(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 
marris: Wow! Those guys are really going at it over there! Thanks for watching my back! Seems like you and some others are doing a good job defending my position. What is that “Hacker” site, anyway?
Could you do me a favour, and piss off the econometricians over there even more, by posting a link to this old post?
The long run scary scenario is that robots replace workers. Presumably this is scary because workers work to earn an income, if robots replace them workers no longer have an income. How is this not a sort of impossible long-run outcome? Who exactly will buy the output of the robots (presumably the output of these robots is owned by some small minority of capital owners)?
Why isn’t the impossibility of this outcome a partial analogy for what is happening now and the reason inequality hurts growth. Capital earned increasing share of national income recently, it seems to me this has hit something of a limit, not just politically, but as a practical economic threshold where now in order to increase its share of the pie, the size of the pie is shrinking as demand from workers reduced incomes shrink.
The short run robot scenario is possibly more scary than the long run (if indeed the long-run scenario is impossible) for all the reasons the past 30 years have been scary for the middle class.
Dan: “Who exactly will buy the output of the robots (presumably the output of these robots is owned by some small minority of capital owners)?”
Assume no robots. Who will buy the output of the workers? Other workers, of course.
Assume no workers. Who will buy the output of the robots people own? Other owners of robots, of course.
Capitalists (owners of robots) are people too!
“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.”
The Jevons paradox, as far as I know, describes a rebound of >100%, which is also called “backfire” in the literature.
“the ‘rebound effect’ is just another name for ‘demand curves slope down’.”
That’s a little misleading, I think. The rebound describes the reaction of fuel demand with respect to changes in fuel efficiency. In a diagram with fuel on the x-axis and Marginal Benefits of fuel use (=demand) on the y-axis, the curve should be downward-sloping; whether there is backfire or not depends on whether an increase in efficiency will move the curve to the North-East (backfire) or to the South-West (no backfire).
Achim: OK, the elasticity of demand may be greater than one.
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.
Right but that’s the catch isn’t it? No one who is concerned about automation taking jobs away is concerned about some overall effect. Of course some people will remain employed and see their real wages increase, but the “nightmare” scenario has always been a distributional issue. That’s not some secondary issue that economists always like to wave away that’s the heart of the matter. It doesn’t help your real wages if you have 0 income. What happens in the long run equilibrium is actually not relevant because people’s lives are destroyed today.
The “fallacy of composition” is not really that much of a fallacy either. You can say that the lower price of goods raises real income which means people who continue to receive income will have more of it to spend. However, the robots still fulfil all demands. It’s not really hard to see that the owners of robots and maybe some robot-related professionals will see their real incomes rise but that doesn’t debunk the nightmare scenario.
Tim Worstall: avoiding collapse was contingent. By luck and pluck We put in place policies to avoid that: getting rid of the Corn LAw thus tranferring income from land to capital. Then, corporate income taxes and its proprietors ot benfiaciaries, then fiscal and monetary policies to promote ” full employment” ( in part employment of paper pushers who then need blue collars to build the bridges into Manhatttan.) We develop higher education where most students learn nothing they will use later and potential leaders of the revolution get an income as professors.
Corn laws were rid off when the capitalists understood that, while landowners where rich like themselves, they had different long-rub interests. Capitalists agrred to share when they needed workers sppport against communism. Now, who is there to accept sharing in nthe name of theit long-run interest?
Revolution? The poors don’t start revolution. They start jacquerie that are easily suppressed.
Revolution start from the rising middle class. Currently, it is not rising.
Dan Thorn:
OK, let’s divide society into two groups, the capitalists and the working class. Imagine the capitalists own a bunch of robots that can replace most or all of the working class’s economic output very cheaply. The capitalists use this to make stuff for themselves and stop hiring the working class. Bereft of income, the working class can no longer buy anything and fall into poverty.
Except, wait a second. Why don’t the working class just doing the jobs they were doing before and selling the output among themselves? Maybe as soon as they do that, the capitalist will undercut them on price, and the workers will lose their jobs again. But, wait, for that to work the workers have to end up getting the stuff they would have made. If the workers all have their own self-contained non-robot economy going, there’s no way the capitalists can make them worse off in aggregate by giving them cheap stuff.
Also, the workers can just make more robots for themselves, and bam, they are all capitalists.
This is where “land” (i.e. non-labor/robot resources) comes in; if production also requires non-labor/robot inputs then the capitalists could buy up all of those inputs and the workers would be unable to execute the plan above. But it’s not really clear that there are such inputs (in an economically relevant way); lots of raw materials on Earth are present in effectively limitless quantities, but require increasing amounts of labor to extract (e.g. oil). Someone above mentioned asteroid mining; that’s another way to transform labor into raw materials (at the very expensive end).
My question would be if capital and landowners create everything and wages continue to drop, then long term won’t that create a giant Keynesian liquidity trap? If people don’t buy as many goods, the capital spent and creation of robots decreases or stops. Then there is no investment needed by business or labor.
Aren’t we still in a relatively global liquidity trap where the preferred savings exceeds investment?
CR
Tiny Tim: ” 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…”
Because it’s not “robots all the way down”. The robots are made out of materials, run on energy and when they wear out become residual wastes — not to mention the wastes produced during their production and the materials consumed and waste produced in the production of goods by robots. It’s throughput, not robots, all the way down.
Considering that capital (robots) embodies labour and land, what happens when it embodies less labour proportionately is that it embodies proportionally more land (capital = land * labour :: land = capital/labour). You can substitute capital for land and you can substitute capital for labour but you can’t substitute capital for land AND labour AT THE SAME TIME. That’s the point I’ve being trying to raise w/regard to the Jevons paradox and the labour “fallacy of composition”. The old expression was “robbing Peter to pay Paul.”
Collin: No. Look at the models. The rate of interest rises over time in the first two models, which is the exact opposite of liquidity trap. In the third model the rate of interest may rise or may fall over time. It depends.
There is investment in robots.
Godofsky,
Assume there is an infinite amount of oil.
Assume that it takes one barrel of oil to feed one worker.
Assume that it takes one worker to extract one barrel of oil.
Well… I would not say “causality reversed” inasmuch as “simultaneously determined”. If we imposed desertification to steadily destroy some land, the interest rate would change anyway. But you’ve hashed out that debate before.
I note there is plenty of technological progress in making the marginal productivity of land larger. It’s right there in the production function, since the number of robots increases.
Anyway, regardless of what pins the down the price of what, if you know the sign of the direction of change in land rents, then you know the sign of the direction of change in the interest rate.
OK, admittedly, I can barely follow any of this. But isn’t the nightmare scenario the one in which
PEOPLE > L
by some significant amount? Or maybe better. Let CAP/0 be the number of people owning capital (including land) who aren’t laborers, CAP/L be the number of people owning capital who also labor and L/0 be the number of people who are laborers but who own no capital. The suppose the path of the mean and total return to capital and labor goes swimmingly well, but due to the displacement of labor by technology and the concentration of the ownership of capital, we end up with.
PEOPLE > (CAP/0 + CAP/L + L/0)
Suppose, specifically, we ended up with something like
PEOPLE = 3 * (CAP/0 + CAP/L + L/0)
Nightmare, no?
david: “Well… I would not say “causality reversed” inasmuch as “simultaneously determined”. If we imposed desertification to steadily destroy some land, the interest rate would change anyway.”
Agreed.
“Anyway, regardless of what pins the down the price of what, if you know the sign of the direction of change in land rents, then you know the sign of the direction of change in the interest rate.”
Disagreed. We know that Price of land = Current land rent/(interest rate – growth rate of rents). But that doesn’t tell us if the interest rate is rising or falling. Price and rents might be growing at the same rate.
Dan: I admit that this post isn’t easy to follow, if you aren’t familiar with growth models.
I think I’m following you. And I think I would say “yes”. For example, if we assumed that everyone was identical, none of my three models would be anything to worry about at all (unless we suffered horrible ennui and moral degeneracy from not really needing to work, because our income from land and robots has increased so much and is so much higher than our income from wages, which is why you need something like fox hunting to make you get up in the morning).
But in an OLG model, if some people do not inherit land or robots, and others do, it’s a very different story.
Way too much to absorb and I’m not facile with this modeling language. I echo the commenter who would like to see it in (manipulable) code. Then we could play with the parameters and not have to rely on our fallible imaginations for the results.
Given that I do not understand the viability of Nick’s assumption: “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.”
He comments in reply to Ritwick: “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.”
Suppose as I think is reasonable (and supported by evidence) that the robots increase by some percent in efficiency (i.e. require less commodities to sustain them) each period. This is happening in industry — energy and materials required are falling.
I can’t see how this could wash out. As robots get older and are less efficient than the frontier at some point it is cheaper to replace them. Humans don’t become more efficient (or at best do so much more slowly) so very quickly we get rid of them too.
More comments later.
Jed: computer simulations are a last resort, when we can’t solve the equations. We don’t need computer simulations here, because I have done the math (well, except in the last little part, but that’s only because I am crap at math, and any competent economist could solve it there too).
If you want to play with the parameters, they are right there in the post!
OK, looked back at the model with this in mind. Obviously (to me) Ritwick and I are talkiing about ‘W’, Nick is replying in terms of ‘a’. Unless there’s some very cute algebra involved, we are talking past each other.
So to put the question in terms of the model: Nick, suppose the robots have a W that declines at some constant rate. What does that do to the modeled results?
Note that the “wages” of computing technology do decline at a significant rate — my iPhone consumes a lot less energy, takes a lot less maintenance, etc. than the same capability would have a few years ago. The commodities required to sustain manufacturing processes also seem to decline but slower — they take less energy, maintenance, space (which needs to be conditioned), etc. So I think this is a reasonable thing to explore.
I’m sure Nick will understand but just to be clear: We are not talking about the resources required for production but the “wages” of robots — i.e. the commodities needed for them to operate and be maintained, just like Sraffa’s circular models.
Jed: W is not a parameter. W is an endogenous variable. You can’t ask that question. You have to tell me what parameter changes, then the model will tell you if W changes as a result, and what else changes too.
Jed: Aha! I get what you are asking. You aren’t talking about W. You are talking about robot depreciation (the resources needed to keep robots functioning).
That’s an easy(ish) question to answer.
Just change by Kdot = I equation to Kdot = I – dK where d is the rate at which robots wear out. This way of modelling it assumes that robots slowly melt, like icebergs, so you need more robots or humans to work at repairing/replacing them.
And then subtract d from the right hand-side of all my equations for the rate of interest. Or is it some multiple of g and d, like d(1-g)?
Yep. I was assuming robots have zero depreciation, or running costs. The whole of robots’ wages W are paid to the owners of robots, just as the whole of a human worker’s wages are paid to the owner of that human worker (himself, if it’s not a slave society).
And if d falls over time, because robots require less and less maintenance, then R rises by an equivalent amount (for given K and L). No effect on W in the first model, a decrease in W in the second model, and no immediate change in W in the third model (but W will fall more quickly over time as people save and invest more now Rc is higher).
OK, I vaguely understand your replies — thanks! But now I need more help.
Taking the last point first, owners of factories staffed by robots could undercut owners of factories staffed by humans, simply by “paying themselves” lower robot wages. And in a competitive environment they will race to the bottom. Humans can’t take lower wages than subsistence so they will be priced out of the game. So all the human staffed factories go out of business, or all the humans get replaced with robots. What’s wrong with that reasoning?
Regarding your first reply about W being endogenous, when laying out the model you explicitly assume robots and humans earn the same wages — I don’t think that’s endogenous. Also I don’t see where you derive wages from any other part of the model. So I don’t know what the parameters are.
Finally the middle point: For humans, wages and “depreciation” clearly aren’t independent. Humans have a minimum wage threshold for “depreciation” or their productive capacity goes to zero — in the extreme case they die, and indeed this happens — see Sen on famines.
You are assuming robots have no such minimum threshold. This makes the rate of dis-employment of humans extreme given the scenario in my first paragraph above — without frictions I guess the economy jumps immediately to an equilibrium where the wages are as low as companies can survive. But even (more realistically) assuming there is such a minimum depreciation threshold for robots I believe it will fall more or less at a constant rate and so we get the same extreme result, just a bit more slowly.
PS: Thanks for making this model explicit! Having the various factors laid out with names helps a lot. Also thanks for staying on the thread and clarifying, so additional factors like depreciation can be added to the model as needed.
Jed: I don’t assume humans and robots are paid the same wages. That is an (immediate) implication of the model. Look at the first equation. Humans and robots are equally productive, therefore humans and robots will be hired by profit-maximising competitive firms at wages equal to their marginal productivity (which is one unit of consumption). If human or robot W ever fell below 1, anyone could start a factory hire humans or robots, and earn a profit, increasing the demand for humans and robots until W increased to one.
Thanks again for clarifying. This is where your ability to interpret the implicit machinery of the model makes it obvious to you but unfortunately mostly opaque to me. Code would help, the machinery would have to be explicit.
What keeps the robots from being “paid” less than subsistence wages for humans — given that their wages are really paid to the owners?
If humans are not being employed, where does demand come from? I think you say somewhere that the owners will take up any slack on consumption, but that seems like a big assumption — though I guess it is pervasive in these models. Diminishing marginal utility (not to mention finite ability to consume) would seem to make that problematic.
I have to go do “real world” stuff for a while so won’t respond further right now but I’m extremely interested in pursuing this.
Jed: OK. In my third model nothing prevents robots and humans being paid less than the human subsistence wage. Rather, it predicts it will happen.
If robot owners get satiated they will stop saving and investing. Why save and invest for a future in which you will have everything you could ever want? In which case nobody builds more robots, so technological change in building robots becomes irrelevant. And economic history grinds to a stop.
I am just wondering why the Marginal Product of Labour for the Cobb-Douglas function wouldn’t be the standard b((N^(1-b))/((K + L)^(1-b)) i.e.
b(N/(K + L))^1-b?
It is not the partial derivative of the production function wrt L?
Kathleen: probably because I have screwed up the math!
Yep. Just checked my notes. I think I did. I will edit the post.
Great! Someone is actually reading, understanding, and checking!
Hi,
I’m fairly knowledgeable about math but less so about economics. I’m having trouble following your first argument.
You wrote: “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.”
It sounds like you’re just assuming that someone’s wage is always equal to their marginal productivity? But for the past 40 years that hasn’t been true in the US at all. And why would the robots be paid a wage at all?
Maybe I’m missing something.
Charlie: profit = P.Q – W.L – other costs where Q=F(L) (Q is output, P is price of output, W is wage, L is number of workers)
Max profit wrt L taking P and W as given. The first order condition is W/P=dF/dL (which is marginal product of labour), and in this model I have assumed P=1 (we measure prices in terms of consumption goods, not money), and dF/dL =1.
The robots get paid a wage because their owners will rent them out to the highest bidder.
Very good post. Highly interesting.
Although, my intuition tells me that something is missing from the first model (although I can’t tell you how I would model that). The thing is that it seems to me only logical that at one point wages should go to zero, not because labour is being substituted for, but because labour is substituting itself. I say that because you assume no population growth, thus I would assume that at one point all workers would become capital owners. It seems reasonable, since as capital owners they could make the same wage (due to the equal MP) as a worker (only that the Marginal Cost of renting out robots is probably way lower than the Marginal Cost of working – thus giving ownership the edge over labouring). Is that reasonable?
Alex1: Thanks!
I think I follow you. Wages per hour (which is my W) would stay at 1, but total wages (W.L) would very probably go to zero eventually, because robots would become cheaper and cheaper to buy, so everyone would own one, and would choose to stop working. If I added any sensible labour supply curve and saving function to my model, that would probably happen.
You say “The robots get paid a wage because their owners will rent them out to the highest bidder.”
It seems like the rent (= wage) will be some amortization of the price of a robot? Otherwise it would be cheaper to buy rather than rent. So wages will decline along with the price of robots.
So it seems that even in your simplest model the falling cost of robots does have an effect on wages.
Jed: Whether to buy or rent a robot depends on the rate of interest. My equilibrium condition for the rate of interest ensures people are indifferent between buying or renting a robot. Or owning a robot and renting it out, vs lending at interest. Or borrowing to buy a robot and renting it out.
It is precisely the falling price of robots, relative to constant wages of robots, that explains why the rate of interest must rise in the first two models.
NR: Who will buy the output of the robots people own? Other owners of robots, of course.
Capitalists (owners of robots) are people too! /end quote
Doesn’t work. Mitt Romney’s income ~=200 times mine. I own one car; he owns two, not 200. I eat three meals a day; I’m pretty sure he doesn’t eat 600.
Increasing inequality in the U.S. over the last several decades has coincided with mostly unimpressive economic growth (Except for a period during the Clinton presidency when both trends reversed, IIRC).
I can’t resist the pun any more. The devil made video-record do it!
Nick Rowe-bot: http://youtu.be/9bjPtoHn_L0
I can’t resist the pun any more. The devil made video-record it!
Nick Rowe-bot: http://youtu.be/9bjPtoHn_L0
NICK: “build a model which shows that (without land). Until then, I will say you are wrong”
(L+R)^b*K^1-b ,where R is robots and K is other forms of capital.
In your first and second scenario, we might as well assume that each individual live on a separate islands (or houses) without any need for any inputs into their production. Each persons production is, by assumption, completely unrelated to what other people do.
In your second example the wage stay the same in terms of consumption (or in terms of the amount of consumption you get the next time period from an hour of work). The present value decrease because you have the technology to transform present consumption into future consumption at a higher rate – but each persons intemporal budget set is strictly larger than in a scenario without robots – so it is hardly a nightmarish scenario (unless you account for relative wealth).
PS: I assumed that the implications of my model were obvious, but to state the obvious.
Some capital is a complement to labor (represented by K) and other forms work as a substitute (represented by R).
This mean that you might see decreasing return to capital investments (d^2Y/d(K+L)^2) and lower interest rates while a bigger share of the output goes to capital owners (and thus a smaller share to labor and lower wages).
PS 2: But in my model there was constant returns, so make it (L+R)^b*K^c instead.
PS 3; Furthermore, assume that the marginal benefit of consumption of goods decrease as consumption increase, but that the marginal benefit of being wealthy is constant (i.e. the benefit of feeling important).
This would mean that the interest rate kept on decreasing until only the richest (wo)man still invested – and most of those investments would not be in new capital, but would instead be him/her buying capital from people with less wealth.
PS 4: Im going to stop now but I just read your last tecnology post, and isn´t (L+R)^b*K^c with b+c<1 the obvious base for the Marxian analysis as well (given my interpretation of your statement of the theoretical problem)?
nemi: “(L+R)^b*K^1-b ,where R is robots and K is other forms of capital.”
Good start, but incomplete.
If that’s on the right hand side, what do you have on the left hand side of the = sign? (What replaces my “C+I/a”? It matters a lot.)
What determines the composition of investment between robots and other capital? How will that composition change over time when robots get cheaper to build?
I was toying with a model like yours for my second model, but chose what I did instead because it’s so much simpler.
As far as I can remember, Marx would want either increasing returns to scale or constant returns to scale. I don’t think I would want decreasing returns to scale at the level of the whole economy either. You can just replicate firms.
But keep going. I reckon you might be onto something.
Sticking land in the model gives you the equivalent of decreasing returns to scale, if you can’t increase land.
Ken Schultz:
Until 2008, the last problem with the US was underconsumption! Overconsumption maybe.
Do you own 1% shares in a private airplane or yacht? Do you eat 100 times as much rice as someone who lives on $1 per day?
If you want to argue against inequality, then do so. But those are incredibly weak arguments.
“Sticking land in the model gives you the equivalent of decreasing returns to scale, if you can’t increase land.”
Sure:
“what do you have on the left hand side of the = sign?”
Y=C+I/a
“What determines the composition of investment between robots and other capital?”
The marginal product of each component has to be equal.
“How will that composition change over time when robots get cheaper to build?”
Higher share of robots -> even lower wages.
“Sticking land in the model gives you the equivalent of decreasing returns to scale, if you can’t increase land.”
Yes – that is a much better model.
But I still think it is reasonable to expect decreasing return. Assume that the cost of production and sale is:
G(K,L)*F(K,L)
where F(K,L) is a constant rate of return production function while G(K,L) is a decreasing rate of return marketing function (or a function that takes a increasing part of the resourses). The more stuff the consumers consume, the less time available to evaluate each product, and the more important marketing will be.
PS: Sorry, The left hand sign should read:
Y=C+I,
and
I=R/a+K
nemi: OK. Lets change it to C + Rdot/a + Kdot = (L+R)^b*K^1-b
So the price of K, Pk=1, and the price of R, Pr=1/a
For a given amount of saving (=Y-C) you now need to figure out the composition of investment between Rdot and Kdot. Will R be increasing over time, or K increasing over time? Or one increasing and the other decreasing?