Very interesting and clear - one of my favourite posts on this blog.
I'm actually interested in how to think about technological changes more generally when depreciation raises the 'hurdle rate' for investment. Doesn't this model imply less capital investment in new technologies (which I will assume has higher depreciation due to faster progress), and possibly even a region where some new technologies don't happen for this reason - is this realistic, what am I missing?
It's a fair point. I was working through pure capital deepening. The comparative static was exogenous, not endogenous. If given the choice, you would never choose the high depreciation capital, given a fixed substitutability. But you maybe would if it comes with better substitutability.
The difference between 'capital share rises' and 'labor share goes to zero' is huge, and I appreciate that you focused on the transition path.
The idea of obsolescence as depreciation seems under-discussed in AI scenarios, since rapid progress raises the hurdle rate.
I also liked your reminder about incidence: if capital is as mobile and flexible as the 'robots build robots' story suggests, capital taxes might be reflected in lower wages or output well before reaching any endpoint.
If the labor share of income goes to zero, who will consume the output of machines? Without broad income distribution—whether through wages or capital ownership—wouldn’t returns on capital eventually collapse?
That assumes capital owners can absorb all output. If the top 1% owns most capital (which is more realistic), their consumption simply can’t scale with production—so where does demand come from, and why wouldn’t returns collapse?
This is a strong and careful piece, and I agree with your central warning about knife-edge endpoints. The jump from “labor share falls” to “labor share goes to zero” does require much stronger assumptions than are often acknowledged, and your emphasis on transition paths rather than endpoints is exactly right.
That said, I think your argument leans heavily on treating capital as primarily reproducible physical capital subject to rapid obsolescence. In an AI-driven economy, a growing share of capital income may come less from MPK in the traditional sense and more from rents — model IP, data advantages, compute chokepoints, ecosystem lock-in, and market power. These returns are not obviously disciplined by depreciation in the same way as hardware.
If capital income increasingly reflects rents rather than reproducible capital returns, the “high depreciation as a stabilizer” mechanism may be much weaker than your framework suggests. In that world, the r > δ + ρ condition can remain satisfied not because capital is endlessly productive, but because it is scarce, protected, or strategically bottlenecked.
So I’m largely with you on the dangers of importing endpoint logic directly into current policy debates. But I’m less convinced that depreciation alone does the disciplining work once capital income shifts from machines to control. I’d be curious how you’d extend this framework to explicitly distinguish reproducible capital from rent-generating AI capital — because that distinction seems central to both the inequality dynamics and the policy implications.
Have you happened to read or at least heard about a few economics papers or reviews of Piketty's big book that claim to show that most of the increase in the returna gap is due to the increases in housing prices? If so, what do you think of the quality of the evidence?
I think I heard about it from Bryan Caplan, but who knows, maybe it was from you. Anyway, I asked ChatGPT 5 about it a few days ago, and this was the beginning of its response:
"Rognlie (2014) A note on Piketty and diminishing returns to capital
Rognlie explicitly frames his note as a critique of Piketty’s predictions about capital’s share and the gap r − g, and then argues that the measured rise in wealth/capital relative to income is dominated by housing."
What’s missing across this debate isn’t another parameter check on substitution or depreciation, but a question about agency.
Both the “labor share → zero” story and the “tax capital to fix it” response implicitly assume a stable locus of decision-making: someone who can still choose accumulation paths, taxation regimes, and redistribution ex post. But the AI dynamics being described—self-replicating capital, rapid obsolescence, highly mobile investment—are precisely the conditions under which agency migrates from actors to structures.
In that setting, inequality doesn’t primarily explode because capital outpaces labor in a growth model; it explodes because decisions are executed without a point where judgment, responsibility, or lived feedback can intervene. Capital taxes then fail not just for incidence reasons, but because they arrive after custody over outcomes has already been lost.
The real fork is “Where, if anywhere, does interruptible agency still sit as the system reallocates work, income, and risk?” Without answering that, both the dystopian endpoint and the policy fix risk being artifacts of a model that assumes authorship long after it has structurally thinned out.
Thanks for the interesting analysis. The problem with the original claim is that it requires that ~90% of the population is fully dependent on the state. This suggests secondary societal effects would soon dominate and any economic modelling will soon fade into background noise. Such a would likely require extreme authoritarianism to function and would be easily captured by those few with capital. This is not the only secondary effect problem. Therefore, this looks more like a manufactured case to support an existing policy preference rather than an experiment that leads to a policy. Still, fun to take it at face value and analyse it!
Brian Albrecht’s essay responds critically to an argument by Philip Trammell and Dwarkesh Patel that AI will vindicate Thomas Piketty’s core thesis: capital will dominate income, labor’s share will fall toward zero, and only a global progressive capital tax can prevent extreme inequality.
Albrecht’s central move is methodological. Rather than extrapolating directly to a futuristic endpoint where labor is irrelevant, he returns to basic growth theory, focusing on the supply and demand for capital. His claim is not that the zero-labor world is impossible, but that it requires a knife-edge set of assumptions that Trammell and Patel largely take for granted.
He distinguishes clearly between two ideas that are often conflated:
Capital’s share rising (e.g. from 30% to 60–70%), which is plausible if AI makes substitution between capital and labor easier.
Capital’s share going to 100%, which is a far stronger claim and requires extreme conditions.
According to Albrecht, labor’s share can approach zero only in two ways:
Perfect substitution: capital and labor are infinitely substitutable, so humans have no comparative advantage in any task.
Unbounded capital accumulation: labor remains productive, but capital grows so fast and so large that labor income becomes negligible.
The essay focuses on the second, Piketty-style path. Albrecht argues that for capital to grow without bound, the return on capital must always exceed depreciation plus households’ required rate of return, at every level of capital accumulation, forever. This is a very demanding requirement.
Here depreciation plays a central role. Rapid AI progress may flatten diminishing returns (supporting capital accumulation), but it also raises depreciation through obsolescence. Cutting-edge AI hardware and models lose value quickly as better versions appear. If depreciation plus impatience implies a hurdle rate of, say, 30%+, then capital’s marginal productivity must stay above that bar indefinitely—an assumption Albrecht finds implausible in standard models.
He therefore outlines three scenarios:
Scenario A (historical): diminishing returns dominate; capital share is stable.
Scenario B (transition): AI makes substitution easier; capital share rises substantially but stabilizes at a finite level.
Scenario C (zero-labor endpoint): capital never hits diminishing returns strongly enough; labor share collapses.
Trammell and Patel, he argues, jump directly from “AI increases substitutability” to Scenario C, ignoring the likely relevance of Scenario B.
The final section critiques their policy conclusion. Even if AI drives capital’s share upward, Albrecht argues that a global capital tax would likely hurt workers, not help them. In a world where capital is highly mobile and supply is very responsive, taxing capital causes it to shrink or fail to accumulate. To maintain savers’ required after-tax return, pre-tax returns must rise—forcing firms to cut wages. The same features that make capital accumulation explosive (easy replication, mobility, elasticity) also make capital taxes ineffective.
His conclusion is cautious but firm: the path matters. We live in the transition, not at the endpoint, and standard economic mechanisms still operate there. Jumping from speculative futures to strong policy prescriptions is unwarranted.
Critique
Strengths
Conceptual clarity
Albrecht’s biggest contribution is analytical discipline. He cleanly separates:
substitution in production vs. responsiveness of capital supply,
rising capital share vs. total capital dominance,
long-run endpoints vs. transitional dynamics.
This alone is a valuable corrective to much AI-economics discourse.
Attention to depreciation and obsolescence
The emphasis on obsolescence is particularly strong. Many AI-driven growth narratives implicitly assume capital that accumulates cheaply and lasts. Albrecht rightly notes that fast progress destroys value as quickly as it creates it, raising the bar for unbounded accumulation.
Internal critique of the policy logic
His argument that Trammell and Patel’s inequality story relies on elastic capital supply, while their tax proposal requires inelastic supply, exposes a genuine tension. This is one of the essay’s most persuasive points.
Respect for uncertainty
Albrecht does not deny radical AI futures; he insists on distinguishing what is plausible, what is extreme, and what follows from which assumptions. This intellectual modesty strengthens his case.
Weaknesses and limitations
Strong attachment to the benchmark growth model
The critique works within standard neoclassical growth theory. If AI fundamentally alters preferences, savings behavior, ownership structures, or the meaning of “capital” itself, the model may be less informative than Albrecht assumes. His argument is strongest as a conditional critique, weaker as a definitive rebuttal.
Underplays political and institutional dynamics
While analytically sound, the treatment of capital taxation abstracts from power, governance, and non-market coercion. In practice, capital taxation debates are not only about elasticities but about institutional capacity, legitimacy, and redistribution through non-wage channels.
Dismisses endpoint thinking perhaps too quickly
Albrecht is right that the path matters—but endpoint analysis can still shape long-run institutional design. If labor income plausibly trends toward irrelevance, the fact that capital taxes are distortionary does not by itself resolve the distributive problem.
Limited engagement with alternative tax bases
He briefly notes consumption or land taxes, but does not fully explore whether AI economies might make non-capital redistribution mechanisms more central, which could weaken his critique of Trammell and Patel’s policy pessimism.
Overall assessment
This is a rigorous, well-argued essay that performs an essential service: slowing down speculative AI economics and forcing its claims through the discipline of growth theory. Albrecht convincingly shows that AI making substitution easier does not automatically imply a zero-labor world, and that the policy leap to global capital taxation rests on fragile and internally inconsistent assumptions.
However, the critique is strongest as a warning rather than a refutation. It shows that Trammell and Patel’s conclusions require multiple extreme conditions to hold simultaneously—not that those conditions are impossible. The essay ultimately defends the relevance of standard economics during the transition, but leaves open the deeper question of what happens if the transition never really ends.
In short: persuasive as economics, cautious on prediction, and most valuable as a reminder that futures thinking still needs models—and models still need assumptions made explicit.
A note here on your model: it oversimplifies savers and their behavior. Some of that is just assuming a flat rate, and you do acknowledge that there is complexity in basically knowing the return rate at which savers abandon complexity.
But what I think you are missing is thinking about where the income that savers are choosing either to save or consume comes from. Namely, in your model that income is either going to come from labor or capital. And that becomes important to think about because savers whose primary income comes from labor is different than savers whose primary income comes from capital.
Essentially, the threshold between saving or spending, what you call ‘patience,’ is not just some fixed constant, but some function of the return to labor (wages) vs. the return to capital (profits/return on capital).
Moreover, savers are not some uniform, equally distributed group; savers have a range of accumulated wealth, and a range of incomes, both of which alter their incentives on how and whether to save or consume. A high wealth, high income individual whose income is 90+% returns to capital has a different set of incentives than a low wealth, low income individual whose income comes 90+% from wages.
Accounting for income and wealth matters too, because it’s not the case that the decision to save is a binary decision between either saving all income or spending all income. There are effectively costs of living, and than costs of lifestyle above that. Effectively with savings we are looking at the concept of discretionary income, and at what split does discretionary income get saved for a return vs consumed. High wealth/high income individuals have more discretionary income, and have as a result much more incentive to reinvest more of their income.
Distribution matters too, because it matters what percent of total discretionary income goes to savings and which to consumption. In other words, if there is existing wealth/income inequality, such that the sum of income is routed more towards high wealth, high income individuals whose income is primarily a function of capital’s share of the economy, then the rate of return those savers will accept before consuming becomes very low. They can maintain lifestyle costs while saving unconsumed discretionary income; if their total wealth/income is large enough, their lifestyle costs may even fall below the return on investment for the unspent (and thus saved) discretionary income. Then the rate of return can functionally approach zero as they have sufficient wealth/income that the low but non-zero return to capital sustains their lifestyle costs. For example, Jeff Bezos can decide he’d rather inverse more incentive his space company than buy a second mega-yacht, even if the space company has very low RoI, without sacrificing much in lifestyle experience.
This all goes to say that the factor you call ‘patience’ on the part of savers amounts to a multi-variate differential equation, where the ‘patience’ rate for investments in capital and labor are functions of (1) the current share of capital and labor in the market (2) the distribution of wealth, (3) the distribution of income, (4) return on investment in labor, (5) the return on investment in capital, (6) the distribution of income between income from labor and income from capital investment.
That is important to realize because that throws the assumption that there is necessarily a steady-state solution out the window. There are very easily initial conditions where that multivariate differential equation could diverge toward infinity, in other words towards a zero-labor outcome.
Your model on depreciation is also flawed. Yes, GPUs are going to depreciate, even become unusable. Similarly with robots and humanoid robots. But the question is not whether there is non-zero depreciation of physical assets— it’s whether those assets continually provide a return on investment over their lifetimes of use above the cost of replacement.
An AI data center is not selling GPU, it is selling compute. So as long as its GPUs are producing compute, it is making profit. The question is whether each installed GPU is producing enough compute to sell over its lifetime to buy a new GPU and produce a profit. As long as that remains true, then the data center is returning a non-zero return on investment in the GPU.
Same story with robots, and other profitable capital investments. As long as the investment produces non-zero RoI, that satisfies the conditions necessary for the scenario of mass wealth/income inequality driving an acceptable ‘patience’ rate to near-but-non-zero. And there’s good reason to believe this can be sustainably true— the cost of compute has sustainably lowered since computation entered the market as a commodity with the invention of computers. Obsolescence depreciation exists precisely because newer GPUs produce more compute for the inflation adjusted dollar. The end product in the AI economy is not the GPU but the compute. As long as compute sustainably gets cheaper over time, then RoI for capital remains above depreciation.
And that is the real ‘robots building robots’ scenario— robots improving their own productivity so that they sustainably maintain return on investment for capital above the ‘depreciation plus patience’ threshold indefinitely.
Combined, these two conditions— extreme wealth/income inequality producing outcomes where the ‘patience’ threshold asymptotically approaches zero but remains non-zero, and robots-building-robots maintaining profitability above depreciation indefinitely— satisfy the conditions you lay out in your own model for the share of labor to reach the ‘zero labor’ condition.
If labor share goes to zero and we don't tax capital to pay for the lost wages, who's gonna consume whatever is produced?. Markets work because most people have a stable income that is not coming from capital gains.
My first issue with this is the abstract treatment of "labour".
The interim scenario where "labour" still has value is that a tiny minority of people have some value and the vast majority have none. This would be a dystopia even if it were possible to extract massive income taxes from the remaining 1% (which seems impossible unless you deny that money is power).
We are not labour. We are people: People who have or do not have jobs.
Very interesting and clear - one of my favourite posts on this blog.
I'm actually interested in how to think about technological changes more generally when depreciation raises the 'hurdle rate' for investment. Doesn't this model imply less capital investment in new technologies (which I will assume has higher depreciation due to faster progress), and possibly even a region where some new technologies don't happen for this reason - is this realistic, what am I missing?
It's a fair point. I was working through pure capital deepening. The comparative static was exogenous, not endogenous. If given the choice, you would never choose the high depreciation capital, given a fixed substitutability. But you maybe would if it comes with better substitutability.
The difference between 'capital share rises' and 'labor share goes to zero' is huge, and I appreciate that you focused on the transition path.
The idea of obsolescence as depreciation seems under-discussed in AI scenarios, since rapid progress raises the hurdle rate.
I also liked your reminder about incidence: if capital is as mobile and flexible as the 'robots build robots' story suggests, capital taxes might be reflected in lower wages or output well before reaching any endpoint.
Thanks for putting this together.
If the labor share of income goes to zero, who will consume the output of machines? Without broad income distribution—whether through wages or capital ownership—wouldn’t returns on capital eventually collapse?
The capital owners consumer in this model.
That assumes capital owners can absorb all output. If the top 1% owns most capital (which is more realistic), their consumption simply can’t scale with production—so where does demand come from, and why wouldn’t returns collapse?
This is a strong and careful piece, and I agree with your central warning about knife-edge endpoints. The jump from “labor share falls” to “labor share goes to zero” does require much stronger assumptions than are often acknowledged, and your emphasis on transition paths rather than endpoints is exactly right.
That said, I think your argument leans heavily on treating capital as primarily reproducible physical capital subject to rapid obsolescence. In an AI-driven economy, a growing share of capital income may come less from MPK in the traditional sense and more from rents — model IP, data advantages, compute chokepoints, ecosystem lock-in, and market power. These returns are not obviously disciplined by depreciation in the same way as hardware.
If capital income increasingly reflects rents rather than reproducible capital returns, the “high depreciation as a stabilizer” mechanism may be much weaker than your framework suggests. In that world, the r > δ + ρ condition can remain satisfied not because capital is endlessly productive, but because it is scarce, protected, or strategically bottlenecked.
So I’m largely with you on the dangers of importing endpoint logic directly into current policy debates. But I’m less convinced that depreciation alone does the disciplining work once capital income shifts from machines to control. I’d be curious how you’d extend this framework to explicitly distinguish reproducible capital from rent-generating AI capital — because that distinction seems central to both the inequality dynamics and the policy implications.
Have you happened to read or at least heard about a few economics papers or reviews of Piketty's big book that claim to show that most of the increase in the returna gap is due to the increases in housing prices? If so, what do you think of the quality of the evidence?
I think I heard about it from Bryan Caplan, but who knows, maybe it was from you. Anyway, I asked ChatGPT 5 about it a few days ago, and this was the beginning of its response:
"Rognlie (2014) A note on Piketty and diminishing returns to capital
Rognlie explicitly frames his note as a critique of Piketty’s predictions about capital’s share and the gap r − g, and then argues that the measured rise in wealth/capital relative to income is dominated by housing."
No. a prgressve consumption tax would work as well to transfer consumption and interfere less with investment and growth.
What’s missing across this debate isn’t another parameter check on substitution or depreciation, but a question about agency.
Both the “labor share → zero” story and the “tax capital to fix it” response implicitly assume a stable locus of decision-making: someone who can still choose accumulation paths, taxation regimes, and redistribution ex post. But the AI dynamics being described—self-replicating capital, rapid obsolescence, highly mobile investment—are precisely the conditions under which agency migrates from actors to structures.
In that setting, inequality doesn’t primarily explode because capital outpaces labor in a growth model; it explodes because decisions are executed without a point where judgment, responsibility, or lived feedback can intervene. Capital taxes then fail not just for incidence reasons, but because they arrive after custody over outcomes has already been lost.
The real fork is “Where, if anywhere, does interruptible agency still sit as the system reallocates work, income, and risk?” Without answering that, both the dystopian endpoint and the policy fix risk being artifacts of a model that assumes authorship long after it has structurally thinned out.
Thanks for the interesting analysis. The problem with the original claim is that it requires that ~90% of the population is fully dependent on the state. This suggests secondary societal effects would soon dominate and any economic modelling will soon fade into background noise. Such a would likely require extreme authoritarianism to function and would be easily captured by those few with capital. This is not the only secondary effect problem. Therefore, this looks more like a manufactured case to support an existing policy preference rather than an experiment that leads to a policy. Still, fun to take it at face value and analyse it!
You said:
summarise and critique
F
ChatGPT said:
Summary
Brian Albrecht’s essay responds critically to an argument by Philip Trammell and Dwarkesh Patel that AI will vindicate Thomas Piketty’s core thesis: capital will dominate income, labor’s share will fall toward zero, and only a global progressive capital tax can prevent extreme inequality.
Albrecht’s central move is methodological. Rather than extrapolating directly to a futuristic endpoint where labor is irrelevant, he returns to basic growth theory, focusing on the supply and demand for capital. His claim is not that the zero-labor world is impossible, but that it requires a knife-edge set of assumptions that Trammell and Patel largely take for granted.
He distinguishes clearly between two ideas that are often conflated:
Capital’s share rising (e.g. from 30% to 60–70%), which is plausible if AI makes substitution between capital and labor easier.
Capital’s share going to 100%, which is a far stronger claim and requires extreme conditions.
According to Albrecht, labor’s share can approach zero only in two ways:
Perfect substitution: capital and labor are infinitely substitutable, so humans have no comparative advantage in any task.
Unbounded capital accumulation: labor remains productive, but capital grows so fast and so large that labor income becomes negligible.
The essay focuses on the second, Piketty-style path. Albrecht argues that for capital to grow without bound, the return on capital must always exceed depreciation plus households’ required rate of return, at every level of capital accumulation, forever. This is a very demanding requirement.
Here depreciation plays a central role. Rapid AI progress may flatten diminishing returns (supporting capital accumulation), but it also raises depreciation through obsolescence. Cutting-edge AI hardware and models lose value quickly as better versions appear. If depreciation plus impatience implies a hurdle rate of, say, 30%+, then capital’s marginal productivity must stay above that bar indefinitely—an assumption Albrecht finds implausible in standard models.
He therefore outlines three scenarios:
Scenario A (historical): diminishing returns dominate; capital share is stable.
Scenario B (transition): AI makes substitution easier; capital share rises substantially but stabilizes at a finite level.
Scenario C (zero-labor endpoint): capital never hits diminishing returns strongly enough; labor share collapses.
Trammell and Patel, he argues, jump directly from “AI increases substitutability” to Scenario C, ignoring the likely relevance of Scenario B.
The final section critiques their policy conclusion. Even if AI drives capital’s share upward, Albrecht argues that a global capital tax would likely hurt workers, not help them. In a world where capital is highly mobile and supply is very responsive, taxing capital causes it to shrink or fail to accumulate. To maintain savers’ required after-tax return, pre-tax returns must rise—forcing firms to cut wages. The same features that make capital accumulation explosive (easy replication, mobility, elasticity) also make capital taxes ineffective.
His conclusion is cautious but firm: the path matters. We live in the transition, not at the endpoint, and standard economic mechanisms still operate there. Jumping from speculative futures to strong policy prescriptions is unwarranted.
Critique
Strengths
Conceptual clarity
Albrecht’s biggest contribution is analytical discipline. He cleanly separates:
substitution in production vs. responsiveness of capital supply,
rising capital share vs. total capital dominance,
long-run endpoints vs. transitional dynamics.
This alone is a valuable corrective to much AI-economics discourse.
Attention to depreciation and obsolescence
The emphasis on obsolescence is particularly strong. Many AI-driven growth narratives implicitly assume capital that accumulates cheaply and lasts. Albrecht rightly notes that fast progress destroys value as quickly as it creates it, raising the bar for unbounded accumulation.
Internal critique of the policy logic
His argument that Trammell and Patel’s inequality story relies on elastic capital supply, while their tax proposal requires inelastic supply, exposes a genuine tension. This is one of the essay’s most persuasive points.
Respect for uncertainty
Albrecht does not deny radical AI futures; he insists on distinguishing what is plausible, what is extreme, and what follows from which assumptions. This intellectual modesty strengthens his case.
Weaknesses and limitations
Strong attachment to the benchmark growth model
The critique works within standard neoclassical growth theory. If AI fundamentally alters preferences, savings behavior, ownership structures, or the meaning of “capital” itself, the model may be less informative than Albrecht assumes. His argument is strongest as a conditional critique, weaker as a definitive rebuttal.
Underplays political and institutional dynamics
While analytically sound, the treatment of capital taxation abstracts from power, governance, and non-market coercion. In practice, capital taxation debates are not only about elasticities but about institutional capacity, legitimacy, and redistribution through non-wage channels.
Dismisses endpoint thinking perhaps too quickly
Albrecht is right that the path matters—but endpoint analysis can still shape long-run institutional design. If labor income plausibly trends toward irrelevance, the fact that capital taxes are distortionary does not by itself resolve the distributive problem.
Limited engagement with alternative tax bases
He briefly notes consumption or land taxes, but does not fully explore whether AI economies might make non-capital redistribution mechanisms more central, which could weaken his critique of Trammell and Patel’s policy pessimism.
Overall assessment
This is a rigorous, well-argued essay that performs an essential service: slowing down speculative AI economics and forcing its claims through the discipline of growth theory. Albrecht convincingly shows that AI making substitution easier does not automatically imply a zero-labor world, and that the policy leap to global capital taxation rests on fragile and internally inconsistent assumptions.
However, the critique is strongest as a warning rather than a refutation. It shows that Trammell and Patel’s conclusions require multiple extreme conditions to hold simultaneously—not that those conditions are impossible. The essay ultimately defends the relevance of standard economics during the transition, but leaves open the deeper question of what happens if the transition never really ends.
In short: persuasive as economics, cautious on prediction, and most valuable as a reminder that futures thinking still needs models—and models still need assumptions made explicit.
Does this flowchart seem about right for what you're talking about?
https://jacgoldsm.github.io/
A note here on your model: it oversimplifies savers and their behavior. Some of that is just assuming a flat rate, and you do acknowledge that there is complexity in basically knowing the return rate at which savers abandon complexity.
But what I think you are missing is thinking about where the income that savers are choosing either to save or consume comes from. Namely, in your model that income is either going to come from labor or capital. And that becomes important to think about because savers whose primary income comes from labor is different than savers whose primary income comes from capital.
Essentially, the threshold between saving or spending, what you call ‘patience,’ is not just some fixed constant, but some function of the return to labor (wages) vs. the return to capital (profits/return on capital).
Moreover, savers are not some uniform, equally distributed group; savers have a range of accumulated wealth, and a range of incomes, both of which alter their incentives on how and whether to save or consume. A high wealth, high income individual whose income is 90+% returns to capital has a different set of incentives than a low wealth, low income individual whose income comes 90+% from wages.
Accounting for income and wealth matters too, because it’s not the case that the decision to save is a binary decision between either saving all income or spending all income. There are effectively costs of living, and than costs of lifestyle above that. Effectively with savings we are looking at the concept of discretionary income, and at what split does discretionary income get saved for a return vs consumed. High wealth/high income individuals have more discretionary income, and have as a result much more incentive to reinvest more of their income.
Distribution matters too, because it matters what percent of total discretionary income goes to savings and which to consumption. In other words, if there is existing wealth/income inequality, such that the sum of income is routed more towards high wealth, high income individuals whose income is primarily a function of capital’s share of the economy, then the rate of return those savers will accept before consuming becomes very low. They can maintain lifestyle costs while saving unconsumed discretionary income; if their total wealth/income is large enough, their lifestyle costs may even fall below the return on investment for the unspent (and thus saved) discretionary income. Then the rate of return can functionally approach zero as they have sufficient wealth/income that the low but non-zero return to capital sustains their lifestyle costs. For example, Jeff Bezos can decide he’d rather inverse more incentive his space company than buy a second mega-yacht, even if the space company has very low RoI, without sacrificing much in lifestyle experience.
This all goes to say that the factor you call ‘patience’ on the part of savers amounts to a multi-variate differential equation, where the ‘patience’ rate for investments in capital and labor are functions of (1) the current share of capital and labor in the market (2) the distribution of wealth, (3) the distribution of income, (4) return on investment in labor, (5) the return on investment in capital, (6) the distribution of income between income from labor and income from capital investment.
That is important to realize because that throws the assumption that there is necessarily a steady-state solution out the window. There are very easily initial conditions where that multivariate differential equation could diverge toward infinity, in other words towards a zero-labor outcome.
Your model on depreciation is also flawed. Yes, GPUs are going to depreciate, even become unusable. Similarly with robots and humanoid robots. But the question is not whether there is non-zero depreciation of physical assets— it’s whether those assets continually provide a return on investment over their lifetimes of use above the cost of replacement.
An AI data center is not selling GPU, it is selling compute. So as long as its GPUs are producing compute, it is making profit. The question is whether each installed GPU is producing enough compute to sell over its lifetime to buy a new GPU and produce a profit. As long as that remains true, then the data center is returning a non-zero return on investment in the GPU.
Same story with robots, and other profitable capital investments. As long as the investment produces non-zero RoI, that satisfies the conditions necessary for the scenario of mass wealth/income inequality driving an acceptable ‘patience’ rate to near-but-non-zero. And there’s good reason to believe this can be sustainably true— the cost of compute has sustainably lowered since computation entered the market as a commodity with the invention of computers. Obsolescence depreciation exists precisely because newer GPUs produce more compute for the inflation adjusted dollar. The end product in the AI economy is not the GPU but the compute. As long as compute sustainably gets cheaper over time, then RoI for capital remains above depreciation.
And that is the real ‘robots building robots’ scenario— robots improving their own productivity so that they sustainably maintain return on investment for capital above the ‘depreciation plus patience’ threshold indefinitely.
Combined, these two conditions— extreme wealth/income inequality producing outcomes where the ‘patience’ threshold asymptotically approaches zero but remains non-zero, and robots-building-robots maintaining profitability above depreciation indefinitely— satisfy the conditions you lay out in your own model for the share of labor to reach the ‘zero labor’ condition.
If labor share goes to zero and we don't tax capital to pay for the lost wages, who's gonna consume whatever is produced?. Markets work because most people have a stable income that is not coming from capital gains.
The whole point is to talk about have happens before labor share gets to zero
"I’m going to hold the number of workers fixed."
Really? Demographic decline is a thing, now, even without AI. How are we supposed to take anything seriously with that prior?
My first issue with this is the abstract treatment of "labour".
The interim scenario where "labour" still has value is that a tiny minority of people have some value and the vast majority have none. This would be a dystopia even if it were possible to extract massive income taxes from the remaining 1% (which seems impossible unless you deny that money is power).
We are not labour. We are people: People who have or do not have jobs.
No NO NO. Do not tax capital or income from capital. Tax consumption.