Is labor a luxury in the long run?

1. Introduction

In every canonical model of automation and growth, if automation is sufficiently advanced, the labor share falls toward zero. Acemoglu and Restrepo (2018) has this implication, for instance. So does Aghion et al. (2019). So do Caselli and Manning (2019), Nordhaus (2021), Moll et al. (2022), and Jones and Liu (2024). Unsurprisingly, ChatGPT believes it, and Gemini, and Claude. The logic is simple: if machines can do everything we can and they outnumber us, their owners will collect more income than we do, just as the world’s, say, non-Italians collectively earn more income than the world’s Italians.

If the labor share will plummet as we approach the limits of automation, this is worth knowing. For one thing, it means that the future will probably be extremely unequal, as discussed in an earlier essay with Dwarkesh Patel, Capital in the 22nd Century.

But as some commentators have emphasized, the argument that robots (or their owners) will collectively make more than human workers, granting that the robots can do all we can and outnumber us, is too quick. This is because some goods are “human-intrinsic”. Part of what it means to put on a concert is to employ human performers, even once we have robots that can just as perfectly (and, if we like, just as imperfectly) produce live music. In other words, though AI researchers give the “full automation of labor” a median date soon after 2100 (Grace et al., 2025)—a prediction Dwarkesh and I took at face value as a premise—we should question it, or even rule it out from first principles.

Fully functional robots would eliminate what is, by far, the primary force that has kept the labor share high historically: that labor has been necessary to produce all our wants and needs. The question is whether the labor share will stay high just because labor stays necessary to produce some of our wants. And if it will, this is maybe even more worth knowing. It means that the literature and the AI reasoning on automation and growth severely mischaracterizes how the most important event in economic history is likely to unfold, and that maybe to prepare for it, instead of investing in Nvidia, you should pick up the banjo.¹

In this essay:

1. In Section 2, I offer a simple illustration of how even a very mild preference for human-intrinsic goods, even in a very narrow range of contexts, can keep the labor share high or even drive it to 1, even as machines get in some sense arbitrarily capable. The idea is that the machines can get very numerous, whereas there is only ever at most one worker per person; and once a machine-provided good or service becomes plentiful enough, the marginal utility it offers starts falling by more than half every time its quantity doubles. I also explain how economic models systematically underrate this possibility.

The premium some place on human-intrinsic goods will at least make the labor share fall more slowly than it would otherwise. Nevertheless,

2. Through the rest of the essay, I argue that the models are probably more or less right on this score in practice: human-intrinsic goods will probably not be enough to keep the labor share high in the long run.² This is because a large and indeed growing number of goods, mostly not human-intrinsic, may likewise remain in limited supply; because some whose supply explodes may remain valuable nonetheless; and because the marginal utility of human-intrinsic goods may fall as the opportunity cost of consuming them—e.g. the time taken away from consuming goods far superior on other dimensions—rises.

It’s only a collection of arguments of varying rigor, and as always, I hope some of them are interesting whatever you think of how to weigh them.

Wages vs. labor share

My focus here is the labor share, not “real wages”. Indeed, according to the most straightforward way of modeling these things, once we have machines that can do all we can, wages will rise. This is because the human body will remain as functional as it ever was, and because, as long as the robots are not better than we are at everything in the same proportion, we will have some comparative advantage that makes room for gains from trade. Italians earn higher wages than they would if they were the only people in the world.

That said, I think it is also possible that even wages fall to zero, e.g. for reasons summarized in Section 4: “Time and other scarce complements”.

Typical wage share low vs. labor share zero

Putting aside concerns about absolute wages, I believe the main reasons some people are concerned (or glad) about the prospect of the labor share approaching zero are the ones explored in the first essay: namely the implications it could have for the concentration of influence over the future, the importance of inheritance, and so on.

But there are two ways the labor share could fail to approach zero without changing these implications much. First, the labor share could simply stabilize at a positive but very low level, say less than 5%. Second, the labor share could stay non-negligible only because of a few top, say, entertainers, so that wages as a share of GDP fall indefinitely, as in a standard model of full automation, once these few are excluded.

Here I am arguing that the labor share will probably ultimately approach toward zero (without taking a stand on whether wages will rise in absolute terms). But I will also note where objections to this stronger conclusion are still compatible with the weaker conclusion that typical wages, as a fraction of GDP, will probably fall to a small fraction of their current level.

2. Why the labor share could stay high or rise

A. Because labor stays scarce

Suppose we consume two goods: [those produced by] capital K and human labor L. Suppose our preferences take the following form:

u(K,L) = 10(1 - e^-K) + (1 - e^-L). (*)

This utility function is not rigged to produce a strong preference for labor. For one thing, labor is not necessary to live and thrive. With enough capital, we can do without labor entirely and enjoy life at “10 utils”; at most, labor can offer us 1 util more. For another thing, on no margin do we ever find a bit of labor extremely valuable. That is, du/dL is never high: its maximum value is 1, which it achieves when L=0.

Nevertheless, if L is fixed and K rises without bound, the labor share rises toward 1. This is because prices should stay proportional to marginal utilities: otherwise consumers can increase their utility by buying less of one thing and more of the other. When L is fixed, here, so is du/dL. But as K rises, du/dK (=10e^-K) eventually falls by more than half for every doubling of K: its negative elasticity to K is eventually greater than one. So spending on K will eventually fall relative to spending on L.

In fact, this is true if we replace the “10(1-e^-K)” component of the utility function with any increasing, concave function with an upper bound. Observe that the edge-case, in which du/dK falls by exactly half each time K doubles, is the unit-elasticity case in which u( · ;L) is logarithmic.

This would be a world in which everyone who works is providing a human-intrinsic good like a musical or athletic performance, and we are all spending essentially all our income on the rich cultural panoply that results.

How macro models tend to underrate this possibility

In a standard macroeconomic model, an awkward chimera of a thing called “output” at time t, denoted Y_t, is produced using various inputs—sometimes framed as tasks, intermediate goods, or factors of production:

Y_t = F(X_1t, X_2t …).

Some of these inputs are capital, or can be produced by capital, of which we have K_t units total. The rest are or must be produced by labor L.

Some fraction of a given period’s output is turned into consumption, C_t. The rest—fraction s of it (s for “saving”)—is turned into capital, for future use in production. If capital depreciates at rate δ, consumption and the rate of net capital accumulation equal

C_t = (1 - s)Y_t, K_t+1 - K_t = sY_t - δK_t.

This model of consumption and capital accumulation implicitly assumes that one unit of new capital always costs one unit of foregone consumption: that is, since the units are arbitrary, that the price of capital goods relative to consumption goods does not change. This assumption is motivated by simplicity and by the observation that, at least until recently, the prices of capital and consumption goods did evolve similarly.

Under this assumption, whether the (competitive) labor share can stay high as capital accumulates comes down to our production function F(·) for “output” across the board. In particular, the labor share only stays high if there is always some input X_i which only labor can provide, and which is “bottlenecking”, in the sense that output is significantly limited by lack of this input. So the labor share, in these models, stays high only while labor remains a bottleneck to the production of capital and consumption alike. This is bad news for the labor share, for two reasons.

1. The notion that labor will always be needed to produce capital goods seems much less plausible. Unless we have a strong intrinsic preference for human inputs deep into the supply chain, capital will be produced by capital once we have machines that can perform all the physical and cognitive functions of the human body.

2. Somewhat paradoxically, if lack of labor does constrain the growth rate of capital, it slows the process by which capital abundance drives down the capital share, along the lines of the previous section.

But the constant price ratio between consumption and capital goods is not a law of nature. Indeed, capital goods have already gotten significantly cheaper relative to consumption goods in recent decades.³ When thinking about the future of automation, I think we should emphasize the possibility of what’s called “investment-specific technical change”—in which the production of capital goods is automated more rapidly than the production of consumption goods—or avoid the chimera of “output” altogether and give capital and consumption separate production functions. In the simplest case, we could posit

C_t = u((1-s)K_t, L), K_t+1 - K_t = sAK_t - δK_t.

Here, capital can self-replicate on its own: A is how many robots a robot can build per period, if it is told to spend all its time building new capital (s=1) rather than assisting with consumption. When A is high, K can thus grow very rapidly. Nevertheless, our preference for human-intrinsic goods may keep labor a bottleneck on the consumption side, e.g. if u(·) takes the form given above.

B. Because labor is a luxury

Part A points out that, when our preferences take a certain reasonable-seeming form (*), the capital share eventually falls if the quantity of capital rises unboundedly but the quantity of labor does not. That is, capital and labor are gross complements in consumption when capital is plentiful. Another feature of these preferences is that labor is (typically) a luxury: fixing the prices of labor and capital, the fraction of one’s budget one spends on labor rises as the budget increases.

Suppose only that the market-clearing price of K is less than 10x that of L. (Recall from part A that, if capital is abundant enough, the “average consumer” will find du/dK arbitrarily less than du/dL.) Then, since the marginal utility of the first unit of K is 10x that of the first unit of L, the poor buy K exclusively. Then you buy some L too when your budget is large enough, and in the limit, as your budget grows to infinity, the labor share of your consumption basket may be very high.

For example, suppose the aggregate supply of K per capita is 5 and that of L is 1, and all but one person has approximately the average budget, which is 1. Then the market-clearing prices will be p_K ≈ 0.1, p_L ≈ 0.5. The last person spends 0% of his budget on L until his budget is at least 0.38, but as the budget rises to infinity, the share of his spending on L rises to around 5/6.

Relatedly, given preferences (*), the labor share ultimately rises if capital starts out more plentiful than labor and both are scaled proportionally.⁴ So, even putting aside the fact that capital can grow more plentiful while labor doesn’t, enrichment across the board—e.g. due to technology that multiplies the quantities of “effective” labor and capital by the same proportion—raises the labor share.

How macro models tend to underrate this possibility

The issue again involves aggregation. Before aggregating consumption and capital goods into “output” comes the step of aggregating different kinds of consumption goods into “consumption”. For reasons we don’t have to get into here, this can only really be done coherently if people have (identical and) homothetic preferences, meaning that nothing is a luxury: the shares of their budgets they spend on each good do not depend on how big the budgets are. So homotheticity is very often assumed for simplicity, even though it makes the prediction that we will not systematically shift our consumption toward labor-intensive goods as we get richer.

3. Many other goods will stay scarce

To summarize Section 2, human-intrinsic goods could sustain or raise the labor share because, unlike other goods, their quantity does not grow fast enough to lower their marginal utility much—perhaps does not grow at all—whereas the quantity of other goods does.

The simplest response to this case for a high labor share is that the share of many other goods, not produced by labor, could rise for similar reasons.

I will assume throughout this section that the quantity and marginal utility of labor stay fixed, as in Section 2A. This will mean that to consider the evolution of the labor share, we can just focus on how non-human-intrinsic goods could also have roughly constant quantities and marginal utilities in the long run, or have marginal utilities that fall more slowly than their quantities grow.

A. Goods whose share could rise because they’re absolutely scarce

The goods (or inputs to production) most closely analogous to labor, as modeled in Section 2, are those whose quantities per capita will not grow, or not grow quickly, in absolute terms. For example:

1. Natural resources for use in production;⁵

2. Natural resources for use directly as consumption, e.g. natural beaches;

3. Historical artifacts;

4. Fast transportation channels for oneself and one’s property, e.g. restricted-access road lanes or cleared flight paths for private jets;

5. Goods sold monopolistically, due to a patent/copyright, trade secret, or natural monopoly; and

6. Newly invented goods which cannot yet be mass produced (even if their markets are competitive).

In principle, any of these could dominate GDP in the long run. They are a long way from doing so now, but so is human-intrinsic labor. To take the first item on the list, in the US, mining alone constitutes 1.2% of GDP. The share of GDP spent on all of arts, entertainment, and recreation is 1.1%, and the wage bill in this sector is less than 0.6% of GDP.⁶

B. Goods whose share could rise because they fuel “contests”

Other goods could stay valuable because what matters is our consumption of them—or businesses or governments care about their use of them—relative to others’, rather than their use of them in absolute terms. Consider

7. Military equipment and services;

8. Hacking (including e.g. for corporate espionage) and cybersecurity;

9. Legal services;

10. Marketing services, including e.g. SEO for promoting products in AI-populated markets;

11. Religious, political, or philosophical evangelism; and

12. Beauty products.

I’ll call these “contest goods”, and assume here that winning the contest is not a human-intrinsic project or one with human-intrinsic inputs. The point that some people may enjoy how much labor they can consume relative to their peers for status reasons is discussed in Section 6: Relative status.

Let c_i denote person i’s consumption of some contest good and C denote its total supply. If c_i/C appears anywhere in i’s utility function—even if a standalone c_i term also appears, e.g. because marketing to some extent grows a market without cannibalizing the competition—then as c_j rises for all j, each proportional increase in c_i is, at minimum, eventually about equally valuable for i. That is, all else equal, doubling C will cause its price to fall by no more than half (relative to labor, if the marginal utility of labor does not change). This arguably seems like a natural central case, and it yields the edge case in which the contest good’s share neither rises nor falls as its quantity C grows. This in turn would prevent the labor share from rising to 1, but it would not drive the labor share to 0.

But in a contest, the value to i of having an extra unit of some good fueling the contest may fall more or less than proportionally to the good’s supply. If it falls more than proportionally, the relative price of C falls faster than its quantity rises, and (all else equal, as above) its share falls. For instance, suppose that once, say, legal expenditures on both sides of a case are high enough, further expenditures are essentially useless: one’s probability of winning is mainly determined by the “true strength” of the evidence and legal arguments. Then as everyone’s use of legal services rises, the legal share will eventually fall. Conversely, suppose that when, say, military expenditures in a war are high enough, the magnitude of the forces deployed overwhelm the sources of noise that sometimes allow underdogs to win, and victory is almost guaranteed to the side with the largest expenditures. Then when C is large, what enters the utility function is more like an indicator function of whether c_i = max_j {c_j}, in which case, if c_i = C/population, the marginal value of increasing c_i does not fall at all as C grows. So in this case the military share can rise indefinitely.

This is important because the labor share approaches zero as long as some capital-provided good(s) come to dominate GDP.

C. Goods whose share could rise because we satiate in them slowly

If there are some capital-provided goods in which u(·) grows faster than logarithmically, then their marginal utility falls more slowly than their quantity rises, so the capital share rises.

When we consider only some fixed set of conventional consumption goods, even goods of much higher quality than any available today, it seems hard to deny that our utility will rise only to an upper bound—so, eventually sub-logarithmically—as their quantities rise. If we all had warehouses full of luxury vehicles, clothes, household appliances, and food of all kinds kept fresh, and robots that could cook the food better than the best chefs, anyone who likes concerts even a little bit would prefer one concert ticket to yet another doubling of everything else.

But there are other “goods” in which some people would probably not satiate. Most straightforwardly,

13. Philanthropy

essentially lower-bounds the marginal value of capital to e.g. total utilitarians⁷ even after everyone’s needs and wants are all met. Suppose we’ve sorted out the relevant engineering and philosophy of mind well enough that we can turn 1 unit of capital into a happy artificial mind, which a utilitarian always values as much as “α < 1 utils” of her own consumption utility (which takes the form (*)). If she allocates fraction p of her capital spending K to creating happy artificial minds, her utility is

αpK + 10(1 - e^-(1-p)K) + 1 - e^-L.

In principle, once capital single-handedly builds capital, a single person accumulating large quantities of capital and failing to satiate in it can drive the capital share to 1.⁸

Some people might likewise have utility that grows less concave than logarithmically in capital due to its ability to provide other goods which they are extremely far from satiating in, such as

14. Years of life;⁹

15. R&D to introduce new consumption goods, and so raise the “utility ceiling” achievable with a large budget (for more on this point, see Section 5: Labor as one good among many); and

16. “Experience size”, and other potential ways of modifying the brain so that it can experience more wellbeing per unit of time.

4. Time and other scarce complements

Throughout Section 3, I assumed that the quantity and marginal utility of human-intrinsic goods stayed fixed. The point was that (A) the same might be true of some kinds of capital, and (B, C) the quantity × marginal utility of some kinds of capital might stay high or rise even as their quantities rise.

Capital accumulation, and technological development that expands what capital can do, doesn’t affect the marginal utility of human-intrinsic goods if the latter are “additively separable” in our utility functions, as in the example of Section 2. But there may be interactions. That is, plentiful and capable capital could change the marginal utility of human-intrinsic consumption at any given quantity. An important interaction of this kind is that it could redirect time, and other scarce “complements of consumption”, away from human-intrinsic goods.

Today, labor is largely used to produce goods we can consume without giving up much of anything else. But in a future where labor is only valuable for the human touch, extracting this value will require engaging with that touch, and paying the opportunity costs of doing so. As those opportunity costs rise, because labor-free experiences are superior on every dimension except human authenticity, the marginal utility of consuming labor can easily fall to zero or below.

Time is the clearest example. As Becker (1965) pointed out, we all have a roughly fixed endowment of time, and the main cost of consuming something is often the fact that it takes time away from consuming something else. Most movies I would pay not to watch, even most movies I would somewhat enjoy watching. Just as people already spend much more in total on movies than on live theater (though a theater ticket is often more expensive than a movie ticket), the GDP share of both would probably fall with sufficiently mind-blowing alternative entertainment, even if the latter were free. Likewise, a Waymo ride is preferable to an Uber ride for many people (I expect for essentially everyone in the long run, especially once it comes with a robot to help with the bags), and the time cost is essentially the only thing keeping many people from taking more rideshare trips (also presumably ~everyone in the long run, once people are rich and cars and electricity are cheap). Rich people who prefer Waymo would not take Uber rides even if they were free, any more than most people would go back to riding slow, bumpy horses even if someone introduced a free Neighmo, at least once the novelty wore off.¹⁰

To illustrate the point formally, if we modify the utility function of Section 2 to

u(K,L) = (1-L)*N(1 - e^-K) + L,

where N indexes what we might call the quality of the capital and L ∈ [0,1] indexes the fraction of our time spent engaging with a human-intrinsic good, it is undesirable to consume any L at all as long as N(1-e^-K)>1.

The same logic applies to other near-fixed complements of consumption, such as

• appetite (one might pay not to eat a meal; every human-cooked dish crowds out a healthier and better-tasting one),

• intoxication tolerance (likewise),

• physical stamina (every human-guided hike up a mountain leaves less energy for a safer and more beautiful one), or

• room around the house (every human-crafted piece of furniture or clothing gets in the way of a more comfortable, functional, and beautiful one).¹¹

And because these constraints are all bottlenecks on utility, means of relieving them—medical interventions that let us sleep less, raise metabolism, increase stamina, etc.—can all be added to the list of capital-intensive goods that might come to swallow GDP rather than human performances.

Incidentally, as Yanagimoto (2026) argues, consumption time costs may be a big part of why people are having so many fewer children than they once did, and why fertility subsidies make so little difference. Even if all the financial costs of having and raising a child were covered by the state, raising a child is only about as fun as it ever was, whereas the other uses of time keep improving.

To be sure, capital accumulation and technological development might change the marginal utility of human-intrinsic goods in other ways as well, and some of these might point in the other direction. Modern A/V equipment makes concerts more fun. But once we have robots that are functionally indistinguishable from people, it seems hard to tell a story for why all this advanced capital wouldn’t tend to improve robot-produced experiences by as much or more.¹²

5. Labor as one good among many

Return to a model like that of Section 2. Put aside all the arguments about goods in permanently fixed supply like natural resources; contest goods; and goods in which we may not satiate, like total-utilitarian philanthropy. Assume that these remain small shares of GDP.

Hubmer (2023) studies the recent history of the labor share in the US in a model that doesn’t feature these possible sources of a high long-run capital share, and allows for both “investment-specific technical change” (declines in the price of capital relative to consumption goods) and nonhomothetic preferences: the two potentially labor-share-preserving forces highlighted in Section 2. Sure enough, he finds that (a) the price of capital goods has been falling relative to that of consumption goods, and (b) at any given time, labor is a luxury: the richer someone is, the larger a fraction of her budget she spends on goods with high-labor-share supply chains. Nevertheless, as the capital has rapidly accumulated and the country has gotten richer, the labor share has fallen. Why?

His answer, in a word, is technology. As capital has accumulated, we have come up with ever more ways for capital to be useful, and in recent decades this has outweighed the two forces above.¹³ Of course, there is no law that uses are found for every plentiful resource so that larger quantities yield larger shares in the long run. Where water is more plentiful, its share is lower. But the easier it is to develop new uses for a thing, the easier it is for growth in its supply, along with advances in technology, to yield a long-run rise in its share. As oil grew more plentiful, we did find new uses for it: what had just been a lamp fuel started being used in cars and jet engines and turned into plastics, and its GDP share rose as its production grew a thousand fold. For capital as a whole, over the last half-century, technology in this sense has succeeded. Superintelligent capital as a whole will be the most versatile product category imaginable.

Hubmer works in a model with a fixed set of 362 goods, so the “increased usefulness” of capital takes the closed form of a rising capital share at the good level. But under the hood, each of these 362 is really a large and growing set of goods, with new (and evidently, on average, more capital-intensive) varieties partially replacing old varieties all the time. And often, of course, new goods don’t just more cheaply provide exactly the same services as the old, but provide services that any quantity of the old goods could not provide. That is, though at any point in time our utility functions might look roughly like (*), with a fixed ceiling (u=11, in the example) on the utility achievable with an arbitrarily large budget, an ever larger capital stock will motivate the design of new goods that raise this ceiling. Furthermore, with advanced AI, we will have intelligent machines to design them. If this “race between preferences and technology” (as Hubmer calls it) continues to be won by technology, the capital share will continue to rise as capital accumulates and we or AI come up with ever better things for capital to do.

This point can be framed in two ways. The first analogizes human-intrinsic goods in the future to a narrow set of varieties in a conventional “expanding varieties” model, in which case the share of these varieties will fall (an elaboration on points #5 and #6 from Section 3). The second reasons from a stylized history of technological development and new products, and might be read as a case for thinking that the long-run R&D share will be high (an elaboration on #15). Since the profits made by selling new goods are largely what support the R&D costs of developing them, these framings are to some extent two sides of the same coin.

My family and other varieties

On the simplest analysis, the labor share falls in the limit of automation because labor and capital are perfectly substitutable. The model of Section 2 overturns this logic by positing that capital is a commodity, homogeneous and ever more plentiful, from which labor alone is differentiated and scarce. But capital is not homogeneous, any more than [capital + labor] is. With the exception of true commodities, every good from every firm is differentiated from the rest to some extent, and its producer doesn’t increase its production willy-nilly, but choose its profit-maximizing quantity.

Suppose there were only two sodas, 7Up and Coke. If the quantity of 7Up on the market grew unboundedly while the quantity of Coke stayed fixed, the market-clearing price of 7Up would eventually fall faster than quantity rose, so the Coke share (within soda) would eventually rise.

The supply of soda per American has grown by a large multiple over the last century, and the Coca-Cola Company can restrict the supply of Coke to the profit-maximizing quantity. This is an even more advantageous position to be in than labor’s position in Section 2: it would be analogous to the case in which labor’s supply per capita is not just capped, or shrinking as people switch to leisure, but set by an aggregate-wage-maximizing union to which everyone in every industry belongs. Nevertheless, the Coke share—the share of Coca-Cola Original in total US soda sales, to be precise—has fallen, from over 50% in 1940 to under 20% today.

This is because the large quantity of non-Coke soda did not all come in the form of 7Up—making this much 7Up would not have been profitable—but consisted of an expanding range of varieties, the supply of each of which grew only to its profit-maximizing quantity, which was well short of satiation. If the new sodas had not been developed, then as soda budgets grew and the cost of producing soda fell, Coke markups would have grown and grown. So would the money to be made by developing alternatives that could substitute, at least for some consumers, at least for the last few units.

Taking the alternative scenario to the extreme, suppose the supply of Coke stays fixed into the future but the Coke share of GDP (not just of soda) stays bounded above zero. If growth continues, and no one is leaving money on the table, this would imply that on the margin, even if we put literally astronomical amounts of matter and energy into the project of creating a single ounce of some drink, there is not a single person who would prefer it to one of her ounces of Coke. But substitution is often possible with enough effort, and so in the long run, individual products in fixed supply tend not to swallow GDP, despite the logic of Section 2. As illustrated by the case of energy sources from animal power to coal to oil to natural gas to solar, and the case of land (from which we have “substituted” by developing ever less land-intensive ways of farming), and indeed by the case of literally every consumer product whose maker has a monopoly on it, we have a long history of developing substitutes for a product once the incentive is sufficiently high.

The main exception has been labor, and goods and services for which it is hard to reduce the labor requirement, like haircuts, nursing, and teaching. And uncontroversially, the main reason for this exception, historically, is the massive “moat” imposed by the fact that human minds and hands have been so radically different from, and more capable than, anything else nature gives us or we can build. The question is whether each unit of labor’s ability to stay preferable to whatever else we can invent with a positive fraction of GDP will survive when this moat is gone, and the only things humans have going for them is their human identity.

I grant that it may. People are willing to spend more in total to watch humans than bots play chess, and it’s hard to imagine we’ll ever pay less to watch humans than bots play football. It’s conceivable that even a quintillion-dollar effort—including, say, on developing systems with their own “personalities” and artificial limitations—would not yield forms of entertainment, however broadly construed, which we prefer to those featuring Messi or Magnus Carlsen.

But if we reason by analogy to most other goods, the identity moat seems very weak. Every product line is identically itself; and though in our nostalgic moments we might be willing to pay some premium for Coca-Cola Original just because it’s the taste we know people have enjoyed for generations, or ale actually brewed by Trappists, or champagne from Champagne, this has not been nearly enough to prevent new sodas and craft brews (many with their own beloved identities) from gaining market share on balance. The new products have sometimes substituted for the old products by scratching a similar itch without perfectly resembling them on a physical level, but either way, new drinks have collectively been economic substitutes for old. And as far as I can tell, the same can be said about essentially every product category, including food, clothing, shelter, and visual entertainment. The world’s most valuable painting—the Mona Lisa—is valued at something like $900m, maybe more than all the world’s prints and replicas of it, but less than The Da Vinci Code grossed in theaters.¹⁴

So I’m more inclined to return to the analogy in which there is a constant number of Italians and they own the world, including its growing population of (robotic) non-Italians. Italians too have an identity, but it would be a mistake to apply the model of Section 2 to “authentic Italian-cooked food” and “other food” and conclude that the Italian food share, among Italians, will go to 1 as other food grows more plentiful. This would be the right model if “other food” were homogeneous. But in Italian-American neighborhoods across the country, as the other food has arrived in ever wider varieties, the Italian share has fallen.

Human-intrinsic goods have not bottlenecked GDP historically

The previous subsection offered some “microeconomic” analogies. I’ll now try to consider the ability of new varieties to circumvent the “human-intrinsic preference bottleneck” at a macroeconomic and long-term scale.

Pick a part of the world and a time in the relatively distant past—say, Mongolia in the year 1000. The local economists could have argued that though very few people yet sing [or offer other labor-intensive performances] for a living, the “song share” of GDP will eventually rise to 1. This is because everyone else is producing things like horses, cheese, and yurts, which we could get more efficient at producing, and in which we will saturate; whereas the labor requirement of a song doesn’t change, so singing will stay valuable on the margin. That is, our utility functions look something like

u(stuff, songs) = 10(1 - e^-stuff) + (1 - e^-songs)

(they might say)—with enough horses, cheese, and yurts, one eventually prefers a song to yet another doubling of one’s stock of horses and so on—so the non-song share will eventually fall to zero.

A millennium of economic growth later, it’s still essentially 100%. Why?

For the most part, I would say, because we came up with new goods which no quantity of horses, cheese, and yurts could make up for either. Unless you have highly unusual preferences, you would eventually prefer the first car or smartphone to yet another doubling of your stock of horses and so on: indifference curves attainable with a large enough budget today exceed the “utility ceiling” imposed by the goods of 1000 Mongolia.

So, though our utility functions in money at any point in time may look something like u($) = N(1 - e^-$), or u($) = N(1 - e^-$/N), for some N>0—or, to separate the human-intrinsic goods from the rest, something like

u = N(1 - e^-K/N) + (1 - e^-L)

—N itself rises over time as we develop new goods. That is, when capital-driven R&D is what raises N, we have something like u = N(SK)*(1 - e^{-(1-S)K/N(SK)}) + (1 - e^-L), where S is the fraction of capital used for R&D.¹⁵ The long history of rising “N”, and the near-infinite space of possible things advanced AI could invent in principle, suggest (to me) that utility will not hit a hard upper bound for an extremely long time—i.e., edge cases aside, that the negative elasticity of du/dK to K will be less than or equal to 1, not greater.¹⁶ This yields a weakly rising capital share as capital accumulates, once capital can do the R&D to invent ever more new goods and build the goods once they are invented.

As an aside, how the R&D share S evolves is a further question. The share of income spent on final capital goods may fall to zero, in the story above, but what would displace it is not labor but capital-driven R&D. This point is explored more fully in a paper in the works with Chad Jones, but for now note that on the account above,
a. technology that expands the range of goods and
b. the inputs (labor/capital) that let us produce units of the goods already invented
are gross complements. In particular, you can’t make up for a lack of technology with lots of quantity. As a result, if (a) less than doubles (in the relevant sense) after every doubling of investment, since “ideas” (in the relevant sense) get harder to find, then instead of scaling up production and R&D proportionally, it will be efficient to let the R&D share rise toward 1. Unlike the live music share, or even the entertainment share, the R&D share has indeed risen appreciably over time.¹⁷ In a conventional growth model, by contrast, technology just multiplies our effective quantities of labor or capital—so we can make up for a lack of technology with lots of labor and capital—and a rising R&D share is harder to explain.

6. Relative status

Section 2 considers the case in which GDP is dominated by the goods which require labor and which we enjoy consuming for their own sake, regardless of how many others get to enjoy them. Some have argued that GDP will be dominated instead by status games, in which the rich of the future spend much of their money on labor-intensive goods simply because labor is in fixed supply. Once we remember how the wealth-weighted distribution of preferences can change, though, I would argue that status games actually give us another reason to believe that the labor share in the long run will fall.

At first, the rich will doubtless compete for status in part by bidding up the prices of goods in limited supply, as many do today. Even this will not necessarily sustain the labor share: labor will continue to be one of the goods in limited supply, but so will all the other goods listed in Section 3A.

But status-seeking consumption and investment lie on a spectrum: instead of paying for an entirely useless monument or entourage, it’s also possible to win status by owning more than one’s neighbors of a “socially legible” (cool!) productive asset. For instance, people often sacrifice some potential returns in buying sports teams, racehorses, media outlets, and famous restaurants or hotels. This was surely part of the spirit in which Elon Musk bought Twitter, and in which he founded SpaceX and Jeff Bezos founded Blue Origin. In its purest form, status competition via investment can take the form of competition over the wealth leaderboard.

As time goes on, wealth will be ever more concentrated among those who prefer to compete primarily “in investment”. In principle, two people competing over their respective capital stocks could be enough to drive the capital share to 1, once capital goods no longer require labor for their production.

Conclusion

On balance, I think our preferences for human-intrinsic goods will probably slow the long-term decline in the labor share but not reverse it. The arguments for labor staying valuable because it is scarce, while capital is plentiful,

1. seem to apply at least as well to many kinds and uses of capital (Sections 3 and 6);

2. will likely fail because amazing capital goods raise the opportunity cost, and so lower the marginal utility, of labor (Section 4); and

3. will likely fail again because intelligent machines can invent new uses for themselves, greatly slowing the process by which they grow less useful as they grow more plentiful (Section 5).
   

Thanks to Bharat Chandar, Tom Davidson, Will MacAskill, Dwarkesh Patel, and Parker Whitfill for comments and relevant conversations.

1. Not that these are entirely exclusive! And not to caricature the high-labor-share scenario: the most valued cases of “human touch” in the future may of course take many forms beyond banjo-playing, including AI-augmented forms of self-expression we have not yet invented. But on this point see footnote 12.

2. I will not explore the possibility that the labor share stays high because labor remains necessary in other ways. I am considering what follows once we have machines that not only build and invent as well as we can, but can start businesses, sift through potential products for those with the best market fit, and predict our tastes as well as one person can predict other people’s tastes.

3. As seminally documented by Greenwood et al. (1997), and more recently by e.g. Hubmer (2023), discussed below.

4. Another way to see it: given preferences (*), each unit increase in K or L induces the same proportional decrease in that input’s marginal utility. So each proportional increase in K and L induces a larger proportional decrease in du/dK if K > L.

5. Earth-based raw natural resources are in fixed supply; extraterrestrial resources can grow at best cubically in the limit.

6. Wage bill series here, GDP series here.

7. That is, those with a cardinal and interpersonally comparable notion of utility and who want to maximize the sum of utility in the universe, including by creating arbitrarily many new animals or artificial minds with positive wellbeing. The same point about non-satiation holds for totalist consequentialists more generally, e.g. those who want to maximize the quantity of vibrant ecosystems or beautiful art.

8. For an illustration using a slightly modified problem which makes the math easier, see ChatGPT’s proof here. The intuition is that our utilitarian (or slow-satiator for whatever reason) has more slowly diminishing marginal utility in income, and thus saves more. By “buying capital” off the others, she eventually keeps the price of capital relative to labor high even as capital grows plentiful.

9. People with a rate of pure time preference ρ > 0 do saturate in years of life: the discounted utility offered by T years at flow utility level u is only u(1 - e^-ρT)/ρ, which rises only to u/ρ as T → ∞. But the value of years of life doesn’t diminish for the fully patient.

10. Of course we still breed some horses, e.g. racehorses, but far fewer than when horses were the best means of transportation. In other words, if the number of horses had stayed fixed instead of falling, we would have been willing to spend less per horse than the cost of maintaining them in a desirable condition. Likewise, wages may fall for all but a few, say, exceptional musicians. On the bright side, for wages, it is possible to “consume a lot of labor at once”, e.g. by watching a musician play a song that took her many years to write, playing an instrument with virtuosity it took many years to achieve. The same can be said for racehorses, but maybe to a lesser extent.

11. Maybe humans could get involved in a mostly-automated production process to do some trivial step without much compromising the good’s quality much on other dimensions, so that consumption of labor does not significantly displace consumption of capital. I think this possibility somewhat stretches the limits of recognizable preferences for a “human touch”—engaging with the work of an artist is one thing; a machine-made sweater with a single human stitch, or a machine-cooked meal with a human pinch of salt, is another—and pessimistically assumes that we will not eventually spend most of our time consuming amazing new goods to whose production a human has as little to add as a horse has to add to a Waymo ride. But intuitions on this point may differ.

12. Likewise, we may invent new human-intrinsic goods, like new kinds of performances for people to engage in, with or without the assistance of capital-intensive technology. But the possible space of such goods is fundamentally constrained by what a human can do, whereas the space of goods producible by all possible superintelligent machines is practically unlimited. This asymmetry is in some sense the converse of the asymmetry that appears in many economic models of automation, in which labor can perform all tasks and capital can only perform a subset.

13. Unlike Hubmer, I would not frame this as capital already being a gross substitute for labor. I think capital accumulation would lower the capital share in the absence of new inventions and entrepreneurship, so that the rising capital share by sector consists largely of equity (imperfectly) compensating its owners for their work coming up with new uses for the accumulated capital. But it does suggest that capital would currently be a gross substitute for labor if R&D and entrepreneurship were automated.

14. The Mona Lisa was assessed for insurance at $100m in 1962, which would be about $900m today. It has not been assessed since. The Da Vinci Code grossed about $800m in 2006, which would be $1.2b today.

15. This function “flattens out the dynamics”, essentially treating history as a single period in which the benefits of R&D accrue immediately. A dynamic setup of the problem makes the same point.

16. But not “knife-edge”, once we look beyond the functional forms conventional in macroeconomic theory. If the negative elasticity of d[N(K)(1 - e^-K/N)]/dK to K is greater than one but falls asymptotically to one, this corresponds to the range of cases in which utility grows unboundedly but sublogarithmically in capital. In these cases the capital share falls.

17. In the US, from less than 1% of GDP before 1950 to 3.5% today (data from FRED). A similar slow but positive trend appears throughout the developed world.