Automation and employment

[Gerald Tarrant]

A question about the trends in manufacturing. This is from the Bureau of Labor Statistics linky (hopefully the page doesn't expire or anything; if it does I'll find the original)



This is the graph form of the linked data. What you see is (ignoring the business cycles and recessions) a general decrease in manufacturing employment. To wit: in 1979 average Yearly manufacturing employment was at 19.4 Million, and in 2000 this had dropped to 17.2 million. (from the linked source). To quote from another paper

Lower investment and export growth during the most recent recession are not the only factorsresponsible for the employment decline in the U.S. manufacturing sector. Amplifying these
short-term factors was the longer-term trend of strong productivity growth in the U.S. economy,and especially the manufacturing sector.


From 1950 to 2000, output per hour of work increased by about 2 percent per year in the nonfarm business sector. Compounded over many years, this means that each hour of work now produces about three times as much real value as it did a half-century ago. Over the same period, manufacturing productivity increased even more rapidly—at an average annual rate of 2.8 percent. As a result, an hour of work in manufacturing produced four times as much in 2000 as in 1950. Slide 5 shows that productivity growth has continued to increase since 2000, surpassing even the rapid rates of the later half of the 1990’s. For example, manufacturing productivity growth increased from 4.0% between 1995 and 2000 to 4.8% between 2000 and 2003.

This rapid productivity growth has substantial benefits. It raises real wages and living standards for American families, so that U.S. workers can buy more for every hour of work. It lowers the cost of production for American firms, improving their competitiveness relative to foreign companies. But rapid productivity growth means that companies can produce more goods without adding more workers.

This rapid growth in manufacturing productivity explains the striking pattern in Slide 6. The share of U.S. employment in the manufacturing sector has fallen dramatically over time. For example, the proportion of workers employed in manufacturing declined from a recorded peak of 32 percent in the early 1940s to just below 13 percent in 2000. But over this period, U.S. manufacturing output has actually increased dramatically, more than eleven-fold from 1940 to 2000.

As shown in Slide 7, this trend of a declining share of employment in the manufacturing sector is not unique to the United States but is also shared by other countries.

The above was from pages 3-4 of this PDF here

So here are the slides








So it seems reasonable to conclude that the decreasing participation in manufacturing is going to continue, especially as more and more automation comes in to play (IIRC the Boeing Dreamliner is made using more automation than previous airframes).

So here are the questions: How is that going to affect the world? How will the Third World fare in all this? The EU? Do you think socialist and communist countries will adapt better? How will more free economies adapt to this? Assume for the sake of the discussion that the energy for continued productivity growth is there. What happens when more and more of a population is in "non-productive" roles?

[Starglider]

Automation accelerates the trend of capital being more important than labour (and indeed, everything else). Eventually we will run out of jobs for non-skilled people to do - and before that happens a good fraction of those non-skilled jobs will be 'personal servant to a rich person'. Unfortunately while technological advancement improves the standard of living of everyone, it will make it harder and harder for large fractions of the population (with neither inherited wealth or valuable skills) to earn a living. Outsourcing was kind of a foretaste of this, but in the long run automation has almost unlimited scope to put people out of work. The only thing likely to slow this down is a massive energy crisis.

[Admiral Valdemar]

You often hear that, should this automated "utopia" arise, those not reaping the benefits of a specialised, often academic career, will be earning their salary by building such robots. The truth of the matter is, I've seen robot factories build other robots. Sure, there are humans in the loop somewhere, but in the future even these people will be cut back as you need less and less in the way of mechanics and have to focus on people who know more about advanced robotics, CNC or hydraulics systems and so on.

So either the Average Joe is going to be earning a pittance with a university level qualification in advanced engineering concepts, or they're going to have to get used to the dole.

I foresee an energy crisis hitting this progress first though, before we get to the point that everything is made by machines you really do need a college level education in just to maintain. Look at modern cars and how limited village mechanics and the like are in what they can do which isn't a simple mechanical replacement.

[Starglider]

You often hear that, should this automated "utopia" arise, those not reaping the benefits of a specialised, often academic career, will be earning their salary by building such robots. The truth of the matter is, I've seen robot factories build other robots.

Even if that were not true, the number of humans required to build the robots* would be vastly smaller than the number of humans they replace over their operational lifetime. Which should be obvious, as they wouldn't be cost effective otherwise. The demand for goods would have to increase immensely to keep up. And while the US has been trying to go in this direction, they are now discovering that if you don't actually pay your population enough to afford all this output, it's unsustainable. Having robots build (and maintain) robots just makes the situation even worse.

* For manufacturing most of job losses are from what most people would consider by 'automated machine tools', full-manipulator robots are mainly for getting the inspection and part joining jobs, we're still working on mobile robots needed to wipe out most of the service jobs.

I foresee an energy crisis hitting this progress first though, before we get to the point that everything is made by machines you really do need a college level education in just to maintain.

Yeah but if civilisation survives that it'll have to confront the problem eventually. Unless an existential risk hits first - and of course widespread robotics and masses of money coming into the field increases the 'runaway seed AI' one from 'dangerous' to 'almost certain'.

Look at modern cars and how limited village mechanics and the like are in what they can do which isn't a simple mechanical replacement.

Given enough energy plus an automated transport infrastructure, 'ship it back to the factory for reconditioning' becomes the answer to virtually every maintenance issue.

[Admiral Valdemar]

That's what I figure, us having to deal with this little issue, because one way or another, if we want to progress we're going to hit this stage, if not this century, then a millennia later.

Once you get machines that can independently look after themselves, you're left with people who design them and maybe the odd repairer guy who can get some others to help fix up anything a robot cannot do. When you get past that and robots can diagnose themselves, repair themselves efficiently and even upgrade their designs, then you really don't need people wasting time looking after them any more just as we don't need loads of people physically writing out copies of books now we have automated printers.

If this goes the way of the Culture, then at the end of the day we all become artists and lead a leisurely life improving ourselves with gratuitous free time (or we can spend more time being dicks to one another. Whichever is more appealing).

It'd be nice if we could transition to the Culture without the crap fest in-between. Or we a) let the machines become sentient/sapient and wipe us out, b) join the machines and push the delete key on boredom and working for a living.

[Starglider]

When you get past that and robots can diagnose themselves, repair themselves efficiently and even upgrade their designs, then you really don't need people wasting time looking after them any more just as we don't need loads of people physically writing out copies of books now we have automated printers.

When you get to that point, unless the 'friendly AGI problem' has been solved (and it's an /extremely/ hard problem that not many people are paying attention to or even taking serious yet), humanity is screwed (as in soon to be extinct) anyway.

If this goes the way of the Culture, then at the end of the day we all become artists and lead a leisurely life improving ourselves with gratuitous free time (or we can spend more time being dicks to one another. Whichever is more appealing).

The main problem with that is the desire to lord it over the less fortunate is built into human psychology. Solution: fix human psychology. Unfortunately people don't like it when you propose mandatory brain modification, and of course powerful fuckwits will also try and hijack /that/ bandwagon to stay in power / get more power (only terrorists complain about mind probes - true Americans have nothing to hide!).

It'd be nice if we could transition to the Culture without the crap fest in-between

So, would you like so sign up to my personal chapter of Evil Geniuses For A Better Tomorrow, taking over the world with Atomic War Robots, then implementing global mind control, for the greater good of humanity? You've just outlined the logic that makes it the only real solution.

[Darth Wong]

Those figures are strictly US figures, right? What happens if you include the foreign labour that is often used to manufacture the goods that are sold in the US? Manufacturing is still quite labour-intensive in many industries; it's just that the most labour-intensive types of manufacturing have been shipped off to China.

[Admiral Valdemar]

When you get to that point, unless the 'friendly AGI problem' has been solved (and it's an /extremely/ hard problem that not many people are paying attention to or even taking serious yet), humanity is screwed (as in soon to be extinct) anyway.

This is the part where we put orphan childrens' brains into the robots to counter our lack of coding prowess. It's cheap and who cares?

The main problem with that is the desire to lord it over the less fortunate is built into human psychology. Solution: fix human psychology. Unfortunately people don't like it when you propose mandatory brain modification, and of course powerful fuckwits will also try and hijack /that/ bandwagon to stay in power / get more power (only terrorists complain about mind probes - true Americans have nothing to hide!).

Generally speaking, any benefit to humanity can be turned to a horrible opposite in no time at all by the more nefarious of our species. Just the way we roll, until such time that we find an evil gene or mental engram and erase it. If only...

So, would you like so sign up to my personal chapter of Evil Geniuses For A Better Tomorrow, taking over the world with Atomic War Robots, then implementing global mind control, for the greater good of humanity? You've just outlined the logic that makes it the only real solution.

Do Republicans like to scandalise their sex lives? Where do I sign?!

Those figures are strictly US figures, right? What happens if you include the foreign labour that is often used to manufacture the goods that are sold in the US? Manufacturing is still quite labour-intensive in many industries; it's just that the most labour-intensive types of manufacturing have been shipped off to China.

I can't help but think Mattel's recent hiccups are going to get businesses giving a long hard think about what they send over to China to be done. Cheap labour is great and all (if you're not the cheap labour), but when kiddies start becoming exposed to risk because of penny pinching corporate suits, it becomes a talking point, admittedly not a major kill-China-economically one, but something China is sitting up for now.

We're getting call centres moving back to the lands they're offering services to, rather than planet India because enough people ranted. Maybe robots will takeover the labour market in the not-too-distant future, when they're less hassle and cost.

Or we can do what Arthur C. Clarke proposed and all have man-servant monkeys. Must've got sunstroke that day.

[Gerald Tarrant]

Those figures are strictly US figures, right? What happens if you include the foreign labour that is often used to manufacture the goods that are sold in the US? Manufacturing is still quite labour-intensive in many industries; it's just that the most labour-intensive types of manufacturing have been shipped off to China.

The only data I found was for the US on the Bureau of Labor site and something from the Treasury Department. The PDF speech I linked had this slide. Japan (which had the slowest decrease) still seems to be experiencing the general decline of percentage of Labor force in Manufacturing. As an aside it's possible that Japan's decrease could be due to the slump they've been in for the decade.



I haven't found anything on this yet, but I would guess that this trend is common to the G-8 in general.

I'm also going to guess that most of the developing world is experiencing the opposite as they become industrialized.

[Darth Wong]

The fact is that a large part of our manufactured goods come from places like China, so any manufacturing job statistics from any first-world nation are going to be quite misleading when it comes to the amount of labour required to produce the goods we consume.

[Gerald Tarrant]

The fact is that a large part of our manufactured goods come from places like China, so any manufacturing job statistics from any first-world nation are going to be quite misleading when it comes to the amount of labour required to produce the goods we consume.

This is manufacturing by year in the United States.



From here

Compare this to the absolute numbers of people employed in Manufacturing in the US and you see growth in productivity. Less people are able to make more; or more is produced per person.

The question I had been interested in was; What are the implications of there being less and less "productive" persons in the developed world? Will this matter at all? This futurist has an unpleasant answer to that question here. Short summary of his view; as more and more production shifts to automation unproductive persons have no recourses and a unhappiness commences. What are your views of this trend? How will the world adapt to this?

[Lord of the Abyss]

How will the world adapt to this?

Well, America is screwed, I think. Any workable solution is likely to involve things that will be labeled socialism, which will spark a huge amount of resistance. America isn't really set up to handle any kind of major shift in the way the economy works, because it's such an ideological matter here.

[Warthog]

Quick question is that monetary value of manufacturing output cost of materials being processed or the sale value of the manufactured good? Because everybody knows Americans overcharge . I've asked a company in America to once quote on making a stainless steel bench, they came back with a 5 figure number and I never spoke to them again.

The other thing that I'm a bit wary of is how do they track the number of jobs in the manufacturing sector? Is this just the Joes and Bobs on the shop floor or does this include people who are needed to support them, logistics and quality.

What I think you'll see is that jobs will shift out of the manufacturing sector to support manufacturing. People will still be needed to commission new robots, they aren't going to set themselves up. This doesn't happen overnight and with the numbers you're probably thinking about, it could be an industry in itself.

The more automation the better the manufacturing process is. This is simply because you can get more consistent product. You not saddled with the variance of the people doing the job. For instance Joe welds left handed while Bob welds with his right, the product is going to be different. I've said that Americans tend to be overpriced, but they sell some good shit, the Chinese on the other hand usually sell crap, if you want something manufactured to tight tolerances the Chinese can amaze you with some of the stuff they bring back, amaze you in a bad bad way. The old adage of cheap, good fast pick two applies. However, until there is a similar quantum leap in robot error checking there will always be people on a line looking for defects. The problem with robots is the consistency they are very consistent meaning if they are producing a flaw everything they make will have that same flaw. See the car industry for example, massive recall issues due to robotic production flaws, usually welding issues that their mechanics will repair.

Design support for robots will also increase, robots aren't going to know how to make a product by themselves or nor are they going to design their own tools to get the job done. You really need to learn some skills to work in manufacturing these days and if you don't want to learn well there's always the retail sector. If your doing a job that anybody off the street can do you're not going to have that much job security anyway.

[Sikon]

A couple centuries ago, most of the population was employed in agriculture. Today, it is as follows:

Labor force - by occupation: farming, forestry, and fishing 0.7%, manufacturing, extraction, transportation, and crafts 22.9%, managerial, professional, and technical 34.9%, sales and office 25%, other services 16.5%

U.S.

The employment situation has survived an orders of magnitude change in agriculture: Employment requirements decreased so much despite far more calories per person, much food exported internationally, and the order of magnitude inefficiency factor of meat production.

As can be seen, the jobs formerly occupied by most of the population were lost. However, there was not a situation of most of the population becoming permanently unemployed. Rather, human desires for more goods and services are more or less unlimited, and those still employed had demand for new services ... a demand satisfied by those losing their agricultural jobs going into new occupations, who in turn had to spend their incomes somewhere. There became far fewer farmers but more doctors, cashiers, lawyers, janitors, and countless other occupations.

Nevertheless, popular concern about automation causing unemployment has been around for a long, long time. The following is one illustration:

To go no further back, let us turn to Adam Smith’s Wealth of Nations, published in 1776. The first chapter of this remarkable book is called “Of the Division of Labor,” and on the second page of this first chapter the author tells us that a workman unacquainted with the use of machinery employed in pin-making “could scarce make one pin a day, and certainly could not make twenty,” but with the use of this machinery he can make 4,800 pins a day. So already, alas, in Adam Smith’s time, machinery had thrown from 240 to 4,800 pin-makers out of work for every one it kept. In the pin-making industry there was already, if machines merely throw men out of jobs, 99.98 percent unemployment. Could things be blacker?

Things could be blacker, for the Industrial Revolution was just in its infancy. Let us look at some of the incidents and aspects of that revolution. Let us see, for example, what happened in the stocking industry. New stocking frames as they were introduced were destroyed by the handicraft workmen (over 1000 in a single riot), houses were burned, the inventors were threatened and obliged to flee for their lives, and order was not finally restored until the military had been called out and the leading rioters had been either transported or hanged.

Now it is important to bear in mind that insofar as the rioters were thinking of their own immediate or even longer futures their opposition to the machine was rational. For William Felkin, in his History of the Machine-Wrought Hosiery Manufactures (1867), tells us (though the statement seems implausible) that the larger part of the 50,000 English stocking knitters and their families did not fully emerge from the hunger and misery entailed by the introduction of the machine for the next forty years. But insofar as the rioters believed, as most of them undoubtedly did, that the machine was permanently displacing men, they were mistaken, for before the end of the nineteenth century the stocking industry was employing at least a hundred men for every man it employed at the beginning of the century.

Arkwright invented his cotton-spinning machinery in 1760. At that time it was estimated that there were in England 5,200 spinners using spinning wheels, and 2,700 weavers—in all, 7,900 persons engaged in the production of cotton textiles. The introduction of Arkwright’s invention was opposed on the ground that it threatened the livelihood of the workers, and the opposition had to be put down by force. Yet in 1787—twenty-seven years after the invention appeared—a parliamentary inquiry showed that the number of persons actually engaged in the spinning and weaving of cotton had risen from 7,900 to 320,000, an increase of 4,400 percent.

Random example

The trend of employment change in the long-term rather than employment loss has continued through recent decades.



The above graph shows the U.S. unemployment rate since forty years ago. See the lack of any vast increase in it.

This is not to say that the loss of U.S. manufacturing jobs is desirable, and the shift from manufacturing to services in employment has some serious downsides. But there is not reason to expect it to cause extreme, permanent unemployment, as history illustrates otherwise.

Some may argue that sufficiently advanced artificial intelligence could someday make past history no longer apply. That's a more complicated topic, although a hypothetical benevolent AI society might recognize that people tend to be happiest when they believe they are accomplishing something. In the meantime, for the more immediate future before such an AI scenario, the trend of history is the best guide: Automation tends not to cause permanent unemployment.

[Drooling Iguana]

The thing with automation is that it's not a bad thing in and of itself. Really, it just improves the work invested:goods produced ratio, resulting in a net increase in wealth within the society. The problem is that, left alone, that wealth will concentrate in the hands of the people who own the automated equipment, increasing the gap between the rich and poor. Automation isn't a problem. Automation paired with unrestricted capitalism is.

[K. A. Pital]

I've already said that solving the problem of "unnecessary people" due to automation can be only done through socialism. If a limited circle of capital owners own the total amount of productive machinery in the world which can supply them well enough, they lose any need in the workers whatsoever.

Why, indeed, make them highly educated and try to create jobs which are outside of physical manufacturing, if physical manufacturing is fully automated and you only need so many people for service?

In such a scenario, either robotic facilities will have to be nationalized, or the following classes will rise: capitalist, serviceman and a huge mass of lumpenized workers.

It's technicaly possible to shift workers to creative intellectual jobs, after all, people transited from agriculture to industry and the transition to 90% intellectual labour share in an automated production environment is not impossible. But this requires a huge incentive from the resource owners to give and support needless manual labour workers in the time of their re-education (the shift can take several decades if not a full generation). The capitalists do not have that incentive since they are already well-supplied by their machines and servicemen.

[Uraniun235]

It's technicaly possible to shift workers to creative intellectual jobs, after all, people transited from agriculture to industry and the transition to 90% intellectual labour share in an automated production environment is not impossible. But this requires a huge incentive from the resource owners to give and support needless manual labour workers in the time of their re-education (the shift can take several decades if not a full generation). The capitalists do not have that incentive since they are already well-supplied by their machines and servicemen.

Couldn't we start to run into limits of human intelligence? A lot of people are basically dumb; is it possible that there will in the future be a large underclass of people who are simply unable, despite the best possible methods of education, to master the skills and knowledge needed to be employable in a job that a robot could not perform?

[K. A. Pital]

Couldn't we start to run into limits of human intelligence?

I think educational methods can be used as artificial selection. In the course of a few generations, even the most dumb would be striving to receive a proper education and skill. Besides, social programs to help the underclass must remain in place for a long time to come (also several decades). We also have technology to augment human intelligence in areas where it is weak, such as computers.

Creative jobs also require low-level technicians - for example, an architect only designs the basic outlines of a building - he needs a little army of ten technicians to flesh out the exact configuration of building, decorations, interior design specs, etc.

[PeZook]

Couldn't we start to run into limits of human intelligence? A lot of people are basically dumb; is it possible that there will in the future be a large underclass of people who are simply unable, despite the best possible methods of education, to master the skills and knowledge needed to be employable in a job that a robot could not perform?

Personally, I'm more worried that there simply won't be enough non-manufacturing, intellectual jobs for all those disenfranchised massess, even if we managed to provide all of them with a proper education.

Some of them can be sponged up by the service industry, sure ; More academics is always good ; But aside from thart, you need to create millions of jobs unrelated to menial tasks which is a gargantuan task.

Shipping them off to build offworld colonies may be the best solution

[Master of Ossus]

So either the Average Joe is going to be earning a pittance with a university level qualification in advanced engineering concepts, or they're going to have to get used to the dole.

I foresee an energy crisis hitting this progress first though, before we get to the point that everything is made by machines you really do need a college level education in just to maintain. Look at modern cars and how limited village mechanics and the like are in what they can do which isn't a simple mechanical replacement.

Henry Ford had the same concerns, but historically capital and labor have ALWAYS been complements. That's also held true in every major economic model, including ones as basic as Cobb-Douglas production functions, which show the relationship empirically. "Average Joe" will actually make more money given automation.

[Gerald Tarrant]

It's technicaly possible to shift workers to creative intellectual jobs, after all, people transited from agriculture to industry and the transition to 90% intellectual labour share in an automated production environment is not impossible. But this requires a huge incentive from the resource owners to give and support needless manual labour workers in the time of their re-education (the shift can take several decades if not a full generation). The capitalists do not have that incentive since they are already well-supplied by their machines and servicemen.

Couldn't we start to run into limits of human intelligence? A lot of people are basically dumb; is it possible that there will in the future be a large underclass of people who are simply unable, despite the best possible methods of education, to master the skills and knowledge needed to be employable in a job that a robot could not perform?

The Flynn Effect might actually be topical here. If you don't feel like reading the entire thing it can briefly be summarized as a general trend upwards in IQ, by an average of 3 points a decade. What's interesting and potentially topical is this

Some studies focusing on the distribution of scores have found the Flynn effect to be primarily a phenomenon in the lower end of the distribution. Teasdale and Owen (1987), for example, found the effect primarily reduced the number of low-end scores, resulting in a pile up of moderately high scores, with no increase in very high scores.[2] However, Raven (2000) found that, as Flynn suggested, data reported by many previous researchers that had previously been interpreted as showing a decrease in many abilities with increasing age must be re-interpreted as showing that there has been a dramatic increase in these abilities with date of birth. On many tests this occurs at all levels of ability.[3] Two large samples of Spanish children were assessed with a 30-year gap. Comparison of the IQ distributions indicated that 1) the mean IQ had increased by 9.7 points (the Flynn effect), 2) the gains were concentrated in the lower half of the distribution and negligible in the top half, and 3) the gains gradually decreased from low to high IQ.[4]

I don't think it eliminates the possibility of underachieving people being left behind; but the Flynn effect, if true, seems to offer some mitigation to those sorts of problems.

[Gerald Tarrant]

Edit: Oh I spoke a little to soon, it seems that the Flynn effect may actually have a peak

The Flynn effect may have ended in some developed nations starting in the mid 1990s. Teasdale & Owen (2005) "report intelligence test results from over 500,000 young Danish men, tested between 1959 and 2004, showing that performance peaked in the late 1990s, and has since declined moderately to pre-1991 levels." They speculate that "a contributing factor in this recent fall could be a simultaneous decline in proportions of students entering 3-year advanced-level school programs for 16–18 year olds."[23]

In 2004, Jon Martin Sundet of the University of Oslo and colleagues published an article documenting scores on intelligence tests given to Norwegian conscripts between the 1950s and 2002, showing that the increase in scores of general intelligence stopped after the mid-1990s and in numerical reasoning subtests, declined.[24]

Some have claimed that the Flynn effect was masking a dysgenic decline in human reproduction and that in developed countries the only direction that IQ scores will now move is downwards. However, even if there is a decline, then this may have other causes than dysgenics. Genetic changes usually happen relatively slowly. For example, the Flynn effect has been too rapid for a genetic explanation.[25] Researchers have warned that constantly greater exposure to industrial chemicals shown to damage the nervous system, especially in children, in industrialized nations may be responsible for a "silent pandemic" of brain development disorders.[2]

Also, if the Flynn effect has ended for the majority, it may still continue for minorities, especially for groups like immigrants where many may have received poor nutrition during early childhood.[citation needed]

However, William T. Dickens and James R. Flynn write in their 2006 paper that Black Americans reduce the racial IQ gap: Evidence from standardization samples that blacks have gained 5 or 6 IQ points on non-Hispanic whites between 1972 and 2002. Gains have been fairly uniform across the entire range of black cognitive ability.[26]

[edit] References

[PeZook]

It was obvious the Flynn effect couldn't have continued indefinitely - there are severe biological limitations on the human brain, most notably the way it stores and processes information.

As for the correlation between employment and automatization, it will hold true for a long time, but it breaks down when the labor investment needed to increase productivity approaches zero.

For example, if the "alpha" exponent in the function is zero (that is - added labor input does not lead to increased productivity), the function breaks and only capital and technology starts counting.

It will happen only if machines are able to produce, service and improve themselves, leading to a completely automated production process.

[Admiral Valdemar]

There are other peaks we've apparently passed now, too. The inventiveness of our species has peaked according to some studies, with less innovation going on for genuinely useful technology, instead, it's variations on things already invented. While this won't kill progress (yet), it does show that fears of an unstoppable march forward like some species-wide Moore's Law are somewhat unfounded if we're not capable of infinite inventiveness or intelligence expansion.

Not that it's much consolation in the here and now.

[Sikon]

As for the correlation between employment and automatization, it will hold true for a long time, but it breaks down when the labor investment needed to increase productivity approaches zero.

For example, if the "alpha" exponent in the function is zero (that is - added labor input does not lead to increased productivity), the function breaks and only capital and technology starts counting.

It will happen only if machines are able to produce, service and improve themselves, leading to a completely automated production process.

While not applicable in the immediate future, even if eventually self-replicating technology allowed almost zero human workforce per million tons produced, like quadrillions of tons output, such wouldn't necessarily mean the end of employment.

Even today, manufacturing is only a limited percentage of the total jobs in a country with mainly service sector employment like the U.S. Elimination of all service-sector jobs from teachers to bureaucrats to psychologists doesn't tend to occur in the foreseeable future.

Besides, if the self-replicating machines are not sapient, the industrial system needs the intellectual labor of humans to have maximum capabilities.

If the self-replicating machines include sapient ones, then there may be a group of artificial people who don't strictly need any assistance from baseline homo sapiens people. Such doesn't necessarily rule out employment for the latter, though. In the current world, the group of people which calls itself the United States doesn't strictly need anything from the people in a number of tiny countries, but that doesn't prevent business arrangements.

A sufficiently advanced sapient AI or upgraded post-human individual might be better at doing any particular job than a baseline human. That doesn't necessarily mean the latter couldn't possibly find employment. In the current world, the average U.S. farmer produces much greater crop yields than the average third-world farmer. But the work of the third-world farmer still produces something of value, and, however limited, it is typically as much (actually more) beyond the food he needs to survive than it was centuries ago.

That's related to the idea of comparative advantage, like this example:

A country can have an absolute advantage in the production of a good without having a comparative advantage. [And an entity like a country or an individual can have a comparative advantage despite being less efficient in absolute terms]. Comparative advantage is what determines whether it pays to produce a good or import it. Assume that there are only two goods, cars and computers, and one productive resource which is some composite of land, labor, and capital. Assume also that producing 100 cars requires two units of the productive resource (PR) in the United States and four units in Brazil, and producing 1,000 computers requires three units of PR in the United States and four in Brazil.

[... In this example,] Americans have an absolute advantage in producing both cars and computers.

It may seem that Americans can realize no gain by trading with Brazilians. Why not produce both cars and computers here? Because it costs more to produce computers in the United States than in Brazil [not in absolute terms but in opportunity cost]. All costs are opportunity costs. The cost of producing computers is the cars that could have been produced. Using the three units of PR required to produce 1,000 computers in the United States requires sacrificing the production of 150 cars. Using the four units of PR required to produce 1,000 computers in Brazil requires sacrificing only 100 cars.

So even though Americans have an absolute advantage in producing computers, Brazilians have a comparative advantage. Compared to what has to be sacrificed, Brazil produces computers for only two-thirds as much as it costs in the United States. The United States, of course, has a comparative advantage over Brazil in the production of cars. Producing 100 cars here costs 666 computers, while producing 100 cars in Brazil costs 1,000 computers.

Clearly the United States benefits from specializing in cars, which it produces more cheaply than Brazil, and trading with Brazil for some of the computers it produces more cheaply. If, for example, the United States produced both cars and computers it might devote 70 units of PR to car production and 30 units to computer production, yielding 3,500 cars and 10,000 computers. If Brazil produced both products, it might devote 56 units of PR to car production and 24 to computer production, yielding 1,400 cars and 6,000 computers. On the other hand, by specializing in their comparative advantages, the United States can produce 5,000 cars and Brazil can produce 20,000 computers, or a total of 100 additional cars and 4,000 additional computers.

example

In the future, perhaps one day any non-upgraded human worker might have inferior productivity to some AI or posthuman workers. But keep in mind that almost any individual human worker already has inferior productivity to some other person (e.g. 99% of electricians aren't the best 1%), such as a relatively unskilled worker versus a skilled worker, yet even unskilled workers can still do work that's worth more than the food they eat.

Besides, short of a scenario with a dystopic society that has people genocided or dying of starvation, people consume food, housing, and more anyway. The society only gains by having people employed instead of having them consume the same resources while producing nothing.

Outside of pessimistic scenarios, a hypothetical future society with almost unlimited self-replicating industrial production would be benevolent and intentionally aim to ensure appropriate employment is available for everyone. For example, if you're converting quadrillions of tons of available raw materials into industrial production, sparing the miniscule portion of that sufficient for paying wages to people and providing great accomodations is trivially easy. What most approaches utopia would be a complicated question, but it would seem to involve less hours of work than today while not having utterly unproductive citizens either, being somewhere in between.

Of course, one has gotten into a far future discussion here, while my past post on historical trends over past decades is more relevant for the near-term foreseeable future: For now, the ratio of human labor requirements to economic output remains very far from zero, automatically demanding employment.