The Concept of an Optimum Labor Force

Everett W. Gross

[A paper presented to Professor Campbell R. McConnell, in partial fulfillment of course requirements. April 1980]

I. INTRODUCTION

It is hoped that the reader of this paper will not expect any success in arriving at numerical values of optimum labor force; only the concept and not numerical value is to be taken under discussion. The reader deserves to be told at some early stage such as this, what the point of the paper seems to be. When it is derived from vague notions that have long haunted the writer, instant clarification for the reader may be remote. A very early idea in the recorded history of thought was that each person occupied or ought to occupy some niche in the organization of production and other services by which society was maintained. Somewhere between then and now, the certainty of a niche (a desirable one, at any rate) for each person has become less than obvious. We give the name 'unemployment1 to this lack of certainty, which has been studied from many angles. And in some schools of thought it is dismissed easily, but I cannot do so. Unemployment usually yields great distress.

An undercurrent of popular thought seems to be that for producers and sellers, the economy is somehow saturated at a point where all of the people (buyers) apparently have their demands supplied before all wares have been sold. There is therefore no market for any more goods and services. And there are left-over people, who for the most part have needs and desires not being supplied by the market activity they see all around them but they have nothing to trade for a share of it except their ability to work. The feeling is that since there isn't any more demand, it might seem less distressing if not so many workers would want to sell their work for a share in the results of selling that which is sold to the ones who do buy, or if producers and sellers did not want to supply so much.

This undercurrent suffers from an internal conflict in the minds of most people I know, since they apparently forget about the demands and needs of the superfluous workers themselves. Part of the problem is handled by economists who use a term 'effective demand' to dispose of the fact that though these superfluous workers have needs, they do not have money to buy what they need and therefore cannot make their demand impinge on the market in such a way as to make it produce the additional supplies to meet those needs. It is an evasion of the problem, however unwitting.

The undercurrent crops out now and then in the form not only of thinking there are too many people, but also in the acts of nations in the establishment of large governmental departments involved in the control and inhibition of immigration. One popular radio newscaster even makes frequent references to the coincidence between the number of illegal immigrants, especially from Mexico, and the number of people thought to be involuntarily unemployed in the United States.

II. ORIGIN

When I first encountered the term optimum labor force, it occurred to me that it could relate to either an explanation or proposed solution to an unemployment problem. One of my fond hopes in starting this project was that I might discover the origin of the expression optimum labor force. The exact person and time and place of first use is not of any particular importance. What is important is the set of problems which seemed to loom before the eyes of the person or persons who first used it. That may have been long ago.

Surely the idea of any optimum comes from the perceived possibility of one or more problems emerging from too much and others from too little. The optimum labor force could grow out of two general classes of possibilities: 1) Optimum population (given a resource base), and 2) Optimum number of people (given a population) to do the work which needs to be done.

In the first class, could too many be too hard on the resource base, and in the second class, could too many result in a reduced product? In either class, could too few result in a lowered standard of living?

III. THE CLUB OF ROME STUDIES

Discussions with colleagues while I was forming my ideas, almost invariably evoked from them some reference to the Club of Rome studies, although I failed to find in that literature even a single use of the term optimum labor force. Nor do those studies deal with the labor force fraction of the total population. They deal with total population which the world can support, from the point of view of pressure upon rates of supply of renewable resources, rates of use in a total sense, rates of use adjustable by adopting lese resource-exhausting styles of living, pollution-correcting capacity of the planet, and psychological distress of insufficient privacy. And nowhere do I find any reference to any problem of living comfort that could arise from insufficient population. All their efforts speak of bringing or keeping a large population just anywhere below an intolerable level. This is hardly the way most of us think of optimum.

It is hard to read the Club of Rome studies without thinking of Malthus and his explanation of economic distress which postulated a geometric population growth rate coupled with linear rate of increase of means of subsistence. His use of mathematical techniques aroused and still arouses degrees of appreciation varying from high admiration to deep contempt. My own appraisal is about mid-range at about the level of a mild chuckle. The deep contempt end is perhaps exemplified by Henry George, of whom I am an avid, but I hope not blind, follower.

The technique of the Club of Rome was to use a computer to project forward into time, the results of the above-mentioned rates (uses of resources, etc.) along with birth and death rates and what is surmised to be the functional pairing of various stock and flow figures. The techniques of systems dynamics were applied to such processes as population growth, DDT movement in the global environment, mercury contamination, natural resource utilization, waste generation, the discovery life cycle of a finite resource, long-term resource availability, carrying capacity of the global environment, among others. The computer print-cuts were shown in graphical form with the quantities as functions of time. They will not be shown here, nor will I review the results in much detail.

The resulting quality of life looks rather uninviting if present trends prevail without conscious redirection by massive exhortation programs or legislative forces. At first thought, one would tend to believe that if some factor necessary to life should come to be in short supply, population would just coast up to its maximum number and approach it as a sort of asymptote. But according to what the computer gets from the assumptions, that is not the way it works out. In almost every case, the mode of reaching a limiting state is the overshoot mode. That is, population density, for instance, (or usage rate of a resource), goes more or less headlong into a totally intolerable figure and then has to drop back catastrophically. The reason is that the time lags in the causal chains in economic and other social phenomena are often quite long. Many of the conditions under which we live had their cause twenty or more years ago. And we can't go back and change that. The solution to a social problem of today often lies outside of the realm of any change in today's behavior. At this point, it would be easy to mistake me as saying that every problem of today is outside of available remedies applicable today; I wish to caution the reader against that interpretation.

Our society is not accustomed to thinking in terms of a future generation to the extent of making any provisions or allowances for same. With respect to our petroleum resources, for instance, it is very rare to find a commentator, news or otherwise, who comments in terns of leaving the most in the ground for future generations. All mental efforts seem to be geared to getting more of it out of the ground now for this generation. One rather minor exception is a feeble effort by some in the United States to keep a little in reserve in case of a military emergency.

Paraphrasing Club of Rome language: We try to be guided by the idea that we ought to maximize the total benefits for all living people. Some of the Western countries believe that this objective is best served by letting each individual be free to pursue his own interest. It is assumed that if every citizen and institution acts to maximize his own position in the short term, the society will benefit. This, however, introduces a strong emphasis on short-term benefits. When an action will bring both benefits and costs over time, individuals use the concept of net present value, and discount the future implications so that they can determine whether an action is profitable ... and hence should be taken. The result is that an essentially zero value is assigned to anything happening more than twenty years from now. In other words, actions will be taken just because the benefits are larger than the costs in the short run (for example over the next decade).

If one chooses to adhere strictly to the objective of maximizing the short-term rewards of the present generation, there are in fact no long-term trade-offs to be made. Continued pursuit of this objective would involve no major change in the present practice of maximizing current benefits and neglecting any future costs. This is the value system that leads in our world model to eventual overshoot and collapse.[1] At the time Malthus wrote, it is doubtful that anyone at all thought in terms of the total exhaustion of any resource. It is also doubtful that anyone dreamed there would no longer be any acceptable place to discard trash, or that emissions into the atmosphere would exceed insignificant figures. Trash was virtually all biodegradable. Even discarded metal objects were reused because a high proportion of metal work was done manually. Their thoughts only needed to be in terms of diminishing marginal productivity of renewable resources. Virtually every item used by man could be thought of as a crop; inroads into the known and suspected reserves were a mere sliver. It was then believed, possibly without empirical support, that more miners in a given mine would produce slightly less coal per miner, but not because the coal was running out.

Since that time we have observed the progress of technology and specialization of labor, and we have seen the rather steady increase of productivity per man hour.[2] It is physically impossible for this to continue along with increasing population, along with higher proportions of people working constant hours, along with product mixes using the same proportions of non-renewable resources. Something has to give. At least one of these rates has to be held back or reduced either voluntarily by some generation in the near future, or under duress by a later one. Failing that, although we expect the death rate to remain one to a person, life could be short and miserable.

IV. PROPORTION OF POPULATION WOHKING

The discussions so far seem to lack something qualifying as the best guess as to the origin of the expression optimum labor force. The subject of gains in labor productivity, however, might be worth following out. There is the widest possible disagreement among economists as to whether this should be expected to produce a higher or lower unemployment rate. This disagreement could be a rather natural consequence of lack of knowledge about what causes unemployment. The fact is that the unemployment rate as a fraction of the known or supposed labor force has remained quite steady with about one notable and rather persistent high mark in the 1930's.

One could imagine a dispute over whether a wobbling number between 4 percent and 10 percent is to be termed remarkably steady or remarkably variable. It almost urges the instincts to suspect that some kind of equilibrium is involved, especially since the wobble is evidently associated with a cyclical or oscillatory behavior of the rest of the economy. But the unemployment rate does not go to zero even on its downward peaks; the lowest on record is somewhere around 3 percent. One occasionally encounters the suggestion that the number of unemployed is just the number by which the labor force exceeds the optimum value. But defining the optimum value in this way does not explain anything. It does not explain why the economy will grow just to the point of being able to hire most but not all of the people who want to work.

Any tenable explanation of unemployment (or of anything else) must pass the test-of not being inconsistent with any observable fact. It isn't that unemployed people can't work. They can work all they want to. They can dig a hole somewhere and fill it in again. It is that they can't find anyone who needs their work and is willing and able to pay for it. The pay and not the work is what is desired.

V. EQUILIBRIUM

There are economists nowadays who doubt the existence of most equilibria; things move around too much. They reason that if an eqilibrium existed, quantities and prices would move rather quickly to their proper values and pretty much stay there. I would suggest that people who argue thus do not interpret the meaning of the term equilibrium the same as I do. There are many equilibria in the physical world which could not meet the requirement of being a stationary state at all. In fact, equilibrium may not really imply a stationary state. It means a position such that if the entity is. displaced from that position, there arises as a result of that displacement, a restoring force tending to return that entity toward that position (i.e., stable equilibrium). There are oc clock pendula and balance wheels which have equilibrium positions, and have run for years without ever stopping there. In fact, the equilibrium position is the point at which motion is the most rapid. And a screen door spring, by virtue of its function, is never allowed to get to its equilibrium position. (In that case, a new equilibrium could be defined as the equality of force of the spring upon the door and force of the door upon the spring, the two forces remaining equal throughout their change with position changes.)

In a modern macroeconomics course, several important determinants of observable quantities are credited to equilibria. Most of them take the form of some quantity demanded being equal to quantity supplied at some price. That point, in turn, can become a variable function of something else or a determinant of yet something else, or both. The whole description can take a number of hours to follow through even in a book as concise and well-written as the one by Bailey.[3] It will be suggested here that there could be a massive equilibrium not mentioned at all by Bailey, or comparable presentations of the workings of the economy.

VI. A COPERNICAN QUESTION

Occasional reference is made to the need to raise a Copernican question. It may be that answers to many distressing questions are not forthcoming from the currently most popular attacks being directed at them. In the Lincoln, (Nebraska) Journal for January 8, 1978, appeared an article by Soma Golden, reporting on the annual convention of the American Economic Association. The article expressed the idea that the economists were lamenting the lack of talent among them of the caliber of Adam Smith and David Ricardo and Alfred Marshall. If they had such talent, it seemed, they could solve the problem of today's stagflation and "...the biggest problem of our time: achieving growth without spiraling inflation." Also, "How, after all, can a tax subsidy compare with an enduring metaphor like Adam Smith's 'invisible hand'? And what does supply management have going for it compared with Ricardo's brilliant insight into the law of comparative advantage?" Is there a remote possibility that some of the needed insights can yet be gleaned from Smith and Ricardo and Marshall? I, for one have never thought that Ricardo's insight into comparative advantage, great though it was, was quite as important as his insight into rent. But the latter could easily have been gleaned from Adam Smith, (Book I, Chapter XI).

Going on with the Golden article: "It was touching to see the 70-year-old Professor Galbraith put aside his usual acerbic comments about the inadequacies of modern economics and try to boost the sagging morale of his fellow economists. He sensed, like many at the meeting, that economists today need, more than anything else, some of the bluster they had - in excess perhaps - in the 1960's. Without some audacity, there will be no leap ahead to new ideas."

Maybe so, but when a new idea comes, will the person who raises it have any easier time of it than Copernicus did? Celestial mechanics was getting as complicated as economics is now. More mathematics was being invented to deal with it. The motions of the stars and planets were getting harder to describe in terms of more circles and more systems of circles superimposed upon circles. Actually, the Copernican question as to what really is at the center, (the sun or the earth) had been raised several times including fairly early in the oft-studied Greek civilization. One of the last anti-moving-earth arguments was that the earth would surely lose its moon. When Galileo, with his new telescope offered to let the academic fathers see that Jupiter had several moons that it had not lost yet, at least one got himself into the history books by refusing to look through the 'stupid (or worse) device'.

It is hard to know in the middle of the story, just what constitutes a Copernican question. This paper will entertain the thought that at least one has already been posed. When we speak of an optimum such as a labor force, we think of something other than the labor force as being maximized for some labor force that is not maximum. The thing being maximized would be someone's well-being as defined by some criterion or other. In other words, who stands to profit more if some laborers who want to work are out of a job? Can the total product be lessened by having a place for more of the people who want a share? Can it be the total well-being of the laborers themselves that is maximized if the ones who do not have jobs lose less thereby than is gained by the ones who do have jobs? Is there more total product to be divided among the total population if fewer people work than there is if more people work? Taking the last question first, we could look around and see many places where an additional worker (call him Mr. A) could work, with the result that only an addition to total product would result. If it is argued that money to pay him would have to be diverted from some place where it would have done more good, it could be replied that the man is already being paid by some kind of dole or relief. He is already surviving by virtue of something diverted from somewhere, but without contributing to the product.

Picture Mr. B who is working, and whose income is already being shared with Mr. A. There would seem to be two possibilities. Either Mr. A could be allowed to lessen Mr. B's work load, to Mr. B's work-leisure advantage, or Mr. A could perform some task to improve Mr. B's (and incidentally Mr. A's) conditions of life (environment in the broadest sense). It could be counter-argued that the cost in additional work equipment and clothing would be greater than the value of the additional work. This would be true in some cases, but the argument holds for the remaining cases. Also, the values and costs and prices upon which these arguments are based, are elements of a total price structure growing out of a vast network of traditions and customs establishing what belongs to whom and on what grounds.

Taking another question: Can the total product be lessened by having a place of work for more of the people who want a share? If we pursue the discussion of the previous question, it is apparent that the answer can go either way. If it were left to private enterprise, some would argue that an entrepreneur would make the decision after weighing the alternatives and would weed out the unfavorable cases. From Adam Smith, we could almost infer that when a voluntary exchange or agreement occurs, it is because each party sees himself as a gainer in the transaction, and therefore, maximum welfare is the result. Is it too far-fetched, to illustrate a principle, to use a hypothetical example from the now supposedly defunct institution of chattel slavery, to say that this may not be true if one considers the alternate opportunities of the respective parties? The slave "voluntarily" remained in submission only because the alternatives allowed to him were even less desirable. There must be many transactions occurring today in which the alternatives for the respective parties are nowhere near equal in (un)desirability by any honest criterion.

From here it would be easy to skip the question about whether the eight percent unemployed lose less by their unemployment than is gained as a result by the other 92 percent. That would not need to be the case in order to provide a natural-sounding explanation for part of the people being unemployed. It may be that the entity which is maximized by the unemployment of one of every twelve persons who need to work, is not necessarily the wages of the other eleven who have found work.

It is far from implausible that the discoverer of a suitable explanation for this miserable phenomenon could be some "grocer's boy" whose name may be doomed to obscurity but whose theory is waiting in the Wings to be clarified. That theory would have to account for, or at least not be in conflict with observations:

• 1) The number of unemployed floats around a percentage greater than zero and never gets to zero;
  
• 2) Government (deficit) spending and easy money monetary policy seem to improve the situation but only temporarily;
  
• 3) Some advances of technology seem to offer short-term relief;
  
• 4) The variation corresponding to the business cycle is rather dependable.

Some classicists of more modern vintage than Ricardo believed that if workers would offer to settle for lower wages, the labor market would clear in much the same manner as other markets. An example is W. H. Hutt.[5] It might be hard to prove or disprove one of those what-would-happen-if statements. Hutt might be correct and the wage rate might cone out below a suitable level. Now, if productivity does not drop, full employment might be the optimum for people other than the workers, but not for the workers.

VII. DOES DISTRIBUTION HAVE ANY EFFECT?

I have not said they couldn't work. I have said they could not get paid enough - if at all. It seems to me that modern discussions are seldom diverted to the logical consequences of certain ideas noted by both Smith and Ricardo. However one states it, the shares of the total product which go as rewards to the furnishers of the respective factors of production cannot be dismissed as not worth considering. It must also be important to understand the market forces which determine those shares. Most macroeconomic discussions in the last eighty years or so, have abandoned the classical concept of three factors of production and in so doing, may have lost some analytical power. The idea has seemed to be that a new enterprise, needing to borrow money to start up, needn't worry about, indeed had no control over, whether his new money would be used to obtain a location or obtain productive equipment. But labor has still kept its place as a separate factor. As a bookkeeping item for an individual enterprise, it isn't important that the price paid for the location is caused by, is subject top and itself exerts, quite different market forces than is the case for capital equipment. In fact, from an analytical point of view, labor and capital have far more in common and more similarities than do capital and land. And yet, capital and land are the ones almost universally called by the same word.

Each location is a monopoly and the prospect of an increase in its future value is an important incentive to hold it idle rather than use it or sell it for use in the present. In order to obtain a location for present use, a would-be entrepreneur must at least match the present owner's estimate of future value, modified by some plausible discount rate.[6]

There could grow out of this fact a massive equilibrium that could overpower and make peanuts out of all of the equilibria mentioned by Bailey.[7] It could mean that the entire economy could be described at all times in terms of an equilibrium involving, on the one hand, all labor and capital, and on the other hand, the status of bare land speculation. If prosperity would be impending or expected for any reason, then an incentive could exist for holders of bare land to hold tighter and not commit their tracts to full development (by sale or their own use). The price they could, and therefore naturally would, hold out for is the price that would separate, a successful from an unsuccessful bidder. If there were no unsuccessful bidders in the picture, the price would be zero. This should be our clue to the unemployment problem.

Government fiscal and monetary policy can wake things up temporarily for reasons other than (or in addition to) those commonly advanced. Bargains that entrepreneurs make to obtain access to locations are necessarily longer-term and more of a delayed-action type. Land owners and land speculators view their investments as long-term things. Government spending and monetary policy are rather more short-term in their effects. Their immediate effect is toward stimulation of gains and rewards for the active factors (capital and labor) through which the multiplier works.

Any arguments that speculation acts alike on the three factors -- labor, capital, land -- must fail on very brief examination. A prospect of prosperity in the near future must bring more capital into existence and cause laborers of all kinds to make some kind of preparation for the coming good times. Such is not the case with land, which offers its owner a maximum if he is able to hold out and recognize that moment just before the majority of people start easing back in expectation of a downturn. The land at that point sells at its highest, which is another way of saying that it places the maximum burden upon the productive forces. It can accelerate a downturn under conditions which might otherwise have produced only a leveling off.

One common counter-argument is that the seller of land (or the collector of land rent) helps the economy by feeding that money back into the income stream. If that is the case, we would get the same result by legalizing bank robbery (and kidnapping for ransom). The bank robber's (or kidnapper's) take is not a payment for a service which comes into being by virtue of the bank having offered that payment. The bank could have done equally well if no such person had existed to collect that payment. The payment is made for the robber to allow some of the bank tellers to survive. Notice the word 'some'. If no robber ever harmed a teller, he would never collect. If the robber always shot the teller, there would also never be a payment.

In an analogy lies the key to a theory of unemployment. Land, exclusive of humanly devised improvements, has no cost of production. Payment to any person cannot cause it to begin existing. People who need to use it compete for its use by outbidding someone else, and virtually no enterprise can exist without it. The existence of any person to collect this payment does not in any way enhance the productivity of land. The amount paid either to buy or rent a site is closely related to the number of unsuccessful bidders. Payment is made for letting part of the people survive.

The seller does not always let the site go to someone; each does his own balancing act between letting it go and holding it for later. It could be said that he can't be expected to build if building pays less than holding it idle. That is true, but the balance point is at the point where part of the people are involuntarily unemployed if we let him profit in any degree by holding it idle or in a low state of improvement.

Now to return to the question of what entity is maximized when fewer than all workers are working. If the foregoing discussion has any validity, then obviously total production is not a maximum for any fixed population figure. Each economic agent is trying to maximize his own net income under the condition that all other agents are acting under a handicap. Each land owner's pecuniary interest is handicapped by the fact that the entire labor-capital network development is arrested by the pecuniary interest of all other land owners. This, then, leads to the appearance of something coming to some kind of natural limit or optimum at the point where only part of the people who need the product and are willing to work for it are employed.

VIII. CONCLUSION

The concept of Optimum labor force could arise from two types of problem: 1) The maximum number of people that could be supported comfortably in a world of finite resources could limit the productive activity permissible, and 2) The structure of traditional property arrangements could bring a halt to the number able to make an acceptable living at any given population level.

NOTES

1. Toward Global Equilibrium; Collected Papers. Edited by Dennis L. Meadows and Donella H. Meadows (Cambridge, Mass., Wright-Allen Press, Inc.) 1973. P 300.
2. A slowing, however, has been noticed in the last few years. Timothy Hannan, of the Philadelphia Fed's Department of Research, discusses the subject very well in an article: The Productivity Perplex: A Concern For The Supply Side, in Business Review. Federal Reserve Bank of Philadelphia, March/April, 1980. Hannan says that aggregate demand considerations don't seem to go very far in explaining it.
3. Martin J. Bailey, National Income And The Price Level, A Study In Macroeconomic Theory. (McQraw-Hill, 2nd Ed., 1971.)
4. W. H. Hutt, A Rehabilitation of Say's Law.(Athens. Ohio University Press, 1974.)
5. Even Marx seldom if ever noted any incompatibility of interest between capital owners and land owners.
6. PV = FVn / (1 + r)n -- where PV = present value; FVn = present owner's estimate of some future value in the nth year; and r = the discount rate that the present owner considers plausible.
7. Martin J. Bailey, National Income And The Price Level. Op.Cit.

BIBLIOGRAPHY

Club of Rome Studies

Meadows, Dennis L. and Donella H., Eds., Toward Global Equilibrium: Collected Papers. (Cambridge, Mass., Wright-Allen Press, Inc., 1973)

Other Works Cited

Bailey, Martin J., National Income And The Price Level, A Study in Macroeconomic Theory, McGraw-Hill, 2nd Ed., 1971)

Hannan, Timothy, The Productivity Perplex: A Concern For The Supply Side. Business Review, Federal Reserve Bank of Philadelphia, March/April 1980.

Hutt, W. H., A Rehabilitation Of Say's Law, (Athens, Ohio University Press, 1974)

Other Works Found Valuable

Gallaway, Lowell E., Manpower Economics, (Homewood, I11., Richard D. Irwin, Inc., 1971)

Hansen, Alvin H., Full Recovery Or Stagnation? (New York, Norton, 1938)

Levitan, Sar A., Our Evolving National Manpower Policy. (Conference Board Record. May 1972)

Owen, Michael S., and Wayne R. Thursk, Land Taxes And Idle Land: A Case Study Of Houston. (Land Economics. August, 1974)

Shannon, Lyle W., Underdeveloped Areas, (New York, Harper, 1957)