A Fleshed Out Example Showing Problems With Piketty
[UPDATE: Note that I clarified the thought experiment to make sure it’s obvious that all physical production is due to labor in an economic sense.]
At Mises Canada I elaborate on an example showing Piketty’s approach is flawed even on its own terms. First I’ll refresh your memory about Piketty’s framework:
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. [Thomas Piketty, pp. 212-213]
And now an excerpt of my response to show why this doesn’t work:
[I]magine a world where there are no physical capital goods, machinery, or tools of any kind. Further, land and other natural resources do not contribute to production in any way that can be appropriated by humans.
In this strange world, the only way people can eat is that workers can jump up and grab (edible) birds as they fly overhead. These birds are the sole source of consumption in this economy. However, there is no advantage to standing in one spot versus another; the likelihood of catching a bird is the same on any particular plot of land.
Notice that in this odd scenario, we have satisfied Piketty’s requirements: Technologically speaking, there is no role for capital goods or physical wealth of any kind to contribute to production. Human labor is the sole source of consumption. Therefore, Piketty would conclude that 100% of GDP every period must be attributable entirely to wages, with the capitalists earning 0% of GDP in the form of capital income (whether in the form of interest, dividends, profit, etc.).
Yet hang on. This isn’t correct. Even within the confines of Piketty’s thought experiment, it’s possible that someone in period 1 accumulates a stockpile of the birds, let’s say equal to 50% of that period’s total catch. [UPDATE: Just to clarify what I had in mind, further assume that the reason this person in period 1 catches so many birds is that he figured out a good technique. Then, in subsequent periods, the other workers copy his technique. At any time, the constraint on catching more birds is how much time a person is willing to put into it. Thus there are no rents accruing to those who captured scarce natural resources; production is entirely attributable to the expenditure of scarce labor.] Thus β which is “capital/income” is 50% of GDP in Piketty’s framework. Now since (by construction) there is no way this stockpile of birds can contribute physically to more output, Piketty wants us to conclude that the real return on capital (i.e. the real interest rate) is zero, so that α = rXβ which is “capital’s share of income” is also zero.
But this isn’t necessarily correct, and the possibility of a counterexample shows that Piketty’s framework is wrong. If we suppose that everybody expects the flow of birds to increase steadily over time, and we further suppose that people have subjective preferences in which there is diminishing marginal utility from consuming additional birds in each period, then in equilibrium we will see a premium placed on present consumption versus future consumption. That is, someone will be able to sell a bird in period 1 for a claim to more than one bird in period 2.
For example, suppose the capitalist who starts out in period 1 with the stockpile of birds is able to sell them for claims to twice as many birds available in period 2. This will be physically possible and in everybody’s interest if the “bird catch” grows enough from period to period. Then the real interest rate in this economy is 100% per year.
If you want specific numbers, imagine in period 1 the total bird catch is 100 birds, and one really lucky worker happened to nab 50 of them. So he starts out period 1 with a “capital stock” of 50% of GDP. Then in period 2 maybe the total bird catch jumps to 200 birds and it’s more evenly distributed among the workers, and moreover everybody saw this coming. So in period 1, the workers who were really hungry might agree to pay 100% on a loan from the rich capitalist. He lends out his 50 birds, then next period out of the catch of 200 total, the other workers pay him back 100 birds.
Thus, a macroeconomist looking at period 2 would say GDP was 200 birds, and the “interest income” of the capitalist was 50 birds (because of the total 100 birds given to him, 50 was interest, the other 50 was payback of principal). Piketty would be forced to say that the entire output of 200 birds went to labor in period 2, because capital has no physical contribution to output. Yet it seems undeniable that from an accounting standpoint, the capitalist earned 50 birds in “real” interest income, meaning that the workers must have only earned 150 of the birds in terms of wages.
If Piketty believes that income from interest is impossible in a world where the physical productivity of capital is 0 then you have proved him wrong. Is there any evidence that he believes this ?
Suppose that the supply of birds doesn’t increase over time – doesn’t that make your model unsustainable ?
Finally, assume that the supply of birds isn’t expected to increase and no-one is inclined to borrow present birds for future birds. The interest rate is zero since no-one can lend at a positive rate even if we assume there are willing lenders , right ? Suppose someone discovers a way of catching more birds that involves the roundabout process of building nets. This creates a demand for borrowing by entrepreneurs who want to build nets to sell. Suddenly the interest rate is positive even though time preference hasn’t changed.
If Piketty believes that income from interest is impossible in a world where the physical productivity of capital is 0 then you have proved him wrong. Is there any evidence that he believes this ?
=========
(1) Piketty believes that if the marginal productivity of capital is zero, then the income flowing to capital is zero.
(2) Piketty believes interest income is a form of income accruing to capital.
Therefore
(3) Piketty believes that if the marginal productivity of capital is zero, then capitalists can’t earn interest income.
=========
What part of the above do you dispute, Transformer? Premise (1)? Premise (2)? Or that conclusion (3) flows from (1) and (2)?
Where does he confirm (2) ? (I don’t remember seeing that anywhere, but it does seems a reasonable thing for him to believe.).
But if he does believe (2), wouldn’t (1) preclude anyone from earning interest in a model where (1) is an assumption ? If so then your example is not an implementation of his model since it violates one of his assumptions.
(If you setup a model where you assume “the income flowing to capital is zero.” then clearly you can’t have anyone earning interest income if interest income is y definition within the model “income flowing to capital”).
BTW: I feel we are getting overly-focused on that one extract you put in that first post. I think that is a side show to the big picture on Piketty, where I probably don’t even disagree with you very much. I would welcome your views on the second part of my comment about what happens to interest rates if someone breaks Piketty’s model by discovering a roundabout process.
Piketty includes interest in his measure of capital (the data). He says it a number of times.
And I suspect that were PIketty to read your post he would be convinced (if he were not already) of the possibility of interest income even when MPK = 0 and (1) would become:
“(1) Piketty believes that if the marginal productivity of capital is zero, then the income flowing to capital is zero (excluding possible interest income)” . And nothing much would change in his model or his theory.
Actually I’m pretty sure Piketty would simply say: loans (whether payable in money or birds) are not net wealth. I owe you 5 birds, payable next spring; an asset in your books, a liability in mine. In aggregate, Beta = 0.
Mind you, I haven’t finished the book; but I’m on page 237 and so far I haven’t seen anything that would suggest another reading.
From the point of view of someone with savings (capital) then the following would be 2 possible ways to make money from your savings
1. Set up a business to make consumer loans of birds and earn interest income
2. Set up a business to build nets to increase bird capture next period and earn sales income.
Both are just ways of generating income by providing services to the market (if both options were available then the risk-adjusted . returns , or interest rate, would tend to be equal between them)
Piketty’s simple model explicitly rules out 2), but for reasons I don’t understand Bob is insistent that 1) is still available. Fine. He clearly thinks that its very possibility says something important about Piketty’s overall theory, but I am not yer sure what this is.
I suspect that Bob’s overall point has something to do with the Austrian view that societal time preference is the sole driver of the interest rate in the economy and physical returns to capital are irreverent. If this is Bob’s point I am not seeing it stated very clearly.
All right, now we’re getting somewhere! That’s the best answer I’ve seen yet Kevin Donoghue in response to my complaints.
Kevin, for real, if you see something about that, let me know because I do have a response. But I don’t want to get into, “now if Piketty ever read my stuff, he might say X, but if he does that, he’s in trouble, because Y…”
Transformer wrote:
But if he does believe (2), wouldn’t (1) preclude anyone from earning interest in a model where (1) is an assumption ? If so then your example is not an implementation of his model since it violates one of his assumptions.
Look what you’re doing in this debate, Transformer. You first admitted that the proposition was false, but challenged me to show you that Piketty believed it. You admitted that if he *did* believe it, then I had indeed shown he was wrong.
So I demonstrated to you that Piketty did indeed believe the proposition. Rather than saying, “Bravo, I’ve learned something from this blog!” instead you all of a sudden starting thinking that maybe the proposition was true after all.
Can you see why this discussion seems rather fruitless to me?
My reply was meant to convey the following simple view.
Either
1. Piketty believes (2) to be true generally but that implicitly there can be no interest income in his model as (1) would be violated if this was true.
or
2. (1) needs to be rewritten to exclude interest income.
I also explained why I believe your example is NOT a true implementation of Piketty’s model.
Anyway, I agree it is fruitless so I shall at this point give up and stop trying to understand what you example is trying to tell us.
Unless by “(1) Piketty believes that if the marginal productivity of capital is zero, then the income flowing to capital is zero.” you believe that he thinks that when mpk=0, there is some (unexplained) reason why time preference can”t line up to allow interest income?
Bob,
I tried to let this go but couldn’t as your last comment annoyed me somewhat.
The proposition you refer to is “Piketty believes that income from interest is impossible in a world where the physical productivity of capital is 0”. Is that correct ?
If so: Where and how do I agree that you have proven this to be true? Your (1) and (2) merely define income in such a way that the proposition would be true if the definitions were true, and I quite clearly reject your definition (1) and suggest a different one that would be consistent with Piketty not accepting the proposition.
Piketty said can imagine a society. Imagine the supply of birds is constant over time. It works. You cannot refute an example with a counter example.
If the supply of birds is constant over time then the capitalist cannot make a return on capital, and also the economy does not grow. Indeed every period is the same as every other so the time dimension collapses and we don’t really have an economy any more.
I am just wondering…
do i understand corectly that Pikkety is assuming that Technology goes in production function into the K?
I though that its generally accepted that technology is harrod neutral so it goes into L…
But its true i dont remember how it is in New theory of growth…
Isnt that like first problém of his analysis? I assume that explain that somewhere in the book?
You have accumulation of human capital, which does contribute positively to production, however you don’t allow ownership of intellectual property … other than for a short time, because people can quickly learn technique from each other. Hmmm that’s a clever setup. The Marxists will be cranky if you allow intellectual property, but if they try to totally outlaw human capital their game will become far too obvious.
If I’m a regular Joe bird catcher and I can catch one bird per day, during the first period, suppose I need to catch 10 birds to survive that period. Then to get through next period, I also need 10 birds but my technique is better, so it only takes me 5 days. Total effort is 15 days work over two periods.
If I choose to borrow from the capitalist, I do no work in the first period, but then I need to make 30 birds in the second period, which also takes 15 days work. I’m no better off, but I suppose I’m no worse off either so yeah it comes down to preferences.
Interestingly, the best result the capitalist can achieve in terms of profits (presuming her customers don’t intentionally make a loss, or offer any charitable donations) is to earn a return on capital at exactly the same rate the economy is expanding. I wonder if that’s an accident?
Bob,
Piketty writes:
“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).”
So he’s talking about a perfect competition model.
“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).”
So within this framework it is possible for the interest rate to be higher than the marginal productivity of capital, once you leave behind the unrealistic perfect competition assumption.
Later on he writes:
“The Notion of Marginal Productivity of Capital
…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.”
Here he explains again that once you leave behind the perfect competition assumption, the interest rate can be higher than the marginal productivity of capital.
That’s kind of odd. If the farmer can earn $100 per week from a patch of land and the rent is $120 per week, why even bother to hang around? No one would rent this land.
… assuming “pure and perfect” competition in both capital and labor markets …
The concept of “perfect competition” is incoherent.
As soon as a consumer chooses to buy something, competition becomes “imperfect”.
Consumer preferences make imperfect competition necessary.
Besides, government regulations are the source of barriers to entry, not laissez-faire:
Anti-Trust and Monopoly (with Ron Paul)
http://www.youtube.com/watch?v=8C4gRRk2i-M
So within this framework it is possible for the interest rate to be higher than the marginal productivity of capital, once you leave behind the unrealistic perfect competition assumption.
In Piketty’s world MPK=0 and he said in that in such a world no one earns interest. If there were imperfect competition in that world MPK would still be 0. He didn’t say anything about imperfect or perfect competition.
Put it another way – if no return on capital is possible because MPK=0, what is there for parties in that world to bargain over?
Richard Moss wrote:
In Piketty’s world MPK=0 and he said in that in such a world no one earns interest. If there were imperfect competition in that world MPK would still be 0. He didn’t say anything about imperfect or perfect competition.
Put it another way – if no return on capital is possible because MPK=0, what is there for parties in that world to bargain over?
Exactly, Richard. It would be as if we quoted an economist who believed in the labor theory of value, but said, “Of course, in practice sometimes the employer will keep some of the earnings from what the worker’s value has produced, but other times he will make a mistake and pay the worker too much. So in practice the market value of a good doesn’t *exactly* equal the labor power put into it, but we can imagine theoretical situations in which it is exact.”
This would obviously be totally screwy. I would come up with simple examples showing, e.g., someone finding a consumer good that no worker produced, and on the other hand I could show that just because people dug ditches and filled them up (lots of labor power), that wouldn’t make something valuable.
In response, the defenders of this hypothetical economist could quote where he said in practice, the value of a good wasn’t exactly equal to the amount of labor that went into it.
“He didn’t say anything about imperfect or perfect competition”
Yes he did. He said it very clearly:
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.”
Etc.
Phillipe quotes;
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).
I’ll ask again – in a model where MPK=0, what does bargaining power get any of the parties involved ? There is no “return on capital” to bargain over.
So, what sense does it make for the model to assume perfect or imperfect competition or not?
For example, he says that:
“…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.”
Phillipe,
Yes – where there is an MPK >0 they can do this – someone, somewhere is earning a return on capital.
NO ONE is earning a return on capital in his model – that is what MPK=0 means.
In Bob’s example the loan is for consumption, not investment.
Phillipe,
This is a joke.
First you said Bob is wrongly criticizing Piketty because Piketty assumes perfect competition in his model.
I show that doesn’t matter given his model.
Now you are saying Bob is wrong because he is assuming a “consumption loan” in his model.
Give me a break.
no,
In Bob’s example MPK is zero but the ‘capitalist’ earns interest on a loan for consumption.
According to Piketty the capitalist can earn this interest if you don’t have perfect competition. And if you look at Bob’s example, the ‘capitalist’ is the only one with a stock of birds to lend out. If everyone had a stock of birds to lend out, the interest rate would be driven down.
In Bob’s example MPK is zero but the ‘capitalist’ earns interest on a loan for consumption.
According to Piketty the capitalist can earn this interest if you don’t have perfect competition. And if you look at Bob’s example, the ‘capitalist’ is the only one with a stock of birds to lend out. If everyone had a stock of birds to lend out, the interest rate would be driven down.
Nah Philippe that’s not what’s going on here. There is “perfect competition” in my model; everybody is paid his marginal product.
The possible escape hatch for Piketty is the one that Kevin suggested, namely that even though there is a guy who doesn’t lift a finger and gets a perpetual stream of consumption from his stockpile of food, that nonetheless Piketty would have to say this economy has zero “net” capital assets and zero net interest income, with the workers earning everything. I think at the very least my example shows there is something very odd then about this accounting framework. But, in any event, *that’s* the way you have to deal with my example, if you want to defend Piketty from it. This has nothing to do with bargaining power and workers getting screwed because they’re not actually getting paid their full marginal product.
… in which case the owner of capital can impose a rate of return greater than the marginal productivity of his capital.
Marginal productivity is derived from consumer’s subjective values and subjective costs.
Since a capital-owner who owns a large portion of a given kind of capital is in a position to raise his prices in the context of increased demand (there’s no value in accepting less money when people are willing to pay you more), it cannot be the case that the capitalist earns more than the marginal productivity of his capital.
The prices that people voluntarily pay ARE the marginal productivity of his capital.
Bob, you’re making it sound like Piketty is saying something highly unusual. But all he is doing is stating the standard mainstream neoclassical view, when he says that:
“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”.
Bob was referring to Piketty’s theory, not the neoclassical one, nor Piketty’s reference to it.
I think that aggregate net worth in Murphy’s example is zero. But there is still interest income.
Interest income does not require physical capital at all or aggregate net worth.
There is nothing in the argument that requires economic growth.
The innovator captures 50% of the birds because of a new technique. The others all catch less.
The rich innovator lends some birds to the others. They are willing to pay interest. In the future they will consume less than they earn, but they are reducing today’s shortfall of consumption.
Next period, they all use the new technique. The innovator catches less next period, but receives the ones he lent back plus interest.
He innovator, saver, and lender, earns less from directly capturing birds. Everyone else, after copying the innovator, earns more than they did in the previous period. They use that to pay the interest. While they could pay all the principle too, we can have the loans for many periods. In fact, that makes much more sense from everyone’s perspective.
Of course, it is ugly (by my tastes) because by construction, innovation doesn’t increase total output at all. It just increases the share captured by the innovator.
If there are lots of birds flying by, and so the innovator catches more the first period, and the others capture the same, then the innovator lends some of the birds to his fellows at interest, and then next period they adopt the new technique and capture more too, then everything is nicer. Everyone gains. The innovator doesn’t enjoy all of the benefits from the added production from the new innovation immediately, but rather shares them. Everyone else is able to bring forward the benefits of the innovation they will copy in the future. Everyone gains due to the innovation. The intertemporal transaction provides added benefits.
Yes, consumption-smootthing services have been provided which add utility just as much as additional birds supplied would have done.
Im sorry maybe i posted coment but i cant find it… so if this is repost sorry abou t hat 🙂
“Thus β which is “capital/income” is 50% of GDP in Piketty’s framework.”
I have problem understanding your model economy, because growth of the technology influence labour and not capital which remains zero. why would β be 50%?
Tel and I previously have noted that Piketty’s model is different than this example.
Piketty is imagining a world where no person is better than another at labor: I think Piketty would argue that what Bob describes in his “advantageous method for catching the birds” is a form of technological capital, which has already been ruled out in Piketty’s example.
As Tel notes above, the real simplifying assumption Piketty requires for his world is that the time dimension is meaningless, i.e. the productivity of land can not be different at any point than it is at any other point.
Another option would be to make labor a sort of sorcery, or a process of pure human will, creating regular income quanta ex nihilo.
Regardless, part of Piketty’s world is a uniformity of production capacity across all laborers: Differences would comprise technological capital.
Nominal profits can remain positive REGARDLESS of what is happening on the real side of the economy.
See Reisman’s theory of profit and interest. This theory of profit/interest makes the most sense to me.
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