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Sorry...is it labour-augmenting technology? Will it change the shape of capital/labor
isoquant of production?
Do you assume imperfect comperition and a elastic demand function and what about eventually for the markups?
And what about excess capacity? Do i have to considerazioni some slack?

beneath: do I need to make any assumptions at all about those things? I'm the one asking the question: "Why doesn't a sub-group form a coalition and go back to the old technology?" If you think some of those things might help you answer my question then go ahead.

"Suppose you have an economic model with (say) two types of people. Let's call them "workers" and "capitalists". OK.

Now suppose you tell me that a new technology comes along that both reduces workers' wages and reduces capitalists' rate of profit."

I would agree that the two-types model will not support the hypothesis offered. It would take at least a four-types model where there would be two types of workers and two types of capitalist. A four-type model would revert to a classic competition model where a new technology would displace an older technology.

Now there is another possibility that we might consider. (I am thinking about climate change here.) What if the new technology is a tax on wages and profits, designed to accomplish a goal? (a carbon tax?) The two-types model could still apply but I think there would be serious questions about how to achieve a fair distribution of hurt.

Roger: I think three is enough. But you need all three to be able to produce goods.

Climate change would also work (in principle). If there are two types of people, but the new technology causes a negative externality, that could do it. (Implicitly, the environment is the third common property resource).

Roger: Interesting, do you mean it is a prisoners dilemma for the workers and capitalists? So their sub groups are better of but as a whole they are worse off? There is of course the a need for the third group, rentiers (landlords), which reaps the benefits?

What if the technology leads to an increase in competition?
There are lots of small retail chains with protected markets and then Walmart or Amazon swoops in. Consumer gets served lower prices (and probably higher quantities), but the rate of profit declines and . You can't put the genie back in the bottle because the new business model has its vested interests. Technology breaks down implicit collusion.
I guess in this example overall welfare is improved and in aggregate either *real* wages or profits grow, but it won't feel that way for many.

Jussi: "...do you mean it is a prisoners dilemma for the workers and capitalists?"

That's why we need a General Equilibrium theorist to explain the link between the core and competitive equilibrium. Because competitive equilibrium is in the core, so that can't happen. You need something like externalities or monopoly power, or something.

Are people really suggesting that robotization is bad for capital as well as labor? I thought the usually story was that it would shift the distribution toward capital to an extent that outweighs (in terms of its effect on labor) the increase in overall income. I might be able to tell a story where it's bad for capital, too, and good for land, broadly understood. Something like: robots are cheap to produce, and their marginal product goes down before you've satisfied the demand for stores of value, so people buy land instead. (Only the market for land has failures, and land is too risky in terms of its consumption value, so secular stagnation, blah, blah, blah.) Not sure if that really makes sense, but that's the direction I would tend to go if I were trying to argue that robots are bad for both capital and labor.

Andy: well, if you argue that robots have been the cause of falling real wages, you need also to explain why real interest rates have been falling too.

Assume three factors of production, and that robots are labour-augmenting and capital-augmenting technology. So they make land rent rise. I have no idea whether that assumption is empirically correct, but you need something like that if you want to use robots to explain recent history.

But people keep talking about robots, never talking about land, or even thinking about the blocking coalition question. It's partial equilibrium, all the way down.

"If it reduces both workers' wages and capitalists' rate of profit, why would workers and capitalists ever adopt that new technology?"

What about air conditioning? The profits of the first adopters may have gone up temporarily, but as it became common, it was a cost that could not be fully passed along to customers, no?

""Stop right there!"" - isn't that Okishio's Theorem right there? I.e. Marx was wrong. But of course Marxists didn't think much about land either.

" "the core" and its relation to competitive equilibrium" - that one's the Edgeworth Conjecture. Every competitive equilibrium is in the core. If the number of agents goes to infinity then, under some assumptions, the core shrinks down to the set of competitive equilibria. It doesn't matter how many or what factors you got.

To be more precise about the Edgeworth Conjecture, the core shrinks down to competitive equlibria if either 1) there's a continuum of agents (that one was proved by Robert Aumann I believe) or 2) the way you increase the number of agents is through "replication". You start with 1 of each of N types of agents and then double the number of agents of each type, etc.

There might be some theorems about the more general discrete case where you're just adding agents of various kinds willy-nilly but it's been a long time since I've peaked at this stuff.

Ooops, I see that some of that is discussed in the pdf you link to. Here is Aumann's paper (I'm pretty sure this has been extended to production economies but don't quote me on that)


And I guess the replication version of the proof was by Debreu and Scarf

Min: But AC makes workers and/or capitalists (or both) better off, presumably. Now it's true that measured wages may fall, but workers' standard of living presumably rises.

notsneaky: "...isn't that Okishio's Theorem right there? I.e. Marx was wrong."

I confess I did have Marx in mind when I wrote that bit, and I vaguely remember Mark Blaug arguing something like this, in his history of thought book. Hadn't heard of Okishio though. And I think it's just one example of a more general theme.

I don't think I need Edgeworth's conjecture. I think all I really need is that CE is inside the core. And even if it's not CE, I think the onus is on whoever says that robots will reduce wages/jobs to explain why workers couldn't form a coalition and secede. Who would they need to persuade to join them in reverting to the old technology? Is it capitalists, or landlords, or skilled workers, or who? (I'm not explaining this very well, because non-economists will think I'm talking about unions going on strike.)

I'm probably not the right person to argue against this since I tend to agree, but I think the thinking goes something like this. There's a (R)obot owner, a (K)apital owner and a (L)aborer. If L and K get together then they produce 1 unit of output. If R and K get together they produce 1+X units of output (robots more productive than workers). Each factor produces nothing on its own. Then the coalition {K,L} cannot block the coalition {K,R} which splits the pie 1+epsilon for K and X-epsilon for R.

Of course the problem is that we've left out the grand coalition {K,L,R}. If workers are redundant with robots - essentially, the production function is Leontief - then it's the same as above. But suppose {K,L,R} produces 1+Z units of ouput where Z > X. Then the grand coalition gives 1+2*epsilon to K, X-.5*epsilon to R and 1+Z-1-2*eps-X+.5*eps=Z-X-(3/2)*eps to L (i think that's right). The grand coalition blocks the capital-robot coalition so {K,R} is not in the core (nor is {K,L}). And then you're right.

That's theory. But of course as Brad DeLong points out (in the original post that Serlin is referring to) some factors DO get pushed out and more or less cease to be factors. Like the horse. Although I think rather than talking about "peak Horse" Brad should've talked about "peak Typewriter" or something since it'd make it clearer that it's something which gets accumulated over time that gets pushed out. I think this needs a more dynamic set up.

[edited by NR to fix (I think) math/typo]

It should be Z-X-(3/2)*eps above.

Yes, yes. "Land." "Rent." But those are just words, Nick. What happens if we use other words (like patents, taxes) to describe "the same things" when they happens elsewhere?

So intellectual property is to land ownership as robots are to soil. Intellectual property is a monopoly granted by the state. Strictly speaking, it is a form of taxation -- a license granted by the state to collect (and keep) revenues.

Why are property owners AGAINST taxation when they are called upon to pay it but FOR taxation when they are privileged to receive it (in the form of rents)?

It seems to me that recent stagnant wages and soft employment, in conjunction with low interest rates, present a puzzle whether or not you want to tell a story about robots. You can give a business cycle explanation (we had a really deep recession and haven't fully recovered), but that is neither here nor there as far as robots go: it's more or less equally compatible with whatever robot or non-robot story you want to tell about how the equilibrium might have changed, since it presumes we're not at the equilibrium. And there are various stories one can tell about how robots might interact with the business cycle.

notsneaky: very good comment. [Check my edit to be sure I fixed your math the way you wanted it.]

But who are the "robot owners"? Are they the people who own the right to use the robot technology?

BTW: here is my old post Production of robots by means of robots where I attempted to build a GE model with robots. (I implicitly assumed the robot technology was a public good.)

Sandwichman: but "wages" are mostly rents too, to roughly the same extent that land rents are rents. Unimproved land and labour aren't much use in producing goods, but some land and some labour can be improved to be much more productive than other land or labour.

Andy: Hmmm. Part of it is clearly the business cycle, but not all of it. Yep. My guess is that land has to be a big part of the story.

Aren't you fixing output here?

Imagine we invent Star Trek replicators, which can replace any arbitrary physical-good production. Initially, this is adopted at the firm level.

Any individual firm will have every incentive to adopt replicators. Their cost of labour reduces dramatically, since skilled workers can be replaced with literal button-pushers. Their cost of goods sold also goes down, as whatever intermediate good they were using is replaced with just the raw energy cost of replication, and by assumption replication is the most efficient manufacturing process.

However, the firm owner cannot maintain their profits in the face of other firms adopting replicators. After the secret gets out, replicators become widespread and the cost of any good falls to approximately its lowest physically-admissible level.

In monetary terms, everyone is poorer. On the other hand, in real terms everyone is richer -- their physical needs can be trivially sated. Have returns on labour and capital gone up or down?

Majromax, that's pretty much exactly what Okishio's theorem disproves. If a factor-saving technique is adopted, then either profits rise or wages rise, it cannot be any other way.

(Where do replicators come from? Are they self-replicating?)

Majro, notsneaky: this isn't about monetary aspects. NGDP could go down, if the central bank responded in a daft enough way, or if we don't need trade any more so all production is home production.

"but 'wages' are mostly rents too, to roughly the same extent that land rents are rents."

All the more reason to abolish wage labour, Nick.

If we ignore the incidental fact that human workers are subjects and treat their labours strictly as commodities, then yes, we can admit that wages are "mostly rents" as long as we also admit that by "rent" we might refer to either a positive or a negative amount. Sort of like a tax credit! We might even call this extraction of negative rent "surplus value" (provided the term hasn't already been adopted by some other analysis).

Wait! Are you confessing that you are a covert Marxist? (If only to get around a few tight corners regarding rent and taxation.)

Are you talking about nominal wages? I mean, if the new technology increases productivity the nominal values such wage and profit can fall, but the ratio wage/commodity and profit/commodity will go up, right? Isn't that desirable?

Maybe I'm being nonsense here, in that case I'm sorry.

I think they are important question.
Let's imagine a Solow-like model with a neutral technology, I mean a tech that doesn't change the shape of isoquant, namely y=A(t)f(K,N). A(t) is a moltiplicative factor that, for sake of simplicity, let's assume increase at a exogenous and costant rate equal to "g".
Solow showed in his 1956 paper, both capital and real wage per worker increase indefenetly.
If we assume another type of technology, namely a labor augmenting tech, production function is y=f(K, A*N) where A is supposed to grow at exogenous costant rate "g".
Here we have real wages increasing at the "g"rate and Y and K at "n+g" rate where n is labor force growth rate.
Even if we assume a very basic Solow model without technology of any sort (i.e. A=1), in a perfect competition market we have that the distributive quote of labor (and capitalist's profit) equals  the labor (capital) elasticity of product. Ex post their sum equals one, anyway.
If we are ongoing to the steady state, and production function shifts upward, whatsoever reason, labor elasticity increases and so do both real wages and labor distributive quote.
Anyway I find it difficult to make the question up in a "pure" classic macro model with perfect competition, too.
With a vertical AS and a loglinear cobb douglas-like aggregate function (y=(1-a)k+an) where k=log Capital and n=log Labor and a is the parameter), an upward shift in the aggregate function (namely a increase in marginal productivity of capital, as technology improves) has a deflationary effect, given the level of AD components, but the parameter which define the labor demand are influenced by those of the aggregate production and labor demand shift upward and its slope increases.
This results in a higher real wage, again.
The only case I can imagine for your question to be realistic is the classical ricardian case of labor applied to a scarse input as land is. But in our post-Ricardo world I think aggregate production function implies less and less use of land than before.

I think that the problem in every case of these is that nominal wage are flexible and models imply full employment of factor.
If we want something to happen we should introduce some rigidity like nominal wage and labor supply rigidities. But in that case we are leaving General Equilibrium models and enter disequilibrium world.
But that puzzles me because your question is addressed to general equilibrium theorist.

Not sure this is an equilibrium story, but one of falling capital costs increasing profits from new technology but also increasing existing capital depreciation, flat to falling prices, but a distributional story, where some, the unemployed and unskilled, are worse off, depending on whether work was better or worse than idleness, others, the employed, are about the same, and a sliver, are spectacularly better off, so much so, it is all they can do to prevent undercutting themselves and are willing to sit on troves and accept no return to avoid doing so.

Bananaman: real wages. better yet, welfare. Yep, nominal wages and prices could go down, if the central bank holds M fixed.

beneath: yep, as a general equilibrium theorist, you are finding it hard to think up an example where *both* wages and profits would fall, without introducing land into the model. Which is my point. That's how it should be. So if someone told you that new technology was causing real wages to fall, and you also observed falling interest rates, you would be rightly suspicious of their explanation.

This is the macro on profits. You may find interesting (not micro though) :)

If we're going to talk about the empirics, we should also note that productivity seems to have slowed considerably (but it may be mismeasured). Offhand, this seems hard to square with any story in which robots are taking over, though maybe productivity would be slowing even more without the robots, or maybe the process of replacing workers with robots involves some kind of adjustment cost that temporarily reduces productivity. Or maybe we're reaching the point where the scarcity of land really starts to drag down productivity.

Bob: thanks but no thanks. That post is totally irrelevant to this post, as well as being wrong.

Andy: Hmmm. Another good point. Unless it's being mismeasured, somehow??


Maybe nitpicking but your condition:

"Now suppose you tell me that a new technology comes along that both reduces workers' wages and reduces capitalists' rate of profit."

Did you mean reduces the growth rate of worker's wages and the growth rate of capitalists' profit?

If so, let me offer the technology of birth control. It may not affect the growth rate of either the individual worker's wages or the individual capitalist's profits but it will over time reduce the growth rate in the quantity of capitalists and workers (and thus the growth rate of worker wages and capitalist profits as a whole).

"And if they did stupidly adopt it, why wouldn't a sub-group of workers and capitalists split off from the main group, go back to the old technology, and earn higher wages and higher rate of profit?"

Because the higher wage and profit growth rates are achieved by the group as a whole, not by the individual members. If the sub-group had a collective mindset, then perhaps they would shun the new technology assuming they as a group were unconcerned with resource limitations.

"note that productivity seems to have slowed considerably (but it may be mismeasured). Offhand, this seems hard to square with any story in which robots are taking over"

It must have taken some time for tractors to replace horses.

I suspect it's the old guys are slowing down and retiring faster than people are figuring out how to replace them with robots. Eventually we'll either run out of boomers or the robots will catch-up (or some combination of that).

Krugman likes to point out that computers didn't show-up in productivity for a long time after they became ubiquitous. It took time to figure out what to do with them (turns out to be big box stores). Could be that we're in that adjustment/learning period for robots.

What about disequilibrium processes?

E.g. say that we have some CRS technology, and then a new technology is introduced -- software -- where someone invents a wordprocessor and can sell a copy to anyone else for a positive price but 0 marginal cost to the seller.

The "capital" in this case is the source code, that must be written. This gives a large return on capital as everyone buys a copy of the wordprocessing software.

Then, as competition sets in and more people drop out of the old economy and create their own wordprocessors to sell. As this happens, the total return to capital falls, because now there are N copies of the source code that need to be created, instead of 1 copy, but each person still has one copy of the wordprocessor (they are all assumed identical). Additionally, N people drop out of the old economy to work on writing software so total output declines.

The terminal state would be such that the returns from writing source code are the same as those from the old old technology, but a large proportion of the labor force will have abandoned production and will be writing source code, but the economy as a whole will not get anything out of it, since they'll each continue to have 1 copy of the wordprocessing software.

It's not clear how the economy would leave this bad equilibrium, other than creating a monopoly on writing word processor software and making it illegal for others to compete in this market.

Patrick: It sounds very plausible to me that it takes a very long time to figure out how to use new technology. But if that were the case here, the effect wouldn't have shown up on wages either, if it doesn't show up in productivity (presumably).

rsj: sounds interesting, but I haven't had coffee yet. Like a rent-seeking equilibrium with unnecessary duplication?

But (I think) you are talking about a one-shot innovation. An ongoing sequence of such innovations might be more plausible.

Frank: "Did you mean reduces the growth rate of worker's wages and the growth rate of capitalists' profit?"

No, I meant levels.

As somebody who read your old article on robots here is my take on the issue:

1) If we are specifically talking about this scenario, I think words like "labor" and "capital" start to lose their traditional meaning. It is impossible to disentangle one from another in any practical example. Even the simple act of buying something, waiting a second and then selling it can be ether viewed as return on capital for duration of one second, or produce of one second labor using advanced capital. Alternatively, spending 1 minute to hire somebody who manages your assets for the rest of your life can be also viewed as return on capital or very advanced job.

2) In "dismal" future there will be people able to use advanced capital in form of robots to reap vastly greater rewards then some other people on Earth. I don't see how is this different from any other era in human history. We currently have a world where we can have incredibly rich people in US living a comfortable modern life earning $30,000 a year using advanced capital and they live "alongside" newly discovered people from hunter/gatherer tribes that would be unemployable in the current market (mostly because they would probably die from common flu) and who have to fear being eaten by wild animals, die of "curable" sickness or even hunger every second of their lives.

So in short, we already have a situation where if you are lucky and you are born in rich country you get to live a comfortable life enabled by advanced capital. If you are unlucky and you are born in a bad place you are quite likely to die before age 1.

JV: 1. I think of raw labour and raw land, and capital as the time-structure of production, and technology as a set of blueprints. A new technology comes along that lets us convert small quantities of land and labour into machines that are close substitutes for labour.

2. It's not obvious to me either why robots would necessarily increase inequality. Cars initially increased inequality (probably) then reduced it as they became cheaper. Self-driving cars (cars+robots) will probably do the same.

Perhaps we could get falling real wages and falling interest rates if society's savings preference shifts in response to the technology.

Consider just-in-time inventory systems taken to their natural limit. Because of a process improvement, businesses no longer need to buffer as much inventory, reducing their overhead and (in partial equilibrium) raising their profits. However, workers who are paid a piece-rate do not see their productivity change and thus see no change in wages.

At the same time, employment that was once fairly steady based on buffered inventory becomes less predictable and more feast-or-famine. Workers seeking to smooth consumption need either easy access to credit or a stock of savings to draw upon. Since credit markets are imperfect (banks can't force repayment in cases of bankruptcy), this means in turn workers will collectively seek to accumulate savings as (at minimum) collateral.

Where do these savings go? Back into investment, but there has been no improvement on the margin. This extra investment necessarily takes the form of marginally less-productive investment, lowering the natural real (marginal) rate of return.

Anyways, just another thought. In fact there was a time where there existed a technology that could cheaply replace human labor. This technology was called slavery. There were societies like ancient Sparta where there were 7 slaves for every legal citizen.

If there is any pattern, then economies that relied on slaves spent most of their time making sure slaves remain subjugated. So yes, if we have economy where robots can replace people then we will leave people with "work" of managing robots. If we can have robots even for that then you have to have people who manage robots who manage robots in the same way you could have slaves that managed other slaves, but ultimately some citizen had to give even those some orders - at least on high level like work this land and bring this much wheat to this granary. Now if we have robots for everything there is no "need" for property - not in a way where private property ensures that all economic actors remain incentivized to maximum production.

Majromax, but if investment goes up then capital goes up (that's how return goes down) which makes the wages go up not down (at least with constant returns technology)


Actually, I think a "defection" is entirely plausible. Imagine society divided into the robot "haves" (the owners of robots) who live in utopian bubble cities, walled off from the hard-scrabble lives of the "have-nots", who use old-fashioned capital + labor to make a living.

You can even imagine a fairly simple model of this, where there are two types of capital, one used in a standard C-D production function z * K^a * N^(1-a), and one "robot" capital z_r * K_r. Now suppose z_r increases over time. Eventually you reach a point where it's not worth it to work or own the old capital. What happens is that at some level of z_r, everyone chooses N = 0 (obviously the marginal disutility of labor can't approach 0 as N -> 0).

Now suppose that (for some reason) a subset of people are excluded from owning robots. Then they will accumulate old-fashioned capital and supply labor. Essentially society has bifurcated into the robot-owners and the non-owners.

(The more extreme version is that these people don't own *any* sort of capital. Then it may not be worth it for the capitalist robot owners to hold any old-fashioned capital, since they need to at least pay subsistence-level wages. Then they either all starve, or fall back on even older forms of capital that they still are allowed to accumulate, like stone spears.)

(p.s. I started writing a model like this for a problem set a year ago, but then decided it was way too hard for my students. But I thought it was pretty cool.)

These sort of discussions always come across as arguing about angels on a pinhead.

- Still stuck within the idea of 'solving' a set of mathematical formula.
- Still stuck in the idea that there is some sort of equilibrium to aim for.
- Still stuck in the idea that there is some magic curve to be discovered.

None of that is true. All this discussion is merely curve fitting aggregated data.

The pre-condition to being allowed to discuss this stuff should be that they have worked in the financial markets and magically 'curve-fitted' enough aggregate data to gain a persistent advantage. Once they have retired with millions in their bank account, then I'll believe they can determine a useful 'curve'.

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