IX Pareto's Law: The Inevitability of Inequality

I X PARETO'S LAW: THE INEVITABILITY OF INEQUALITY THE benefits of popular education, which, though we are apt to forget this, is an institution of quite recent times, are only now being felt. We are admittedly still experimenting with education, qnd it is as well to remember that the presence of thousands of millions of people on the earth who can read and write and think is an experience denied to previ.ous generations, including even the Victorians. This may be one of the reasons why we are all so actively and vigorously engaged in seeking new ways of living and exploring various forms of revolution, all of them quite untried and most ofihem necessarily unworkable. A new world that can read and write looks back upon the old and sees in it much cause for complaint; im-· patient of waiting for that degree of knowledge and analysis by which alone it can understand the origin and· nature of present evil, it sets to work in all its ignorance, with a fund of youthful enthusiasm, to put things right.

It would be amusing, were it· not in some ways so serious, that a whole generation of people should flatter themselves that to them at last has come the revelation; that the world and the people in" it from the beginning of time have been all wrong; that there was no wisdom in the past and that it has been reserved for 'us, the THE INEVITABILITY OF IN~EQUALITY 155 twentieth-century OlympIans, to receive the gift of wisdom with an abundance denie,d to the lo~g pro cession of our forefathers. The next gener.ation of economists will, in all proba bility, realise that the past is worthy of far more atten tion .than it has hitherto received. Present-day writers on political economy may be divided into four classes. There are, first and most numerous, those who frankly set out to create some new social system; secondly, and less numerous, those whose researches and writings are designed to find fresh ways. of raising the means, through taxation, to develop and extend the service of that modern fetish called the State. The third class is smaller still, and consists of those very rare creatures, . the pure economists, concerned solely with the dry-as dust science of analysing and defining the economic structure of society. Lastly, and this is the smallest class of all, comes the handful of writers on economic subjects whose object is the study and defence and extension of the existing order of things,who are im pressed with the wonderful strides that have already been made in the difficult work of civilisation, and who believe that in the experience of the past are to be found the fact and the wisdom upon which the progress of the future may be assured. It is greatly to be hoped that this class will increase in numbers a hope likely to be realised as the follies of the larger class of experimentalists become more obvious.

If the effort which is put into the study of new ideas could for a time be diverted to the study of the basis of the present order,so that we might be as thoroughly acquainted with the workings of what is called Capital ism as we are with the theoretical workings of some of the new systems, so eloquently recommended, we should acquire a practical proficiency in economic matters which is at present sadly lacking. _ 156 THE CONFESSIONS OF A CAPITALIST The eternal problem, the great single question, which is facing us and has always faced the human race, is the problem of the poor man. Our method of approaching that problem to-day does little credit to our intelligence. We see on the one hand a man who is poor, and on the other one who is rich, and we jump at once to the con clusion that the two phenomena are related, and that the solution of the difficulties of the poor man is to be found in the spoliation of the rich. We are helped towards that simple solution by a combination of the natural human instincts of pity on the one hand and envy on the other. A little more thought, deeper study, and a more genuine desire to get down to the real truth of the matter might bring us to the view that the salva- ,.

tion of the poor man is to be found in some scheme , which would enable him to follow in the steps of the rich, and which would thus offer, or so it would seem, a prospect of riches for all, instead of what appears to be the only prospect held out by the other alterna tive-poverty for all. The Italian economist and mathematician, Vilfredo Pareto, stands out" among the more distinguished of those who have attempted serious work along these lines. Pareto's Law lays it down that: (I) In all countries and at all times the distribution of income is such that the upper ranges of the income-frequency-distribution curve ~ may be described as follows:-If the logarithms of income sizes be charted on a horizontal scale and the logarithms of the numbers of persons having an income of a particular size or over be charted on a vertical scale, then the resulting observational points will lie approxi mately along a straight line.

(2) In all countries and at all recent times the slope of this straight line fitted to the cumulative distribution (that is the constant m in the equation y= bxm) will be approximately I. S. Pareto was an Italian economist who wrote much during the latter part of the last century and left THE INEVITABILITY OF INEQUALITY 157 behind him the law as to the distribution of wealth briefly stated above.. I venture with great trepidation to suggest that, perhaps unconsciously, there has been something in the nature of a conspiracy to suppress Pareto. If he has come anywhere near the truth he disposes once and for all of any economic system based on Socialism. As we are all of us, from Diehard Tories leftwards, afflicted with a tenderness towards Socialis;m, which in some ways does us credit, no one seems to have thought it worth while to say much about Pareto. I cannot find (and I have made a serious. search) a sympathetic explanation of Pareto's Law in the whole of the national economic literature. I discovered Pareto, almost by accident, through a very casual mention by Marshall in one of his heaviest volumes and an even morec'!sual reference by Sir Josiah Stamp in his valuable work, British Incomes and Property. But no English writer that I have yet disco,:ered has been at any pains to translate Pareto, or to give us an English version of Pareto's Law. The above summarised trans lation of the Law appears in a volume entitled Incomes in the United States, published by the National Bureau . of Economic Research, New York-.-another illustra tion of American superiority in economic research and thought.

It must be said in extenuation of English economists that Pareto's Law is admittedly imperfect. It is based upon mathematics, an exact science, and Pareto has been found, indeed he found himself to be, unable to stand the searching cross-examination of the higher mathematicians. Put into the simplest terms, Pareto's Law, if true, would, prove that there must be degrees of wealth; that we must go up in stages, and that we all go up and down together; that economic equality is a scientific impossibility and ~that to raise the lower grades we must ISS THE CONFESSIONS OF A CAPITALIST also raise the higher, or, vice versa, that in damaging the higher grades we cannot avoid corresponding damage to the lower. It would appear to .be universally admitted that Pareto's Law is true in so far as it brings within the terms of a definition the accumulated experience of the past. Those who hope for some new economic order are not prepared to admit that what has always been is necessarily a guide to what will be in the futu,re. There is, of course, plenty of room for -differ ences of opinion, but the point I desire to make is that the future would be easier, if not safer, if we had the advantage ·of a closer, more scientific and more thQrough knowledge of the economics of the past.

All I can· hope to do, for I am no mathematician, or indeed economist, is to tempt better qualified students to apply their minds to the doctrines expounded by Pareto. Would it not be possible, for instance, to begin a discussion as to the scientific possibility or impossibility of equality? Forgetting economics, let us take some simple exampIe that everyone can· understand. Take, for instance,a heap of sand. Imagine the sand in an hour-glass,. the small, smooth particles of which fall into their natural and ordinary position as more and more run through and are added to the pile. Such a heap will assume a conical formation; being widest at the base and having at its apex a single grain of sand. Its height will roughly be equal to the diameter of its base, and the 'largest number of grains will be at the base. For the sake of simplicity let us say that the heap has reached 100 grains of sand high and that there arrives another, grain which desires to place itself on the very top of the heap. The heap will thus become 101 grains high, but, in order that the ambitious grain may remain at the top, it will be found necessary to add to the heap THE· INEVITABILITY OF INEQUALITY 159 as a whole no less than 5,250 grains. 102 of these find themselves on the bottom layer and 101 will be deposit~d on the second layer from the bottom; 100 on the third layer; 52 on the 5I st layer; 27 on the 76th ; 4 on the 99th, and finally our ambitious grain will take its place at the top of the heap. In this simple exercise it will be demonstrated bey'ond possibility of doubt or misunderstanding that a single grain of sand, desiring to be at the top, has to arrange for 5,250 grains to be settled in appropriate positions below, and that the absence of a single grain at any stage lower down the heap will bring the topmost grain out of position. A similar little experiment could be under taken with a few tennis balls. The conclusions to which it would lead would be the same.

If four tennis balls are arranged in the form of a miniature pile, three will be necessary on the· bottom layer and one at the top. In order to make the pile higher, it will be found necessary to add three more to the bottom layer, two to the next and one at the top, and, further to increase the pile, \ve must add four to the bottom, three to the next row, two to' the next, and one at the top. As the heap increases in height, balls must" be added to each row in numbers varying in definite proportions to the height of the pile. Thus a single tennis ball, desiring to raise itself a grade higher, must arrange for the maintenance of a num ber of others in appropriate positions, and this would seem to suggest that one way at least of providing for the prosperity of the many lies in the encouragement of the enterprising and the ambitious. If it may be assumed by way of argument that there is some scien tific similarity between the construction of society and the heap of sand 6r the pile of tennis balls, it would appear to be advisable to inquire a little more fully into Pareto and his law.

160 THE CONFESsIoNS of A CAPITALlsT That the heap of sand is a good analogy seems to be demonstrated by the test of my own business. Many a small newspaper is produced by a proprietor-editor manager with the assistance of an office boy and a clerk. The heap in that case takes the form: Proprietor-editor-manager. Office Boy. Clerk. Canvasser. Messengers. Editor. Typist. Clerks. As the enterprise develops and prospers, the heap grows; the number of grains in it increases, and it forms up somewhat as follows: Proprietor. Manager. Secr~tary. Office boys. Reporter. Sub-Editors. When, in the course of time, the little paper becomes a big one, an enormous heap emerges, with the pro prietor presiding over a board of directors, who in turn require the assistance of a news editor, a night editor, a foreign editor, a city editor, with correspond ing grades of managers and publishers and, further down the scale, large armies of subordinates, all arranged in order of importance. The proprietor perched at the head of such an organisation will have much more to do than the little proprietor-editor manager who produced his paper with the assistance of an office boy anq. clerk, and ought therefore to be blessed with a good deal more of this world's goods; but it appears that he can only· attain such a position on condition that he makes and maintains numbers of other positions grading naturally down the scale, and that the solidity of the whole structure will depend upon the largest proportion of the benefits or proceeds reaching down to and remaining at the base of the undertaking.

THE INEVITABILITY OF INEQUALITY 161 It is, of course, admitted even by the Communists that there must be something in the nature o( social status or grading. Thus an army is unthinkable with out its due proportions of varying ranks from Field Marshal to Private. If the heap of sand or tennis ball test is applied to the army it will be seen that a Field Marshal cannot exist with.out a number of Generals, a larger number of Lieut.-Generals, a still stronger body of Major-Generals, who in turn require Colonels com manding battalions with appropriate Lieut.-Colonels, and so downwards through the company officers to the lowest ranks. The same kind of structure is to be found in a Church or in a Government department. Thus it would seem to be the natural formation for society equally as for sand: all of which seems, to some extent, to justify Pareto. It will be noticed that Pareto is very sweeping and very definite. He pronounces judgment upon all countries and all times, and he commits himself to a formula and a fraction which, although guarded with the word " approximate," are both very exact. Such discussion as has been concerned with Pareto's Law, and there is all too little of it, has centred round the slope of the straight line and the 1.5, and has suc ceeded in showing that 1.5 should sometimes be I.3 or even 1.6. That is to say, that while Pareto gave us the line AB it has turned out that CD or EF may in some circumstances be the correct delineation.! But the difference in the angle of all these lines is imma terial to his general contention as to the distribution of wealth.

A still more complicated and technical discussion has ranged round the ends of the line, and nobody seems to be able to tell us with any degree of authority what really happens to the very very big and the very very 1 See diagram I, page 16z. L 162 THE CONFESSIONS OF A CAPITALIST small incomes. For these technical reasons, Pareto is at a discount among the higher mathematicians. That, however, does not seem to prevent them from making use of him for the practical everyday work of life, and, although we have apparently still to find an exact formula to cover the economic distribution of all D B Diagram I. incomes, Pareto comes in handy in such. a matter as the collection of taxes. I understand that Pareto's formula is used by the Inland Revenue authorities, who graph their returns as directed by his law, and in that way profess to be able to detect any serious tendencies towards evasion and any serious flaws in their system of assessm'ent.

Pareto therefore has his uses. That being so, it would appear to be a profitable undertaking for others. besides mathematicians and tax~collectors to Jook more carefully into the Pareto theory. If it is a fact that " in all countries and at all times " the income line runs as shown on Diagram 2, THE INEVITABILITY OF INEQUALITY 163 then whether the angle is 1.5 or 1.3 would appear to be a matter of detail which for the purpose of more -general discussion can be safely ignored. A hundred years ago we had a population of 8,000,000 and probably not more-than a score of them with in comes approacing £10,000 a year. To-day we supDiag~am 2. port no less than 47,000,000 souls, and Pareto would seem to say that it is therefore necessary for us to have at least some of our fellow-citizens in enjoyment of incomes of millions. Applying the same theory at the other end, we get some economic light upon recent happenings in Russia.

The wiping out of the wealthy would seem, according to Pareto, to require the physical disappearance of a much larger number of persons lower down the scale. And whether Pareto is right or not, that is undoubtedly what has happ~ned. Large numbers of our people believe that by taxation and legislation it is possible to approach equality of 164 THE CONFESSIONS OF A CAPITALIST wealth; still larger numbers hold that by these means inequalities can be graded less steeply, while all hold that the burden should be regulated according to ability to bear. Pareto would seem to say that these ideas are more attractive than workable, and to lead one to doubt whether the following of them is not in itself respons ible for the slow progress of that general well-being which they are intended to promote. If the increase of the wealth of the millionaires by 10 per cent. would mean a corresponding increase in the wealth of all of us, and is indeed a necessary scientific condition of our securing that improvement, then the sooner we know about it the better.

To advocate the encouragement of millionaires as a cure for social ills sounds a little out of tune with modern political thought, but, having regard to the failures of the immediate past, the idea is surely worth investigating. I am not concerned about the million aires, but I do want more of this world's goods for the rank and file. If Pareto is right, we must have both or neither. There is an opportunity here for a student of econo mics who will take up this question of millionaires and give us new light upon it. Everyone is interested in the millionaire, but interested only in his millions and what he does with them. Nobody seems to bother about the other millions which must necessarily have accrued to. the rest of us before the millionaire could attain to his high position. If there is anything at all in my sand heap theory it would seem that a good many thousands of millions must be distributed among us by anyone who succeeds in himself becoming a millionaire.

Guy Morrison Walker, in an interesting (if rather American) book called The Things that are Ctesar's, has a good deal to say on this subject: THE INEVITABILITY OF INEQUALITY 165 Take the record of the life of James J. Hill, who constructed thou sands of miles of railroad and opened up millions of acres of land that were formerly wild and inaccessible; who bettered the conditions and raised the wages of hundreds of thousands of men and women by the opportunities for work that he created. Look at the cities, whose creation and growth he inspired, and the wealth and prosperity of a half-dozen states which his vision conceived and which his work made possible. Which was the greater worker, a Roosevelt, who railed' at swollen fortunes, malefactors of great wealth, and who sowed discontent and envy among the masses of the people, or a Harriman, who took the bankrupt Pacific railroads off the hands of the Government and by his genius for management and development not only recreated them and made them efficient servitors of the States through which they ran, but, by improving their service and reducing their transportation costs, brought prosperity to a score of States and increased the wealth of the people of those States which were dependent upon them, by a sum not less than twenty-five billion dollars?

The fortune that Mr. Harriman left is a mere pittance compared to the wealth which he created for others. A commission so small when expressed in percentage of the money that he made for others, that if the ordinary man were offered business on the same percentage he would spurn it with contempt. The foresight and courage of Commodore Vanderbilt in the organisa tion and consolidation of the original scraps of road and in the con struction of the missing links that created the New York Central and Hudson River system, was what determined the leadership and pre-eminence of the State of New York in population and wealth in our country. Every man who is proud of the fact that the Empire State is the first State of our Union in population and wealth owes a debt of gratitude to old Commodore Vanderbilt. The paltry millions that fell to him were an infinitesimal part of the total wealth that his work gave to this' State and its people.

. . . Our people have so long been relieved from the primitive methods of harvesting and are so ignorant of the use of the hand-sickle, or of the flail, or of the threshing floor, that they do not realise how much of labour has been saved"and how much of wealth has been created for the farmers by the invention of harvesting machinery. The money made by the harvesting companies is a small percentage of what their devices and machinery have saved not only the farmer but all the people who consume farm products; yet our people have been taught that the International Harvester Company is the last word in plundering practice, thievery, and unfair tactics.

166 THE CONFESSIONS OF A CAPITALIST ... can anyone estimate the value of the services rendered to society to the world and the billion and a half of people in it, by Mr. Rocke feller, who, by making safe and cheap the use of petroleum and by huilding up· an economical system of distribution, has spread the use of illuminants throughout the world, turned the night into day, banished ignorance and superstition, and done more to make possible reading and study, and the spread of education and culture, than all the men who lived in the world before his time? Who can measure the value of the services to mankind of Thomas Edison, with his many inventions? Or'a Philip D. Armour, who, by the development of refrigeration and cold storage, has brought within the reach of the poorest in the land a quality of meat that was not only out of reach of the richest, but was absolutely unknown until he introduced his methods into the packing-house business? Or who shall say what it was worth to the world to discover the method of refining sugar, that reduced it from its original cost of 25 cents, or a shilling, a pound, when that represented a day's work, to its recent price of 5 cents a pound, which, in our country at least, is not over one-hundredth of the wages for a day?

If we could agree that we must all go up or down together; if it could be shown that it is impossible for anyone of us to -go up or down without bringing the restup or down with us, economic discussion wopld be very much simplified. Pareto shows us that this has always been the experience of the past, and, if it is to' be the experience of the future, what a deal of trouble we could save ourselves by· that knowledge. The figures on page 167, giving the numbers of incomes of six different sizes which were listed by the Inland Revenue authorities in 1895 and in 1920, seem to support my contention. It will be noticed that judged by money figures we have all of us been going steadily up. The number of persons with £3 a weekhqsmultiplied by 14, and the number of persons with over £50,000 a year has in creased in proportion.. The various classes have been mltltiplied by the figure shqwn in the last line of the table, and it will be seen that this varies from 14 to 12.

THE INEVITABILITY OF INEQUALITY 167 Increasein Numbers at certain Incomes ---£160 to £600 to £800 to £1,000 to £10,000 Over £3 00 £700 £1,000 £2,000 £5 0 ,000 No. in 1895. 222,693 5,591 6,672 I 11,069 1,314-56 No. in' 1920. 3,194,100 74,850 86,560 , 142,870 16,720 660 No. of times increased. It 13·5 j 13 j 13 I 1-3·5 I 12 If Pareto's law is absolutely true, the multiplier should be 14 or 12 all the way through, and the slight dis crepancy which my figures show points either to a weakness in Pareto or, as is much more likely, to a very natural inaccuracy in the Inland Revenue figures. These figures do, however, demonstrate beyond ques tion that twenty-five years of legislation which have in'cluded death duties and super-tax, which have seen the full development of the modern theory of placing the burden on the shoulders best able to bear it, which have reduced the public finances to the position in which two million persons are nominally paying the whole of the taxes, and which have .led the wage earning classes as a whole to believe that salvation is to be found through the spoliation of the rich, have, in fact, done nothing whatever to alter the slope of the line to which, so Pareto argues, we must all conform.

What has been happening is that while the poor have been getting less·poor, the rich have been getting more rich, notwithstanding a political effort, unequalled in its force in the whole of history, to arrive at something pleasingly called equality. If it should be a fact that inequaLity is inevitable; if 168 THE CONFESSIONS OF A CAPITALIST it may be admitted that society cannot exist except it be graded; if it is necessary that some of us must ge on top and some below-and surely even the Com munists admit all this-then the discussion reduces itself to the question: How best is this. grading pro cess to be performed; how best can the lower grades be arranged, so that each of us may fall ~aturally into the position in which we can function to the greatest advantage of ourselves and the rest? . Hitherto we have relied upon the .process which may be described as the money test, the competitive system or Capitalism. That is only another way of saying that each of us has been subjected to the test of the opinion of our fellows. Under Capitalism every act performed by anyone of us is tested and found good or bad by the judgment of those whom it affects. Capitalism might be defined ~s the economic interpretation of the ideal democratic theory.

Discarding theory for the moment, we ,can, in the light of the experience of 'the last few years, look at the matter in a wholly practical way. We know, of course, that it is possible to select the higher grades of society as they have been chosen under the present regime in Russia. We know that there are serious students of Communism who believe that, by some system of training, super-men can be evolved who will naturally occupy the first positions in society. It is even suggested that we might resort to scientific breed ing for the purpose of recruiting the necessary upper classes. But we of this generation have had the good fortune to enjoy practical experience of the workings of some of these principles, which should surely help us to form a sound judgment upon them. I suspect. that Fascism and M ussolini are not alto gether unconnected with the writings of Pareto; a suspicion which does not strengthen the appeal of THE INEVITABILITY OF INEQUALITY 169 Pareto to my democratic soul. It strengthens, however, my impression that there may be wisdom and experi ence to be found in Italy, of which we ought to avail ourselves if we are serious in our search for,the best. .in economics.

I hope to see some such enthusiasm as that which brought Karl Marx out of Germany and built upon his writings a whole new literature of political economy, applied to the even more useful and promising task of unearthing Pareto from Italy and, on his foundation, building up a literature and a method of thought which will lead us to a constructive policy making for the general well-being of the whole community.