"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!

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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.