Labour Defended Against the Claims of "Human Capital"

According to Guang-Zhen Sun, "Xenophon discussed in somewhat [sic] details the sexual division of labor within a family, a topic that was to be picked up by Thomas Hodgskin (1827) and Marxists in the 19th century and nicely integrated into a neoclassical theory of human capital in the 20th century (e.g., Becker 1985)." Except that Hodgskin's analysis of the topic was not "nicely integrated into a neoclassical theory of human capital." It was adamantly ignored because the point of human capital theory is to naturalize ideological claims about the utility maximizing motives of individuals and returns to factors of production attributable to their marginal contribution to production.

In Labour Defended Against the Claims of Capital, Hodgskin stated explicitly that the purpose of his essay was to refute the arguments of John Ramsay McCulloch and James Mill to show that: "the effects attributed [by them] to a stock of commodities, under the name of circulating capital, are caused by co-existing labour." In a prefatory note, Hodgskin wrote:

In all the debates on the law passed during the late session of Parliament, on account of the combinations of workmen, much stress is laid on the necessity of protecting capital. What capital performs is therefore a question of considerable importance, which the author was, on this account, induced to examine. As a result of this examination, it is his opinion that all the benefits attributed to capital arise from co-existing and skilled labour. He feels himself, on this account, called on to deny that capital has any just claim to the large share of the national produce now bestowed on it. This large share he has endeavoured to show is the cause of the poverty of the labourer; and he ventures to assert that the condition of the labourer can never be permanently improved till he can refute the theory, and is determined to oppose the practice of giving nearly everything to capital.

In Marx's discussion, in Capital, of the division of labour, he cites a passage from Hodgskin's "admirable work" in support of "The fact that the detail labourer produces no commodities." It is worthwhile quoting Hodgskin in full, here, with the passage cited by Marx highlighted in bold:

Whatever division of labour exists, and the further it is carried the more evident does this truth become, scarcely any individual completes of himself any species of produce. Almost any product of art and skill is the result of joint and combined labour. So dependent is man on man, and so much does this dependence increase as society advances, that hardly any labour of any single individual, however much it may contribute to the whole produce of society, is of the least value but as forming a part of the great social task. In the manufacture of a piece of cloth, the spinner, the weaver, the bleacher and the dyer are all different persons. All of them except the first is dependent for his supply of materials on him, and of what use would his thread be unless the others took it from him, and each performed that part of the task which is necessary to complete the cloth? Wherever the spinner purchases the cotton or wool, the price which he can obtain for his thread, over and above what he paid for the raw material, is the reward of his labour. But it is quite plain that the sum the weaver will be disposed to give for the thread will depend on his view of its utility. Wherever the division of labour is introduced, therefore, the judgment of other men intervenes before the labourer can realise his earnings, and there is no longer any thing which we can call the natural reward of individual labour. Each labourer produces only some part of a whole, and each part having no value or utility of itself, there is nothing on which the labourer can seize, and say: “This is my product, this will I keep to myself.” Between the commencement of any joint operation, such as that of making cloth, and the division of its product among the different persons whose combined exertions have produced it, the judgment of men must intervene several times, and the question is, how much of this joint product should go to each of the individuals whose united labourers produce it?

Hodgskin was defending labor against the (illegitimate) claims of capital. Becker was extending the claims of capital into the household. One of these things is not like the other.

Hume & Kapp, et al.

Over at MaxSpeak, Sandwichman didn't get any response to his provocation that "human capital" was cooked up by the Chicago boys as a way of side-stepping the fundamental methodological critique posed by the institutional analysis in the tradition of John R. Commons and J. M. Clark, which dominated American labor economics -- and presumably labor economics journals -- in the 1940s and 50s. I particularly wanted to mention cost-shifting as an issue that "human capital" evades. This passage from  The Foundations of Institutional Economics by K. William Kapp highlights some of the central motifs of institutionalism's critique of conventional theory. It also has the merit of mentioning the contribution of David Hume, among others and thus enabling the pun in the title.

Institutional economists have raised some very specific objections to the dominant conventional theory; and while it is not necessary to analyze in minute detail all the well-known aspects of this critique, it will be useful to review some of the exceptions taken by representative institutionalists to certain methodological procedures of conventional economics, if for no other reason than to make clear the distinct perspective and mode of thought which have guided them from the beginning. These exceptions will illustrate clearly and fundamentally how institutionalism conceives the task of economic analysis in a radically different manner than the traditional, pure theory of valuation, value, and price.  

Starting with a brief outline of the evolution of the theory of value from its classical origins, we shall illustrate our thesis by brief references to the institutional critique, with particular emphasis on those elements of the critique that demonstrate the alternative perspective of the institutional approach. Both Adam Smith and David Hume made deliberate use of inherited concepts of natural order and natural law to show that the system of private enterprise, or "natural liberty," was not only theoretically conceivable and practically workable, but at the same time morally superior and more efficient in the use of given resources to the preceding mercantile system. Not only did this system tend to regulate itself, it also produced terms of exchange that possessed many, if not all, of the characteristics of a "just price," as the term was conceived and propagated by medieval thinkers; it guided labor, resources, and capital into the occupations and lines of production which corresponded to the wishes and preferences of the consumer. The labor theory of value, together with the hypothesis of maximizing behavior -- both major and central hypotheses of classical political economy -- asserted that market prices would gravitate around natural prices of goods and services at their normal level, or the level at which they covered their costs of production. Prices and wages could thus be considered just and equitable, and as such did not need to be controlled. If the labor theory of value, understood as an equilibrium, seemed to guarantee the theory of distribution, the maintenance of some form of macroeconomic balance or equilibrium was shown to be guaranteed by the principle of the conservation of purchasing power, which both Adam Smith and Jean-Baptiste Say considered self-evident. 

The classical theory of Smith and his successors borrowed the equilibrium concept from mechanics and supplemented its notion of natural order, natural liberty, and natural law with an increasing dependence on the quantitative, utilitarian psychology of Jeremy Bentham as a basis for its explanation of human behavior, and particularly of economic behavior. By measuring and aggregating all input and output magnitudes in terms of prices (at equilibrium levels), and by identifying the social output as the sum total of these values at market prices, the theory and system supposedly provided their own quantitative yardsticks for measuring the performance and growth of the economy over time. The economy was also said to produce the greatest sum of pleasure possible to the greatest number of people, by allowing every individual economic unit to choose goods, occupations, and investment outlets according to its own preferences. Thus, what began as an exercise in objective analysis ended in a system of normative and political conclusions, formulated without apparent or explicit value premises. This unprecedented achievement, unparalleled in any other discipline, is the outcome of a specific procedure. By first defining the scope of the analysis and postulating specific behavior patterns, the position of equilibrium is endowed with characteristics that give it the appearance of an objective optimum. Used in this fashion, the concept of equilibrium lends itself to a superficially convincing defense of the laissez-faire system of natural liberty. Philosophers, aware of the presupposition of classical and neoclassical analysis, have shown the logical limitations and weaknesses of the concept of natural order and natural law; they have demonstrated that such doctrines have been used repeatedly to support open and hidden valuations of the greatest variety and mutual incompatibility and shown that the ideology does not exist that cannot be defended by an appeal to the laws of nature. 

Institutional economists have developed their own analysis of the philosophical premises of classical and neoclassical economic theory into a thorough critique of their preconceptions. Veblen criticized the non-causal teleological character of the analysis in contrast to the viewpoint of modem science, and Gunnar Myrdal showed that conventional equilibrium analysis has continued a long tradition of normative (political) thinking while professing a commitment to a positive (value-free) and objective account of the natural world. In fact, both radical and conservative economists have been inclined to shape and use their economic analysis to support their political objectives and perform the logically untenable feat of arriving at normative political conclusions without explicit political premises. The political objectives of classical and neoclassical economists were those of anti-mercantilism, anti-regulation, and non-intervention. Theoretical economists appealed to natural order and natural law, based on a theory of man later reinforced by the utilitarian calculus. Aided also by the analogy to mechanics and stable equilibrium (i.e., under static conditions where no new “forces" produced changes in motion), they have developed a system of conclusions that make economic and political processes appear to work towards common goals and a maximization of "social welfare." Levels of equilibrium are so defined that processes of production and distribution, under the impulse of the forces of self-interest, tend automatically and in a self-correcting manner towards a socially desirable and optimal outcome. What was initially introduced as a simplifying assumption for the abstract representation of reality for purely analytical purposes is thus subtly converted into the idealized norm of a perfectly competitive market, providing direct criteria for economic policies without further diagnosis of the specific situation, and without explicit normative or moral value premises. This logically untenable feat of arriving at political conclusions without political premises is, however, achieved with the aid of logical fallacies, the norms and teleology derived from pre-analytical visions and ideologies have forced upon economics specious concepts, definitions, and assumptions. Thus, normative and ideological elements have shaped the concepts, language, distinctions, and modes of thinking of conventional economics. Institutional economics has made major contributions to identifying these fallacies, and in doing so has produced both a critique of conventional economic theory and a clear picture of the modern character of institutionalism itself, as a distinct approach to economic analysis. The most notable points of the institutional critique are the fallacies of the utilitarian foundations of economic theory, the fallacy of the doctrine of the sovereignty of the consumer, and the fallacy of the means-ends dichotomy.

Larry Summers Tells It Like It Is

From the unedited transcript, "Future of Work in the Machine Age" policy forum:

Third, when I was an undergraduate at MIT in the 1960s there as a whole round of concern about this -- will automation displace all the employment? And what I was taught as an undergraduate was that basically the people who thought it would were a bunch of idiot Luddites and that obviously there would eventually be enough demand and it would all sort of work itself out, and if people got more productive they'd be richer and they'd spend and maybe we needed some transition assistance, but that it was all basically going to be okay. That was what I was taught. That's what Bob Solow thought; he was a hero and the other people were all a bunch of a goofballs was kind of what I learned. (Laughter)

I actually believed that for many years and actually repeated it often. It has occurred to me that when I was being taught that about six percent of the men in the United States between the age of 25 and 54 were not working. And that today 16 percent of the men in the United States between the age of 25 and 54 are not working, and it won't be very different even when the economy is at full employment by any definition. And so something very serious has happened with respect to the general availability of quality jobs in our society and we can debate whether it's due to technology or whether it is not due to technology. 

We can debate whether it's the cause of dependence or whether it is caused by policies that promote dependence. But I think it is very hard to believe that a society in which the fraction of people in -- choose whatever your most prime demographic group is that should be working, whatever that group is, a society in which the fraction of them who are not working is doubling in a generation and seems to be on an upward trend is going to be a society that is going to function well, or at least function well without major social innovations.

And I would want to leave you with that concern as there whether you think it's due to technology or whether you think it's due to globalization, or whether you think it's due to the maldistribution of political power, something very serious is happening in our society.

"The Future of Work" has a Chequered Past

The Hamilton Project had an event to discuss the Future of Work in the Age of the Machine. Lawrence Summers was there, along with Robert Rubin, Erik Brynjolfsson and Andrew McAfee, Laura D. Tyson and David Autor. Round up the usual suspects. They didn't invite the Sandwichman. No one ever invites the Sandwichman to these events.

The Hamilton Project's "framing paper" on the future of work takes its historical bearings from a fable about events that happened two centuries ago. Wouldn't it make sense to rely instead on documents from within our own lifetime? How credible are predictions about the future based on fictions about the past?

Writing in Fortune magazine 61 years ago, Daniel Seligman predicted achievement of the four-day week by 1980. He based that prediction on projection of historical trends. It didn't happen. Apparently a lump of labor got in the way -- the same fixed amount of fiction that the Hamilton Project framing paper frames the Luddites of 200 years ago with.

"Prediction is very difficult, especially about the future." Attribution is even harder. Niels Bohr? Yogi Berra?

At least Larry Summers got it right.

Fortune and the Four-day Workweek

What economists of the 1950s and 60s disparaged with the "lump-of-labor" hand, they typically celebrated with the "inevitable", "productivity gains", "income-leisure choice" hand. Based on past trends, the four-day week could be expected to arrive by 1980 -- presumably without legislative or collective bargaining "coercion." By now, 2015, workers would be enjoying the three-day, 21-hour week or, alternatively, three-month annual vacations. Didn't happen. But what's odd is how little thought is given to why it didn't happen and to what happened instead. The dots do connect. Rising inequality, financialization, economic instability and precarious employment -- all these cannot be entirely unrelated to the euthanasia of union arguments for shorter hours.

The Four-day week: How soon?

Daniel Seligman
Fortune -- July 1954

How far off is the four-day week? The standard five-day week has been lodged in American life for only a decade or so. Yet for some reason it is widely regarded today as something natural and immutable. Recently, Fortune mailed a questionnaire about the feasibility of a four-day week to fifty large industrial firms (more than 30,000 employees) and fifty medium-sized companies (300 to 3,000 employees). If there is a single U. S. company whose spokesmen are willing to affirm that a four-day week is possible and desirable in the fairly near future, it has not been found.

The fact that most American businessmen regard any future four-day week with misgivings and even hostility does not, of course, mean it is never coming. A quarter of a century ago there was a great debate about the five-day week. Speaking for the affirmative, but almost alone among businessmen, was Henry Ford. He had introduced the five-day week, he said shortly after the event, “because without leisure the working men— who are the largest buyers in the country—cannot have the time to cultivate a higher standard of living and, therefore, to increase their purchasing power.” Virtually all the businessmen who addressed themselves to the subject found differently. In general, they had three major objections to the five-day week: the cost would be prohibitive; the workers would not know what to do with their leisure time; and there was Biblical sanction for the six-day week.

An important reason for the cautiously noncommittal attitude of business men today is that their employees have been unionized. To declare that a four-day week might soon be feasible would be to give, gratis, a large bargaining counter to the union. On the other hand, to suggest that employees cannot look for any more leisure time would be inept public relations.

Labor leaders also appear to he preoccupied elsewhere. It is true that both the major labor federations have clearly defined ideas about affording more leisure for the American worker. But these do not include the four-day week—yet.

If both labor and management are uninterested in the four-day week, what good reasons are there for talking about it? Briefly, two kinds of reasons might be adduced: The four day week would be desirable, both for business and employees; and it would almost certainly be attainable.

The major reason for thinking a four-day week feasible is, of course, the continually increasing productivity of U. S. industry. Productivity—i.e., output per man-hour—has been rising by 2 or 3 per cent a year, taking the economy as a whole, for more than fifty years now. And, barring a war or a prolonged depression, Americans clearly have some further benefits in store. The question is whether they will take these benefits in the form of increased income, increased leisure time, or in a combination of both.

A calculation made by Fortune for the years since 1929 suggests that in the past quarter-century U. S. workers have been taking about 60 per cent of the productivity pie in the form of income, about 40 per cent as leisure. Assuming that the four-day week for non-agricultural employees will be attained when the total work week is in the vicinity of 32 hours, that productivity continues to increase at an average of 2 or 3 per cent a year, and that something on the order of the recent 60-40 ratio for income and leisure continues in effect, the 32-hour week should be spread throughout the whole non-farm economy in about 25 years.

If the four-day week seemed sufficiently appealing, of course, it could be achieved much sooner. A lot of Americans might, in other words, he willing to work nine hours a day. That, theoretically, would enable them to enjoy the four-day week when total hours of work were down to 36. If they made such a decision—if they traded the eight-hour day for the three-day weekend—then the great event would he scheduled to arrive, not around 1980, but in the 1960’s.

A large number of business men maintain that the four-day week has no applicability to their own operations. The following problems are suggestive of the wide variety of “insurmountable” obstacles that would he encountered:

• Manufacturing companies with three-shift operations would run into formidable scheduling difficulties if the nine-hour day were introduced.  
• Companies whose total hours of operation could not be reduced would have to hire more employees.
• Retailing provides a peculiarly difficult situation. To remain open six days and give their employees a four-day week, department stores would have to hire 25 per cent more workers than they now employ. 

A final question must be considered. Do workers really want more leisure? Many employers are still convinced they do not. Now there is no doubt that, given more time off, some workers might drink too much, or beat their wives, or go insane watching daytime television. Others might work themselves to death on second jobs. But the $30-billion leisure market, the remarkable emergence, almost from nowhere, of a huge, new do-it-yourself market, and even the familiar Sunday-afternoon sight of cars crawling along bumper to bumper, suggest strongly that most American workers have a pretty good idea of what to do with their time off.

Meanwhile, in the income-leisure choice for the years ahead, there will be one strong pressure for leisure: The workers who have been energetically pushing their way into the middle-income class have, naturally, become increasingly preoccupied with federal tax demands. "If we get more dough," said one AFL man recently, "the government can take back part of it. But they haven’t yet figured out a way to tax your day off."

"Unemployment and Shorter Hours" -- Howard G. Foster

The excerpt below presents a hypothetical example of how reducing the hours of work can create jobs without assuming a fixed amount of work. It was developed by Howard G. Foster -- then a teaching assistant at the New York State School of Industrial and Labor Relations at Cornell -- and published in the April, 1966 Labor Law Journal. It can best be understood as a direct reply to arguments in the pamphlet, The Shorter Workweek by Marcia L. Greenbaum, published three years earlier by Cornell ILR. Both Foster and Greenbaum went on to distinguished careers as labor arbitrators.

from "Unemployment and Shorter Hours"

Howard G. Foster

A common reason given by economists who reject the proposal of a shorter workweek is based on what they call the "lump of labor" fallacy. Labor's analysis, they suggest, assumes that an employer has a fixed amount of work that must be done. If hours are reduced with no cut in weekly pay, the employer will react just as he would to any wage increase —that is, cut back output until marginal cost (which has risen) again equals marginal revenue. To suppose that the employer will maintain production in the face of a substantial cost hike is said to be clearly fallacious. ...

But does it follow that a rise in cost is a necessary concomitant of a cut in the workweek? A moment's reflection leads one to answer "no." The key to such a conclusion is the assumption that productivity is continually moving upward. This means either that a firm can produce more goods and/or services with the same amount of input than it could before the productivity increase, or that it can produce the same amount with less input. ...consider the following hypothetical situation.

Suppose a company employs 100 men who work 40 hours a week. Suppose further that average hourly pay is $1.00. Thus the average worker grosses $40 a week and the employer's total weekly payroll is equal to $4,000 (ignoring, for the moment, other employment costs such as social security payments, fringe benefits, etc.). Now let us assume that the union contract is about to expire, and during the course of the contract— two years—the company's productivity has risen by 5 per cent. This is not an unreasonable assumption, as the average annual productivity increase in American industry is estimated to be about 3.2 per cent. Now what might happen at the negotiations for a new contract?

Since productivity has risen by 5 per cent, the union will demand a share of the gains. If returns to all factors of production are to remain constant, labor would call for a 5 per cent increase in hourly wages. This is the same as saying that labor will receive the same amount relative to sales as before. Let us assume, however, that product demand has not changed. Total payroll, therefore, will have to remain at $4,000. Since hourly wages should be boosted by 5 per cent, then weekly pay can be maintained with a 5 per cent drop in weekly hours. This works out nicely, since the workers can still produce as much as before because of the productivity increase. To illustrate:

One might wish to interject at this point, "So what? You haven't improved the employment situation at all. The work force still numbers 100." This is all very true indeed, but it might be useful to reflect on just what would have happened had this particular sequence of events not occurred. Whether or not the union demands an hourly wage increase, the employer finds himself in a position where he can meet his production needs with 5 per cent fewer man-hours. So what are his alternatives? He can either cut back hours by 5 per cent or cut back men by 5 per cent—in other words, lay off five men. In the first instance he did the former. He can just as easily do the latter, as illustrated in row (b) of the table below:

In this situation, there are fewer men working at a higher weekly wage. Since we have proceeded from the premise that a certain number of men working at, for example, 38 hours is better than fewer men working at 40 hours, we must conclude that situation (a) above is preferable to (b). 

What is the significance of this? It is true that employment has not been increased in situation (a), but obviously the hours reduction has forestalled a decrease in employment. If hours were not cut, then five more men might be out of work. In policy terms there is little difference between steps to decrease unemployment and steps to prevent it from increasing. Furthermore, it should be noted that it appears to make little difference to the employer whether he cuts man-hours through cutting men or hours. It might be argued that in situation (a) the company is obliged to incur some extra cost over situation (b) in the form of fringe benefits, social security and unemployment compensation payments, and other costs which are dependent on the number of workers employed rather than the number of hours worked. It should be added, however, that the employer has the advantage in situation (a) of retaining men who are experienced and whom he could use in case of a spurt in demand without going to the trouble of hiring and training additional workers. At any rate, both of these factors would seem to be relatively minor cost considerations, since only 5 per cent of the work force is involved. Now let us expand the argument a bit. In the foregoing, it was assumed that demand for our employer's product had remained constant. It is not unreasonable to assume that in some cases demand will have risen. For the sake of simplicity, let us assume that sales have increased by 5 per cent, the same amount as the productivity increment. In such a situation, the employer will want to retain the same number of man-hours as before, since by definition the same input can turn out 5 per cent more output. Thus the company might simply raise hourly wages by 5 per cent, and everything would be fine. The situation would look like this (assuming that in 1963 8,000 units had been sold at $1.00 apiece, and that in 1965 the market will take 8.400 units at the same price):

Now suppose the union forces the company to cut the standard workweek to 38 hours. In such a case total payroll will have remained the same. Since the employer was willing to pay out an additional $200 in wages in the first place, he should have no objection to using that money in order to hire the extra workers he needs to meet the demand for his product. Thus we have the following situation:

At this point a critic might protest that the marginal cost of hiring five additional workers is greater than simply the total of their wages. There are administrative costs, benefit and tax costs, and training costs. This, of course, is a valid objection, but the problem is not insuperable. One way the difficulty could be circumvented might be to allow the employer sufficient leeway in the hours reduction to meet the extra costs. In other words, the union might agree to cut weekly hours by only 4 per cent, with no increase in weekly wages, allowing the employer 1 per cent of total payroll with which to pay the expenses of hiring new workers. Thus, again, it should make little difference to the employer how the complement of man-hours is composed— of 100 men and 40 hours, or 105 men and 38.4 hours (that is, a 4 per cent reduction of hours). Two possible situations have been examined, and with each two alternative ways of facing them have been suggested. First it was hypothesized that weekly sales had remained the same, and second, that sales had increased. It should be obvious that any other possibility can be reasoned out in the same manner. If, for example, sales should increase by, say, only 2.5 per cent, then the alternatives would look like this:

Tables representing situations in which sales are held to be any other amount may be similarly devised. Two points might be noted and emphasized here. First, it is evident that any increase in sales concurrent with a productivity increase opens the possibility of creating jobs. The more that sales rise, the more jobs can be found. Secondly, in all the above examples, the standard workweek was reduced without a rise in unit labor costs. This should at least suggest that in principle hours reduction might indeed be an instrument by which to alleviate the unemployment problem and is worth further study.

Finally, the hypothetical situations described above assumed that the employer's annual rate of productivity increase was 2.5 per cent. To be sure, all companies do not enjoy such good fortune. Since the average rate has been estimated at 3.2 per cent, however, some industries must have a rate of increase that is even higher; and in these areas of the economy, hours reduction should have its greatest effect. In industries with low rates of productivity gains, the proposal will be less effective. It seems reasonable to suggest, however, that any company willing to grant a wage increase in the first place, for any reason, can do it just as easily by cutting hours as by raising weekly wages. As stated above, productivity is the key to the shorter-hours proposal in that productivity is the principal factor which enables wage increases in any form to be granted. So long as productivity in American industry continues to rise, hours of work can be cut without inflating unit costs and in this way labor may indeed be able to "create jobs" at the bargaining-table.

UPDATE: Addendum to Foster

A small wrinkle that Foster left out is the observation that, within a certain range of hours, a reduction in working time may often be expected to contribute to productivity by reducing fatigue, etc."The days are gone," wrote Lionel Robbins in 1929, "when it was necessary to combat the naïve assumption that the connection between hours and output is one of direct variation, that it is necessarily true that a lengthening of the working day increases output and a curtailment diminishes it." Below is the hours and output table presented by Sydney Chapman in his 1909 "Hours of Labour" paper:

Assuming that this table is an educated guess, the productivity "rebound" from reducing the daily hours of labor works out to be around one-third. It takes time to realize that productivity gain so it would be safer to say that over a two-year period, a two percent reduction in working time would add an additional one percent to productivity growth (or half a percent per year). With Foster's baseline productivity gain of 2.5% per year, this adds up to a productivity gain --  in the second two-year period -- of 6%. Assuming again that sales grow at the same rate as productivity produces the following table:

The work force continues to grow. Wages increase modestly and so do weekly earnings but per unit costs remain unchanged to slightly lower. Not a lump in a carload!

*************************************

Five years after Foster's article was published, H. D. and N. J. Marshall wrote in their textbook, Collective Bargaining:

The arithmetic of the theory is simple. lf there are 50 million people presently working forty hours per week, let them now work for only thirty-five hours. The resulting reduction of 250 million hours of labor will create openings for more than 7 million (250 divided by 35) additional workers.  

Few businessmen or economists have been convinced of the validity of this reasoning...

The arithmetic IS indeed simple, just not so stupid. The Marshalls' argument is even simpler: ignore the argument that is made; substitute a flimsy straw man; knock down the straw man. Few businessmen or economists are not convinced of the validity of their reasoning. Witness the Hamilton Project's February 2015 framing paper, The Future of Work in the Age of the Machine.

Break Their Haughty Frames

They have taken untold millions that they never toiled to earn,
But without our brain and muscle not a single wheel can turn.
We can break their haughty power, gain our freedom when we learn
That the union makes us strong.

The Hamilton Project bills its "The Future of Work in the Age of the Machine" as a "framing paper." The "frame" (or frame-up) appears on page two of the paper:

The Luddites, as they were called, were revolting against a phenomenon that would fundamentally alter the economies of the world. Technological change would dramatically increase the productivity of labor, creating new possibilities in manufacturing, agriculture, mining, and transportation. While these changes ultimately raised the standard of living in industrialized countries, the Luddites, and many others, saw their jobs disappear (Easterly 2001).

Those "Luddites" (as they were called) were notorious for breaking frames. They were also framed.

From the report of the proceedings of the trial of George Melior (or Mellor), William Thorpe and Thomas Smith for the murder of William Horsfall of Huddersfield, Yorkshire, it would appear (to this reader at least) as though the defendants were indeed guilty as charged. So in what sense am I claiming they were "framed"? The prosecutor, Mr. Richardson saw fit to present his "general observations on the case" -- unsupported by the testimony of witness -- regarding a certain "delusion that has prevailed... amongst the lower orders."

Mr. Horsfall is represented to me to have been a man, who had upwards of four hundred persons at work under him, extremely beloved by his men, and they greatly attached to him. He had very large manufactories, of course, from the employment of so many men; and he employed the machinery which was the object of the abuse of these misguided people. I have not the means of making such observations as I have frequently and lately heard made, upon the delusion which has prevailed upon that subject, amongst the lower orders. It has been supposed that the increase of the machinery by which manufactures are rendered more easy, abridges the quantity of labour wanted in the country. It is a fallacious argument: it is an argument, that no man, who understands the subject at all, will seriously maintain. I mention this, not so much for the sake of you, or of these unfortunate prisoners, as for the sake of the vast number of persons who are assembled in this place. 

I hope that my learned Friend on the other side, will give me credit, that I mean to state no facts as bearing upon the prisoners at the bar, that I shall not, as I conceive, bring home to them. But I cannot help making general observations upon the subject, to draw their Lordships' attention, and yours, to the case itself. I would rather, for perspicuity's sake, go to the facts which constitute the crime, and then apply it to the prisoners. Mr. Horsfall was a man, I understand, of warm feelings*, of great and good understanding, and who saw the fallacy of these arguments; and he, perhaps imprudently (though I do not think so, for I do not think any man acts imprudently in stating his sentiments on a subject which has been under his full consideration) he, I say, stated he would support this species of machinery, because he was sure it was advantageous to the country. He was perfectly well known, in consequence of the part he has taken in reference to these disturbances; and it was proposed by some persons, that he should be taken off.

* What Mr. Richardson meant by "warm feelings" is not what one might suppose. The "warmth" doesn't refer to compassion or tenderness. It alludes instead to Mr. Horsfall's taunt that he wished to "ride up to my saddle girths in Luddite blood."

Catch that? "I have not the means of making such observations..." "I mean to state no facts as bearing upon the prisoners at the bar, that I shall not, as I conceive, bring home to them." In short, this peroration was a digression. It was admittedly incidental to the matter at trial. But it was politically crucial. Not only was Mr. Richardson concerned with securing a conviction for murder but, perhaps even more urgently, with establishing, for the record, the collective guilt of those "lower orders" for "outrages" arising from their delusion and their fallacious argument. Those lower orders had no grounds for complaint.

The authors of the Hamilton Project framing paper cited William Easterly as the source for their digression on the Luddites (as they were called). Easterly called his passage on the Luddites "an aside about the Luddite fallacy." Apparently not having consulted Mr. Richardson's Indictment, Easterly claimed that "the intellectual silliness came later":

Some people believe labor-saving technological change is bad for the  workers because it throws them out of work. This is the Luddite fallacy, one of the silliest ideas to ever come along in the long tradition  of silly ideas in economics. …  

The original Luddites were hosiery and lace workers in Notting  ham, England, in 181 1. They smashed knitting machines that embodied new labor-saving technology as a protest against unemployment (theirs), publicizing their actions in circulars mysteriously  signed “King Ludd.” … The intellectual silliness came later, when some thinkers generalized the Luddites’ plight into the Luddite fallacy: that an economy-wide technical breakthrough enabling production of the same amount  of goods with fewer workers will result in an economy with—fewer  workers. Somehow it never occurs to believers in Luddism that there’s another alternative: produce more goods with the same number of workers.

Actually the allegation of intellectual silliness came three decades earlier -- in the form of a pamphlet by the Lancashire magistrate, Dorning Rasbotham, Thoughts on the Use of Machines in the Cotton Manufacture. Accusing frame breakers of irrational techno-phobia became a commonplace in industrializing Britain. That way you don't have to acknowledge or deal with their grievances.The Luddite fable serves the same purpose today  Opponents of austerity, pension cutbacks, neo-liberal trade policies and labor-market deregulation, along with proponents of work-time reduction can be glibly dismissed without having to acknowledge their arguments. Those lower orders are all deluded. They assume that their is only a fixed amount of work to be done. There's no point listening to their silly ideas or reasoning with them.

Above all, forget about the masterful lampoon and exposé of this dodgy frame by Marx in section 6, chapter 15. volume I of Capital, "The theory of compensation as regards the workpeople displaced by machinery":

It is an undoubted fact that machinery, as such, is not responsible for "setting free" the workman from the means of subsistence. It cheapens and increases production in that branch which it seizes on, and at first makes no change in the mass of the means of subsistence produced in other branches. Hence, after its introduction, the society possesses as much, if not more, of the necessaries of life than before, for the labourers thrown out of work; and that quite apart from the enormous share of the annual produce wasted by the non-workers. And this is the point relied on by our apologists! The contradictions and antagonisms inseparable from the capitalist employment of machinery, do not exist, they say, since they do not arise out of machinery, as such, but out of its capitalist employment! Since therefore machinery, considered alone, shortens the hours of labour, but, when in the service of capital, lengthens them; since in itself it lightens labour, but when employed by capital, heightens the intensity of labour; since in itself it is a victory of man over the forces of Nature, but in the hands of capital, makes man the slave of those forces; since in itself it increases the wealth of the producers, but in the hands of capital, makes them paupers-for all these reasons and others besides, says the bourgeois economist without more ado, it is clear as noon-day that all these contradictions are a mere semblance of the reality, and that, as a matter of fact, they have neither an actual nor a theoretical existence. Thus he saves himself from all further puzzling of the brain, and what is more, implicitly declares his opponent to be stupid enough to contend against, not the capitalistic employment of machinery, but machinery itself. 

No doubt he is far from denying that temporary inconvenience may result from the capitalist use of machinery. But where is the medal without its reverse! Any employment of machinery, except by capital, is to him an impossibility. Exploitation of the workman by the machine is therefore, with him, identical with exploitation of the machine by the workman. Whoever, therefore, exposes the real state of things in the capitalistic employment of machinery, is against its employment in any way, and is an enemy of social progress! Exactly the reasoning of the celebrated Bill Sykes [the villain from Dickens's Oliver Twist]. "Gentlemen of the jury, no doubt the throat of this commercial traveller has been cut. But that is not my fault, it is the fault of the knife. Must we, for such a temporary inconvenience, abolish the use of the knife? Only consider! where would agriculture and trade be without the knife? Is it not as salutary in surgery, as it is knowing in anatomy? And in addition a willing help at the festive board? If you abolish the knife — you hurl us back into the depths of barbarism."

***

Is there aught we hold in common with the greedy parasite,
Who would lash us into serfdom and would crush us with his might?
Is there anything left to us but to organize and fight?

For the union makes us strong.