Piketty on the Marginal Product of Capital
I’m not going to comment on this right now; I have a big article on capital theory coming out next week, and you guys should read that first as foundation. So I’ll wait.
In the meantime, however, let me go ahead and type out the following excerpt from pp. 212-213 of Thomas Piketty’s blockbuster Capital in the Twenty-First Century. This will be like the puzzles in the kid’s menu at a restaurant: “Can you find what’s wrong in the picture below?”
Technology naturally plays a key role. If capital is of no use as a factor of production, then by definition its marginal productivity is zero. In the abstract, one can easily imagine a society in which capital is of no use in the production process: no investment can increase the productivity of farmland, no tool or machine can increase output, and having a roof over one’s head adds nothing to well-being compared with sleeping outdoors. Yet capital might still play an important role in such a society as a pure store of value: for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine or perhaps for purely aesthetic reasons (adding piles of jewels and other ornaments to the food piles, perhaps). In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero. In that case, the share of capital in national income, α = rXβ, would also be zero. In such a society, all of national income and output would go to labor.
As Obama would say, now let me be clear: The above is fundamentally, totally, utterly wrong. Piketty doesn’t even know how to conceptually think about capital and interest income in a simple thought experiment. Since Piketty’s whole book is about capital and interest income, that’s kind of a big deal. (It helps to be an Austrian to see why, but you don’t have to be; Nick Rowe could come up with an example of two guys and an apple tree to show the problem.)
Bob: you are right. That passage you quote is so horribly muddled. Just because there are no investment opportunities doesn’t mean the rate of interest is zero. Take an economy with land, for example.
I would want to see the context in which he is using this thought experiment before passing judgement.
It appears he’s imagining a society where everything is produced by labor alone (no machines and perhaps land is in super-abundant supply). Maybe they pick berries by hand for food and pick up shells from the beach for jewelry. Its like a hunter-gather society with no tools.
In this model “capital” (as he has defined it) would just be the stored value of any fruit and shells.
There might even be lending (of fruit and shells) for interest in such a society.
But there is no reason in this model why all the fruit and shells gathered in certain time period would not all go to the laborers who had done the gathering so I see no immediate problem with “In such a society, all of national income and output would go to labor.”
(Happy to be proven wrong on this).
I can see that the stored fruit and shells may provide a stream of food and jewellery services that would mean that the return on them is not zero, but that seems separate from the production process (via gathering) where they play no role.
You’re getting warmer, Transformer. Now what if someone *lends out* his stockpile of apples in period 1, in exchange for a perpetual stream of apples that come out of what the workers gather in periods 2, 3, … ? That sure looks like real interest income on that initial stockpile of capital, doesn’t it?
I don’t think apple trees can exist in this world, since they are not “of no use as a factor of production.”
He’s establishing a meaningless tautology by creating a world without capital and then saying that capital has no value there.
Tavish wrote:
He’s establishing a meaningless tautology by creating a world without capital and then saying that capital has no value there.
Ah, but no he’s not. He admits that “capital/income” is positive in this hypothetical example. So capital has value. It just earns no income, he thinks, because its marginal physical product is zero.
I can’t see any difference between that kind of interest from lending and the kind I mentioned before. These are just trades of present for future goods. I guess you can define it as the “real interest income on that initial stockpile of capital”.
How does this relate to “marginal product of capital” though ?
People just go out and gather stuff, which they then divide up amongst themselves. Then they save some of this output. No capital is involved in this process, though the resulting savings becomes part of “capital” (on which interest can potentially be earned).
As no capital is involved in production it seems reasonable to say “the marginal product of capital” is zero and “all output goes to labor”.
I guess you also have to assume that there is no other income (from interest or trade) to further claim “all income goes to labor”.
So stated more simply:
If Pikerty makes the additional assumption that no lending takes place and savings is just deferred consumption then I see no issue with his simple thought experiment.
Transformer wrote:
I can’t see any difference between that kind of interest from lending and the kind I mentioned before. These are just trades of present for future goods. I guess you can define it as the “real interest income on that initial stockpile of capital”.
How does this relate to “marginal product of capital” though ?
!!! But that’s the crux of the argument, Transformer. This is what the Cambridge Capital Controversy was about (though you need to read Wikipedia, not Piketty’s 3-page discussion, to learn that).
The UK Cambridge people (and the Austrians, incidentally, which is why Peter Klein and Jamie Galbraith agree on Piketty’s confusion) deny that interest income in a market economy is due to the marginal product of physical capital goods.
To get a positive real interest rate, you need to have a present unit of consumption good having a higher market value than a future unit of consumption good.
In the Solow growth model and other mainstream default models, there is only one good, so you don’t see these subtleties. The math is right, but the economic intuition and concepts built around the math are wrong–they were exploded by Bohm-Bawerk in the 1800s.
You’ve lost me. I’m confused what it is you think Pikerty has got wrong.
I agree that “To get a positive real interest rate, you need to have a present unit of consumption good having a higher market value than a future unit of consumption good.” sounds reasonable.
However it also seem intuitive that the higher the physical productivity of capital the more people are likely to defer current consumption so they can build capital goods that will allow higher consumption in the future. What effects this will have on interest rates though seems like it would be a complex thing to calculate.
Not sure what this has got to do with Pickerty’s model, where there is no point building capital goods by definition but where the interest rate could be non-zero simply as a result of the above definition.
The savings in Picketty’s thought experiment can still generate a return, despite their lack of “physical” productivity. If the fruit being piled up is cheap to produce in summer and expensive to produce in winter, piling up fruit in the summer frees labour to produce other goods in winter, increasing total output and generating a return for savers. He even hints at this when he mentions a “future famine.”
If it even prevents one famine, the marginal productivity is greater than zero.
Piketty above: “In the abstract, one can easily imagine a society in which capital is of no use in the production process”
No, that isn’t easy for me to imagine. The value of an analogy is to simplify thinking about something, to distinguish what “capital” brings to production. An analogy that assignes equipment, land, and technique a value of zero and has people sleeping on the ground refers to something that is not in any way a part of anyone’s experience. So, how can that analogy be useful?
More amazing is the summary of what Piketty has written. “(If we specify that capital has no effect whatsoever, that leaves labor as the only factor of production. In that case, all production would be earned by labor.)”
Tautologies are always impressive because they are absolutely correct. Piketty is shamelessly nipping at the heels of that other great socialist, tautologist, economist John M. Keynes.
The Political Dictionary: Keynesian Economics
=== ===
Keynes said that the total income (production) in a society is consumption plus investment. When there is unemployment and unused productive capacity, one can only increase employment and total income by first increasing expenditures for either consumption or investment.
Translation. The total production of a society is what it consumes (eats) and what it invests (doesn’t eat). When there are unemployed resources (people and machines), you can increase employment and production only by increasing what you eat and what you don’t eat. To restate, you can increase production only by increasing what you produce.
This insight made Keynes the most famous and influential economist of all time.
=== ===
“In the abstract, one can easily imagine a society in which capital is of no use in the production process”
Then there is no such thing as capital, capital goods being those goods being used for the productive process.
Whoops.
Not entirely. When people write IOU notes, they are claims on future labour, and you can save up those notes. Thus, the notes must be capital, not labour.
However, they aren’t used in the production process.
Why are they writing up IOU notes? Presumably, they are promising future production for current goods. And those current goods are used to sustain them while they produce now up to that future date.
So… used in production process.
I don’t think it’s fair to regard “used in the production process” as equivalent to “somehow came in contact with the production process however tangentially”. At least, I doubt that’s how most people think of it, especially not Piketty’s readers.
Hmmm, suppose a young man issues IOU notes against his own labour while he is studying to obtain skills (similar to a student loan if you like) and then repays those IOU notes later in life with the benefit of more powerful abilities. That’s a plausible enough scenario, without anything that would be traditional “plant” type capital (i.e. no factory, machinery, infrastructure, whatever).
You could argue those IOU notes annotate the human capital invested in the man… yeah, it kind of works. That’s speculative of course because we don’t know whether that investment is going to return good value, but that’s largely a problem for the holder of those IOU notes. Hmmm still kind of works, because most capital investment is risky.
Also, every definition I can find goes something like this:
“n economics, capital goods, real capital, or capital assets are already-produced durable goods or any non-financial asset that is used in production of goods or services.”
A claim on future labor or resources is not capital of itself.
Well the financial industry does seem to believe their instruments represent capital. They might be wrong, but that’s a pretty heavy discussion when you think about the implications of that.
How much of our existing capitalism runs on IOU notes (in one form or another) ?
Here’s something to think about…
I ran through a thought experiment: we have one million people, and each week they write an IOU note for one hour of their time and put the notes into a lottery. Randomly, one thousand winners are drawn and each of these receives one thousand IOU notes, each for one hour of labour.
Repeat the experiment for fifty weeks a year over twenty years (thus one thousand lotteries in all) and we get these statistics:
* 36.8% of the population end up putting in one hour per week of labour and get nothing back, they lose.
* 36.8% of the population break even exactly, for every hour they put in they get one in return.
* 18.4% of the population come out ahead by one hour per week.
* 6.1% of the population come out ahead by two hours per week.
* 1.5% of the population come out ahead by three hours per week.
* 0.4% of the population get four hours per week or better (the winners).
Is it fair to play a lottery game like that? Well, obviously we end up with inequality, but you don’t see too many big government statists wringing hands and shutting down those lotteries that rake in a lot of tax dollars.
The game itself is completely fair, in as much as everyone has an equal chance of winning.
The average wage is zero in this case, because it’s a zero sum game, the median wage is also zero. If you change the rules a bit you can get a median wage above or below zero.
By the way, this economy is not growing, nor is there any capital investment. There is nominal capital in the form of IOU notes (i.e. a claim on future labour), but it merely changes hands between people and is then consumed.
How did you manage to make each hour of labor equall
By making the assumption that they are equal. The participants might have decided that amongst themselves at the start.
Bob: “Piketty doesn’t even know how to conceptually think about capital and interest income in a simple thought experiment.”
Nick: “Just because there are no investment opportunities doesn’t mean the rate of interest is zero. Take an economy with land, for example.”
You’ve lost me guys. Piketty doesn’t mention interest income, or the rate of interest, in that passage.
But at Nick’s request, I’m visualizing an economy with land, lots of land (and a starry sky above). A vast, vast planet, in effect a sphere of infinite radius. On it stand a few thousand hominids, gobsmacked by the prospects for agricultural development. Their God has commanded them to increase and multiply and fill the earth, but they can see it’s going to take rapid procreation from now until Judgement Day to fill even a fraction of it.
So, apart from having sex, what are they to do? What conclusions do you draw about the rental return on land? And what in Heaven’s name are you asserting about the rate of interest?
Kevin.
1. If land has a positive value marginal product, land rents will be positive, and not all income will go to labour.
2. Taking a dynastic-Ricardian example: the rate of interest in that economy will equal the rate of time preference proper (rho) plus the intertemporal elasticity of substitution of consumption times the growth rate of consumption. It can easily be strictly positive.
Or just draw an Irving Fisher diagram, with a rectangular PPF (no investment opportunities), with the rate of interest equal to the slope of the indifference curve (which is how Bob is looking at it above).
If an economist writes a whole book about capital and the functional distribution of income, you would think he would at least understand the very basics of the theory of capital and interest. He does not.
Bob is absolutely write about this. How come anyone takes this stuff seriously?
But did some lefty heterodox economist reviewers also say he doesn’t get capital theory right? If so, they were right too.
What Kevin seems to be saying is that with large amounts of land and few people, there’s no way to command rent. The guy just moves somewhere else and uses that land. Lots of supply, limited demand => low prices. Possibly still greater than zero if you want to quibble over commas.
It is admittedly a difficult thing for modern people in crowded cities to imagine, but in principle it could happen, suppose there was a great plague or something.
Tel, that’s it exactly.
Seriously Nick; do you think Piketty needs to be told that if land has a positive value marginal product, land rents will be positive?
What’s the French for “No shit, Sherlock?”
Kevin: Piketty says: “In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero. In that case, the share of capital in national income, α = rXβ, would also be zero. In such a society, all of national income and output would go to labor.”
If there are no additional investment opportunities with a positive return, that does not imply that the rate of interest is zero, and nor does it imply that all of national income would go to labour.
Land is one counterexample. Positive rates of time preference and consumption loans is another counterexample (those lenders will earn part of national income).
I can only interpret him as assuming that the real rate of interest is equal to and determined by the MPK. And that labour’s share of income will be one if MPK=0.
Nick, look at pages 150-151 please. I’ll sign off now.
Here’s pages 150-151:
tinyurl.com/piketty150-151
Thanks Keshav!
Kevin: OK, have now read pp150-151. He doesn’t say anything (obviously) wrong there. But it does not clear up the muddle in the paragraph Bob quotes.
He is using the word “capital” to include land, which is a loose sense but OK. But when he talks about “the return on capital” being zero he is talking about the return on additional investment in newly-produced capital goods in the strict sense.
Just because the return on additional investment in the strict sense is zero does not mean the rate of interest is zero nor that the income from capital in the loose sense is zero.
“I can only interpret him as assuming that the real rate of interest is equal to and determined by the MPK.”
This makes sense to me in a world where MPK > 0. But he assumes its zero. But if time preference exists then the real rate of interest is potentially > 0.
So I think real rate of interest is > MPK and not determined by it in his simple model.
(I think he is assuming that there are literally no investment opportunities that will allow capital to be used in production – all lending that takes place would be for consumption. I think he also implicitly assumes that land is not a scarce resource).
I think I am on the same page as Transformer. But I need to draw an Irving Fisher diagram with a pointy PPF to explain it clearly. The slope of the intertemporal indifference curve at that point determines the rate of interest.
It’s a bit stronger assumption than that, he assumes all resources are in plentiful supply. As soon as anything becomes scarce there would be rents again, and once rents exist you are back to having a return on capital somewhere in the system.
Piketty is assuming away all types of natural scarcity… no fishing spots are better than any other, all land has plentiful water, there’s always a forest nearby to hunt game and collect wood, for any natural transport corridor several others will exist in parallel to prevent toll booths, minerals are available in a large number of locations, etc.
It’s a bit stronger assumption than that, he assumes all resources are in plentiful supply.
But not labor. (I’m not just being picky. He’s also ruling out a pure endowment economy where manna falls from heaven, because he has labor earning 100% of GDP.)
Yes that’s correct, not labour.
However, skilled labour is certainty ruled out (or at least, any skill you can learn is ruled out) otherwise there would be scope for financial instruments and investment in human capital (e.g. student loans and similar). Such financial instruments would violate the “no return on capital” constraint.
Kevin, I know exactly how this debate is going to go. It will be just like Krugman and Dean Baker with the “gov’t debt doesn’t burden our great-grandkids” thing.
(1) The big gun throws out some sweeping claims that are demonstrably false, and gives “intuition” that is also wrong to try to show why the sweeping claims are true.
(2) Nick and I present very simple counterexamples isolating exactly why the sweeping claims and the accompanying “intuition” are demonstrably wrong.
(3) The defenders of the big guns get mad at Nick and me, saying we’re either nitpicking, missing the point, and/or changing our examples to something else, where it’s not as obvious that the big guns were wrong.
(4) Nick and I explain what’s going on in the new models suggested by our critics, and show once again that yes the big guns were wrong.
(5) The defenders move the goalposts and redefine what the debate was originally about, defending a different claim from what the big guns said and what 99% of their readers took away from their claims.
(6) The defenders get mad at Nick and me for wasting everyone’s time by digging in our heels when the big guns were right all along.
Kevin, I’m coming to your conclusion. Piketty has assumed that technology does not exist, in any form at all, and self improvement is impossible, and all available natural resources are in plentiful supply. There is nothing for these people to do, and possibly we could argue this is not sufficient to even be regarded as an economy at all.
Why would they trade? None of them have any skills beyond what they are born with (that would imply human capital) thus division of labour is impossible. If it takes Adam an hour to pick berries then it also takes Barry an hour to pick berries so there’s no way to make a profit on any transaction.
Tel,
I think we’re pretty much in agreement on this. It’s clear that Piketty is discussing a logical possibility, not a realistic case. The next paragraph after the one Bob quoted begins: “Nothing prevents us imagining such a society, but in all known human societies, including the most primitive, things have been arranged differently.”
There are problems with Piketty’s approach I’m quite sure. But Bob hasn’t found one here.
I will now resume reading where I left off (page 168). Whether I’ll end up liking this book or not I’m not sure, but I’ve no regrets about buying it. It’s essential reading.
I would go one step further and say that the “no return on capital” constraint must by necessity destroy most of the things we would recognise as an economy. Not only is it an unrealistic assumption, but it is such a powerful assumption that there is nothing remaining to study after making that assumption.
Bingo. This is a devastating point.
Indeed, it is an interesting (ludicrous) proposition that someone would keep something of zero market value (“capital is of no use in the production process”) as a “store of value.”
The more I read about Piketty, the more obvious it is that his greatness (like Keynes?) is that he says what the ignorami want to hear, not something profound or even well thought out.
One cannot get by the full first sentence of that quote without knowing Piketty is wrong. Piketty has done no more than taken the Marxian pig and put new lipstick on it. Same old pig. But, the looney left goes ape over this new evidence that socialism will at last be made to work. God help us, and they vote too.
Pikerty has invented a simple model to demonstrate a world where no capital is used in production perhaps because literally no “roundabout”processes exist.
He doesn’t specify but I think he has an implicit assumption that land is a non-scarce resource.
MPK = 0 in this world.
However as he allows capital to exists (as savings from deferred consumption) his model introduces the possibility of a positive interest rate on consumption loans and interest income. This means that capital earns a positive rate of return even in this model (which may be at odds with his MPK = 0 point). He could probably introduce other assumptions (no lending ?) to make his model more consistent.
As this seems like a simple thought experiment (of the kind Nick and Bob use all the time) to demonstrate a world where capital is not important in production it seems a bit like uncharitable nit-picking to critique this particular model in this way. (I haven’t read it so perhaps the rest of the books justifies this approach ?)
Transformer wrote:
Pikerty has invented a simple model to demonstrate a world where no capital is used in production perhaps because literally no “roundabout”processes exist.
He doesn’t specify but I think he has an implicit assumption that land is a non-scarce resource.
MPK = 0 in this world.
However as he allows capital to exists (as savings from deferred consumption) his model introduces the possibility of a positive interest rate on consumption loans and interest income. This means that capital earns a positive rate of return even in this model (which may be at odds with his MPK = 0 point). He could probably introduce other assumptions (no lending ?) to make his model more consistent.
As this seems like a simple thought experiment (of the kind Nick and Bob use all the time) to demonstrate a world where capital is not important in production it seems a bit like uncharitable nit-picking to critique this particular model in this way. (I haven’t read it so perhaps the rest of the books justifies this approach ?)
But Transformer, he is using the example to show us *why* interest is equal to the MPK. He is saying the income flowing to capital must be zero, because (by assumption) the MPK is zero.
So when you say, “Now maybe there is interest income in this world too…” you are giving away the whole game.
Nick and I aren’t nitpicking by pointing out that his own example proves he’s wrong.
“But Transformer, he is using the example to show us *why* interest is equal to the MPK. He is saying the income flowing to capital must be zero, because (by assumption) the MPK is zero.”
But could he just say something like “everyone has exactly the same time preference so there is no lending” and then r = mpk = 0 ?
Once he introduces productive capital into his model then even if everyone has exactly the same time preference then there is a reason to save and both r and mpk will be > 0.
“Technology naturally plays a key role”
I think this is a true statement. I think the “skimmers” , middlemen, bureaucrats, burdensome regulation, tax policy, Fed inflation and other takers suck up most technological gains before average producers reap the rewards.
IN a nutshell, most of us are a whole lot more less wealthy then we would and should otherwise be…
I think the Austrian answer is that the reason for the existence of interest is time preference. Productivity of capital is neither necessary or sufficient.
I think this is true, though it is important to emphasize that the productivity of capital (technologies that make round about methods more productive) impacts the exact level of interest.
I don’t think consumer loans create capital.
Bill wrote:
I think this is true, though it is important to emphasize that the productivity of capital (technologies that make round about methods more productive) impacts the exact level of interest.
Sure. Just like capital goods affect the productivity of labor and hence wages. But nobody would say, “Wages are due to the productivity of capital.”
In Piketty’s world I know I can pick berries whenever I want, I know that everyone picks berries the same way I do, and no one will ever invent a berry picking machine. I know the berries will never run out, and I know nothing ever changes in this world.
So where does time preference come from, in the Piketty world? For that matter, where does time itself come from?
Importantly, a scarcity of berries is also not created by berry-picking.
The necessary assumption about land is not even as simple as it being non-scarce, but that all land is always equally productive across time: If labor on a piece of land could create scarcity on it, previous quibbles come into play.
A better assumption is not that land is non-scarce, but rather that labor is a sort of sorcery which creates income ex nihilo.
So, labor is a productive act of sorcery with no requisites beyond human will, of which all humans are precisely equally capable at all times and in all places.
Piketty is right! That is a super-easy world to imagine.
Oh; Is Piketty just talking about the Fed?
Yeah, I agree, you need to basically eliminate the time dimension completely in order to satisfy Piketty’s constraint. You can’t have good years and bad years or else someone could profit from buying cheap, then stockpiling and selling during times of hardship, which would be return on capital. You can’t even have seasons.
And yeah part of eliminating the time dimension is that whatever activity you do cannot in any way change the environment (neither for better, nor for worse).
[Note: I edited some of the numbers below from what I originally posted.]
The thing is, everyone, I can easily come up with a model in which physical capital goods and land have zero marginal physical product and hence earn no rents. The only physical production accrues because of labor. And yet, in this world I can have a person in period 1 who starts with a collection of consumption goods equal to, say 50% the amount of consumption goods produced by the workers, i.e. 50% of GDP. Piketty himself in his quote in the OP would thus say that capital/income in period 1 is 50%.
Then I can choose preferences such that after everyone optimizes the owner of the capital (shall I call him a “capitalist”?) can sell his stockpile of goods in period 1, for claims entitling him to a perpetual flow of 25% of GDP for periods 2, 3, ….
So Piketty agrees capital/income is 50% in every period in this model (I’m making it stationary after period 1), and yet the fact that the owner of this capital gets to consume 25% of GDP forever because of the interest income on this initial capital, while the workers forever get to consume only 75% of GDP, nonetheless means that alpha is zero, because the workers earn all income and the capitalist earns nothing. So Beta is 50%, but alpha is 0%, because the stockpile of consumption counts as “capital” for Piketty, but the perpetual flow of real income that that capital generates does not count as “income to capital” for Piketty.
If this type of example doesn’t get you to see that Piketty’s framework is totally screwed up, then nothing will.
I get what you are saying.
But I still think its nitpicking (possible because I haven’t read the book).
Piketty is clearly saying :”image a world with capital that is non-productive”. Implicitly this excludes capital from being used to provide consumption-balancing services (lending). Implicitly I think he assuming that such services are not profitable (perhaps no-one ever wants to borrow), just as much a building a capital good would be non-profitable.
But as he doesn’t explicitly exclude this kind of use of capital you pounce and say “what an idiot – can’t he see that even in such a world there could be return on capital”).
Perhaps there a more subtle point about interest rates and mpc that I am missing. If so please explain.
Those this with a high propensity to save will over time gain a bigger share of capital goods. If capital can be made productive by physically producing goods, providing consumption-balancing services etc then this imbalance will also affect incomes. I assume that is Piketty’s point.
He appears to be saying that, in his example, food is just stored for possible future consumption (i.e. not loaned to anyone). Or that people just accumulate things like jewels for purely aesthetic reasons.
“Yet capital might still play an important role in such a society as a pure store of value: for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine or perhaps for purely aesthetic reasons (adding piles of jewels and other ornaments to the food piles, perhaps).”
If you store food for a possible future famine, you don’t lend that food out.
Until there’s a famine, at which time you can lend it out at significantly high rates.
see my reply below.
I agree, it does, and think of the implications… Every period must be the same as every other, in order to prevent speculative profits by lending. In other words, the hypothetical system contains no time at all, nothing changes.
“Every period must be the same as every other”
He mentions that the future might be different to the present:
“for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine”
Anyway, as he says, it’s an abstract thought experiment:
“In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero.”
If the future was different to the present, then speculators could write future contracts and those contracts could be sold as financial capital and the capital might make a positive return. Thus contradicting the original requirement that capital does not make a return.
Even without financial instruments available, a physical stockpile can make a profit if it was purchased during time of plenty and resold during times of hardship. Thus also contradicting the requirement that capital does not make a return.
Which does not bypass the need for self-consistency otherwise it becomes a fantasy experiment, rather than a thought experiment.
“If the future was different to the present, then speculators could write future contracts and those contracts could be sold as financial capital and the capital might make a positive return. Thus contradicting the original requirement that capital does not make a return.”
You seem to be missing the point. Piketty says: “In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero.”
He doesn’t say it’s impossible to imagine a world in which the return on capital is not zero. Saying that you can imagine a world in which the return on capital is not zero, is not a way to “disprove” his point.
The world you imagine must be consistent with itself. Piketty can have any fantasy world he likes, where any detail can be fixed up by just saying, “I don’t want that to happen.” but that would not be economics, it would be novel writing.
In order for the thought experiment to be meaningful, it can’t contradict its own assumptions. Piketty makes the assumption that capital does not produce any return, as I have pointed out, this is a strong assumption. You can’t just “imagine” that it works whenever you feel like it, you have to either support the assumption completely or abandon it.
You could make a weaker assumption, that some particular types of capital don’t make a return, in which case humans would naturally invest in those types of capital to do make a return.
Bob, I haven’t read Piketty’s book and have no idea how he would respond.
But it seems to me that your example isn’t that relevant to Piketty’s point in the quote you posted.
He says:
“In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero.”
You respond to this by saying “hang on, I can imagine a society in which the return on capital is not zero! Therefore Piketty is wrong!!”
What I was trying to say – but much clearer !
Philippe:
Piketty did not merely pose such a possible interpretation. His whole theory is riding on it.
I’ll just post one more here because I’m sure we will be arguing this in future posts…
Guys, the central point of dispute is that Piketty flips back and forth between “capital” as a sum of financial wealth denominated in money units, and also physical things that contribute to the production of real output. It is clear from the book that he thinks the marginal product of physical “capital” (and land) is intimately related to the financial income flowing to the owners of financial “capital.”
This is wrong. The easiest way to show it is to use his own approach, of imagining a world where the marginal productivity of physical capital is zero. And yet, people who own a stockpile of capital (measured in money terms) can earn a flow of real income. I.e. the real interest rate can be positive even if MPK=0.
You guys are trying to plug the chink in his armor in the thought experiment above by adding in the assumption, “Present goods don’t trade at a premium for future goods” even though Piketty didn’t say that. Instead he is focusing on the marginal productivity of physical goods and land. I don’t think that’s just because he was interested in brevity, i think it’s because he doesn’t realize that interest isn’t really about the marginal product of physical capital at all.
I’m also (based on the reviews I’ve seen) suspecting that Piketty has some unsustainable views on the return to capital.
I just don’t think you have shown this in your critique of his simple thought experiment.
Yes, its possible to get a return from capital just by lending it out.
But
1, Piketty (in the quoted passage) never discusses this at all so how do we know he disagrees ?
and
2. Such a return is contingent upon lending opportunities existing. They may not in Piketty’s model (or he may have intended to exclude them by assumption)
3. If one adds the possibility of “roundabout” production process into the model then this increases the benefits of savings. As Bill Woolsely says above the resulting interest rate will be a combination of time preference and productive possibility. (I’m guessing you may agree with this and think it all time preference ?). In any case the returns from lending capital and from using in directly in production processes (risk adjusted) will tend to be equal. Piketty may get this horrible wrong in the rest of the book but its not even mentioned in the passage in question.
” i think it’s because he doesn’t realize that interest isn’t really about the marginal product of physical capital at all.”
Consider this thought experiment.
Take Pijketty’s model and add in the assumption that everyone has the same Time Preference so no lending takes place (both MPK and r = 0)
Someone discovers a production process that means that by savings in the present more can be produced in the future.
At this point entrepreneurs have a reason to borrow from people who previously had no-one to lend to and interest rates go positive.
Isn’t this an example where MPK drives an increase in r ?
Bob, here’s the rest of the section your Piketty quote is taken from:
p.212:
What Is Capital Used For?
Using the best available historical data, I have shown how the return on capital evolved over time. I will now try to explain the changes observed. How is the rate of return on capital determined in a particular society at a particular point in time? What are the main social and economic forces at work, why do these forces change over time, and what can we predict about how the rate of return on capital will evolve in the twenty-first century According to the simplest economic models, assuming “pure and perfect” competition in both capital and labor markets, the rate of return on capital should be exactly equal to the “marginal productivity” of capital (that is, the additional output due to one additional unit of capital). In more complex models, which are also more realistic, the rate of return on capital also depends on the relative bargaining power of the various parties involved. Depending on the situation, it may be higher or lower than the marginal productivity of capital (especially since this quantity is not always precisely measurable).
In any case, the rate of return on capital is determined by the following two forces: first, technology (what is capital used for?), and second, the abundance of the capital stock (too much capital kills the return on capital).
Technology naturally plays a key role. If capital is of no use as a factor of production, then by definition its marginal productivity is zero. In the abstract, one can easily imagine a society in which capital is of no use in the production process: no investment can increase the productivity of farmland, no tool or machine can increase output, and having a roof over one’s head adds nothing to well-being compared with sleeping outdoors. Yet capital might still play an important role in such a society as a pure store of value: for example, people might choose to accumulate piles of food (assuming that conditions allow for such storage) in anticipation of a possible future famine or perhaps for purely aesthetic reasons (adding piles of jewels and other ornaments to the food piles, perhaps). In the abstract, nothing prevents us from imagining a society in which the capital/income ratio β is quite high but the return on capital r is strictly zero. In that case, the share of capital in national income, α = r × β, would also be zero. In such a society, all of national income and output would go to labor.
Nothing prevents us from imagining such a society, but in all known human societies, including the most primitive, things have been arranged differently. In all civilizations, capital fulfills two economic functions: first, it provides housing (more precisely, capital produces “housing services,” whose value is measured by the equivalent rental value of dwellings, defined as the increment of well-being due to sleeping and living under a roof rather than outside), and second, it serves as a factor of production in producing other goods and services (in processes of production that may require land, tools, buildings, offices, machinery, infrastructure, patents, etc.). Historically, the earliest forms of capital accumulation involved both tools and improvements to land (fencing, irrigation, drainage, etc.) and rudimentary dwellings (caves, tents, huts, etc.). Increasingly sophisticated forms of industrial and business capital came later, as did constantly improved forms of housing.
The Notion of Marginal Productivity of Capital
Concretely, the marginal productivity of capital is defined by the value of the additional production due to one additional unit of capital. Suppose, for example, that in a certain agricultural society, a person with the equivalent of 100 euros’ worth of additional land or tools (given the prevailing price of land and tools) can increase food production by the equivalent of 5 euros per year (all other things being equal, in particular the quantity of labor utilized). We then say that the marginal productivity of capital is 5 euros for an investment of 100 euros, or 5 percent a year. Under conditions of pure and perfect competition, this is the annual rate of return that the owner of the capital (land or tools) should obtain from the agricultural laborer. If the owner seeks to obtain more than 5 percent, the laborer will rent land and tools from another capitalist. And if the laborer wants to pay less than 5 percent, then the land and tools will go to another laborer. Obviously, there can be situations in which the landlord is in a monopoly position when it comes to renting land and tools or purchasing labor (in the latter case one speaks of “monopsony” rather than monopoly), in which case the owner of capital can impose a rate of return greater than the marginal productivity of his capital.
In a more complex economy, where there are many more diverse uses of capital— one can invest 100 euros not only in farming but also in housing or in an industrial or service firm—the marginal productivity of capital may be difficult to determine. In theory, this is the function of the system of financial intermediation (banks and financial markets): to find the best possible uses for capital, such that each available unit of capital is invested where it is most productive (at the opposite ends of the earth, if need be) and pays the highest possible return to the investor. A capital market is said to be “perfect” if it enables each unit of capital to be invested in the most productive way possible and to earn the maximal marginal product the economy allows, if possible as part of a perfectly diversified investment portfolio in order to earn the average return risk-free while at the same time minimizing intermediation costs.
In practice, financial institutions and stock markets are generally a long way from achieving this ideal of perfection. They are often sources of chronic instability, waves of speculation, and bubbles. To be sure, it is not a simple task to find the best possible use for each unit of capital around the world, or even within the borders of a single country. What is more, “short-termism” and “creative accounting” are sometimes the shortest path to maximizing the immediate private return on capital. Whatever institutional imperfections may exist, however, it is clear that systems of financial intermediation have played a central and irreplaceable role in the history of economic development. The process has always involved a very large number of actors, not just banks and formal financial markets: for example, in the eighteenth and nineteenth centuries, notaries played a central role in bringing investors together with entrepreneurs in need of financing, such as Père Goriot with his pasta factories and César Birotteau with his desire to invest in real estate.
It is important to state clearly that the notion of marginal productivity of capital is defined independently of the institutions and rules—or absence of rules—that define the capital-labor split in a given society. For example, if an owner of land and tools exploits his own capital, he probably does not account separately for the return on the capital that he invests in himself. Yet this capital is nevertheless useful, and his marginal productivity is the same as if the return were paid to an outside investor. The same is true if the economic system chooses to collectivize all or part of the capital stock, and in extreme cases (the Soviet Union, for example) to eliminate all private return on capital. In that case, the private return is less than the “social” return on capital, but the latter is still defined as the marginal productivity of an additional unit of capital. Is it useful and just for the owners of capital to receive this marginal product as payment for their ownership of property (whether their own past savings or that of their ancestors) even if they contribute no new work? This is clearly a crucial question, but not the one I am asking here.”
Philippe wrote:
Bob, here’s the rest of the section your Piketty quote is taken from:…
Right, and seeing it in the bigger context makes it even more clear that he is thinking that “marginal productivity of capital” is due to its technological ability to physically increase output. I can’t believe you guys aren’t agreeing with me on that. It is crystal clear. He says it explicitly, and then all of his examples involve physical production.
(BTW I had seen the bigger context originally; I read this entire section before blogging about it. It’s why I’m so confident in what he is trying to say in the smaller part I quoted here in the OP.)
I don’t know how you guys are remaining agnostic as to whether he is restricting “marginal product of capital” to a physical concept. Look again how he introduced it:
=====
Technology naturally plays a key role. If capital is of no use as a factor of production, then by definition its marginal productivity is zero. In the abstract, one can easily imagine a society in which capital is of no use in the production process: no investment can increase the productivity of farmland, no tool or machine can increase output, and having a roof over one’s head adds nothing to well-being compared with sleeping outdoors.
=====
You guys are saying, “Maybe he also had in mind that nobody wanted to borrow 100 apples to eat today to pay back 105 apples next year, just as a pure consumption loan,” but that seems very unlikely. He is clearly thinking in terms of how capital contributes *physically* to output.
He says that
“the simplest economic models, assuming “pure and perfect” competition in both capital and labor markets, the rate of return on capital should be exactly equal to the “marginal productivity” of capital”
In another post, in which you were criticizing mainstream neoclassical economics, you wrote:
“In mainstream economics, it is commonplace for people to say that in a competitive equilibrium, the interest rate equals the “marginal product of capital.”
http://consultingbyrpm.com/blog/2013/01/interest-does-not-equal-the-marginal-product-of-capital-even-in-equilibrium.html
So Piketty is stating the mainstream view, which refers to the unrealistic perfect competition model.
‘He is clearly thinking in terms of how capital contributes *physically* to output.’
Isn’t that a reasonable way of looking at it ? Obviously time preference will determine which physical process are exploited and to what extent. And there won’t be a one-to-one mapping between r and increase in physical output (which would be impossible to measure in most cases).
But you seem to be asserting that time preference is all and increased physical output none of the reason for r being at what ever level it is in a given economy and that seems untenable to me.
Bob,
As a point of reference can you explain how you think Piketty’s views differ from your description of Rothbard’s ?
“A capitalist will be willing to hire an additional unit of a productive resource so long as its rental price is lower than its discounted marginal value product (DMVP). The marginal value product (MVP) is the additional revenue that can be imputed to the marginal unit of a productive factor. The discounted MVP is then simply the present market value of the (future) MVP. For example, if an additional hour of labor will generate $110 of additional revenue in one year’s time, a prospective employer will pay no more than $100 today to hire this worker if the interest rate is 10 percent.
Although many authors stress the importance of variability in the proportion of inputs, it is actually the relative specificity of factors that allows a unique determination of DMVP.
The MVP is determined by the marginal physical product (MPP) times the price of the product. That is, the prospective buyer estimates the increased physical output (i.e. quantity of the good to be sold) due to an additional unit of a factor, and multiplies this by the market price of these extra goods. (To the extent that the market price of the final product declines as additional units are produced, the true MVP will actually be less than this computation would suggest.)”
I assume that in your view the interest rate used for calculating the DMVP is determined “exogenously” (as it were) by TP alone totally independent of the MPP itself – is that it ?
Transformer wrote:
As a point of reference can you explain how you think Piketty’s views differ from your description of Rothbard’s ?
OK guys, I realize I need to be less snarky. But I promise you, you are overlooking something so big here that it’s hard to even get across how you’re missing it.
Rothbard is explaining the *rental price of a capital good (or other productive factor) per unit of time*. That is NOT the same thing as the rate of interest the owner of that capital good enjoys over that same time period.
So, who’s going to be coming out with a book titled “The Failure Of The New-New Economics?”