(Sorry about the title. The devil made me write it.)
What are we afraid of? Let's think about the worst-case, nightmare scenario for the distribution of income.
Assume that all capital is robots, and robots are perfect substitutes for human workers. One robot can produce everything and anything one human worker can produce. And that includes producing more robots.
And assume that every year the technology of robot production improves, so that it takes less and less time for one robot to produce another robot.
That sounds nightmarish, right? Because robots will get cheaper and cheaper, and drive down human wages?
Well, no. They won't. Or rather, it all depends. It depends on whether we add other forms of capital, or land, to the model.
Labour and Robots only.
Let's start out by ignoring land. And the only form of capital is robots. You can produce everything with just human or robot labour.
The production function is: C + I/a = L + K and Kdot = I
where C is consumer goods produced per year, I is robots produced per year, a is a parameter which increases over time as technology improves and robots get easier to produce, K is the stock of robots, and L is the number of human workers.
There's another way to look at the parameter a. It's the rate at which robots can reproduce themselves if they aren't producing consumption goods instead. (I'm assuming that robots can't, er, reproduce and make chewing gum at the same time.)
Let's measure wages in terms of consumption goods. Because consumption is what people care about. Robots and humans earn the same wages. Since both robots and human workers produce one unit of consumption goods per year (or per day, or per hour, or whatever) their Marginal Products and wages will be one unit of consumption goods too.
W = 1
In this simple model, improving technology for producing robots has no effect whatsoever on wages.
Not at all nightmarish, is it?
It will however have an effect on the rate of interest.
We know that the price of a robot in terms of consumption goods will be 1/a. (That's because I have assumed a linear PPF between consumption and robots, so the opportunity cost of producing one extra robot is always (1/a) units of consumption).
Suppose a is rising over time, so (1/a) is falling at rate g. We know that each robot earns 1 unit of wages per year. So the rate of interest (measured in terms of consumption goods) Rc must equal the rate of return on owning a robot, which is annual robot wages (1), divided by the price of a robot (1/a), minus the rate of capital losses from the falling price of robots, so:
Rc = a – g.
In this simple model, the rate of interest is determined by the rate at which robots reproduce, and by the rate of change of the rate at which robots reproduce. The bigger is a (the quicker robots reproduce) the higher the rate of interest. The faster a is rising (the quicker the rate of technological change in robot reproduction) the lower the rate of interest. If g is positive but constant, the rate of interest will be rising over time.
It's simpler if we measure interest rates in terms of robots, Rr, because then we can ignore the fact that the price of robots will be falling over time. Since one robot can produce a robots per year,
Rr = a
The interest rate, measured in terms of robots, will be rising over time if technological change increases the rate at which robots reproduce.
Labour and Robots plus other Capital.
Robots are a form of capital goods that are perfect substitutes for labour. What happens if we introduce a different form of capital that is a complement to labour?
The simplest way to do this is to assume there is a one-year lag between humans and robots doing the work and the extra consumption and new robots being produced. So the production function now becomes:
C(t) + I(t)/a = L(t-1) + K(t-1)
The wage, measured in terms of current consumption, now becomes the present value of the (future) Marginal Product of Labour:
W = 1/(!+Rc)
The rate of interest Rc must equal the rate of return on owning a robot, which is the wage of a robot 
divided by the price of a robot (1/a), minus the capital losses from the falling price of robots, g:
Rc = a/(1+Rc) – g
I think (somebody please check my math) that Rc, as before, is increasing in a and decreasing in g. That means that if a is growing at a constant rate, the rate of interest will be rising over time.
And, since W=1/(1+Rc), that means that wages (in terms of consumption) will be falling over time.
OK. That's a much more nightmarish scenario. For those who only own their own labour.
But it's not very realistic, for recent years, because real interest rates (deflated by the CPI) have not been rising. They have been falling.
Labour and Robots plus Land.
OK, let's scrap the lag in the production function, but put land (Natural Resources, N), along with labour plus robots, into a Cobb-Douglas production function:
C + I/a = (L + K)b.N1-b
It's a constant returns to scale production function, but holding land fixed we get diminishing marginal returns to labour plus robots. (I have implicitly assumed, by making the PPF between C and I linear, that producing consumption goods and robots are equally land-intensive.)
The human (or robot) now earns a wage equal to the Marginal Product of Labour:
W = b(N/(K+L))1-b [edited to fix math error spotted by Kathleen.]
As the number of robots increases, the wage gets driven down by diminishing returns, just as in Malthus/Ricardo, except it is the robot population that is increasing over time, if people save and invest in building more robots.
With a little bit of math, we can show that human plus robot workers earn a constant share b of total output, and landlords earn the remaining constant share (1-b). But as more robots are built, and the robot/human ratio K/L rises, human workers earn a decreasing share of b. And as total output expands, land rents per acre rise.
And the rate of interest is:
Rc = ab(N/(K+L))1-b – g [edited to fix math error]
To figure out whether Rc is rising or falling over time we need to figure out if the growing stock of robots is making the denominator grow more or less quickly than the numerator of the first term. And that will depend on people's consumption/savings choice, which in turn depends on their intertemporal consumption preferences. The math is beyond me, but I'm pretty sure the effect could go either way. (To figure it out, we need an additional equation representing intertemporal preferences in which Rc is an increasing function of the growth rate of consumption.)
Anyway, if you are looking for a nightmare scenario that is at least vaguely realistic, robots alone won't do it. I think you need to go back to Malthus/Ricardo, and put land back into the model.
That's what I was trying to say way back in this old post. I've just said the same thing with more math.
(I don't do micro, dammit, or growth theory (which is really micro, despite what the macro textbooks say). Why am I doing micro?)
Worthwhile Canadian Initiative 
Nick,
Instead of these mathematical models where it’s always hard to tell when the underlying critical assumptions diverge from reality, why don’t we try an elementary analysis of a hypothetical world without land rent?
Suppose we invent a technology that enables us to open portals towards an infinite number of uninhabited parallel Earths in other dimensions, at negligible cost. Now if you want oil, you just need to pay the cost of the drilling machines and labor, teleport them for free into the empty Arabian desert of a parallel Earth, and oil will be flowing through the portal. Or, if you want a house, you just pay the contractors to go to a parallel world with the materials and build it, and afterwards you commute through the portal from home to wherever you want to go.
Imagine now this no-land-rent economy at a technological level otherwise similar to the early 21st century developed world. What would be the possible consequences of the robot scenario?
I’m very busy right now, but I’ll post my own analysis later tonight.
Nick, back to your point that “oil is land, too”: the math gets quite a bit more complicated once you start trying to factor in greenhouse gas emissions and climate change scenarios. Also, you’re not going to be able to use your Cobb-Douglas if you actually want to consider the interdependency of the inputs (Costanza, Ayres and Kneese) rather than pretending they are independent, which of course they are not.
Before indulging in all that complicated math, though, it might be worthwhile contemplating that the machinery question and the fuel efficiency/rebound paradox are two sides of the same coin. Malthus was “wrong” about peak population because of peak coal and Jevons was wrong about coal because of petroleum. Maybe Hubbert will be wrong about peak oil because of climate change — which will make Malthus right about population after all!
Vladimir: Two thoughts:
1. That hypothetical world is rather like my first model.
2. The real world is partly like that model, if technical change is “land-augmenting”, which to some extent it is. Stick another technology parameter in front of N, and suppose it increases over time. That’s how we have driven back the Malthusian spectre. So far!
Here’s the proposition, the creation of wage-labor “jobs” is coupled with the consumption of hydrocarbon-based fuel. This is an historical-empirical fact that anyone can confirm for themselves by looking at the data for the last 200 odd years. It is neither rocket science nor brain surgery.
Although it may be theoretically possible –“in principle” — to uncouple or decouple job creation from fuel consumption, no one has done it or shown how it could be done. It is science fiction. But economists persist in assuming that it will happen “automatically,” so to speak, through market-generated technological substitution. Or, in plain language, someone will invent a perpetual motion machine. That isn’t even theoretically possible!
The Robots symbolize the age-old anxiety about machinery displacing human labor, throwing people out of their jobs and thus depriving them of their livelihood.
The Rift refers to the metabolic rift between town and country, between industrial processes and natural rhythms, biomes and landscapes. Even a good thing can become too much of a good thing toxic in the wrong place at the wrong time.
The Rebound is a descriptive synonym for what is otherwise known as the Jevons paradox, the idea that increases in the fuel efficiency of machinery will paradoxically lead to increased consumption of the fuel because it will make the fuel, in effect, cheaper. And, as Dorning Rasbotham proclaimed 232 years ago, “A cheap market will always be full of customers.”
The robot and the rebound are tied to each other continuously in a kind of metabolic Möbius strip. On “one side” are fuel efficiency and consumption and on the other are labor displacement (by machinery) and re-absorption (through market extension). But an ant — or an unemployed worker — crawling along this strip would eventually return to its starting point only after traversing both sides.
http://ecologicalheadstand.blogspot.ca/2012/12/the-robots-rift-and-rebound.html
Sandwichman: one quick thought: the “rebound effect” is just another name for “demand curves slope down”.
I feel OK with my model if N is farmland or building land. I feel much less sure it’s OK if N is oil.
Nick, the most nightmarish scenario is the one where cost of reproduction of robots is lower then the subsistence wage. It takes many years of feeding and sheltering and training until your average human becomes productive, and then there is more of the same. If robots could do exactly same things for lower costs than is the level of human subsistence, then we end up in a potentially nightmarish scenario. People will become horses of this dystopia – too expensive and too much of a hassle to bother using for a real work.
Nick:
But what if robots are not just perfect substitutes for humans, but increasingly superior to humans, not just in volume of output and productivity, but in quality – in a non-substitutable way?
Say like car makers don’t let human welders near their cars, because robots are welding so much better. Or Apple won’t allow humans to assemble the iPhone 6, because machines are orders of magnitude more precise.
If that happens – and every sign is telling us that it’s happening on an increasing scale – then the friendly co-existence of robots and humans in your equations ends quickly and possibly exponentially.
In that case human labor will not compete against a rising robot population size, but will compete for a rapidly shrinking pool of jobs that robots cannot do yet or which humans can still do.
The “nightmare scenario” is then for most of humanity to be in that large group – with wages eventually driven below subsistence.
The Hunger Games, anyone?
JV: But a falling price of robots does not necessarily mean a falling wage for robots (or humans). Look at my first model, where the cost of reproducing robots keeps on falling but has zero effect on the wage. Instead it causes the rate of interest to rise.
Nick: Yep. And “demand curves slope down” is just another name for “a cheap market will always be full of customers.”
Anon: build a model which shows that (without land). Until then, I will say you are wrong.
Nick:
Put differently, the “nightmare scenario” is not humans competing against robots and the rent of land.
The nightmare scenario is a growing human population competing not against robots, but against other humans, for the rapidly shrinking pool of jobs that robots have not monopolized via their superior work quality yet.
In other words, the worst effect of robots is not price, but the (relative) erosion of the human skill set that can be used by humans to get a job – any job.
Anon: until you buil;d a model showing that, I still say you are wrong. Suppose someone owns a robot that can produce everything they need and want. OK, they buy nothing from the rest of us, but they can’t sell anything to the rest of us either, because we can’t afford to buy it. So waht? That person is better off, but the rest of us just keep on trading among ourselves, doing as well as we were before.
That’s why you need to build a model. Because until I built that model above, showing people were wrong, everyone (I conjecture) was saying “If robots get cheaper to produce, that means the price of robots will fall (correct), and that means wages will fall (incorrect).
Nick, a simple model would be something like:
C_h = L/r
C_h is consumer goods produced by human workers. L is human workers. “r” is the “robot quality factor”, which increases in time as robots improve.
Robots produce:
C_r = K r
Where K is the stock of robots. Let’s keep K constant for simplicity, and only increase r as robots are getting better.
Robot productivity goes up in time, human productivity and wages go down.
The “nightmare”: if r is high enough for human worker marginal product to drop below subsistence.
Anon: “C_h = L/r
C_h is consumer goods produced by human workers. L is human workers. “r” is the “robot quality factor”, which increases in time as robots improve.”
Stop right there. You have just assumed that the new technology makes human workers less productive than before. If that were the case, why wouldn’t human workers say “Stuff this, let’s go back to the old technology, and let the robots do what they want!”?
Nick: you are right, the “rest of us” will be trading amongst ourselves mostly – with inferior goods and almost no ownership of anything of value to owners of robots, such as land or resources, right?
That is a “nightmare scenario” below subsistence, isn’t it?
Nick: Your model is correct that falling robot prices don’t mean that wages will necessarily fall. But what actually happens to wages depends on exogenous variables of investment and the rate of interest, whose adjustment is not “automatic.” See Marx: “The Theory of Compensation as Regards the Workpeople Displaced by Machinery” and Keynes, “Is the Economic System Self-Adjusting?”
http://ecologicalheadstand.blogspot.ca/2012/04/efficiencys-promise-too-good-to-be-true.html
http://ecologicalheadstand.blogspot.ca/2011/02/self-adjusting-economic-system.html
Anon: No. That’s my first model. Those who own robots get richer; those who don’t own robots stay the same. They get relatively poorer sure; but not absolutely poorer.
Or maybe i misunderstood your 6.22 comment. In my third model, with land, yes, wages will get pushed down to/below subsistence.
Nick: those who own robots get richer, those who don’t, stay the same.
Isn’t that very similar to what I’m saying? In a finite world that dynamic means that robot owners will own a rapidly increasing share of resources and land.
The rest will own – and earn – a rapidly shrinking share of resources and land. They will get poorer in absolute terms – in terms of resources.
When their share drops below subsistence, people start starving and dying.
Nick: but it’s not human workers that determine the technology used, it’s the owners of capital.
Nick: Sorry my bad. I was already assuming land in the model. If we have infinite space to expand and there are only robots and humans and everybody capable of human labor can create things from nothingness with ever increasing productivity, then obviously we will get richer and richer.
Add land or some other rent-like production factor (holders of patents etc.) and you will end up with owners of this production factor owning everything and everybody will be else driven to starvation because their wage will be vastly lower then their productivity – with surplus being captured by our rentier.
Nick:
Correction: my “in a finite world” qualifier introduces “land” in essence – turning it into your second model.
So I guess we agree: robots, in the simplest model with a finite universe, are leading to a nightmare scenario for humans.
The only question appears to be: “at what rate will it happen?”
“Anyway, if you are looking for a nightmare scenario that is at least vaguely realistic, robots alone won’t do it. I think you need to go back to Malthus/Ricardo, and put land back into the model.”
But if you’re looking to avoid the nightmare scenario, you only need to go back to Marx and “wake up from the dream.”
“Our programme must be: the reform of consciousness not through dogmas but by analyzing mystical consciousness obscure to itself, whether it appear in religious or political [or Cobb-Douglas production function] form. It will then become plain that the world has long since dreamed of something of which it needs only to become conscious for it to possess it in reality. It will then become plain that our task is not to draw a sharp mental line between past and future, but to complete the thought of the past. Lastly, it will becomes plain that mankind will not begin any new work, but will consciously bring about the completion of its old work.”
In reality robots would produce significantly more than humans would, although the prices for these products might only fall so far because of price floors on the underlying natural resources due to limits. I don’t see how your model says wages would be unaffected, seems like as people are simply put into unemployment human wages to go zero in the sectors that the robots produce in.
CBBB: suppose a new technology lets one new robot produce twice as much as one human worker. That is the same as my parameter “a” doubling; we just call the new robot two old robots.
My model says you are wrong. Do you have a different model?
But then why are any humans going to be working any way? Suppose you’re a commercial airline and have access to robots that replace pilots. You don’t hire any pilots and you just have robots fly all your planes. You still have to pay for fuel etc. and so there are some savings to pass onto customers but the price of a ticket doesn’t fall to anywhere close to zero no matter how cheap robots get. The pilots are totally replaced though so their wages go to zero.
Now, this is happened in industries before as technology has made certain professions obsolete. But of course if the robots could do just about any job this effect would occur across all sorts of sectors. Perhaps wages of still working people wouldn’t change but significantly fewer people would be working.
“My model says you are wrong. Do you have a different model?”
I say “Let the robot economists build the robot economic models!”
http://ecologicalheadstand.blogspot.ca/2012/07/thoughts-and-dreams-about-machines-new.html
The comments seem to have missed it out, but I think Rowe is trying to link it back to the argument invoking real interest rates. We can all make up plausible stories regarding income inequality and Farewell-to-Alms-style horse obsolescence.
Anyway. In the land model, surely the real interest rate must track the rate at which the real value of land rises? Otherwise you would borrow and buy land, or vice versa.
[Stop right there. You have just assumed that the new technology makes human workers less productive than before. If that were the case, why wouldn’t human workers say “Stuff this, let’s go back to the old technology, and let the robots do what they want!”?]
It happens, and the simple answer is “because the workers are just workers, not management, and not owners.” And by the way, the new technology does on occasion make human workers less productive – measured separately from that technology, which economists don’t seem to have thought to do heretofore – but it certainly makes them less valuable, since it provides a cheaper alternative to that labor, where it’s an alternative at all. And if an aggregate production function is improved, even while the human worker becomes less productive, the new technology is at least economically justified. Morally or ethically, no, but economically, yes. At least to those who make this call. And, surprise, those people are not often economically literate; they do things that don’t make sense. But they do like gadgets – new technology is nothing if not gadgets. They like new technology like first graders like shiny new toys.
I build models, too. They’re called “software.” And they’re readily tested, unlike yours. One of those is the Apache web server that your blog is running on:
Server: Apache
X-PhApp: oak-tp-web042
X-Webserver: oak-tp-web042
Vary: cookie
Keep-Alive: timeout=300, max=100
Content-Type: text/html; charset=utf-8
X-Pad: avoid browser bug
Date: Fri, 14 Dec 2012 04:38:29 GMT
X-Varnish: 1454707643
Age: 0
Via: 1.1 varnish
It seems to me you’re hypothesizing about how things might be – but it seems you’re doing it in an effort to discount how things actually are. That alone makes your model not just wrong, not just worthless, but damaging. If you want to build a model, build one that can actually be descriptive of the real world – really descriptive of it, not just limited to your admittedly meager math skills.
My models do real things, like run your blog. Yours, at this level, are like first graders drawing with crayons. So you can complain all you want, “my model says you are wrong,” but all that complaint does, in my opinion, is make you sound like a first-grader.
It really seems to me you haven’t tried very hard to look around you and see what this new technology actually does – even just for you. And if you haven’t looked, you haven’t measured, and if you haven’t measured, your model can’t possibly be realistic.
The real economic issue isn’t robots – which, by the way, are now even driving cars and flying planes without human occupants. The real economic issue is that there’s no such thing as a workplace without a computer in it, pretty much anywhere. When I first started programming, folks were talking about the reasonable claim, at the time, that there would never be a need for more than a dozen computers in the world. I have more than that myself. And just about any literate person in the US these days has or uses at least one.
Your model reminds me of that “no more than a dozen computers” claim.
It doesn’t take much of an impact to explain unemployment rising from, say, 4% to 10%. But that much of an impact – from whatever combination of causes – is apparently not one that should be ignored. And you’re doing nothing if not trying to ignore one of those factors.
And John provides a demonstration of why growth theory is macro: because the argument isn’t about microscopic labour-market interactions at all. The argument is about the sign of the real interest rate!
In your model, the production of robots increases exponentially. The result in the limit is that consumption goods relative to all goods and human labor relative to all labor both go to measure 0. At that point you can make no prediction about them, since they are statistical anomalies. Of course this is a ridiculous outcome, but to prevent it, production of consumer goods has to increase and their price has to decline, or their production has to consume more labor. In any case the human share of total labor marginal product goes to 0. If labor is paid according to marginal product, then the human share of labor pay goes to 0, even if it remains constant in absolute terms. At some point human labor will of too little use to bother with. Robots are much easier to manage than humans.
Labor will also be worse off if the cost of living increases relative to marginal product, but it’s hard to make a prediction about this.
Nick,
With the portals-to-infinite-land world, I was aiming for a situation of the second kind in your list, i.e. one where capital is important, but not land. I’ve been trying to map your scenario of rising interest rates and falling wages to this world, but the more I think about it, the less sense it makes. Take for example robots whose reproduction is very labor-intensive so that “a” is only slightly above 1, and that it’s roughly constant, so that “g” is close to zero. Your model then implies interest rates given approximately by the golden ratio. But why?
I’m sure I’ll manage to figure this out eventually, but it’s already 2am and I’m half asleep…
Nick
In your model 1:
“Since both robots and human workers produce one unit of consumption goods per year”
Why? Why aren’t you letting robots produce consumption goods faster than labour over time?
Only a miro-economist would try to prove that nobody needs to worry about robots driving down wages. Then admit as an aside that if land exists the robots can drive wages below subsistence level. You may live in a landless world. The rest of us don’t.
Nick, re land.
YES. That is the problem. Perhaps you have noticed the recent increase in commodity prices. Land NEEDS to be put back into models.
are those who foresee a nightmare scenario envisaging the robots are owned by a small minority of people?
if we do go down that road, I wouldn’t be surprised if there has to be some sort of revolution to redistribute the fruits of our amazing technological production sector. After all, we have to get from here, to here: http://en.wikipedia.org/wiki/The_Culture
Both C and L are functions of t so the model as it stands is underdetermined. Obviously C matters. Constant C and C growing proportional to K are rather different.
what if the robots are really small and require very little land and are perfectly happy in the middle of Mongolia, or maybe everything is built on floating platforms in the ocean or sky, and raw material are mined from asteroids.
I feel these are the really important questions.
david hits the nail on the head. I’m just going to edit his comment slightly, to get:
“And John [and many commenters] provides a demonstration of why growth theory is [general equilibrium theory]: because the argument isn’t about [partial equilibrium] labour-market interactions at all.”
You can’t use partial equilibrium reasoning to solve a general equilibrium question. Classic fallacy of composition. “If robots can do my job the demand for my labour falls, and my wages fall, therefore if robots can do everybody’s job the demand for everybody’s labour will fall and everybody’s wages will fall!”
“If I sit down in the theatre I will see worse, therefore if everybody sits down everybody will see worse”.
If robots can do my job, my wages fall, but the price of the goods I am producing falls too (relative to the general price level). That raises everybody else’s real wages.
“Assume that all capital is robots, and robots are perfect substitutes for human workers. One robot can produce everything and anything one human worker can produce. And that includes producing more robots.
And assume that every year the technology of robot production improves, so that it takes less and less time for one robot to produce another robot.
That sounds nightmarish, right? Because robots will get cheaper and cheaper, and drive down human wages?”
The bit I don’t understand. If the robots are building the robots that build the robots and doing so ever more cheaply. And it becomes robots all the way down. The the price of consumer goods becomes spit. Because no one has to do any labour in order for there to be a cornucopian world. Everything’s made by the machines at the extreme. True communism has arrived in fact.
Another way of putting this is to look at wages in terms of consumption. If the result of the robot farm, mill, baker and truck delivery to the house is a loaf of bread at 1 cent then who the hell cares that wages to humans have fallen by 98%?
And the only way that entirely robotic production isn’t going to cause a collapse in prices is if “capital”, those owners of those robots, can collude to stop it.
We’re back with Smith and “businessmen seldom” etc.
Further, we’ve actually seen this happen before. With farming. Once that mechanised then shouldn’t all of the money have gone to the landowners? They just have to use machines after all: exactly analogous to “capital” with the robots. We should have ended up with the landowners having all the money and the rest of us none.
But we didn’t. We actually have to subsidise the farmers now as competition using the new technology drove food prices down. Mechanisation of farming produced the greatest rise in the living standards of the average man ever.
I’m simply not getting why anyone thinks that the mechanisation of manufacturing (or of services, whatever) won’t produce the same result.
Peter N: “Both C and L are functions of t so the model as it stands is underdetermined. Obviously C matters. Constant C and C growing proportional to K are rather different.”
That is partly true. Given K(t) and L(t), all my 3 models are fully determined at time t, except for the mix of output between C(t) and I(t). We need to add some sort of savings function (intertemporal preferences) to determine the C/I mix, and how the economy will evolve over time.
Note that I had to assume a linear PPF between I and C to determine the price of robots and the rate of interest. If I had instead assumed a more general non-linear PPF I would have needed an extra equation for the savings function to determine those two variables (and also to determine W, in the second model).
Tim: my guess is that you are implicitly assuming a representative agent model. Which is OK, but may leave some stuff out. The representative agent would have growing C, and stagnant of declining W, so if leisure is a normal good (it seems to be) the income and substitution effects combined will lead to labour supply falling towards zero.
If you instead do classical class analysis (workers, capitalists, landlords), treating the functional distribution of income as equivalent to the personal distribution of income, you would get a different perspective.
The truth is somewhere in between, of course. Like me: I belong to all 3 classes, until I retire.
“The bit I don’t understand. If the robots are building the robots that build the robots and doing so ever more cheaply. And it becomes robots all the way down. The the price of consumer goods becomes spit.”
What’s your numeraire? The price of consumption goods in terms of what? Note that I am taking consumption goods as the numeraire.
Luis: “are those who foresee a nightmare scenario envisaging the robots are owned by a small minority of people?”
Yes. I think so. And maybe many implicitly assume that the functional distribution of income is the same as the personal distribution of income. They have a class analysis that would apply to 18th/19th century England.
If production by robots was less land-intensive than production by human labour, I think that would change my third model a lot. I haven’t done the math though.
Ritwik: “Why? Why aren’t you letting robots produce consumption goods faster than labour over time?”
I can put my parameter “a” underneath I or in front of K. It doesn’t make any difference, except for vintage effects. My way of doing it handles the vintage effects better. Old robots don’t get better over time. But new robots are better than old robots. So if two new robots are twice as productive as one old robot, but cost the same to produce, it’s easier to redefine robots so that one new robot is really two robots, each costing half as much to produce.
Vladimir: If humans have a comparative advantage over robots in producing robots, and robots have a comparative advantage over humans in producing consumption goods, then:
1. Robots aren’t identical to human workers (I assumed they are).
2. The PPF between C and I will be convex, and so you won’t be able to figure out the price of robots in terms of consumption goods (and the rate of interest) without knowing the C/I ratio, which will depend on savings preferences.
(BTW, I was re-reading your old comments on my old post that I linked to above. They were good comments.)
david: “Anyway. In the land model, surely the real interest rate must track the rate at which the real value of land rises? Otherwise you would borrow and buy land, or vice versa.”
That is true, but you have causality reversed (in this model). We know that land rents will be rising over time as the stock of robots+human workers increases over time. And it is true that the rate of return on owning land must equal the rate of return on owning robots, and both must equal the rate of interest. But whereas the price of robots is pinned down by the linear slope of the PPF between C and I (in this simple model), there is no technology for producing more land, so the price of land is not pinned down by technology. The rate of interest determines the price of land, not vice versa.
(For a very different model, see my old post on Dutch Capital Theory, where the price of land is pinned down by intertemporal preferences (or jointly determined by preferences and the curvature of the PPF for producing new land).
BTW, speaking of Dutch capital Theory, where are the English Capital Theorists? I would have thought they would be all over the comments by now, given that title? Maybe they are plotting strategy for an attack en masse.
Please excuse John. He grew up watching big guys push kilobytes through the intertubes and earn good wages. Now he’s seeing robots push gigabytes for less. You can’t placate him by pointing out that bandwidth is cheap for everyone.
Nick, have you noticed an uptick in traffic recently? Your thermostat post was posted on Hacker News [http://news.ycombinator.com/item?id=4915751] a few days ago. The comments on your post are closed. I think the ycombinator ones are still open. Enjoy!
Daphne: “Only a miro-economist would try to prove that nobody needs to worry about robots driving down wages. Then admit as an aside that if land exists the robots can drive wages below subsistence level. You may live in a landless world. The rest of us don’t.”
jeeez! Talk about missing the whole point of this post! That bit about land wasn’t an aside. That was the main point of the post! Plus, you accuse me of living in a landless world? I’m the one that keeps yammering on about land! (And how many acres do you own?)