by Quetelet and is now carried for- ward with zeal by anthropologists and bio- metricians, has established that physical qualities are distributed according to the Gaussian law. " We have very definite evi- dence that the normal curve suffices to de- scribe within the limits of random sampling the distribution of the chief physical charac- ters in man." ^ (2) Several years ago Sir Francis Galton began his studies of inheritance on the assumption that the mental and moral qualities of man are distributed according to the same law as are physical qualities. Professor Pear- son's laborious investigations of mental char- * Karl Pearson : Biometrika, Vol. II, p. 395. Wages and Ability 77 acters proceeds upon the same assumption: " We have . . . selected, as the normal scale of intelligence, that which would be given if the frequency distribution of intelli- gence followed the normal, or Gaussian, curve of errors. Whatever the true scale may be, it can only be a more or less — prob- ably less — distorted form of this scale." ^ (3) It has been pointed out that industrial effi- ciency is dependent upon physical, mental, and moral qualities, and these qualities, ac- cording to tfie preceding paragraphs, there is good reason for regarding as being dis- tributed according to the Gaussian law. Professor Edgeworth has demonstrated a theorem to the effect that "... if a varia- ble thing obey the normal law, a function of that thing will obey the normal law." '^ Professor Edgeworth however gives the warn- ing that " this property holds only com- monly, not universally." ^ Karl Pearson : Biometrika, Vol. V. p. 106. " An a priori justifica- tion of the scale may be found in the fact that the plotted points of the regression curves are for a nunaber of pairs of characters, within the limits of random sampling, on a straight line when such a scale of intelligence is used." Ibid., pp. 106-107. ■^ Journal of the Royal Statistical Society, December, 1898, p. 676. 7S Laws of Wages The Expression of the Gaussian Law in a Form that ivill facilitate the Testing of the Differential Theory of Wages. In the subsequent part of this chapter we shall refer to the theory concerning the law and cause of the distribution of general wages among the members of the labor group as the differential theory or the differential hypothesis of w^ages. The statement of the differential hypothesis by the most approved authorities contains four leading prop- ositions : — (1) The labor force in a country of varied indus- tries is a force of varying efficiency per la- borer unit ; (2) The character of the industrial organization of a particular time and place determines the nature and degree of segregation of laborers into groups of varying efficiency. The two most fundamental groups are those of skilled and of unskilled labor ; (3) The laborer of least efficiency in each group receives a wage which constitutes the mini- mum wage of the group. This minimum wage is not less than the hig-hest wasje that could be earned by the least efficient mem- ber of the group in the other forms of em- ployment w^iich are open to him ; (4) The more efficient laborers within a group re- ceive the minimum wage of the group plus Wages and Ability 79 a supplement proportionate to the exce^ of their efficiency over that of the least capahle laborer in the same group. We have assmned that the distribution of abihty among a large group of laborers foUows the Gaussian law. But this law is a generalization applying to an infinite number of measurements, whereas the statis- tics of wages are aTailable for only a finite number of laborers. Furthermore, according to the differential hypothesis, wages are distributed among laborers proportionately to their differential ability. But the Gaussian law gives the law of the distribution of abOity for the aggregate of laborers : it do^ not de- scribe how the individuals in the aggregate differ from each other. It is therefore necessary to derive from the Cranssian law a formula that will be applicable to a finite group and will express the average differences in ability among the members of such a group. In 1902 Sir Francis Galton proposed to British mathematicians this problem : ^ A certain sum, say i£100. is available for two prizes to be awarded at a forthcoming competition ; the larger one for the first of the competitors, the smaller one for the second- How should the ^100 be most suitably divided be- tween the two ? What ratio should a first prize bear to that of a second one ? Does it depend on the number of competitors, and if so, in what way? Similiar questions may be asked . . . when the number of prizes exceeds two. What ^ould be the 80 Laws of Wages division of the £100 when three prizes are to be given, or four, or any larger number ? " ^ Mr. Gal- ton's investigation suggested " that when only two prizes are given in any competition, the first prize ought to be closely three times the value of the second." The novelty and interest of the problem led him to conclude : " I now commend the subject to mathematicians in the belief that those who are capable, which I am not, of treating it more thoroughly, may find that further investigations will repay trouble in unexpected directions." Professor Karl Pearson answered the appeal to mathematicians and undertook the solution of the problem in this general form : " A random sample of n individuals is taken from a population of JV members which when JSf is very large may be taken to obey any law of frequency expressed by the curve y = N(f){x), ydx being the total frequency of individ- uals with characters or organs lying between x and x + dx. It is required to find an expression for the average difference in character between the p^^ and the {p + 1)''' individuals when the sample is arranged in order of mao;;nitude of the character." " I propose to call this general problem : Francis Gallons Individual Difference Prohlem in StatisticSy or, more briefly. Gallons Difference Prohlem. It will be seen at once to carry us from the consideration of the means and standard deviations of mass aggregates ^ Francis Galton, F.R.S. : " The most Suitable Proportion between the Values of First and Second Prizes." Biometrika, Vol. I, p. 385. Wages and Ability 81 and arrays to the average interval between individuals of those aggregates. We may still deal with averages, but we fix our attention no longer on the whole pop- ulation, but on definite individuals in its ordered array. This I believe to be a real advance in statistical theory." The solution of the problem " provides us for the first time, I believe, with most probable relation- 'ships between individuals forming a random sample." ^ One would think that this mathenaatical problem had been formulated and solved with a view to the appHcation of the results to our problem of the dif- ferential hypothesis of wages ! For the knowledge of the average difference in ability between each of 1000 laborers and his less efficient neighbor, when the whole number are ranked according to their ability, would afford data for determining the average dif- ference in ability of the 999 laborers over their least efficient associate. Moreover, if the 1000 laborers were separated into two groups, the one composed of the less efficient, and the other the more efficient, thus giving rise to a minimum wage in each group, the knowledge of the average difference in efficiency in the population of 1000 would suffice for the computa- tion of the average difference in efficiency of the members in each group over that of the least efficient member of the same group. To solve our problem of wages, the first need is the construction of a Standard Population in which the average differences in ability ^ Karl Pearson : " Note on Francis Galton's Problem." Biometrika, Vol. I, pp. 390-399. G 82 Laws of Wages of its members are computed. Such a Standard Population, judiciously used, would supply the means with which to obtain a first approximation to the solution of several questions in the dynamics of wages. The Standard Population. In the Appendix to this chapter are two mathe- matical tables: Table I, Average Differential Ability in a Population of One Hundred ; Table II, Standard Population of One Hundred. A detailed account of the construction of these tables is given in the Ap- pendix. Before proceeding to the description of Table II, upon which the investigation of this chapter is based, it may be observed that Table I enables us to answer the question as to the form of distribution of wages when the incomes of laborers are apportioned entirely according to ability. For example, in 1900, in the manufactures of the United States, the average wage of males over sixteen years of age was $ 11.43 per week. The aggregate received by a population of 100 would therefore be $1143. Assuming the minimum wage to be $3.13 ^ then, if wages were dis- tributed entirely according to ability, each of the more sagacious and energetic laborers would receive the minimum wage $3.13, plus a supplement propor- tionate to his differential ability. That is to say, 99 laborers would each receive $3.13 plus a share of $ 830 (1143 — 313), which would vary proportionately 1 The reason for this assumption will appear later. Wages and Ability 83 to the excess of his ability over that of the least capa- ble member of the group. The $830 would there- fore be distributed according to the conditions of columns IV and VIII in Table I. The ablest man would receive $3.13 plus (830) (.02) which is $3.13 plus $16.60 =$19.73. Similarly, the wages of the other laborers would be ascertained. A graphic de- scription of the resulting distribution is given in the accompanying Figure 12, where wages are taken upon the axis of x and the relative frequencies of the sev- eral rates of wages are plotted parallel to the axis of y. The Gaussian curve traced upon the figure is practically an exact fit ^ to the data. Table II, The Standard Population of One Hundred, is designed to meet the difficulty of the segregation of labor, in actual industry, into groups of skilled and of unskilled labor. It is based upon the knowledge of the average differences in ability between members of a group of 100. The total population of 100 is divided into an upper group corresponding to skilled labor, composed of the fifty ablest members ; and a lower group corresponding to unskilled labor, com- posed of the less capable members. The two groups are then treated separately, just as the whole popula- tion was treated in Table I ; that is to say, each group of fifty is considered as forming a separate population. The average differences in ability of the fifty ablest members over the ability of the fifty-first member — 1 According to the Pearsonian test, n^ = 17 and x^ — -94:2782, which is a perfect fit. 84 Laws of Wages 05 <^ rv (0 "i * Wages and Ability 85 who is the ablest member of the lower group — are then computed. Likewise the average differences in ability of the members of the lower group over the ability of the least capable member of that group are ascertained. In columns III and VII these differences are expressed in terms of the standard deviation of the group, and in columns IV and VIII the same individual differ- ences are respectively expressed as percentages of the sum of the differences. The method in which this table is used to bring to a statistical test the differ- ential hypothesis as to the distribution of wages will now be rendered clear by means of examples. The Application of the Tlieory of the Standard Popu- lation. Certain principles must be observed in selecting data to test the theory : — (1) The differential hypothesis is based upon the assumption of perfect competition of laborers. To meet this specification, (a) we have taken data only from adult male laborers in man- ufacturing industries, where competition among laborers is keenest, and (b) have made a supplementary hypothesis — designed to meet the difficulty of non-competing groups — to the effect that the labor force is divided into two groups, the members of each of which receive the minimum wage of their respective groups plus a supplement proportionate to their differential ability. 86 Laws of Wages (2) The differential hypothesis is based on the assumption of conditions of wage earning in a limited area — " in neighboring places/' to use Professor Marshall's phrase. Ac- cordingly, in order to avoid complications of differences due to geographical separa- tion, the following data refer, as far as pos- sible, to conditions in homogeneous areas. (3) The differential hypothesis is based upon the assumption that opportunities for work are sufficiently varied to permit each laborer to exploit to the full his special degree of sa- gacity and energy. By confining the selec- tion of data to general manufactures instead of particular trades, this condition of the theory is approximated. We shall now consider in detail the application of the theory. {a) Wages in France. In Vol. I of the report of 1893 on Salaires et duree clu travail dans Vindustrie frangaise, p. 496, there is the following table giving the distribution of wages in the Departe7)ient de la Seine : — Wages and Ability 87 TABLE I. — DisTRiBUTiox of Laborers according to Rates OF Wages per Day. France Rate in Francs NuMBEtl Rate in Francs Number 2.75 and less 173 7.25- 7.75 1,3.59 2.75-3.25 137 7.75- 8.25 552 3.25-3.75 453 8.25- 8.75 232 3.75-4.25 1,172 8.75- 9.25 133 4.25-4.75 1,271 9.25- 9.75 76 4.75-5.25 2,182 9.75-10.25 137 5.2.0-5.75 1,351 10.25-11.25 30 5.75-6.25 1,551 11.25-12.25 15 6.25-6.75 6.75-7.25 1,403 1,-558 More than 12.25 Total 19 13,804 This table describes the actual conditions of wage receiving among 13,804 representative workmen. In order to apply the differential hypothesis we must first settle upon the wage to be used as a mini- mum wage in the lower group of the Standard Popu- lation. The total range of the Standard Population of One Hundred is 5.02 times the standard deviation (2.52 + 2.50), which gives a half-range of 2.51 times the standard deviation. If, now, we refer to a table of the values of the probability integral in terms of the standard deviation, ^ we find that, on the average, six cases in a thousand exceed 2.51 times the stand- ard deviation. Consequently, in order to make the Standard Population of One Hundred applicable to the French schedule affecting 13,804 laborers, we have substracted from each end of the total series 83 members, that is, (.006) (13,804). This would 1 The best table is that of W. F. Sheppard : " New Tables of the Probability Integral." Biometrika, Vol. II, pp. 174-190. 88 Laws of Wages leave 90 members in the lowest group and 118 in the group 9.75—10.25. If the lowest limit of actual wages be supposed to be 2 francs, we should then find the theoretical minimum for the Standard Popu- lation from the following proportion 173 : .75 : : 83 : cc. As X in this proportion is 36 centimes, the theoreti- cal minimum wage is 2.36 francs. Similarly, the superior limit of wages in the actual figures would be reduced to 10.18 francs. The modified schedule would then appear as in the first and second columns of the following table : — TABLE II. — Percentage Distribution of Laborers according TO Daily Rates of Wages in the Departement de la Seine AND IN the Standard Population Department de la Seine Standard Population I n III IV V Kale ill Francs Number Percentage liate in Francs Number 2.55 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50 9.96 90 137 453 1172 1271 2182 1351 1551 1403 1558 1359 552 232 133 76 118 .66 1.00 3.33 8.59 9.32 16.00 9.91 11.38 10.29 11.42 9.96 4.05 1.70 .97 .56 .86 2.36 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7..50 8.00 8.50 8.98 9.31 9.91 1 2 4 6 10 13 14 12 11 9 7 4.5 3.5 1 1 1 Total 13638 100.00 Total 100 Wages and Ability 89 Having determined the theoretical minimum wage for the Standard Population, we now find by means of the first and third columns in the above Table II that the average wage in the manufactures of the Departement de la Seine was 5.864 francs per day, and that the first fifty per cent of the laborers — that is the less capable laborers — received 39.819 per cent of the total wage dividend. These three facts, to wit: (1) the theoretical minimum wage of the Standard Population (2) the average wage, and (3) the percentage of the wage dividend received by the less capable group, are all the facts that are neces- sary in order to apply at once the theory of differen- tial wages. We shall now proceed to determine what the dis- tribution would be according to the theory of reward in proportion to ability and shall then compare the theoretical distribution with the actual distribution. Since the average wage is 5.864 francs, the whole wage dividend to be shared by the Standard Popula- tion of One Hundred is 586.40 francs. As the less capable group receives 39.819 per cent of the total dividend, the first fifty members of the Standard Pop- ulation will divide between them 233.50 francs, and the more capable fifty will receive 586.40 — 233.50 = 352.90 francs. The minimum wage in the less effi- cient group is 2.36 francs, and since, according to the differential hypothesis each of the fifty members of this group will receive the minimum wage of the group plus a supplement proportionate to his dif- 90 Laws of Wages ferential ability, the total amount to be divided among the fifty laborers in the form of supplemen- tary payment is 233.50 - (50) (2.36) = 115.50 francs. The resulting distribution in this group will therefore be computed by means of column VIII in Table II of the Appendix to this chapter. For example, the fifty-first laborer — who is the ablest member of the less capable group — will receive 2.36 + (115.50) (.029083) = 2.36 + 3.3591 = 5.72 francs. In a simi- lar manner the amounts received by the other mem- bers of this group may be computed. The dividend of the more capable group is 352.90 francs. The minimum wage of the group is the highest wage that could be earned in the lower group, which, as we have just seen, is 5.72 francs. This method of estimating the minimum wage of the more efficient group is regarded as in harmony with actual practice where the minimum wage in a group is equal to the highest wage that could be earned in other forms of employment open to the laborer. According to the differential hypothesis the mem- bers of the abler group receive likewise the minimum wage of their group plus a supplement proportionate to their differential ability. As the minimum wage is 5.72 francs, and the total amount shared is 352.90 francs, the amount distributed in the form of sup- plementary payments is 352.90 -(50) (5.72) = 66.90 francs. This sum 66.90 francs is distributed accord- ing to Table II of the Appendix, column IV. For example, the ablest member of the Standard Popula- Wages and Ability 91 tion receives as total wage 5.72 + (66.90) (.062670) = 5.72 + 4.1926 = 9.91. The fiftieth laborer receives 5.72 + (66.90) (.000622) = 5.72 + .0416 = 5.76 francs. The wages of the other members of the more efficient group are computed in the same way. The resulting distribution of wages in the total Standard Popula- tion may be seen in columns IV and V of Table II printed in the text. To what degree is the differential hypothesis of wages borne out by the facts of wage receiving in the French Departement f If the figures in Table II for the actual distribution of wages in the Departement de la Seine and for the distribution in the Standard Population were plotted just as they are, it would be seen that the approximation is very close, but, because of the zigzag shape assumed by each series of figures, the measure of the degree of approximation would be rather vague. The result of the method which I have adopted to bring out the degree of ac- cordance between fact and theor}^ may be seen by referring to Figure 13. In this figure the zigzag line gives the actual percentage frequencies of wages as they appear between limits 2.36 and 10.18 in the French report. The dashed smooth curve, computed by Professor Pearson's method of moments, is the curve fittina; best the actual fio;ures. The continuous smooth curve is the best fit to the tabulated wages of the Standard Population. The fact that the smooth curve of the actual data is practically congruent with the smooth curve of the Standard Population shows 92 Laws of Wages / V' A / y 7 ,^ ^ ^ :^ / ^ < / / s J K ^ ^■^ "S \^ ==-^ ^"^^ -^r^-. Vx ^. ^ 1 o> «v I J 151 r I il M ■{^ - \ % <3 I I ^ c3 ■I I ^ .-2 I I Wages and Ability 93 that in this particular case, a doctrine of pure econom- ics is statistically verified. " La valeur relative du salaire . . . depend essentiellement de la rarete des aptitudes intellectuelles et physiques necessaires k I'ouvrier, du degre de developpement de ces memes aptitudes qu'exigent les diverses professions." The words of the French report are now the accurate de- scription of an economic law. (b) Wages in Massachusetts. As the distribution of wages in the Departement de la Seine presents only a small degree of skewness, we shall offer a further test of the differential theory of wages by taking a case in which the distribution is characterized by a considerable degree of asymmetry. Table III of the text, which exhibits data for Massa- chusetts, has been constructed in a similar manner to that of Table II referring to the Devartement de Iq, Seine. The crude data of the table were taken from the Census of Manufactures, 1905, Bulletin 93, p. 109. Figure 14 illustrates the degree of correspondence between theory and practice. ^emarh upon the Preceding Demonstration. The equal division of the Standard Population of One Hundred into two groups needs justification. The asymmetry of a wage curve is due to the influence of several factors, among which are the relative num- bers of laborers at different ages, the increasing value of high degrees of efficiency due to the increasing con- 94 Laws of Wages Wages and Ability 95 TABLE III. — Percentage Distribution of Laborers accord- ing TO Weekly Rates of Wages in Massachusetts and in THE Standard Population Massachusetts Standard Population I II III IV V Eate in Dollars Number Percentage Eate in Dollars Number 2.79 1414 .44 2..58 1 3.50 4176 1.29 3.68 1 4.50 8920 2.75 4.50 2 5.50 13,937 4.31 5.50 4 6.50 22,104 6.83 6.50 6 7.50 28,055 8.66 7.50 9 8.50 28,425 8.78 8.50 11 9..50 39,951 12.34 9.50 13 10..50 27,084 8.36 10.50 8 1L.50 24,705 7.63 11.50 7 12.50 22,239 6.87 12.50 6 13.50 19,754 6.10 13.50 6 14.50 17,216 5.32 14.50 5 15.50 14,748 4.55 15.50 5 16.50 12,603 3.89 16.50 4 17.50 9958 3.08 17..50 3 18..50 8098 2..50 18.50 2 19..50 6203 1.92 19.50 2 20.50 4541 1.40 20.50 2 21.50 3164 .98 21.64 1 22.50 2020 .62 22.81 1 23.50 1162 .36 24.92 1 24.50 1041 .32 25.50 921 .28 26.50 800 .25 27.40 546 .17 Total 323,785 100.00 Total 100 96 Laws of Wages centration of industry,^ the temporary monopoly of particular grades of skill, and the strategic advantage in bargaining enjoyed by trade-unions. It is not pos- sible at present to determine how far these factors are respectively effective in raising wages, and the equal division of the Standard Population into two groups is simply a means of giving expression to the joint effect of a number of factors whose individual influence has not yet been determined. It would be more philosophic but less simple to assume that this " joint effect " to the advantage of efficient laborers is a linear function of their differential efficiency. 1 See Chapter VI. Wages and Ability 97 APPENDIX Notes on the Construction of Table I. I. The table is composed of eight columns. Columns I and V, marked p-, give the rank of the individual in the total population of 100. Columns II and VI, marked — , give the difference between each individual and the next in order of rank divided by the standard deviation of the whole group. Columns III and VII give the difference, in terms of the standard deviation, between each individual of the group and the last member of the group. The first entry in column III is obtained by summing the entries in columns II and VI. The second entry in III is obtained by subtracting from the first entry in that column the first entry in column II. Similarly of the remaining entries in columns III and VII. Columns IV and VIII are obtained by expressing each entry in columns III and VII as a per- centage of the sum of the entries in columns III and VII. For example, the total of columns III and VII is 251.4425, and the first item in column III, 5.02885, is .02 of 251.4425. II. The mathematical derivation of — is explained in the "Notes on the Construction of Table II." 98 Laws of Wages l> Ph lOinKtiioioio-^-rfH^ti-rti-rttcocooioi'— ioo5<»r^o Cn05C505CiC10jCSC350500COCOCOa3COOOCOGOI^t^ ooooooooooooooooooooo ooooooooooopooooooopo > S o ? £ (MGOOCOrHiOr-ICOOCOl^COCOOOi-H'THOCOCO.-l os.-HOiooojc-it^'— (wcsi— iiooj'— loooiOOiOii^ci CO CO t-- lO CO ^H t^ CO t^ 03 >— 1 O t^ CO O O Ct> CO 1^ CO o ^H CO ^H CO >— 1 o o lo oi CO CO CI lO o; (M ic CO o oi -ti o O t- O Ol O l>- lO Ol Ol I— -^ Ol 05 CO -^ •— 1 CO CO CO o t^ O ■* -^ -^ -^^ CO CO CO C^I Ol (M_ Ol ^ ^ "-^ ^ p p O O Ci o\ o\ c\ (m' (m' (n" oi (M* (m' c^' Difference Xp TflCOl^CNCO-^COCOCM'— li— lOCOO-^t^-^t^t-i^t^ t-05C005COirauOOOCOCOCOCOa)(NO;GOr-(CO-rH>0 o o i-H --I iM CO ^+1 o t^ GO o oi -ti t^ 05 oi CO C5 CO ';:■ ci lO o m ira o iQ o «o i.o lo CO CO CO CO CO t^ i^ 1-. CO CO c5 CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI CI ppppppppppppppppppopp > a, 1— icicO'+Hiccot^cocR.O'HCico-tiiocot-ooajo^ lOiooioiOiooioiococococococococococoi-^t^ > a ^ 0-+ICO.— iuticoo5eocoT-i-*co-#cDcoi>Tticoiococo OCOCOCDCOIQ'— (CI'Ot— lOOt^t-OOOCOt^T— ICOrHt^ O lO t^ rH t^ CO O t^ -f CI O t^ i.O CO CI O CO l^ >Q 'Tfi CI OCOI^t^COCOCOOlOlO-+l-*-^^-+l-^COCOCOCOCO ppppppppppppppppppopp s s § 1 i CO Bh OCOCICOCOCIOSOClCO-flCOCOCOlO-tHCO'-HOCOCO iC CO CI 1^ Oi O lO CO O' O C;. -f >0 O 05 CI -^ CO O -ti -f CO GO CI -ti l^ CO CI -f CI CO CO lO >C CO CO 'O -ti 05 CO c: CI O) l^ l^ CI 1-- T-i t^ CO CO -H t- 1^ -t< t^ CI O CO CO O CO CO CI CO CO CI o .— 1 CI ira CO CI CO ^H CO ^H t^ '^1 CO -+I T— 1 1^ CO p o -^H CO CI i-i p p CO CO 1^ t^ o p >-0 iq -*H Tjj ^ CO CO kO-Tli-^Tji-^-^-^COCOCOCOCOCOCOCOCOCOCOCOCOCO - Difference Xp 8 '+l-HCOO'#COOiGOOiOiCOOOCOr-l,— ICIi— l-^OCO coiO'ttcooj-^oii.ooiOT^iojirai— (i^co-— co'QOco COO-Hi— IO5C0t--COCOl0>O-rl"^-TtH-ti-^C0C0COC0C0 cociT-;.-Hppppppppppppppppp - - 1— icicoTtiiccoi>.coa50i— icico-^iracot^cooso^H I-I.-IT— lrH.-HrHrHT-Hi-l.-HCICI Wages and Ability 99 '^(CMOCOlOCMOJCDOiaDCOCOtMCOCi.— IC^J(Mr— IOO^t^iX)TjC0050Tt<'*005t^CDlOCMC^O)CDt~000'-MOO'*^00'* 1— (Oi.Q'rOiOOSiOOJOOiraT— iOC^l'OTti020iC-Thi'-tHO:Ci-*i>Ot^'MCD COtOCOlO-^'— I02l0 0-*OOOJ001'^>— l'*'*T— I^OllOOt^T— (CDt— lO ^^HCOlOCNaSLOGMOJLQ,— It^-^CSlO^^COi— ICDO-*t-0.— (C^OCDCD OS05000000t^l:^t^<:OQ3COlOiO^-^-*COCO(M(Mr-(0005COt^lOCO l:^(MOO-^i— ICOt^COt— 00.— ll0OC0CD(M01»-H0ilC'. OI'TflOOOSCDt^CDOS OOOt— (fMCMCO-*iiOCDC003T— (CM-^l^ClCOCD.-Ht^-TtiCCi-O-^'^tOO OOOOOOOOOOOOOOOOOOOOOOOO.— It— lOlOO l^t^t^l^t^t-t^t^OOCOaOOOCOQOCOCOOOGOCiOSOiOiCOCiClOiOSOS CO^COOOt^t^OlCOCOCO^iOCDaiCMt^COOlCD^CM.— (005C»C»OiO CO O t- Ji CI Oi t^ lO ^ C-1 T— I O CD GO t:^ t^ !» CO iC lO lO O O lO ^ Tti 'rti ■* lO T— lOCOt^CO'^COOjT— lOCiCOOira^COCMi— (OCSCDl^CDLO-rflCOCMT— lO C0C0C.1OJC>IC)(MO)(M(Mt— I^Ht— ii— irH^HT-tT— It— lOOOOOOOOOO T— IrHl— It— Ir-ll— It— iT-li— It— It— ItHt— It— l>— IrHi— It— (1— li— 11— It— It— It— It— li— I'l— (1— (.— I ooooooooooooooooooooooooooooo Ot— (■Tt^'^lOcocDco05■"#l:^o«503l.!:5 0'^•r^^co(^JO^-oi>.ooi^^oc^co cDOoi.— lOiTticooit^cio-TtiiocoTtiiocscoioc^icot^c^jioascocoira lO 1^ CO o (M CO T— I ■* oj -^ t— 1 T— I iQ CI c^] o o r-- r^co^Hioot^-^c^ii— loc^ C0CSCD'*IC0CM(M(MC0-^i»00OC0CDO5C0COO-ti0iC0C0 01t^0al-^0)C0 ococoot^^T— icoioojoico^T— ico>-racoocoiO(MOt^iorMOi--iocj cooiOJOiT-jT— It— iooociosoic^oqcocqa3i~--i--;»--;i--;<:DCD':DCD>OLOio CO CO CO CO CO 00 CO CO CO CO (^i oi (^^ ci oi oi cj oj oi c4 oj <>i oi O) (^^ c^ oa oi (>i oit^ool<^ll:^o^^lOt^^^T^^l:^-*ocooT-l,— icMcoco^ooit^co-^ico COCOCOt^Ol-T+iT— (OiO-^COt— l0005CMCX)CC>COCOCOOOlO»OCDC&COCRl--5g t^CDT— i-^COOlt^fMr-COCOCOtMOSt^-rhliMOCOt^iO-^COOlT^'— lOOO CO (M Ol T— I O O 05 Oi 00 CO t^ t^ t^ CD CD 03 CO CO l-O l-O lO l-O lO >0 lO lO VO lO IQ CO CO CO CO CO CO CM CM (M (M (M (Ol OJ O) C3CD1>-C020 CMdCMlMCMCMCMCMCOCOCOCOCOCOCOCOCOCO-*-*-^'^'*-^-^'*'*''^'" 100 Laws of Wages Notes on the Construction of Table II. I. The table is composed of eight columns. Columns I and V, marked jt?, give the rank of the individual in the total population of 100. Columns II and VI, marked ^, give the difference between each individual and the next in order of rank, divided by the standard deviation of the whole group. Column III gives the difference, in terms of the standard deviation, between each of the first fifty members of the group and the fifty-first member. The first entry in the column is obtained by summing the en- tries in column II. The second entry in column III is ob- tained by subtracting from the first entry in that column the first entry in column II. Similarly of the remaining entries in column III. Column VII is constructed from column VI in the same way that column III is constructed from column II. Column IV is obtained by expressing each entry in column III as a percentage of the sum of the entries in column III. Similarly column VIII is con- structed from column VII. For example, the total of column III is 40.321478, and the first item in column III, 2.526958, is .06267 of 40.321478. II. In computing the successive differences between the first six members of the Standard Population, Pro- fessor Pearson's formula for ^^ was used. where s is the standard deviation. (See Biometrika, Vol. I, p. 396, formula XXVII.) III. Since, by Stirling's formula, when p is large, \p= V27rppPe-P, the factor X?^!^Z!l^, in the above for- Wages and Ability 10 i mula for %^, approximates to unity with increasing values of p. The last factor, {1 4- ^ ^ 1 I>. a> TJH § b- '-^ ^ Ol ^ '-J o o -^ CO t~ CO Ol lO t>. o CO o O ,-1 i- i£ < CO o T-l C- CO oi 1—1 CO 1—1 >-0 as o ■^ v—/ ^ -" ' -^ ' ^^ cs -si cs 7i _, CO O o o t^ CO " 1 CI _: S -- o s § CI o o t- CO S CI ci =■- 5 CJ a CO ^ 1^ o 3 •^-y ^-^ v»^ ^~\ ^_^ ^-^ a 1^ l^ CO :^ e CO '"' ^^ CO O CO .^5 o CO r-i s t- 05 O i~ in t- T— I 2) lO CI CO o V— ' V— ' s ,-^^ K 'X /^N CO « ^, <^ CO t~ ^1 o Si o CI -rtl CO "2? CO CO 00 Cl t~ 1— 1 ^ ""-^ ^w/ H i i ^ V ^ /^\ ^^- CO H o t CI CO ;^ ^ 05 CO !>• -!ti »-^ «M^ CI 05 -*1 ^.^ ,_^ < o 7 eo CO O CO CO CO ^1 CO -i- CO o CO c; o CI o co o6 1—1 &. CJ 1^ o ■w- 1 ^^' &3 ^,^ ,,-^ ,,-^ 5 o -* CO S5 o CO '^ CO t-: >— ' '"? CO a t- oj CO CO CI UI CO g C4 CO S i '-< -^ •* CO C5 ^ CO '-^ ^ P^ -^ ^ \ ^ _ o CI 2§ CI =» CI o CO CO :2 c 1 - O -5 "S 1— -§ >> r— O ^ ? A* O O -f2 1 ^ ' TJ sa^uis qoiqii. ui siuaanisi[qBis3; 1 suop -■EZTUB^JO Joq^i^q pajapjo S9:5uig jo araooiiio 112 Laws of Wages that the strength of labor organizations is propor- tional to their control of trade disputes, Table II will likewise supply an answer to the question as to whether the strength of labor organizations has any- thing to do with the outcome of strikes declared by org;anizations. The construction of the talkie will be made clear by an illustration. In the first column of the body of the table marked " Below 20," the figures 389 signify that, in all of the industries covered by the official report, 389 establishments in which strikes occurred were in industries in which labor organiza- tions declared below 20 per cent of the total strikes of the industry. In case of 211 of these 389 estab- lishments the strikes failed ; in 67 of the establish- ments the strikes were compromised; and in 111 of the establishments the strikes succeeded. It will be observed that the table refers only to the outcome of strikes ordered by labor organizations. All of the data in the official summary have been included ex- cept the material referring to " domestic service " and to " miscellaneous." From this table two conclusions will be drawn: (1) as to the nature of the association between the out- come of strikes and the degree of control of trade disputes on the part of labor organizations, and (2) as to the measure of this relation. The method employed in extracting the conclusions from the data is the method invented by Professor Pearson for the derivation of the coefficieut of mean Wages and Strikes 113 square contingency. An indication of the significance of the coefficient of mean square contingency, as a measure of association, is given by the following con- sideration : The total number of establishments in which strikes occurred is seen, from the entry in the next to the last column and the bottom row, to have been 156,459. Of this total number of establishments 53,512 were establishments in which the strikes failed ; 24,943 were establishments in which the strikes succeeded partly ; and 78,004 were establish- ments in which the strikes succeeded. The last column marked " Chances " gives the ratio of these numbers, respectively, to the total number 156,459. If, now, the outcome of the strikes in the 389 establishments recorded in the first column had been similar to the outcome in the whole of the establishments enumerated, the number of the establishments in which the strikes failed would have been (389) (.3420193) = 133.05 ; the number in which strikes succeeded partly would have been (389) (.159422) = 62.02 ; and the number in which strikes succeeded would have been (389) (.4985587) =193.94. Numbers derived in this way will be referred to as the numbers given by inde- pendent probability. Now it is clear that the numbers actually occurring in the subgroups differ from those given by inde- pendent probability. In case of the establishments in which strikes failed, we have in the first column 211-133.05= +77.95. And in case of the estab- lishments in which strikes were successful, we have 114 Laws of Wages 111 - 193.94 = - 82.94. That is to say, in industries in which labor organizations were weakest, — in the sense of controlUng only a small percentage of the strikes that occurred in the industries, — the outcome of strikes, in establishments in which strikes occurred, was such that there was a positive deviation from independent probability of +77.95 in case of strikes that failed ; while, in case of strikes that succeeded, there was a negative deviation from independent prob- ability equal to - 82.94. If, in a similar manner, the column marked " Above 80 " is examined, it will be found that, in case of establishments in which strikes failed, there is a neg- ative deviation equal to — 5809.57, while, in establish- ments in which strikes succeeded, there is a positive deviation equal to 7888.86. We find, therefore, that for weakly organized in- dustries, the successes are fewer and the failures are more than would be given by independent probability ; while for strongly organized industries the contrary relation proves to be true. These two extreme columns suggest that the outcome of a strike is in some manner related to the degree of union control of the industry, and it is required to determine rigidly from all of the data of the table the quality and the degree of association betw^een the two variables. The deviations from the independent probability of the same sign, or some function of the deviations may be taken as a measure of the association. But, as in other forms of relation the coefficient of correlation Wages and Strikes 115 has been used to measure the degree of association, it is desirable — in order that types of association like that with which we are dealing may be compared with types in which the coefficient of correlation is the appropriate measure of association — to choose from the many possible functions of deviations from independent probability such a function that, in case of normal distribution where the two methods may be applied, the measure of association remains the same, whether it is computed by the newer method or by the method of the coefficient of correlation. The coeffi- cient of mean square contingency, which is a function of the squares of the deviations from independent probability, and the coefficient of mean contingency, which is a function of the deviations of the same sign, are two functions that fulfill the above conditions. If the former coefficient be represented by C^ and the latter by C2, then, in case of normal distribution when all three methods may be applied, 0^= C.2 = r, where r is the coefficient of correlation. The range of value of Ci and C2 is from zero to unity. Their signs must be determined by special methods.^ When the association or contingency between the degree of union control of strikes and the outcome of strikes is computed from our Table II by means of the contingency coefficients, we obtain for the coeffi- cient of mean square contingency (7i = .232 ; and for the coefficient of contingency €2= .30. 1 Karl Pearson : On The Theory of Contingency and its Relation to Association and Normal Correlation. 116 Laws of Wages The conclusions from the investigation are, there- fore: (1) The greater the degree in which labor organizations control the disputes of an industry, the more likely is the outcome of a strike declared by labor organizations to be faA^orable to the interests of laborers ; (2) The measure of the association between the degree in which labor unions control trade disputes and the outcome of strikes declared by organizations is C, = .232 and C, = .30. Figure 15 illustrates the association between the two variables. The diagram is constructed ork the assumption that the variable which measures the out- come of strikes is distributed according to the normal law.^ The origin is taken at a line separating estab- lishments in which strikes " succeeded partly " from establishments in which strikes " failed." The zig- zag line is the line of the means of the respective cate- gories. It is seen that the mean outcome of strikes, in industries in which below 20 per cent of the strikes were called by labor organizations, was a failure ; while in industries in which above 80 per cent of the strikes were called by labor organizations, the mean outcome of strikes was a success. As the degree of control of trade disputes by labor organizations increases, the general trend of the mean outcome of strikes moves from failure, through compromise, to success. There is need of great caution in the interpretation 1 Let it be observed that no point in the argument is dependent ■upon this assumption. This form of diagram was invented, I believe, by Professor Pearson. Wages and Strikes 117 s; I I O o o 6 118 Laws of Wages of these results. It is not to be inferred that the relation between the strength of labor unions and the outcome of strikes is a relation of cause and effect. The low value of C^ precludes the hypothesis of a direct cause and effect relation. The two phenomena may be joint effects of a common cause. Moreover, the results have been determined from data as to all industries and as to all causes. The mixing of the material in this manner introduces an element into the problem the influence of which it would be dif- ficult to measure. Suppose that the outcome of strikes is dependent upon the nature of the particular causes for which the strikes are called, that is to say, suppose that the probabilities of the outcome of strikes being in favor of the laborers vary according to the nature of the causes. Then, if labor organizations in weakly organized industries are predisposed to strike for causes that are likely to fail, while the stronger unions enter into trade disputes for more promising causes, the results that we have obtained would find their explanation not in the degree in which labor unions control trade disputes, but in the wisdom with which strong unions choose the grounds of the disputes into which they enter. Before taking up these considerations, we may note another relation that has a bearing upon the outcome of strikes, as far as the outcome is affected by the strength of labor organizations. Is the result of a strike the more likely to be favorable to the interest of the laborers, the greater the length of time the Wages and Strikes 119 laborers hold out ? Or is the contrary the case ? If the duration of a strike and its outcome are either directly or inversely related, what is the measure of the degree of association between the two ? TABLE III. — Contingency between the Duration of Strikes AND THE Outcome of Strikes. Germany, 1899-1905 L»AYS OF DuKATlOiV Total 1-5 6-10 11-20 21-30 31-60 61-100 101 or over H H S H O a m a to Succeeded 1134 353 275 122 80 57 14 2035 Succeeded partly 1106 601 577 364 336 299 124 3407 Failed 1563 598 517 344 434 438 181 4075 Total 3803 1552 1369 830 850 794 319 9517 TABLE IV. — Contingency between the Duration of Strikes AND the Outcome of Strikes. France 1890-1905 Days of Duration Total 7 or under 8-15 16-30 31-100 101 or over < s H CO O BS « to Succeeded 1522 285 132 98 4 2041 Succeeded partly 1665 618 379 328 36 3026 Failed 2131 613 337 337 51 3469 Total 5318 1516 848 763 91 8536 120 Laws of Wages Tables ^ III and IV, referring respectively to the history of strikes in Germany from 1899 to 1905, and to the history of strikes in France from 1890 to 1905, supply material for answering these questions. In case of the figures for Germany C^ = .22; C, = .26. In case of the figures for France, C^ = .16; C.^ = .19. It may be concluded that — (1) the greater the duration of the strike, the less likely is the outcome of the strike to be favor- able to the interests of the laborers ; (2) the measure of the association between the duration of strikes and the outcome of strikes is, in case of Germany, C-^ = .22 ; in case of France, (7i = .16. Here again caution in the interpretation of the results is very necessary. Is it to be inferred from the above conclusions that protracted strikes tend to end contrary to the interests of laborers because the greater duration of the struggle exhausts the funds of trades-unions and weakens their fighting capacity ? The inference is not warranted by the data. The low coefficients of contingency suggest the unwisdom of drawing any conclusion from the data as to cause and effect. Besides, the lumping of the results of all causes of strikes leaves room for an indefinite number of hypotheses as to the specific cause of the relation that has been established. May it not be true that ^ The tables are taken from the Report for 1906 on Strikes and Lock- outs, pp. 859, 840. Wages and Strikes 121 strong unions, when they do enter into trade disputes, strike for causes that are likely to end quickly in the interests of the laborers, while the weaker unions vainly protract their disputes through ignoring economic laws in the choice of the time and grounds of their strikes ? Outcome of Strikes as Limited hy Econom,ic Law. This discussion brings us to the consideration of the role of economic law in determining the out- come of strikes. In searching for the influence of economic laws in this particular field the first ques- tion that one is led to ask takes this form : Is the outcome of a strike, so far as the interests of the laborers are concerned, independent of the nature of the cause of the strike ? This question may be put more concretely. The Bureau of Labor of the United States classifies strikes according as they had their origin in one or more of fourteen causes. Is it found, from the record of the Bureau, that strikes succeed, succeed partly, or fail in the same proportion of cases, no matter what the cause of the strikes may be ? Or is it true that certain causes of strikes are more likely to lead to success- ful issues than other causes ? The answering of these questions will put one in the way of con- necting the outcome of strikes with economic causes. Table V, which was compiled from the Report on Strikes and Lockouts, p. 63, makes possible the computation of the contingency between the causes 122 Laws of Wages o o H O a H H 02 cq H t^ CO hJ CO CO CO CO 3 C» I— 1 o_ 1— 1 H O ecT o~ oT f-H H 10 r-( '*! (M >. m f£5 =5 ® +J ^ fc. c -C -d 1^ g 10 t^ CO CO 1— t t- CD 10 CO I— ( 00 CO CC r^ ^ I— I -* CD 5-l« tiO aa a. a be a a .2 .3 -3 CD CO Oi oncer Work onditi ,nd El 00 c^ CO CO T-H t— 1 CD I— 1 CO o ■ o « ^ bo B „ C « 3 ,o "S a « s t^ 00 TiH 05 ^ ^ ^ s (M CO ^ CO 2 ° ,'?' 2 tH 03 -^ ling tion and ules t^ »o CO CO 'A S H 9 « CD 1— !once: ecogi Unic nion CO CO 05 cd~ H 1-H 1—1 CO V « 'S 1:2 Cm O <« M _^ ;o a S i; Oi vf5 CO t^ <) ■5 2 g I— 1 O "1 •^ 1—1 CO 00 r- .2 t> t- IC 10 3 ^ t- •* 05 1— I IS t^ 1:- 1^ CO CO T— 1 CD t-T t- tH fc( 3 tn 05 t^ (M CO CO CO Oi 05 Agai Eedu< of W; CO CO -H 'Tt* CO I— 1 10 >— 1 o\ »> (M >— 1 h '« "+1 t^ (M ^ 1^ I— 1 (M^ 05 CO i-T CO 'o CO .— I 1—1 CD fe 'd •n ■73 Ti 0) ■D ^ -5 OJ 0) u cj Ja c3 c3 CJ ;3 § ^ Ph 03 CO H sasiaxg HOiH.ii ni sxnaivHsnayisg ssHiaxc! AO awoaxno Wages and Strikes 123 of strikes and the outcome of strikes. The table includes the results only of strikes that were under- taken for single causes; it does not deal with the results of strikes in which the causes were mixed. The computation of the contingency coefficients gives C, = .298 ; C, = .33. With these values defi- nitely ascertained, it cannot be denied that the out- come of a strike is associated with the kind of cause for which the strike is undertaken. From Table Y, it is also possible to derive values that will throw light upon the ranking of causes according as they are the origin of strikes that are likely to succeed, to succeed partly, or to fail. If the percentage deviations of the actual figures in the subcontingency groups are computed from independ- ent probability, then the magnitudes and signs of the percentages will supply indices of the rank of the causes. For example, in case of the group in the upper left-hand corner, the actual frequency is 30,142, the theoretical frequency given by independ- ent probability is 28,360 ; the relative deviation is therefore ^ — = + .0628. For the sub- 28360 group in the upper right-hand corner the relative deviation is ^-^^-- = - .5599. In the first 2988 case, that is to say, in case of strikes for an increase of wages, there is a positive deviation of the success- ful strikes equal to 6.28 per cent, while in case of sympathetic strikes, there is a negative deviation of 55.99 per cent. 124 Laws of Wages TABLE VI. — The Rank of Causes of Strikes according as Strikes undertaken for the Particular Causes devi- ated, IN their Outcome, from Independent Probability Succeeded Succeeded Partly Failed (1) Concerning recog- (1) For increase of (1) In sympathy nition of the union wages. with strikers and union rules. elsewhere. (2) For reduction of (2) Against increase (2) Concerning em- hours. of hours. ployment of cer- tain persons. (3) Against increase (3) Against reduction (3) Concerning of hours. of wages. working rules and conditions. (4) For increase of (4) For reduction of (4) Against reduc- wages. hours. tion of wages. (5) Concerning work- (5) Concerning work- (5) Concerning rec- ing conditions and ing conditions and ognition of union rules. rules. and union rules. (6) Against reduction (6) In sympathy with (6) For reduction of wages. strikers elsewhere. of hours. (7) Concerning em- (7) Concerning em- (7) Against increase ployment of cer- ployment of cer- of hours. tain persons. tain persons. (8) In sympathy with (8) Concerning recog- (8) For increase of strikers elsewhere. nition of union and union rules. wages. In Table VI, the causes of strikes are ranked according as strikes undertaken for the particular causes deviate, in their outcome, from independent probability. It is found, for instance, that a strike for the recognition of the union has been the most likely to succeed ; a strike for an increase of wages has been the most likely to be compromised ; and a strike in sympathy with workers elsewhere has Wages and Strikes 125 been the most likely to fail. The other causes rank in the order of their sequence in the table. An examination of Table V also discloses that, during the period covered by the Report, the most important causes of strikes were " For an increase of wages " and " Concerning recognition of the union and union rules." These two causes of strikes, to which were due more than 50 per cent of all the strikes that occurred between 1881 and 1905, will be subjected to further treatment. TABLE VII. — Percentages of Total Strikes that were CALLED, respectively, FOR AN INCREASE OF WaGES AND FOR THE Recognition of the Union and Union Rules Tear For AN Increase of Wages Concerning THE Kecogni- tion of the Union and Union Eules Year For an Increase op Wages Concerning THE Recogni- tion of the Union and Union Eulbs 1881 61.15 5.73 1894 30.54 12.45 1882 54.41 5.95 1895 41.98 12.35 1883 45.40 7.53 1896 26.80 21.93 1884 29.57 6.77 1897 35.81 12.99 1885 37.52 7.44 1898 36.36 15.72 1886 41.69 8.73 1899 38.84 19.53 1887 33.64 15.60 1900 32.94 15.35 1888 2.5.94 13.69 1901 29.04 27.98 1889 29.95 12.65 1902- 32.86 25.27 1890 31.48 12.88 1903 31.57 23.24 1891 26.67 14.27 1904 23.19 32.42 1892 29.12 15.25 1905 28.07 30.86 1893 24.21 13.72 Table VII, which was taken from the volume on Strikes and Lockouts, 1906, p. 56, gives the per- centages of total strikes that were undertaken for 126 Laws of Wages I -A > r / \ \i \\ ^ ^ ' \ y N \ \ V I > ■< ■^ \^ \ < « y \ \ \ \ \ > < t V [^ \\ ^ 1 ^ ^ / ) 1 i 15J § 5^ % ^ ^ Wages and Strikes 127 these two causes between the years 1881-1905, in- clusively. When these figures are plotted, as in Figure 16, it is observed that the general trend of the percentage of strikes undertaken for an increase of wages has been downward, while the general trend of the percentage of strikes for a recognition of the union rules has been upward. Furthermore, there is an inverse correlation between the deviations in the tv/o cases, that is to say, when the percentage of strikes for an increase of wages rises above the general trend, the percentage of strikes for a recog- nition of the union tends to fall below the general trend and vice versa. The coefficient of correlation between these deviations from the general trend is^ 7- =-.228. An additional light upon this very same question of the relation of these two causes is afforded by Table VIII, which is taken from the same Report on Strikes and Lockouts, p. 622. The table gives the percentages of total strikes that were successful when the causes of the strikes were, respectively, for an increase of wages and for a recognition of the union. The general trend — Figure 17 — of the percentages of total strikes that were successful was downward, in case of strikes for an increase of wages, 1 No argument is dependent upon the absolute value of this coefficient. It contains a spurious element. The equation to the general trend, for the percentages of total strikes that were called for an increase of wages, is 7/ = 34.4:3 — .6466 x ; and for the percentages called for a recognition of the union, ^ = 15. .57 + .8967 x, the origin in both cases being in the middle of the year 1893. 128 Laws of Wages Is «M R § ^ § ^ Wages and Strikes 129 and upward, in case of strikes for a recognition of the union. Moreover, the percentage deviations from the general trend ^ in case of successful strikes for the recognition of the union were inversely corre- lated with the percentage deviations from the gen- eral trend in case of successful strikes for an increase of wages. The coefficient of correlation is r= — .207. TABLE VIII. — Percentage op Strikes that were success- ful WHEN THE Causes of the Strikes were, respectively, FOR AN Increase of Wages and concerning the Recog- nition OF THE Union and Union Rules Year For an Increase op Wages Concerning THE Recogni- tion OP THE Union and Union Rules Yeak For an Increase op Wages Concerning the Recogni- tion OF THE Union and Union Rules 1881 73.62 40.74 1894 31.04 75.84 1882 56.86 50.00 1895 37.11 74.19 1883 74.31 17.50 1896 62.15 68.78 1884 57.25 30.00 1897 40.92 92.17 1885 61.13 50.75 1898 60.60 87.67 1886 66.44 40.58 1899 53.06 62.43 1887 48.97 53.41 1900 37.60 31.66 1888 63.53 47.64 1901 53.92 57.26 1889 53.45 46.85 1902 56.29 55.14 1890 45.64 45.25 1903 46.98 66.48 1891 37.01 69.46 1904 39.22 36.60 1892 55.01 13.09 1905 45.73 43.83 1893 47.39 82.01 Thus far it has been possible to establish that strikes for an increase of wages decreased in relative 1 The equation to the general trend of the successful strikes for an increase of wages is ?/ = .52.45-.8614x; and for the recognition of the union, 2/ = 53.55+ .9848 x, the origin in both cases being in the middle of the year 1893. 130 Laws of Wages importance in the interval 1881-1905; that the per- centage of successful strikes for an increase of wages decreased during the same period ; that during the same epoch there was an increase in the relative number of strikes for the recognition of the union and an increase in the percentage of successful strikes for the recognition of the union. Furthermore, it has been established that the percentage deviations from the general trend are inversely correlated both in case of the relative importance of the two causes of strikes and in case of the percentage of successful strikes due to the two causes. In view of the dominant importance of these two causes of strikes and of their interrelation, it is clear that if the outcome of strikes for either cause could be shown to be dependent upon economic law, a large part of the theory of strikes would be brought into intimate and real relation with the general theory of distribution. Table IX has been compiled from the data contained in M. Francois Simiand's work : Le Salaire des oimriers dee mines de charbon en France. On pages 351-365 of that work M. Simiand has given the results of strikes relative to wages and conditions of work in the coal mining districts of the basins of Loire, Nord, and Pas-de- Calais. I have computed, for these three districts, in Chapter III, on '^ Wages and the Produc- tivity of Labor," the equation to the general trend of the ratio of wages to the value of the product per laborer per day, and I have given the percentage Wages and Strikes 131 deviations of these ratios, for eacli year, from the gen- eral trend, during the period 1848-1901. By means of these two bodies of results Table IX has been con- structed. The 112 strikes recorded by M. Simiand have been classified according as they fall into the sixteen subcontingency groups of the table. TABLE IX. — Contingency between the Rate of Wages AND THE Outcome of Strikes Pekoentage Deviation of Wages from THE General Trend Total Above +4 to +4 to -4 Below — 4 s W E-i O H O o f u O Successful 3 5 12 7 27 Very Favorably and Favorably Compromised 1 5 1 7 Compromised 6 1 11 2 20 Failed 18 10 26 4 58 Total 27 17 54 14 112 When the coefficients of contingency are computed, it is found that (7i = .327 and C.2= between .36 and .37. The conclusions are — (1) The outcome of strikes for the causes affect- ing wages or the conditions of work is 132 Laws of Wages related to the deviations from the general trend of the ratio of wages to the value of the product, that is to say, the outcome of strikes affecting wages and the conditions of work is likely to be favorable or unfavorable to the interests of the laborers according as the prevailing share of the laborer in the value of the product is below or above the general trend of that share ; (2) The measure of this relation is (7i=.327; C,= M-.S7. But the above coefficients relate to M. Simiand's entire number of strikes between the years 1848-1901. The causes of the tabulated strikes were, however, mixed causes. M. Simiand has included all causes affecting wages and conditions of work, and conse- quently such causes find their place in his table as payment for supplies, hours of work, employment of foreigners, conduct of overseers, and dismissal of work- men. But we have established that the outcome of strikes varies according to the causes of strikes, and therefore it is desirable to narrow the investigation and to inquire whether there is any relation between the rate of wages and the outcome of strikes for an increase of wages. Table X has been compiled from M. Simiand's data by including only those strikes that had their origin in a demand for an increase of wages. The material has been treated by the Pearsonian method for evalu- Wages and Strikes 133 ating the correlation ratio when one variable is given by alternative categories and the other by multiple categories. The percentage deviations from the gen- eral trend of the ratio of wages to the value of the product per laborer have been assumed to conform to the normal law. TABLE X. — Correlation between the Rate of Wages and THE Outcome of Strikes for an Increase of Wages Outcome of Strikes Total Succeeded Succeeded Partly Failed a Above general trend 3 1 10 14 Below general trend 8 6 11 25 Total 11 7 21 39 The value of the correlation ratio is 17 = .370, which is the highest degree of relation that we have found in this chapter. The conclusions are (1) that the out- come of strikes for an increase of wages is related to the deviations from the general trend of the ratio of wages to the value of the product per laborer ; (2) the degree of the relation is measured by 17 = .370. The outcome of a strike for an increase of wages is likely to be favorable to the interests of the laborers when the ratio of wages to the value of the product per laborer is below the general trend of that ratio. The outcome is likely to be adverse to the interests of the laborers when the prevailing ratio is above the general 134 Laws of Wages trend. The general trend itself, as we discovered in the chapter on " Wages and the Productivity of Labor," is conditioned by the degree and nature of the organization of capital and labor in production. Summary. In beginning this chapter it was assumed that both labor organizations and economic law affect the out- come of trade disputes as to wages, and the scientific task that was imposed was to measure, as far as possible with available data, the relative importance of the two factors in the determination of the result- ing rate of wages. The conclusions of the investiga- tion may be summarized under two headings ; {A) The influence of labor organizations ; {B) The influence of economic law. {A) The influence of labor organizations. (1) The results of strikes ordered by labor organizations are more favorable to the interests of the laborers than the results of strikes that are not ordered by labor or- ganizations. The measure of association between the outcome of strikes and the calling or not calling of strikes by labor organizations is given by 17 = .218. (2) The greater the degree in which labor organ- izations control the trade disputes of an industry, the more likely is the outcome of a strike declared by labor organizations to be favorable to the interests of laborers. Wages and Strikes 135 The measure of association between the degree in which labor organizations control trade disputes and the outcome of strikes declared by labor organizations is given bj (7i = .232. (3) The greater the duration of a strike, the less likely is its outcome to be favorable to the interests of the laborers. The measure of association between the duration of strikes and the nature of the outcome of strikes is (7i = .22 in case of Germany, and (7^ = .16 in case of France. (B) The influence of economic law. The relations summarized under (A) must not be assumed to be relations of cause and effect. The low coefficients measuring the degrees of association preclude any inference as to causal relations. Moreover, the results are aggregate results of mixed causes and mixed conditions. A complete investigation would require a segregation of the material and its treatment according to differing conditions and causes. The results of this preliminary study, which goes as far in the direction of seg- regation of materials as the present sources will admit, are as follows : — (1) The outcome of strikes is associated with the kinds of causes for which strikes are un- dertaken. The coefficient measuring the degree of association is (7i = .298. 136 Laws of Wages (2) The causes of strikes may be ranked accord- ing as they have been the origin of strikes that succeeded, succeeded partly, or failed. (3) The most important causes of strikes have . been " for an increase of wages " and " for the recognition of the union and union rules." (a) The general trend of the ratio of strikes "for an increase of wages" to total strikes has been downward ; the gen- eral trend of the ratio of strikes " for the recognition of the union" to total strikes has been upward. (6) The general trend of the ratio of success- ful strikes " for an increase of wages" to total strikes " for an increase of wages" has been downward; the gen- eral trend of the ratio of successful strikes " for the recognition of the union" to total strikes "for the recognition of the union" has been upward. (c) There is an inverse correlation between the percentage deviations from the general trend of the ratio of strikes "for an increase of wages" to total strikes, and the percentage deviations from the general trend of the ratio of strikes " for the recognition of the union " to total strikes. Wages and Strikes 137 (d) There is an inverse correlation between the percentage deviations from the general trend of the ratio of successful strikes "for an increase of wages" to total strikes "for an increase of wages," and the percentage deviations from the general trend of the ratio of suc- cessful strikes " for the recognition of the union" to the total strikes "for the recognition of the union." This intimate connection of the two most important causes of strikes led to the attempt to connect one of the causes with the economic laws that have been established in a preceding chap- ter. It was found that — (4) The results of strikes for general causes affecting wages and conditions of work are associated with the percentage devia- tions of the laborer's share of the product from the general trend of that share. The outcome of a strike for general causes affecting wages and conditions of work is likely to be favorable to the interests of the laborers when the laborer's share in the product of industry is below the gen- eral trend of that share. The outcome of the strike is likely to be adverse to the interests of the laborers when the laborer's share is above the general trend. 138 Laws of Wages The coefficient measuring the association is Ci = .327. (5) The outcome of a strike " for an increase of wages " is related to the percentage devia- tion of the laborer's share of the product from the general trend of that share. The result is likely to be favorable if the la- borer's share is belovv^ the general trend ; it is likely to be adverse, in the contrary case. The measure of the relation is 77 = .370. This last coefficient is based upon a small num- ber of cases and consequently the probable error is high. From the nature of the data examined there is reason for supposing that, with a larger number of cases, the correlation ratio would be much higher. CHAPTER VI WAGES AND THE CONCENTRATION OF INDUSTRY " II mettere in luce 1' influenza dell' impresa e dell' eta dell' operaia suir altezza dei salari, ci sembra ricerca della maggiore importauza teorica e pratica." — La Donna Nell' Industria Italiana, p. ix. The investigation upon which we are about to enter as to the influence upon the status of the laborer of the concentration of industry in large establishments is of both theoretical and practical importance. Its practical value lies in the answer to the question as to whether the form of selection of laborers entailed by the survival in competition of large establishments places the employees upon a better plane of living than the one occupied by their fellow-workers in smaller establishments. Its theoretical interest lies in the answer to the query as to whether the pro- ductivity hypothesis will explain the results to which the investigation will lead. We shall approach our problem by considering the relation of the size of the establishment (1) to the rate of wages, (2) to the amount of employment, (3) to the continuity of employment, and (4) to the length of the working day. Because of the complexity of the undertaking, there is great likelihood of obtaining spurious re- 139 140 Laws of Wages suits in consequence of the mixing of heterogeneous data. The following cautions should be observed as far as possible in selecting material upon which to base the investigation : Data should be segregated (1) referring to different sexes; (2) referring to la- borers of different ages ; (3) according as the data are drawn from different geographical districts ; (4) ac- cording as they are drawn from city and country; (5) referring to industries bearing the same generic name but producing different commodities. Unfor- tunately, statistics appropriate to the solution of dif- ficult economic problems cannot be had for the ask- ing, so that, in the treatment of several points in this chapter, I have been compelled to use data that do not in all respects fulfill ideal requirements. Wages as Affected hy the Concentration of Industry. The first three tables in the Appendix to this chap- ter refer to the daily wages of women, above fifteen years of age, employed in the manufacture of textiles in Italy. ^ We obtain, (1) from Table I, the coefficient of mean square contingency between the size of the estab- lishment and the rate of wages, Ci=.318; ^ The tables in this chaptei' that present Italian data are drawn from the publication of the Ufficio del Lavoro : La Donna Nell' Indus- tria Italiana, Roma, 1905. Wages and the Concentration of Industry 141 (2) from Table II, the coefficient of mean square contingency between the rate of wages and the age of the worker, C,= M; (3) from Table III, the coefficient of mean square contingency between the age of the laborer and the size of the establishment, C, = M. With these crude coefficients of contingency, it would be possible to evaluate, by the method of mul- tiple contingency, the net relation between wages and the size of the establishment. But such a net coefficient would not be an adequate index of the real connection between the phenomena. The de- tails of the computation of the above coefficients have made it abundantly clear that the interrela- tions between the size of the establishment, the rate of wages and the age of the laborer cannot be suffi- ciently described by the simple linear laws that are obtained in the usual cases of correlation. Let us first endeavor to find the law of the varia- tion of wao;es with the a^re of the laborer. Tables I and II of the text have been computed from Table IV of the Appendix. ^ Knowing the mean ages of the laborers in the separate wage groups and the mean wages earned by laborers in the same 1 Table IV of the Appendix was copied from the publication, La Donna NelV Industria Italiana, pp. 99-100. 142 Laws of Wages TABLE I. — Mean Daily Wages of Italian Women accord- ing TO THEIR Ages and the Sizes of the Establishments in WHICH they were AT WORK Age of Employees Mean Daily Wages received in Establishments with Less than 20 Employees 20-99 100-499 500 and Over 15-20 .87 .93 1.04 1.24 20-35 1.09 1.10 1.21 1.50 35-55 1.05 1.12 1.17 1.48 Above 55 .92 .98 .98 1.16 TABLE II. — Mean Ages of the Employees in the Several Age Groups of the Four Classes of Establishments. Textiles. Italy. Size op Establishment Age Groups Above 15 15-20 20-;35 85-55 Above 55 Less than 20 employees 28.23 17.32 25.82 44.43 58.20 20-99 25.63 17.30 25.33 44.72 57.53 100-499 25.14 17.30 25.22 44.89 57.58 500 and Over 24.32 17.31 25.34 43.63 57.49 groups, we can deduce the approximate law of the variation of wages with the age of the laborer. Fig- ure 18 is the graphical description of the variation of wages with the age of the female workers, above Wages and the Concentration of Industry 143 fifteen years of age, engaged in the manufacture of textiles in Italy. The four curves upon the chart give the variation of wages with the age of the la- borer, for the establishments of different sizes. The curves show : — • (1) That the law of the variation of wages with the age of the laborer is, in general charac- ter, the same in establishments of different sizes : There is a rapid rise of wages to a maximum, between twenty-five and thirty- five years of age, and a slow descent to old age. (2) That the larger the establishment the higher the wages at all ages. (This may be partly due to the fact that data from the whole of Italy were mixed in the summary table that has been used.) (3) That in case of the smaller establishments — establishments "less than 20 employees," and between "20 and 99 employees" — the wages of the old employees are higher than the wages of the young employees, while the contrary is true of the larger establish- ments. (Compare the columns in Table I of the text.) (4) That the descent from the maximum wage is more rapid in the large establishments.^ (Compare the curves in Figure 18.) ^ The above method and conclusions are submitted as contribu- tions to Professor Max Weber's problem : " Es ist eine der wichtig- 144 Laws of Wages &l/// a/pasffSJc/)£0 S'aiS&y///ec7 Wages and the Concentration of Industry 145 Why should the law of the variation of wages with age take this peculiar form ? Why should there be a rapid rise to a maximum between twenty-five and thirty-five years of age and a slow descent to old age ? And why should the graphs descriptive of the operation of the law in the four classes of estab- lishments be disposed in the same order as the sizes of the establishments ? The productivity hypothesis supplies the proper answer to all of these questions. We shall consider first the bearing of the produc- tivity hypothesis upon the shape of the age-wage curve. In Chapter IV we found that the efficiency of the laborer is dependent upon a balance of physi- cal, mental, and moral qualities, and that the wage of the laborer is dependent upon his industrial efficiency. In the present chapter we have discovered the law of the variation of wages with the age of the laborer. If the productivity hypothesis be the true explanation of wages, it would follow that the efficiency of the laborer — his balance of physical, mental, and moral qualities — must vary with age in a manner similar sten Aufgaben, fiir die einzelnen Industrien, innerhalb ihrer die ein- zelnen Arbeiterkategorien und fiir diese wieder nach den einzelnen ethnischen, sozialen iind Berufs-Provenienzen festzustellen : wie schnell oder langsara sie ein solches Mass von Leistungsfiihigkeit erlangen, dass ihre Verwendung als Vollarbeiter rentabel wird, wann sie den Hohepunkt ihrer Leistung erreichen, wie lange sie sicb auf dieser Hohe behaupten und -wann ihre Leistungsfahigkeit so weit sinkt, dass sie nicht mehr als Vollarbeiter, oder schliesslich iiberhaupt nicht mehr fiir die betreffende Arbeitsart verwendbar sind." " Zur Psychophysik der industriellen Arbeit," Archiv fiir Sozialwissenschaft unci Sozialpolitik, 1909, pp. 270-271. 146 Laws of Wages to the variation of wages with age : it must rise rapidly to a maximum between twenty-five and thirty-five years of age and then descend slowly to old age. There can be very little doubt, I think, that among the mass of laborers industrial efficiency varies with age according to this law. The study of certain physical measurements is confirmatory of this belief. In a paper by A. 0. Powys on " Data for the Prob- lem of the Evolution in Man," ^ the following im- portant truths are discovered : — (1) The law of the variation of stature with age, in case of the experience of New South Wales, is that stature increases rapidly from the age of fifteen to a maximum between twenty-five and thirty years of age and then decreases slowly to old age. (The maxi- mum stature of men is reached at about twenty-eight years of age and of women at about twenty-five.) (2) " The modal fertility of Victorian women is at 27 and of Victorian men at 32. For New South Wales women the modal fertility 24.4, two to three years less than for Victoria. We have not the data for New South Wales men, but they would probably show a mode of about 29-30 instead of 32. Thus we see that the age of maximum fertility at any rate approaches, if it does not coincide with, the age of most fully developed stature. As 1 Biometrika, Vol. I, pp. 30-49. Wages and the Concentration of Industry 147 Mr. Powys remarks, this tendency of maxi- mum stature age to coincide witli that of maximum fertility can hardly be fortuitous. It seems probable that in man, as in other types of life, the age of maximum fertility is the age of most fully developed physique." ^ The law of the variation of wages with age is therefore similar to the law of the development of physique, and both fertility and industrial efficiency reach their maxima, in the mass of laborers, at about the period of most fully developed physique. This resemblance in the general character of the law of the development of physique and the law of the vari- ation of wages with age, together with the approxi- mate coincidence of the periods of fully developed physique, maximum fertility, and maximum industrial efficiency leaves very little room for doubt as to the intimate causal relation of the phenomena. The facts are all in harmony with the a priori doctrine that the laborer's income is dependent upon his efficiency, and that consequently the law of the variation of his income is similar to the law of the variation of his efficiency. We may now consider the manner in which the productivity hypothesis supplies the answer to the question as to why the graphs descriptive of the varia- tion of wages with the age of the laborer are disposed ^ Remarks of Professor Pearson upon Mr. Powys' data, Biometrika, Vol. I, p. 48. 148 Laws of Wages upon the chart in the same order as the sizes of the establishments. Two points may be made : — (1) The large establishments select the more effi- cient laborers. Referring to the payment of higher wages in large establishments, the French report Salaires et duree du travail dans V Industrie fran^aise makes the following observation : — " Cette tendance ne se manif este pas senlement en faveur des industries qui, comme les mines, les usines metalkirgiques, les compagnies de transiDort, sont le terrain propre de la grande industrie : on Vohserve encore dans (Vautres groupes ou les grands etablisse- ments compensent, par des avantages economiqties certains, la contrainte morale que la concentration des entreprises impose d la ptopidation ouvrih'e, laquelle ne renonce pas sans regret ci la vie plus irregulih'e, mais en un sensjjlus independante, de Vancienne industries ^ (2) Because of the use of large fixed capital in large establishments, the more efficient workers are more valuable to the large than to the small establishments. '^ We have hitherto supposed that it is a matter of in- difference to the employer whether he employs few or many people to do a piece of work, provided his total wages-bill for the work is the same.' But that is not the case. Those workers who earn most in a ^ Vol. IV, p. 22. I have italicized the part of the quotation that I wish to emphasize. Wages and the Concentration of Industry 149 week when paid at a given rate for tlieir work are those who are cheapest to their employers (and ultimately to the community, unless indeed they overstrain themselves, and work themselves out pre- maturely). Yov they use only the same amount of fixed capital as their slower fellow workers; and, since they turn out more work, each part of it has to bear a less charge on this account. The prime costs are equal in the two cases ; but the total cost of that done by those who are more efficient, and get the higher time- wages, is lower than the total cost of that done by those who get the lower time-wages at the same rate of piece-work paj'^ment." " This point is seldom of much importance in out-of-door work, where there is abundance of room, and comparatively little use of expensive machinery ; for then, except in the matter of superintendence, it makes very little difference to the employer, whose wages-bill for a certain piece of work is £100, whether that sum is divided between twenty efficient or thirty inefficient workers. But when expensive machinery is used ivhich has to be loroportioned to the number of workers, the employer ivould often Jind the total cost of his goods lowered if he could get twenty men to turn out for a wages-bill of £ 50 as much work as he had previously got done by thirty men for a ivages-bill of £40.''^ We infer from the quoted facts that the higher wages paid in the larger establishments are due to the greater productivity of a personnel which, age for age, is superior in a balance of physical, mental, and moral qualities. 1 Marshall: Principles of Economics, 4th edit., pp. 631-632. The part of the quotation that I wish to stress I have italicized. 150 Laws of Wages The next detail to be examined is that of the dif- ferences in the age grouping of the operatives in large and in small establishments. The curves descriptive of the frequency distributions according to the age of the employees in establishments of different sizes may be deduced from Table IV of the Appendix. The method that I have adopted may be understood from the following illustration. Table IV gives the infor- mation that, in establishments employing at least 500 women, 41.9 per cent of the employees were between 15 and 20 years of age ; 47.3 per cent between 20 and 35 ; 9.8 per cent between 35 and 55; and 1 per cent over 55. Assuming that no employee was over 65 years of age, the preceding age distribution may be expressed in cumulative form as follows : 100 per cent were over 15 years of age ; 58.1 per cent over 20 years of age ; 10.8 per cent over 35 ; 1 per cent over 55 ; and zero over 65. By fitting a parabola of the fourth order to the age distribution in the cumulative form, the equation to the age distribution is found to be y = 7.167674 - .518268 x + .028171 x' - .0023708 x^ + .000064577 x\ where, the origin being taken at 40, (40 + x) repre- sents the age and y the cumulative percentage frequency. By differentiating the equation and changing the signs of the quantities, the frequency distribution according to age is obtained in the usual form. The equation in the differential form is y = .518268 - .056342 x + .00711 24 x' - .0002583 x\ Wages and the Concentration of Industry 151 From this latter equation, since the origin is at 40, the mean of the distribution may be found from /a yxdx 40 + £yd^. and the standard deviation of the distribution from I yx'-dx r / yxd. tlA Jb j ydQ ydx Inas- much as the lower age limit in the four groups of establishments is 15 years of age, h, the lower limit of integration, is - 25. The upper limit of inte- gration, a, is determined by the point where the curve cuts the axis of x and is different in the four types of establishments. By utilizing this method, Table III of the text is derived. TABLE III. — Means and Standard Deviations op the Ages OF Employees, according to the Sizes of the Establish- ments Size op Establishments Below 20 Employees 20-99 100-499 500 and Over Mean Age 28.23 2.5.63 25.14 24.32 Standard Deviation . . . 12.25 10.84 10.59 9.37 We see from this table that — (1) the larger the establishment, the lower is the mean age of the employees ; 152 Laws of Wages f 1 h Jj. 1 il ''lif il / 1 1' <^ 1 / ^ / y ^ ^ 1t^^ .^ V /^ ^r "^^ ^ < y '^ CJ <0 N to lO th <>> Wages and the Concentration of Industry 153 (2) the larger the establishment, the smaller is the " scatter " about the mean age. It follows from these two facts that the bulk of the adult personnel in the four classes of establish- ments is younger, the larger the establishments. In Figure 19 the percentage distribution of the operatives in the four classes of establishments is roughly indicated by a series of broken lines. The most marked feature of the graphs is that above forty years of age the percentage frequencies are in inverse order of the sizes of the establishments — the smaller establishments having at all ages above 40 a larger percentage of workwomen than the large establishments. Amount of Employment. We come now to the consideration of the relation of the size of the establishment in which laborers are at work to the amount of employment afforded by the establishments in the course of the year. We shall seek to know whether the mean num- ber of days in which the laborers are employed in a year bears any relation to the size of the estab- lishment in which they are at work. The material used in the investigation is again drawn from the admirable report, La Donna NelV Industria Italiana. In the Appendix, Table V, which was compiled from the Italian report, summarizes the data relating to the manufacture of textiles. From this Table V two contingency tables — Tables IV and V of the 154 Laws of Wages TABLE IV. — Contingency between the Amount of Employ- ment AND THE Size of Establishments. Textiles. La Donna Nell' Industria Italiana. Mean Number OF Days, pek Establishment, worked in A Year Number of Women in Establishments OF Sizes given Below Total Less than 20 20-99 100-499 500 and Over 245-255 1167 25,007 26,174 255-265 62,930 62,930 265-275 999 6789 7788 275-285 3772 3772 285-295 3744 25,700 29,444 295-305 4936 16,269 21,205 Total 2166 32,523 93,566 23,058 151,313 text — have been constructed. Both of the contin- gency tables refer to the relation of the amount of employment to the size of the establishment, but they differ in respect to the system of weighting the amount of employment. The original Italian report ^ gives the number of establishments of various sizes, the mean number of days, per establishment, worked during the year by the establishments of the several sizes, and the total number of workwomen over fifteen 1 Pages 54-62. Wages and the Concentration of Industry 155 TABLE V. — Contingency between the Amount of Employ- ment AND the Size of Establishments. Textiles. La Donna Nell' Ixdustria Italiana. Mean Numbek OF Dats, per ESTABLISHME^fT, worked in a Yeae Number of Establishments of Sizes given Below Total Less than 20 Employees 20-99 100-499 500 and Over 24.5-255 116 613 729 255-265 462 462 265-275 123 11 134 275-285 92 92 285-295 99 130 229 29.5-305 27 26 53 Total 239 804 619 37 1699 years of age employed in the establishments of the several classes, on the 30th of November, 1903. In the contingency Table IV, the mean number of days worked in a year, per establishment, is weighted in each case, with the number of workwomen em- ployed in the establishments of the class in question, on the 30th of November, 1903. For example, 1167 women over 15 years of age were employed, on the 30th of November, 1903, in establishments in which the mean number of days' work, per establishment, in the preceding year, was between 245 and 255. 156 Laws of Wages In the contingency Table V, the mean number of days worked in a year, per establishment, is weighted in each case with the number of establishments of the various sizes falling within the limits of the par- ticular "days worked" group. For example, 116 establishments employing less than 20 women each worked on the average between 245-255 days, in the year from December 1, 1902, to November 30, 1903. When the coefficients of contingency are calculated in the usual way from these two tables, we find that — (1) in the first system of weighting, Table IV, Ci = .791; (7,= .89; (2) in the second system of weighting. Table V, (7i=.785; Co = .88. These very high coefficients are marked indications of the gains to laborers, in the way of amount of em- ployment, that accrue in consequence of the superior management necessitated by the investment of vast capital in enterprises producing upon a large scale. Continuity of Employment. The third aspect of our problem as to the relation of the status of the laborer to the size of the estab- lishment in which he is employed is concerned with the variability of the amount of employment in course of the year. It has just been proved that the larger the establishment, the greater the amount of annual employment. We now inquire as to whether the Wages and the Concentration of Industry 157 amount of employment afforded by the establish- ments of the various sizes is more or less variable, from month to month, in the larger establishments than in those of the smaller types. Table VI of the text, referring to the manufacture of textiles in Italy, was summarized from the report that has proved so valuable in the other investiga- tions of this chapter. It gives, for establishments of various sizes, the monthly indices of employment, in the more important subdivisions of the textile indus- try, together with the minimum, mean, and maxi- mum monthly variations, in the year December 1, 1902, to November 30, 1903. The method of presenting these results is due to Professor Bagni,^ who had charge of the preparation of the report. La Donna NelV Industria Italiana. Before commenting upon the data of Table VI, we shall consider the method of computing the monthly indices of employment. For every establishment investigated, the Italian Bureau of Labor had data showing, for each month in the year December 1, 1902, to November 30, 1903, the number of days in which the establishment was in operation and the mean daily number of work- women who were employed. It was, therefore, pos- sible to compute for each class of estabhshments the total number of workwomen-days-work in each month. For, obviously, the number of workwomen- days-work in establishment X diu-ing the month T 1 La Donna Nell' Industria Italiana, p. ix. 158 Laivs of Wagss i-< o << CD Jo & >H a a b o I-" rl a, » 6 ^ I?; o h] i-I tt K O ^ ^ □ 1 B I— ( p o C) oj o c^i ci O z; c3 rH CO tH _^ 2 S C3 05 cs -* "* iri OS O .—1 '^ 5 t^ 3 Cl cc 1-; IC a "a oi r-H H S > o p p t— 1 c^ CO ^ CO 1—1 ^ o o o ^ rH 1—1 1—1 o (N C^J ■^ "S o id (TJ c~ O T— ( tH 1— 1 o 1—1 1—1 1—1 1—1 t^ o OS If: c. 05 OS o OS OJ O' 1—1 o o OS ^^ 2 Ol Ci P ■^ H bi 00 o CO ■<* !z; :3 o I— ( 1—1 o -« T— I 1—1 1—1 ki _X CI CO CI CI g o OS uo ci 1-3 »? o o 1— t P-( cc rH 1— ( 1—1 f—i S W « o H 05 "* o o fe 3 o ^ 00 d o 1-5 g CO CO lO OS 02 < F4 O >> '^tl p CO Cl Q o3 s 00 tA id ^ (^ OS OS OS o 1— i 1-5 ^ ^ t- ^ p CJ C:. CO CO id C7 H "< o o o o o 1—1 1—1 '— ' ^ o GO CO (M •^ rt OJ CO t^ id 05 o O OS ''' 1— ( 1—1 p O] OS p fJ^ '^ t^ CO id fcl a OS OS OS' O] CO ^ OS n .-5 CO CO o 1-5 o 1—1 OS OS o 1—1 03 lO CO o S ^ ,_^ 00 CO Q OS OS 00 OS o ;- ca 5c ^^ CN OJ o C) o r- o ict> o o o o o o o o C5 1—1 O o CD 1— 1 I— 1 1—1 1—1 ■-I 1— 1 1—1 o CO ■ 1—1 en CO T— 1 t- Oi la CO CO en lO Oi t-- r- 1—1 CD CO CO CM 1—1 !>. CO tH o o o 1—1 o o o 1—1 o O 1—1 1^ 1—1 1—1 1—1 1—1 1—1 1—1 1—1 CO t- CO o CO CO CO lO t- lO ^ t- CO T— 1 CO Y— ( CM CO 05 t- CO CM ,__, 00 o o Ci o o CI en en o o o CD '"' 1-H '"' 1—1 1—1 >-H o lO t^ o kO ^ o CO 00 CO t- ^ o 00 o (OJ 00 1—1 en t- -rti 1—1 OI CD o o en o o en o a> w o o o 05 >— 1 I— 1 1— ( >j 1—1 1—1 1—1 1-1 1—1 t- CO (M o t- CM CD CO t^ CO CD CO CO CO t^ t^ o -tH lO CD ^ I-. CO ■* CD t- o o O o o o o o ^ o o o o I— 1 I— 1 •^ '"' 1—1 I— 1 1—1 1—1 H 1—1 1—1 1—1 "* 00 05 t^ C>J o -* t^ CO CO 1—1 t- ^ -* -* CO 1—1 CD '^ t^ k lO '^ CO CM CO 05 en 05 f OJ CD en en < 02 CD Ol CD o 00 CO 00 -:t< CO 1—1 lO CO o >o (M o en Cl oi o O z; C5 CD en CM o CO LO o en C5 o O -< en CD en O o en o o T—t 1—1 a '"' "-^ ^ 1—1 oj CM CO 00 H o CO o lO CO o en t- <33 o 1—1 o CO ^__( o 1—1 b o 1—1 1—1 CO C» o o o CD o o o Z o o o o T— 1 '-' rH 1—1 1—1 ^ 1—1 '-' '-' "-I -* CO 1—1 CD 00 OI CD CD T— 1 en CO CO CO 05 o 00 r^ CO O o SI CO CO o 1—1 05 (Ji o en en o o o en CD o o '-' 1—1 '-' 1—1 I— ( lO o -# en o CM 1—1 CO -*i 00 (M CO CO CO lO ,_! TtH -tH CO CO t- CM 05 ^ 00 C2 en Cl en en Ol en 00 en 00 Oi litl eo en lO ^ -* CO o t^ IC 't' ^ o 00 o 00 1—1 en 1—1 CM CD CO ifi CM CD Oi o 1—1 CD o 1—1 en o O 00 en t- 05 en CI CO 1—1 OJ CM Tj^ -*i CM -* 00 (M CO "* CD CO lO o CO CM o lO 00 05 05 OS Oi en en o en en 05 o i^ O 1^ o !- (M en ^ (M en > CM en en Oi n J3 en Oi o en CD 6 ^ 1" -ri en ■* tS en 1 -T! o A c 4J o += o o S "5 Cl o cS M CM <3i c« CO CM o 1— ( O tH O 1—1 O O lO J o J 160 Laivs of Wages was equal to the number of days the establishment was in operation multiphed by the average daily number of workwomen employed that month. By means of this method the number of workwornen- days-work in each of the four groups of establish- ments was computed for each month of the year and for the whole year. The monthly numbers were afterwards expressed as fractions of the correspond- ing annual numbers, and the fractions were then multiplied by 1200. The resulting numbers are Pro- fessor Bagni's monthly indices of employment. The maximum, mean, and minimum variations are meas- ured from 100.^ We may now examine Table VI. By referring to the last two columns we observe that — (1) As the size of the establishment increases, the general trend of the mean variations of the index of employment is downward. (The silk industry is an exception to the rule.) (2) As the size of the establishment increases, the general trend of the maximum deviation is downward. (The silk industry is again an exception to the rule.) (3) In all of the groups, the mean deviation and maxinmm deviation in the largest establish- ments are smaller than the corresponding deviations in the smallest establishments. ^ The objection to this method is that spurious monthly diiierences are introduced in consequence of not taking into account the differ- ences in the length of the calendar months. The defect in the method does not invalidate the inferences in the text. Wages and the Concentration of Industry 161 Length of the Working Day. The fourth aspect of the problem as to the relation of the status of the laborer to the size of the estab- lishment in which he is employed is concerned with the length of the working day. Up to this point the researches of this chapter have been based upon the data relating to the textile industry in Italy. It would be highly desirable to have all of our conclu- sions bearing upon the concentration of industry re- late to one industry at a given time and place. But TABLE VII. — Mean Duration of Daily Hours of Work, CONSIDERED IN RELATION TO THE SiZE OF ESTABLISHMENTS, IN THE Mines of France producing Coal and Other Fuel LOOALITT Mean Duration of Daily Hours of Work according as the establishment had a Number op "Workmen Exceeding 999 From 500 to 999 From 100 to 499 From 25 to 99 From 1 to 24 Region Nord et Pas-de- Calais 8f 9i H Region Est 8f 9 101 Region Centre .... 9 9J 9i 10 Region Sud 9i H 10 Region Sud-Est .... 8i 10 H Region Bouches-du-Rhone 8i 8i 162 Laws of Wages I do not know of the existence of material jjresenting a classification, according to sizes of establishments, of the hours of labor in the manufacture of textiles in Italy. In default of appropriate Italian figures, we may refer to the investigation embodied in the French report : Salaires et duree du travail dans V Industrie fpan<^aise. Table VIP is given as a favorable in- stance of the findings of the French statisticians. This table eliminates the differences in hours of labor arising from the differences in locality, and it clearly shows that as a general rule the hours of labor decrease as the size of the establishment increases. The conclusion that is drawn from this illustration is the conclusion of the French report as to the general trend in the whole of the French provincial manufactures. The conditions of production in Paris are exceptional, and statistical study of the relation of the size of the establishment to hours of labor is rendered difficult because of the classification under the same name of industries that are radically differ- ent in character. " En province, an contraire, les fabrications sont plus courantes, les divers etablisse- ments groupes sous le meme nom d'industrie forment des groupes plus homogenes. On pent meme les etudier, et on observe nettement une amelioration des conditions du travail dans les grandes entreprises. Dans leur ensemble, la duree du travail est plus courte."^ 1 This table is taken from Vol. IV, p. 100. ^ /j/j.^ p, oo. Wages and the Concentration of Industry 163 We started out to find the relation of the concen- tration of industry to the changing status of the laborer, and we proposed to investigate that relation from the four points of view of (1) the rate of wages, (2) the amount of employment, (3) the continuity of employment, and (4) the length of the working day. Our investigation has yielded the definite result that, as the size of the establishment increases, the condition of the laborer improves in all directions — his wages rise, he is employed a greater number of days in a year, his employment varies less from month to month, and his hours of labor, per day, -decrease. We have found that the law of the variation of wages with the age of the laborer is similar in estab- lishments of all sizes, and that the general character of the law has its explanation in the law of the de- veloping physique and capacity of the laborer. The differences in the graphs representative of the law of the variation of wages with the age of the laborer in the four types of establishments are due to the large establishments selecting the more capable workers. The large establishments are able to carry out the work of selection because, in consequence of their large capital and better organization, they offer op- portunities for the more capable laborers to reap the reward of their differential ability. 164 Laws of Wages APPENDIX TABLE I. — Contingency between the Daily Rate of Wages AND THE Size of the Establishment in which Employees WERE AT AVORK. TEXTILES. ItALY. Kate of Wages in Lire and Centesimi Number of Workwomen in KsxAULisuiiE^TS with Totals Less than 20 Employees From 20-99 From 100-499 500 and Over Up to .50 150 545 1030 96 1821 .51-.70 443 6303 9356 1103 17,205 .76-1.00 873 12,863 30,523 3718 47,977 1.01-1.50 645 11,239 45,113 10,605 67,602 1.51-2.00 214 1843 7097 6396 15,550 2.01-2.50 30 519 1755 1482 3786 Over 2.50 6 177 613 413 1209 Totals 2361 33,489 95,487 23,813 155,150 Wages and the Concentration of Industry 165 TABLE II. — Contingency between the Daily Rate of Wages AND THE Age of the Laborer. Textiles. Italy. Rate of Wages IN Like and Centesimi Number op Employees whose Ages weke in the Age-gkoups Totals 15-20 20-35 35-55 Above 55 Up to .50 1425 228 105 63 1821 .51-.75 11,000 4063 1478 664 17,205 .76-1.00 21,903 18,843 6049 1182 47,977 LOl-1.50 24,905 33,884 8010 803 67,602 1.51-2.00 4184 9103 2109 154 15,550 2.01-2.50 555 2511 676 44 3786 Above 2.50 98 807 289 15 1209 Totals 64,070 69,439 18,716 2925 155,150 166 Laws of Wages TABLE ITT. — Contingency between the Age of Employees ANO THE Size of the Establishment in which they were AT Work. Textiles. Italy. AliK IN Ykaks NUMliEU OK WOKKWOMEN IN KslAUl.ISllMKNT8 W ITIl Totals Less than 20 Employees 20-99 100-499 500 and Over 15-20 778 13,453 39,851 9988 64,070 20-35 1005 14,831 42,367 11,230 69,439 35-55 471 4543 11,367 2335 18,716 Over 55 107 602 1902 254 2925 Totals 2361 33,489 95,487 23,813 155,150 Wages and the Concentration of Industry 167 TABLE IV. — Classification of Workwomen according to THEIR Ages, their Rates of Wages, and the Sizes of the Establishments in which they were employed. Textiles. La Donna Nell' Industria Italiana, pp. 99-100 Size or the ESTABLISU- WENT8 Percentage of Workwomen, over 15 Years of Age, RECEIVING THE FOLLOWING EaTE OF WaGES. [Kates are expressed in Centesimi and Lire] Age Groups Up to .50 .51- .75 .T6- 1.00 1.01- 1.50 1.51- 2.00 2.01- 2.50 Above 2.50 Total Per- centage Less than 20 Employees 4.0 8.5 12.1 7.0 1.3 32.9 15-20 1.3 6.4 15.0 13.3 5.4 1.0 .2 46.6 20-35 .5 3.0 8.2 6.0 2.1 .3 20.1 35-55 .5 .9 1.7 1.0 .3 4.4 Above 55 6.3 18.8 37.0 27.3 9.1 1.3 .2 100.0 20-99 1.2 11.1 15.6 11.2 .9 .2 40.2 15-20 .2 5.9 16.5 17.1 3.3 1.0 .3 44.3 20-35 .1 1.6 5.4 4.8 1.2 .3 .2 13.6 35-55 .1 .3 .9 .5 .1 1.9 Above 55 1.6 18.9 38.4 33.6 5.5 1.5 .5 100.0 100^99 .9 6.5 14.9 17.1 2.0 .2 .1 41.7 15-20 .1 1.9 12.4 24.1 4.3 1.3 .4 44.5 20-35 .1 .9 3.9 5.5 1.0 .3 .2 11.9 35-55 .5 .8 .5 .1 1.9 Above 55 1.1 9.8 32.0 47.2 7.4 1.8 .7 100.0 500 and Over .3 3.7 9.1 19.5 8.1 1.1 .1 41.9 15-20 .1 .6 4.9 20.5 15.8 4.1 1.3 47.3 20-35 .2 1.3 4.1 2.9 1.0 .3 9.8 35-55 .1 .3 .5 .1 1.0 Above 55 A 4.6 15.6 44.6 26.9 6.2 1.7 100.0 168 Lairs of Wages Ei: H s ir; H u S u s o Wl < rr) (h >7; a W X < ■•^ >- A Pi r. = f^ >- >< r- ^ g E 5|| X i. :i ;-; ~ C :^ ^ S m s o 55 O 12; - -/: < »-■ > Lj 1-^ V H ^ ^■* O s <; V5 K sc t; ^ < ~ - ^ ^ ^ ii X >^ ^"^ '/: ^, ? <; 1 '/^ > _ r^ a » 0 o i-H Ol o CO s Ol o o CO x ^ tii! ^ (M CO ^ "^ iZ >> ^ -^ CO CO 00 C o CO >-0 -rt< 5 &: (M CO K ^ 5 t- t- o s ^ CO CO Tt< =3 o CJ S ■^ t^ w CO ^ X 6i 1— ( ^ 0) « Ji ^- ho J: >. s o g 3 12; s ^ <1 O 33 5 3 £ c "S CS 4^ S "cS >^ — c3 OQ a> cc 13 ■4^ C3 'c a s C o O 03 >^ ^O °o £ CHAPTER VII CONCLUSIONS " Womit wir es hier zu thun haben, ist eine kommunistische Gesellschaft, nicht wie sie sich auf ihrer eigenen Grundlage entwick- elt hat, sondern umgekehrt, wie sie eben aus der kapitalistischen Gesellschaft hervorgeht; die also in jeder Beziehung okonomisch, sittlich, geistig, noch behaftet ist mit den Muttermalen der alten Gesellschaft, aus deren Schoos sie herkommt." — Karl Marx. In the preceding chapters we have been concerned entirely with the scientific aspects of the subjects that came before us, and no attempt was made to indicate the practical bearing of the results that were established. But the economist, least of all scientists,\ can feel content with the simple understanding of ' the laws of his subject matter. He desires to see what guidance they may afford in the complicated life of his own time. This summary will, accord- ingly, be concerned primarily with the relation of our results to actual practice. We may notice first the practical character of Sta- tistical Economics. It was pointed out in the first chapter that in its scientific character, Statistical Economics proposes this twofold object : (1) to bring >^ to the test of representative facts the hypothe- ses and theorems of pure economics ; (2) to supply > 169 170 Laws of Wages data, in the form of general facts and empirical laws, for the elaboration of dynamic economics. Its prac- tical service is performed in a similar way ; for, in giving a statistical summary and interpretation of the material relevant to the economic subject under investigation, it supplies the means by which general reasoning may be brought to bear upon the problems of industrial legislation. A short account of the way in which this form of economic science has come into being will indicate more clearly its scope and bearing. Just half a century ago, in an inspiriting address ^ on " The Progress of Economic Science during the Last Thirty Years," William Newmarch summarized what he regarded as the greatest achievement of the science during the period covered in his survey. " Looking back at the changes and the experience of which this is a rapid outline, it appears to me that I shall not be in any danger of misleading the Sec- tion if I suggest that probably the most conspicuous and important fact to be found in the history of Eco- nomic Science during the last thirty years is this ; namely, that while there has been no change in the objects to which it is directed — no change in the purposes intended to be worked out — while these objects and these purposes remain the same in their broad and general aspect as they have been from ^ Newmarch gave the address as President of Section (F) of Eco- nomic Science and Statistics of the British Association for the Ad- vancement of Science. The address is published in the Journal of the Statistical Society, 1861, pp. 451-467. Conclusions 171 the time of Adam Smith, there has been a marked change in the Methods according to which Economic Science is cultivated. It has ceased to be an abstract science, — it has ceased to be a system of subtle and ingenious reasonings. It has little by little, and by a process cautious and full of promise, become a science almost entirely experimental. We have learned that in all questions relating to human so- ciety — in all controversies where the agency of hu- man beings has to be relied upon for working out even the smallest results — we have learned that in these inquiries the only sound basis on which we can found doctrines, and still more the only safe basis on which we can erect laws, is not hypothetical de- duction, however ingenious and subtle, but conclu- sions and reasoning supported by the largest and most careful investigation of facts. This vital change of method, this substitution of observation and ex- periment (and for our present purpose the two words mean very much the same thing) for deductions ar- rived at by geometrical reasoning, seems to me to be the most prominent fact of the last thirty or forty years, as regards the progress of the branches of knowledge which more immediately interest us in this Section." The negative attitude of Newmarch with regard to theoretical economics I, of course, do not share. The quotation has been made in order to stress his point of view as to the relation of economic science to legisla- tion. The two pervading ideas of the address are. 172 Laws of Wages first, that effective legislation must be based upon ex- perience, and, secondly, that experience must be interpreted by the statistical method : " we claim for Statistics . . . that it is the application of the Exper- imental or Baconian method to the several divisions of inquiry which relate to man in society. We say that where there is no careful application of the Statistical method — in other words, where there is an absence of observation and experiment, so far as observation and experiment can be applied to men in Societies — there can be but faint hope of arriving at the truth in any line of research connected with social problems." ^ In the works of Stanley Jevons is found the devel- opment of the ideas of Newmarch upon this subject. Jevons observed that legislation in England did not proceed without what is commonly called statistical evidence, but the statistics were not always of the right sort, nor were the statistical inquiries always conducted according to "true scientific method."^ Furthermore, using the hint in Newmarch's address, he called the method of legislation he approved " Baconian legislation," and he thus described the principle upon which it should proceed : " What I venture to maintain is that Baconian legislation will always proceed by reasoning from the most nearly proximate and analogous experience which is avail- ^ Newmarch: Journal of the Statistical Society, 1861, p. 457. 2 Essay on "Experimental Legislation and the Drink Traffic." Methods of Social Reform, p. 256. Conclusions 173 able. We cannot possibly dispense with general rea- soning, hut ive should use it as sparingly as possible. We shoidd choose, as it were, the loivest logical elevation in sight." ^ The part of the quotation that 1 have itahcized presents the point of view I should hke to urge. According to the argument of the chapter on " Statis- tical Laws," the statistical economist proceeds by a progressive synthesis from individual facts to general facts, and from general facts to statistical laws. He expresses the laws in their mathematical form, and, where it is possible, he measures the degrees of asso- ciation between the related phenomena, expressing them as coefficients of correlation, correlation ratios, or coefficients of contingency, as the case may be. Now in Baconian legislation, the interpretation by means of general economic reasoning of the statistical laws and coefficients of association constitutes " the lowest logical elevation in sight" upon which legisla- tion can be effectively based. The practical work of the statistical economist bridges the gap between general reasoning and the crude facts.^ ^ Jevons : The State in Relation to Labor, p. 24. 2 This conception of Statistical Economics, theoretical and applied, is receiving a most promising development in the contemporary Italian school, whose organ of publication is the Giornale degli Econoniisti. Following Professor Pareto's attempt to give concreteness to the theory of distribution by basing his reasoning upon a statistical law summar- izing approximately the distribution of income in modern societies, numerous essays appeared, particularly in Italy, in which Pareto's method was applied in the treatment of other social phenomena. Pro- fessor Pareto himself, asserting, in 1907, that " the progress of polit- ical economy in the future will depend in great part upon the investi- 174 Laws of Wages Coming now to the detailed consideration of the practical bearing of the preceding chapters, we may observe with reference to the two theories, which for the sake of brevity we may refer to as the subsistence theory and the standard of life theory, that their per- sistence in economic literature gives color to the be- lief that wages may be increased in other ways than through an increased effective productivity of the laboring class. This is particularly true in regard to the doctrine of the standard of life, because in sup- port of false views, Ricardo's authority may be cited : " The friends of humanity cannot but wish that in all countries the labouring classes should have a taste for gation of empirical laws that are derived from statistics" (Giornale degll Economisti, Maggie, 1907, p. 36G), has spent much of his time in perfecting the inductive, statistical tool by means of which the em- pirical laws are summarized in mathematical form. But the formal conception of an Inductive Economics, utilizing as means of investigation modern statistical methods, is found in the work of Professor Benini and of Professor Bresciaui. In his inaugural address as Professor of Statistics in the University of Rome, Professor Benini outlined his conception of " Una possibile creazione del metodo statistico. L'economia politica induttiva" {Ibid., Gennaio, 1908). His volume on Principii di Statistica Metodologica may be regarded as his description of the method to be employed in the treatment of this aspect of economic science. More recently, Professor Bresciani, in his inaugural address as Professor of Statistics in the University of Palermo, has treated a phase of the same subject under the title " Sul carattere delle leggi statistiche " (Ibid., ]\Iarzo, 1910). In the series of articles on correlation and frequency distributions, published in 1909, Bresciani has described to his co-workers the methods of Pro- fessor Karl Pearson. A marked indication of the influence of this constructive group of younger economists is seen in the change in the name of their journal. Since 1910, the title of this admirable review is no longer simply Giornale deyli Economisti but Giornale degli Economisti e Statistica, thus establishing a formal attempt to bring theoretical and statistical economics into intimate relation. Conclusions 175 comforts and enjoyments, and tliat they should be stimulated by all legal means in their exertions to procure them." ^ It is entirely possible with ingenuity to interpret Ricardo's meaning from the context so that it would seem to be in harmony with the modern doctrine, but, without doubt, the vigorous statement is both misleading and false : misleading, in conse- quence of wrong emphasis in centering attention upon increasing wants while ignoring the inevitable price of their gratification; and false, in consequence of lumping together the " laboring classes," and infer- ring that it is true of all grades of labor that there should be an artificial stimulation of wants. In order to seize the degree of truth in either of the two theories that we are considering, it is necessary to reason about laborers not as a class that may be represented as a whole by a more or less fictitious " average laborer," but as made up of groups which, in regard to wages, may possibly be subject to differ- ent laws or to different degrees of effectiveness in the working of the same law. If, with this conception, we begin our investigation by considering the two theories with reference to their relevancy to the groups of skilled and of unskilled laborers, we are brought to practical conclusions of considerable importance : — (1) It cannot be said that in the territory covered by our figures the wages of unskilled laborers 1 Ricardo : Principles of Political Economy and Taxation, McCullochs' edit., p. 54. 176 Laws of Wages are determined by the cost of the means of subsistence, that is to say, a fixed mode of life. This negative statement is a fortiori true of the wages of skilled laborers ; (2) There is a close correlation between the wasfes of unskilled laborers and their stand- ard of life, but the correlation is not so high as to justify the inference of a cause and effect relation ; (3) The correlation between the wages of skilled and of unskilled laborers is much higher than the correlation of the wao;es of unskilled laborers with their standard of life. These facts, which are inductively established, lead to the following reflection : the wages of both skilled and of unskilled laborers are determined by other causes than the adherence of the laborers to a fixed mode of subsistence or to a variable standard of life. The chief determining cause is the specific productive efficiency of each group, as is illustrated in Chapter III : the efficiency of the unskilled group yields a wage that affords a variable standard of life, and because of the great supply of labor of this character, both the wage and the standard of life vary within narrow limits. The wages of the skilled group are likewise dependent upon the specific productive effi- ciency of the skilled group, but, because of the oppor- tunity enjoyed by employers in an open market of substituting, within limits, unskilled for skilled labor, Conclusions 177 the strategic advantage of skilled laborers is affected by the wage received by unskilled laborers, as is in- dicated in Chapter IV. It is submitted that these facts have a fundamental bearing upon the theory of wages, upon the conception of the solidarity of in- dustry, and upon all projects having in view the bettering of the state of the laboring class by the establishment of a legal minimum wage with the necessary concomitant regulation of the supply of unskilled labor. ^ The idea of the solidarity of industry receives in- creased illumination from the conclusions of the chapter on " Wages and the Productivity of Labor." It was there established — (1) that average wages increase with the specific product of labor ; (2) that the more rapid the increase of capital in the industry, the more rapidly do wages increase ; (3) that the fluctuations of wages about their general trend are inversely correlated with the machine-power with which the laborers work. It is true that these points were es- tablished only with reference to the one industry for which we could obtain adequate data, but there is the great satisfaction of kjQOwing that the inductive findings with regard to this one industry are in complete 1 Cf. The Minority Report of the English Poor Lmo Commission, 1909. 178 Laws of Wages accord with the conclusions of a priori reason- ing. The very high coefficients of correlation measuring the relation between the variables that figure in these three propositions compel the acceptance of the idea of solidarity which sympathetic supporters of the cause of the laborers too frequently ignore. It is clearly indicated that one of the most valuable services that can be rendered by labor organizations consists in using their power to induce and compel the highest possible efficiency of plant and industrial organization. The resulting increased productivity will supply the fund from which increased wages may be obtained, and a permanently increasing wage can be secured only by increasing the flow of the specific products of labor. It has been said that the results of Chapter III compel the acceptance of the idea of solidarity of industry. It is not useless to add that this does not by any means suggest that the present form of soli- darity is the best that is conceivable. There is a perplexing statement in this connection in Professor Clark's Distribution of Wealth : ^ — " For nothing, if not to protect property, does the state exist. Hence a state which should force a workman to leave behind him in the mill property that was his by right of creation, would fail at a critical point. A study of distribution settles this question, as to whether the modern state is true to its principle. Property is protected at the point of its origin, if actual wages are the whole product of labor, if interest is the 1 Page 9. Conclusions 179 product of capital, and if profit is the product of a coordinating act." When this introductory statement was followed by the admirably lucid and cogent proof with which we are familiar that each factor in production does) tend to get what it produces, one could scarcely avoid a sense of baffled enthusiasm in recalling the words that have just been quoted. Of course the solution of the difficulty lies in the apprehension that the introductory statement and the argument take for granted the present forms of own- ership of property and the present social and technical conditions of production. It is entirely conceivable that a form of distribution of property which when tested by any familiar standard of equity would be pronounced inequitable, could coexist with each factor, in production tending to get what it produced. The social and technical conditions of production might cooperate to reduce the national dividend to a mini- mum and still that minimum would be distributed according to the specific productivity of the several factors. The same difficulty takes a visible form in the treatment of the problem of production and distribu- tion by a series of simultaneous equations, as, for example, that problem is treated by Professor Mar- shall^ and Professor Pareto.^ The problem of distribu- 1 Marshall : Principles of Economics, 4th edit. Appendix, particu- larly notes XTV, XXI. ^Pareto: Cours d'economie politique. Vol. I, Principes d'e'conomie politique pure. 180 Laws ,of Wages tion is shown to be determinate if the following facts are known : (1) the effective demand schedules of the members of the community, which result from their desires and their wealth ; (2) the supply schedules of the factors of production, which result from the amounts of the factors in existence and the needs and dispositions of their possessors ; (3) the functions descriptive of the technical conditions of production, w^hich depend upon the state of invention and the legal and other social conditions under which industry is carried on. Whatever may be the character of the functions of these three items, it is shown that under the hypothesis of least cost or of perfect competition, each factor will tend to get what it produces. But that fact is not assumed by either Professor Marshall or Professor Pareto to be any justification of the par- ticular forms that may be assumed by the functions. This observation brings us to a perception of the further practical bearing of the results of Chapter III. In order that the problem of distribution of income may be determinate, it is necessary that the number of equations in the problem shall be equal to the number of unknown quantities. Now a consider- able number of the necessary equations are dependent upon the proof that under free competition, or the hypothesis of least cost, each factor in production gets what it produces, and the results of our chapter show that so far as labor is concerned this tends to be the fact in the present industrial organization of society. That is to say, an important part — but Conclusions 181 only a part, let it be understood ^ — of the momentous problem of the organization of industry and the dis- tribution of income is worked out as it should be in the present industrial society. This point is of extreme importance, and its signifi- cance should not be misunderstood. There are two distinct questions ^ in the theory of the socialization of the means of production : (1) as to whether it is socially expedient for the state to assume control of any particular form of the means of production, and (2) as to the principles upon which the ministry of production in a collectivist state should organize and carry on industry with the means of production placed at its disposal. Postponing the discussion of the first question until we come to the consideration of the ^ Marshall : Principles of Economics, 4tli edit., p. 588. " Subject to conditions which are indicated in the foot-note, but are not important for our main purpose, the wages of every class of labour tend to be equal to the net product due to the additional labour of the marginal labourer of that class. " This doctrine has sometimes been put forward as atheory of wages. In reply to any such preteusion, it may be objected that the doctrine that the earnings of a worker tend to be equal to the net product of his work, has by itself no real meaning ; since in order to estimate net product, we have to take for granted all the expenses of production of the commodity on which he works, other than his own wages. " But though this objection is valid against a claim that it contains a theory of wages, it is not valid against a claim that the doctrine throws into clear light the action of one of the causes that govern wages." 2 In this paragraph, I follow Professor Barone, who, utilizing the suggestions of the earlier work of Pareto, has given a mathematical demonstration of the proposition under discussion, in his substantial articles on ^' II ministro della produzione nello stato collettivisto," which were published in the Giornale degli Economisti, 1908, pp. 267- 293 ; pp. 391-414. 182 Laws of Wages results of another chapter, we may observe that if in a collectivist state the minister of production should seek to maximize the national dividend of the com- munity, he must so apportion the means of production that their marginal productivity shall be the same in different forms of production, and he must place values upon the units of the several factors that are propor- tionate to their respective marginal productivities. The latter principle of valuation is the principle of reward according to specific productivity that tends to be realized in the present industrial state. In reviewing the results established in the chapter on " Wages and Ability," we shall see that they lend additional force to what has just been said. I should like first, however, to amplify an idea to which refer- ence was made a moment ago. In summarizing the results of the chapter on " Wages and the Standard of Life," the importance of distinguishing in theory between the qualities of different groups of laborers was dwelt upon. One of the invaluable services that the newer statistical methods are likely to render to pure economics is to liberate speculation from the bondage to the average in which it has labored since the beginning of the science. The syndicalist Georges Sorel has shown how, influenced by the special conditions of production in the large manufacturing industries of England and by the prevailing forms of physical science, the nine- teenth century economists disregarded the qualities Conclusions 183 that differentiate laborer from laborer and conducted their reasoning with regard to " units of labor " and " laborers of average capacity." "On arriva ainsi a penser que, dans I'industrie la plus avancee, il devenait inutile de tenir compte des qualites pro- pres des hommes et qu'on pouvait considerer les travailleurs comme des atomes de qualite moyenne, susceptible d'etre seulement distingues par des grandeurs matliematiques, en sorte que toute I'economie devint une science des quantites de travail raises en jeu par les capitalistes." ^ The most marked development of science in the latter half of the nineteenth century took its de- parture from the study of deviations from the average rather than of the average itself, and economists will, of course, adjust their theories in the light of this newer evolutionary science. There can be little doubt that egalitarian doctrines of the past century were fostered through the inadequate method of reasoning by vaguely conceived averages and the ignoring of the law of the natural differences between individuals in any large group. That there is a law of natural differences between individuals in any large group, no one who is ac- quainted with the results of recent biometric and anthropometric work will deny. The point that con- cerns us, however, as practical economists is to know whether this law of natural differences finds its ex- pression in the actual earnings of laborers. Accord- ing to the productivity theory of wages the distribu- tion of general wages among the groups making up 1 Georges Sorel : Introduction a Veconomie moderne, p. 29. 184 Laws of Wages the class of laborers should be according to the pro- ductive efficiency of the respective groups. The re- sults of our investigation have established that the law of the natural difference in ability between individual laborers does find its expression in the ap- portionment of earnings among laborers in the present industrial state, and that, furthermore, the congruence is remarkably close between the actual distribution of wages and distribution as it should be according to a priori theory. As a rule, the curve descriptive of the distribution of wages among a large group of laborers employed in numerous occupations is skew in a positive direc- tion. This skewness is generally, but not always, a sign of improving conditions in the laboring class. When the industry grows more productive and earn- ings are such as to justify an increase in Avages, the more intelligent and better organized laborers are the first to perceive and to take advantage of the improved conditions. The more prompt adjustment of wages of the abler laborers to the increased productivity gives the wages curve a greater measure of skewness. The subsequent changes in the degrees of skewness are de- pendent upon the degree of friction in the adjustment of the wages of the less able laborers and upon the improving or declining general conditions of industry. In a collectivist state conducted upon the principle of rendering a maximum the product of available labor and capital, the differences of earned incomes of the members of the state must conform to the very Conclusions 185 same law that obtains in the present industrial order. It is a mark of the great progress in the scientific treatment of social questions that upon this funda- mental point economist and socialist are in agreement. Writinyi; under the influence of the idea of Marx that is quoted as the motto to this chapter, Sorel observes " que c'est par un mecanisme emprunte a I'ere capital- iste que le socialisme compte regler la repartition," ^ and then, touching upon the question before us, he says : " Le capitalisme . . . tend a produire une cer- taine ^galisation du travail entre les diverses parties de I'usine ; mais comme il a besoin d'un nombre con- siderable d'hommes particulierement actifs, attentifs ou experiment's, il s'ingenie a donner des supplements de salaire aux hommes qui lui rendent ainsi plus de services ; ce n'est point par des considerations de justice qu'il se regie dans ce calcul, mais par la seule recherche empirique d'un equilibre regie par les prix. Le capitalisme arrive done a resoudre un probleme qui semblait insoluble, tant qu'il avait ete etudie par les utopistes ; il resout la question de I'^galit' des travailleurs, tout en tenant compte des inegalites naturelles ou acquises qui se traduisent par des in- egalites dans le travail." The only " socialist revolution " of which we have knowledge is the revolution in the opinions of lead- ing "scientific socialists "^ — their abandonment of ^ Sorel : La Decomposition du Marxisme, p. 44. 2 The right to refer to Sorel as a socialist can scarcely be denied in view of his claim to teaching le Marxisme de Marx. 186 Laws of Wages their doctrine of the cataclysmal destruction of capi- talism and their apprehension of the necessity of reg- ulating distribution in a collectivist state by means of a mechanism borrowed from the capitalist era. The most critical practical questions concerning the income of laborers are the questions as to the effect upon wages of strikes and of the concentration of industry in large establishments. It is by means of the pressure of labor organizations, which in its acute stage takes the form of strikes, that laborers expect to compel an increase of wages ; and it is from the growing magnitude of the aggregations of capital which tend more and more to control the output in the market that they expect to find their greatest opposition. These two subjects form the topics of our last two chapters, the results of which, as to their practical bearings, we shall consider in se- quence. Since the attitude of the public toward industrial disputes, in the matter of public sympathy and public control, must change with the degree of relevant scientific information that is available, it will be well to consider our great progress during the last half century in the understanding of the nature, causes, and effects of strikes. Fifty years ago the dominant school of economists was united in its insistence upon a vicious, radi- cally fallacious doctrine of wages which contained as corollaries : — Conclusions 187 (1) the doctrine of the impotence of trades-union- ists to increase their wages through combi- nations and strikes ; (2) the doctrine of the impotence of laborers to increase their wages through the increase of their productive efficiency ; (3) the doctrine of the impotence of laborers to better their condition by exerting pressure, through combination, upon the employers to the end that they should increase the efficiency of their plant and organization. This theory of wages was so hypothetical and so vague that it was impossible to put it to an inductive test. Indeed the nebulous character of the theory was one condition of its persistence ; for, as soon as pre- cision was given to the terms in which it was ex- pressed, it was seen that the modicum of truth in the doctrine was but little more than a pedantic elaboration of a platitude. The successful middle class that had risen in wealth and power during the period following the industrial revolution was predisposed, in consequence of its industrial interests, to accept the economic doctrine of the wages-fund with all of its corollaries. Accord- ingly, strikes and labor combinations were regarded as being impotent to achieve the effects sought by trades-unionists and as being, moreover, conspiracies against public order. In the meanwhile strikes in- creased in number and extent and bitterness of con- 188 Laws of Wages flict, and, notwithstanding the enormous pubhc interests at stake, no public authority concerned itself with the collection of adequate material bear- ing upon the origin, causes, and outcome of strikes, which material alone, when properly interpreted, could possibly afford guidance in the direction and control of this form of industrial warfare. During the interval of fifty years, the progress in the understanding of the labor question has been such as to lead to a reversal of attitude upon all of these points. A new theory of wages, definite in form and admitting of empirical tests, has been developed as a part of a general efficiency theory of distribution. So far as its fundamental propositions have been tested it has been found that the theory tends to be realized in actual practice. The essential idea of the new doctrine is that, with a definite tech- nical and social organization of industry, the laborer tends to get what he produces. Corollaries to the doctrine are : — (1) that whatever leads to an increase in the effi- ciency of the worker will tend to increase his wages ; (2) that if increased wages do not follow upon in- creased efficiency of the industrial worker, the labor combinations can, through strikes, force the cession of the increased product ; (3) that without the increased efficiency no amount of striking will result in a permanent increase of wages ; Conclusions 189 (4) that labor organizations, through their powers of putting pressure upon the employer to increase the efficiency of his plant and or- ganization, have a means not only of in- creasing wages, but of enlarging the national dividend. Pubhc opinion is in the process of adjusting itself to the new light. The vagaries of early economists have discredited a priori opinions as to industrial matters ; it is insisted that economic truths like all other truths can be reached only by treating scien- tifically the relevant facts that are laboriously accu- mulated. Accordingly, in nearly all of the states of Europe, public bureaus have been established for the purpose of collecting and interpreting the facts bear- ing upon the labor question. The material available at present is neither satis- factory in classification nor adequate in amount for a complete treatment of the question of strikes. But the results in Chapter Y show — (1) that the outcome of strikes is subject to statisti- cal and economic laws ; (2) that the scientific apparatus in the form of economic theory and statistical mathematics has been developed to such a degree of power as to be equal to the handling of this com- plex problem ; (3) that there is reason for beheving that if data of satisfactory quality and quantity were 190 Laws of Wages supplied, the whole subject could be placed upon a scientific foundation admitting of the prediction of average results in a way that would approximate the actuarial calculations of life insurance. Public opinion, as has been said, is adjusting itself to the newer light. Public opinion is unalterable in its condemnation of the form of industrial treason that is manifested in a general strike. Its condemnation is unalterable because there is absolute certainty that no economic service rendered by the aggrieved class is comparable to the economic loss that would follow upon a tolerated general strike. Public opinion is in sympathy with or in opposition to strikers according as it is made clear that the strikers have or have not created a value that is appropriated by the employer. It would therefore seem obvious that since public opinion does utilize the degree of knowledge that is available, and since adequate scientific knowledge could be supplied, if only the facts were properly collected and analyzed, we should not be far from the solution of a problem that many have regarded as in- soluble. Our progress during the last fifty years justifies this belief ; the importance of the question justifies the exertion of any degree of pressure upon an industrial group that should either withhold the facts, or pollute the sources of knowledge for the purpose of exploiting an opportunity created by public ignorance or misinformation. Conclusions 191 In the matter of the attitude of the state toward economic activities, we have made the distinction ^ between the question (1) as to what forms of capital should be socialized, and (2) as to the principles that must be followed by a collectivist minister in the direc- tion of production and distribution. With regard to the latter question it has been shown to be demonstrable that, if a collectivist state is to have any degree of stability, the principles followed in the apportionment of labor and capital in production and in the distri- bution of the product of industry must be the same in the collectivist state as in the present industrial state, and that when recent socialist thinkers have attempted to give definiteness to their proposals for collective control and administration, they admit this fact. We have further shown that when competition tends to be realized — in the technical sense of the word competition — or when through collective bar- gaining results approximating competitive standards are reached, the presumption is against any attempt at socialization of the industry concerned. The results of Chapter VI on " Wages and the Concentration of Industry" will throw some light on the first of the two questions into which we have divided the problem of socialization ; viz., what forms of capital should be socialized. As we have shown that the presumption is in favor of the present order of production when competitive standards are 1 Barone made the distinction in 1908 in his articles on " II mi- nistro della produzione nello stato collettivisto." 192 Laws of Wages realized, it is quite clear that the ground for belief in the expediency of socializing any form of concentrated industry must be found in the deviation of the facts of industry where concentration obtains from the standards that would be realized under competitive conditions. We are therefore led to inquire in what respect, so far as the laborer is concerned, do the facts of industry where masses of capital and labor are aggregated differ from the facts where labor and capital cooperate in the same industry upon a smaller scale. Concentration of industry, in the sense in which the term is used here, viz., of aggregation of capital and labor in the same establishment, does not by any means imply the abrogation of competition. But it is a normal form of transition from competi- tion to monopoly and for that reason deserves especial investigation. The researches of Chapter VI have been under- taken with a view to discovering the effects of con- centration of industry upon the status of the laborer. The broad general results of the chapter are ^ — ' A technical detail affecting the comparison of the wages received in large and in small establishments is of sufficient importance to justify a note. When such comparisons are made, spurious differences that are due to several causes are obtained. A common form of spurious dif- ferences has its origin in the lumping together of wage statistics from different geographical districts, as, for example, when the wages paid in the manufacture of cotton in the northern and southern states of the United States are massed in a classification of rates of wages ac- cording to the size of establishments (cf. Earning.<< of Wage-earners, Census of Manufactures, 1905, Bulletin 93, pp. 73-81). In this case, a comparison between the mean rate of wages in large establishments Conclusions 193 (1) That as regards the four critical items — rate of wages, amount of employment, continuity of employment, and length of the working day, the status of the laborer improves with the increasing concentration of industry ; (2) That the greater complexity of production fol- lowing upon the concentration of labor and capital creates new opportunities for efficient laborers to exploit their differential ability ; (3) That, when the degree of the concentration of industry increases, the similarity and the differences in the operation of the law of the variation of wages with the age of the and the mean rate in small establishments would show a difference in favor of large establishments. But this difference would be spu- rious so far as concerns the effect of the size of the establishment upon the rate of wages. The fact that the large establishments are situated in greater number in the northern states where a high rate of wages prevails would be an explanation of a difference in the rate of wages paid in the large and in the small establishments. A more subtle form of spurious difference is manifested when wage statistics are presented without reference to the age grouping of the laborers. That is to say, increasing concentration of industry implies a form of industrial selection of laborers which shows itself, in one way, by the different age groupings of laborers in large and in small establishments. The constants in the equation expressing the law of the variation of wages with age vary not only with the degrees of concentration of capital and labor in the same industry but also from industry to in- dustry. In both cases these variations should be taken into account before comparisons are instituted between the rates of wages in dif- ferent industries and in establishments varying in size in the same industry. It is suggested that in the presentation of wage statistics a plan should be followed similar to the procedure of the English Registrar General, in his comparison of death rates in different places where the age groupings of the populations are different. 194 Laws of Wages worker are explicable by means of the hypothesis that the laborer tends to earn an income proportionate to his efficiency in production. These inductive findings not only reenforce the belief that, so far as the welfare of the laborer is con- cerned, concentration of industry is no ground for the socialization of industry, but they place in clearer light the solidarity of industry and illustrate how the increasing welfare of the laborer is dependent upon the skillful management of large capital. We finally reach our question as to what forms of capital or economic institutions should be socialized, meaning by socialization the administration in the common interest of society. We need a principle upon which to make the decision, and we need a method by which each institution may be put to the test of our principle. In our quest of a principle we may start from two propositions which I think will be accepted by both economist and socialist. We may assume first, that, so far as it is compatible with the acquisition of better things, it is desirable to have the national dividend of wealth a maximum ; and, secondly, that those who take part in the creation of the dividend should receive shares that are proportionate to their contribution to the total product. Our principle is implicit in these propositions, and it may be worded as follows : the economic resources of a state should Conclusions 195 be so utilized as to render the national dividend of wealth the maximum that is compatible with the acquisition of better things, and the dividend should be so distributed that each contributor to its pro- duction should receive a share proportionate to his services. The method of applying this test of an efficient economy is a combination of synthetic economics ^ and statistical economics. We have shown in an earlier part of this chapter that, according to recent economic theory, the problem of production and dis- tribution of wealth is determinate, if we admit the hypothesis of least cost or of perfect competition and have a knowledge of three facts : (1) the effective demand schedules of the members of the community, which result from their desires and their wealth ; (2) the supply schedules of the factors in production, which result from the amounts of the factors in existence and the needs and dispositions of their possessors ; (3) the functions descriptive of the technical conditions of production, which are depend- ent upon the state of invention and the legal and other social conditions under which industry is carried on. Starting from this hypothesis and the knowledge of these three facts, it may be proved that under the assumed conditions the national dividend is a maximum and the owners of the factors of ^^^oduction are re- 1 Barone refers to the type of economic theory in which the conditions of production and distribution are simultaneously presented in a series of equations as L'economia sintetica. 196 Laws of Wages warded ivith shares jproioortionate to the contributions of the several factors to the production of the dividend. The words that are italicized in the preceding de- scription are critical for the application of the test of an efficient economy. The test requires that the re- sources of the state shall be so utilized as to render the national dividend the maximum that is compatible with the acquisition of better things, whereas in the above economy, the national dividend is rendered a maximum under the assumed rights of ownership of the factors of production and the existing technical, legal, and other social conditions of production. Furthermore, the test requires that the individuals in the community should receive shares of the dividend proportionate to their contributions in its production, whereas the above economy cedes to the owners of the factors of production shares proportionate to the contributions of the factors. Whether, in these two points, there is a great or small discrepancy between the ideal and the actual depends upon the concrete form of the premises upon which the theory rests. It is the task of synthetic economics to supply a general solution of the problem as to the effects upon the size of the national dividend and its resulting distribution of any alteration in the hypotheses or the premises upon which the theory rests. It is the task of statistical economics to give concrete form to the premises and the general solution by summarizing in mathematical form the relevant facts in the present order of production and distribution. 'T^HE following pages contain advertisements of a few of the Macmillan publications on kindred subjects The Law of the Employment of Labor By L. D. CLARK Cloth, i2mo, $i.6o net In all the realm of economics it is strange that heretofore no book has been published dealing specifically and authoritatively with the legal as- pects of labor. Mr. Clark has realized this, and his book covers the whole field of law as it affects the employment of labor in the United States. By the citation of an adequate number of representative cases and statutes, the principles of common law in their most important phases as well as the nature and trend of legislation are discussed and illustrated in so far as these are applicable to workmen and their employers. By SCOTT NEARING, Ph.D. 0/ the Wharton School, University of Pennsylvania Social Adjustment Cloth, 3Y7 pages, $1.50 net "It is a good book, and will help any one interested in the study of present social problems." — Christian Standard. " A clear, sane gathering together of the sociological dicta of to-day. Its range is wide — education, wages, distribution and housing of popula- tion, conditions of women, home decadence, tenure of working life and causes of distress, child labor, unemployment, and remedial methods. A capital reading book for the million, a text-book for church and school, and a companion for the economist of the study desk." — Book News Monthly. Wages in the United States Cloth, i2mo, $1.25 net This work represents an examination of statistics offered by various states and industries in an effort to determine the average wage in the United States. As a scholarly and yet simple statement it is a valu- able contribution to the study of one side of our social organization. THE MACMILLAN COMPANY Publishers 64-66 Fifth Avenue New York PRINCIPLES OF ECONOMICS By F. W. TAUSSIG Henry Lee Professor of Economics in Harvard University Cloth, 8vo, 2 volumes, $4.00 net per set This book, which is addressed neither to specialists nor to chil- dren, but to students and the educated public, states simply but fully the main principles of economics and their application. It does not avoid difficult or severe reasoning, but centers attention on the larger problems and the important trains of reasoning and treats these liberally and fully. The book deals with the present day ; there is very little of economic history, very little about the phenomena of semi-civilization or barbarian society. The expe- riences and problems of countries of advanced civilization are pri- marily kept in view. American problems naturally receive con- siderable attention, but the author is chiefly concerned with those principles which are of general application in all of the leading countries of modern times. ECONOMICS By SCOTT NEARING and FRANK D. WATSON Boik instructors in Political Economy in the Wharton School of Finance and Commerce, University of Pennsylvania Cloth, 8vo, 4QJ pages, $i.go net The book discusses the whole subject of prosperity of the factors which enter into the complex economic life of the nation. A young man who wishes to read even the daily paper with full in- telligence would find time spent in reading this book well em- ployed for the help which it would give him in understanding current discussions of such topics as the standard of living ; the natural resources of the country and their conservation ; the relations of labor and immigration ; of the labor of women and children to industrial progress ; of organization in business and its tendencies ; of the growth and functions of large corporations ; of public ownership ; of the various experiments which have been tried at different times, or the programmes which social leaders are now proposing for the remedy or the prevention of economic injustice. THE MACMILLAN COMPANY Publishers 64-66 Fifth Avenue New York Law for the American Farmer By JOHN B. GREEN, of the New York Bar Decorated cloth, xvi -\- 438 pp., i?idex, $1.50 net; by tttail, $1.63 " A volume that bears the marks of painstaking effort to present information that will be useful to those engaged in agriculture. In no sense is the book intended to take the place of counsel, but merely to fit the owner of a farm to cope with legal ques- tions which may arise any day in the conduct of his farm. Any person who will make himself famihar with the contents of this book will possess a liberal education." — Boston Globe. A Living Wage : its Ethical and Economic Aspects By Rev. J. A. RYAN. Cloth, \2mo, $1.00 7iet ; by mail, $1.12 " A clear and concise study of the wage problem," The Labor Movement in America By RICHARD T. ELY. \2mo, half leather, $1.25 net A historical and critical sketch of the struggle of the day-by- day working population of North America for the betterment of their condition. Labor Problems By THOMAS S. ADAMS and HELEN L. SUMNER 2>vo, cloth, gilt top, $1.60 Jiet " Invaluable as presenting in convenient and accessible form necessary material that would else have to be searched for in widely scattered sources." — Providence Journal. Federal Power over Carriers and Corporations : A Study of the Sherman Anti-Trust Law By E. PARMALEE PRENTICE. \2mo, cloth, $1.50 net This is an exhaustive study of the Sherman Anti-Trust Act and of the Federal powers upon which the Act is based. THE MACMILLAN COMPANY Publishers 64-66 Fifth Avenue New York Wage-Earning Women By ANNIE MARION MacLEAN Professor of Sociology in Adelphi College Cloth, leather hack, i2mo, $1.25 net; by mail, $1.35 "This book needed to be written. Society has to be re- minded that the prime function of women must ever be the perpetuation of the race. It can be so reminded only by a startUng presentation of the woman who is ' speeded up ' on a machine, the woman who breaks records in pack- ing prunes or picking hops, the woman who outdoes all others in vamping shoes or spooling cotton. . . . The chap- ters give glimpses of women wage-earners as they toil in dif- ferent parts of the country. The author visited the shoe- shops, and the paper, cotton, and woollen mills of New England, the department stores of Chicago, the garment- makers' homes in New York, the silk mills and potteries of New Jersey, the fruit farms of California, the coal fields of Pennsylvania, and the hop industries of Oregon. The author calls for legislation regardless of constitutional quibble, for a shorter work-day, a higher wage, the estab- lishment of residential clubs, the closer cooperation between existing organizations for industrial betterment." — Boston Advertiser. Making Both Ends Meet : The Income and Outlay of Ne. -^. .^v^^ <> '^^ ^4 ^/, '/• ,v\