GDP and prosperity across technology paths

1. Introduction

It would be great to have a single number that captured something like how big our economy is, or how far our useful technology has advanced. In a word, it would be good to be able to put a number to our prosperity. A number like this would be especially useful these days, as we sit at the cusp of what seems like it will probably be the biggest technological and economic transformation of all time. We desperately want a way to quantify (and debate) how quickly the transformation will go and how far it’s already come.

It’s very common, among both economists and AI forecasters, to talk as if we have such a number, and that the number is real GDP, or a productivity number like TFP that takes real GDP as an input. There are certainly some people who understand the many ways that real GDP (etc.; throughout this introduction I’ll just say “GDP” as shorthand) can fail to track what we mean by prosperity—or indeed anything else we might care about—and who use it only carefully, for lack of a better alternative. But many more people use it because of the impression that its flaws are relatively minor: that it’s highly correlated with whatever ideal index of economic or technological progress we might want to construct.

This post argues that that is incorrect.

What confuses people about this, I think, is that GDP really is highly correlated with intuitive prosperity on three fronts:

• across regions, at a given time;

• within a region, over the short run; and

• within a region, over the long run.

Put another way, in any given year, if you were going to be dropped into (a life in) a random country with high GDP or one with low GDP, you should almost always hope to land in the higher-GDP country. And fixing a region, if you were going to be dropped into one of two random years in some given decade—or one of two random decades, or centuries—you should almost always hope to land in the higher-GDP one.

But these correlations do not imply that GDP is strongly—or even positively!—associated with intuitive prosperity

• across possible technology paths.

And I will argue that this association is weak. Put another way, if we were going to get a phone call from 2046 telling us which of two random possible futures has unfolded, we should often hope that it’s the one in which GDP grew more slowly.

Making a precise claim about the correlation between GDP and some notion of prosperity, across possible technology paths, would require a distribution over possible technology paths. I do think that the correlation would be weak for the distribution we should currently have over possible paths of technology and GDP over the next n years, for any large-ish n—say, at least 20—and likewise for the distribution a well-informed person should have had throughout the past century. But coming up with a “prior over future tech paths” we can all agree on seems next to impossible, and I won’t try. Instead I’ll just illustrate, with a few examples, why the future of GDP growth and the future of prosperity are less connected than many realize.

I’ll first summarize why GDP really is a good “measure of prosperity” under certain stylized conditions, namely when everyone in the economy has common, homothetic preferences, and why the objections people raise to it most commonly—including that it leaves out home production, free goods, and nonmarket goods like health—are fixable in principle without taking GDP out by the roots. I’ll then explain what I see as the “deep issue” GDP faces when these conditions fail. I’ll point out how this deep issue can completely decouple GDP from prosperity across possible technology paths, without doing so across countries, short periods, or long periods within a given “timeline”. I’ll argue that this decoupling is not just a theoretical curiosity but significant in practice, and likely to become even more significant in the future. Once we have self-replicating, general-purpose robots, we could very well see an explosion in anyone’s definition of prosperity without an explosion in GDP, or vice-versa.¹

2. Real GDP and its cousins

2.1 Real consumption under common, homothetic preferences

Suppose that at time t the economy produces n consumption goods, in quantities x_1t, …, x_nt​. Let c_t denote “real consumption” at t: some aggregation of these n quantities. “Real consumption growth” at t, which I’ll denote g_t, is defined as the spending-share-weighted average of the goods’ quantity growth rates g_it:

g_t = Σ_i σ_itg_it,

where σ_it is good i’s share at t of total consumption spending, so that the shares sum to one. For example, if some consumption good accounts for 20% of spending, a 1% increase in its quantity adds 0.2% to real consumption.

A “real consumption series” constructed in this way will be well-behaved under certain narrow conditions: when everyone in the economy has the same preferences, and they’re homothetic.² Your preferences are homothetic when they’re representable by a utility function U(·) that exhibits constant returns to scale (CRS), meaning that for any consumption bundle x and any k ≥ 0, U(·) satisfies U(kx) = kU(x).

Since U(·) here is just a way of ranking bundles, this doesn’t mean that if you consume twice as much of every good, you enjoy “twice as much utility” in any meaningful sense. But it does mean that if you prefer bundle x to bundle y (i.e. U(x) > U(y)), then for any k ≥ 0, you prefer bundle kx to bundle ky (since U(kx) = kU(x) > kU(y) = U(ky)). And this in turn means that when everyone has the same preferences and they’re homothetic to boot, then they all adopt the same budget shares across goods: if one person spends 1% of his budget on some good i, so does everyone else. If my favorite affordable bundle is x and your budget is k times as big as mine, your favorite affordable bundle must be kx.

After a 1% increase in the quantity of good i, therefore, if people’s budgets stay the same in relative terms, everyone will in equilibrium consume 1% more of i. Under these conditions, it’s natural to say that a 1% increase in i at t grows real consumption by 1% × σ_it, as the formula above requires. In absolute terms, consumers’ collective willingness to pay (WTP) for this extra consumption of i is (1% × x_it)p_it, where p_it is the price of i at t. This can be seen from a demand curve, like the one below. As a share of consumption, this willingness to pay is 1% × σ_it, since σ_it = x_itp_it/c_t.

When I say that the resulting real consumption series will be “well-behaved”, what I mean is that more real consumption will always be better, and changes to real consumption will not be path-dependent. To illustrate this second point, suppose that

• real consumption growth from year 1 to year 2, as defined above, is 1%, driven by the growth of good 1; and

• real consumption growth from year 2 to year 3 is 2%, driven by the growth of good 2.

By definition, real consumption will be approximately 3% higher in year 3 than in year 1. The subtle point is that we can imagine an alternative timeline, on which the growth of good 2 happens first (from year 1 to year 2) and the growth of good 1 happens next (from year 2 to year 3), and on this alternative timeline, real consumption will again be ~3% higher in year 3 than in year 1.

This should not be obvious, because the growth of one good can affect the consumption share of the other. If an abundance of good 1 raises the consumption share of good 2, but not vice-versa, then on the timeline in which good 1 grows first, real consumption will “grow more” across the two years! This is because the growth of good 2 will happen to occur when it is a larger share of consumption, so its growth will contribute more to real consumption growth.

These bizarre interactions cannot happen in an economy of common, homothetic preferences. To see why, let U_i(x) denote the marginal utility of good i at bundle x, and observe that as long as consumers are optimizing and price-taking, price ratios must equal marginal utility ratios. Real consumption growth then precisely equals the growth of our CRS utility representation U:

g_t = Σ_i σ_itg_it = Σ_i (p_itx_it)/[Σ_jp_jtx_jt] · g_it …

and if consumers are all enjoying some multiple of the bundle x_t at t, then p_it/p_jt = U_i(x_t)/U_j(x_t) for any pair of goods i and j, so

… = Σ_i (U_i(x_t)x_it)/[Σ_jU_j(x_t)x_jt] · g_it = Σ_iU_i(x_t)x_itg_it/U_t = dU_t/U_t = g_Ut,

where the denominator simplifies to U_t by Euler’s homogeneous function theorem and the fact that U(·) here is CRS, i.e. homogeneous of degree 1.

So, more real consumption means more utility. And since U just depends on x_t, it can’t exhibit any path-dependence, so real consumption can’t either.

2.2 The “deep issue” with real consumption absent common, homothetic preferences

Preferences obviously differ from person to person, and everyone’s preferences are obviously non-homothetic. Elon Musk spends a smaller share of his budget on basic calories than someone starving.

In the absence of common and homothetic preferences, “real consumption”, as defined above, is path-dependent and has no necessary relationship to utility. One way the two can become disconnected, which is especially simple and I think especially important, is that introducing new goods that grow in quantity no more quickly than average raises our utility but does not pull up real consumption growth. Worse, slower-than-average-growing goods can raise our utility but pull down real consumption growth, since again, it is the share-weighted average of goods’ growth rates.

An example (adapted from here). Suppose the economy begins with a single good (f, for “food”). Eventually at some date t*, a new good (s, for “string quartets”) is invented; its discovery is exogenous in this example. Utility is the sum of the utility from each good: U_t = u_f(c_t^f) + u_s(c_t^s), and the utility from each good is given by a bounded utility function. You only get so much utility from eating a bunch of apples or repeatedly watching the same violin performance on a given day:³

u_i(c) = ū_i + (c + c̄_i)^1–θ /(1–θ) where θ > 1.

The c̄_i term is chosen so that u_i(0) = 0.⁴ The good-specific utility function looks like this:

The quantity of food grows 5%/year. Once the quantity of string quartets is non-negligible, it grows 1%/year. (String quartets must initially grow at an “infinite rate” to grow from zero units, but because their GDP share will be ~0 while ~0 units are being produced, this does not produce an explosion in real GDP growth. See Appendix A of the paper for details.)

After t*, string quartets have been invented, so real GDP growth falls from 5% to some weighted average of 5% and 1%. In fact, in this example, the string quartet share of GDP approaches 1 over time, so real GDP growth falls all the way to 1% in the limit. This occurs because the fast growth of food drives down the marginal utility of food, while the slow growth in string quartets means that their marginal utility (and thus their relative price) falls more slowly.

This demonstrates that real GDP can become arbitrarily decoupled from welfare.

It also demonstrates that real GDP is path-dependent. Real GDP is lower after years of string quartets than it would have been without them, even though we’re enjoying just as much food as we would have without them. But then, if—having introduced the string quartets and thus lowered the growth rate—we take the string quartets away (i.e. they exhibit negative growth, all the way to a quantity of zero), real GDP can only fall further! With or without our temporary foray into string quartets, we wind up in the same place, with a lot more food than we had earlier and nothing else. But real GDP is lower if, on the path there, we introduced the string quartets and then took them away.⁵

2.3 From real consumption to real GDP and other measures

Suppose we do have common, homothetic preferences, and have defined real consumption growth in the way described above. Then, putting aside government spending and international trade, we can

• define “real GDP” to be what real consumption would be if we did no saving,

so that the saving rate is the fraction of potential real consumption that is foregone. We can then

• define various measures of productivity as real GDP divided by various inputs to production: labor productivity, for instance, is real GDP divided by hours worked.

Finally, we can define measures of welfare or prosperity that increase in real consumption, real GDP, or productivity, but also incorporate the value of other desirable things, like leisure, lifespan, education, or equality. Consider for instance

• the human development index,

• the genuine progress indicator, or

• the welfare index proposed by Jones and Klenow (2016).

As long as we haven’t introduced any new sources of incoherence, all of these new variables will be well-behaved as long as real consumption is. But if real consumption isn’t well-behaved, real GDP and all the other variables constructed from it inherit its deep issue.

2.4 Mere measurement issues

If we had common and homothetic preferences, real GDP (and so on) would be well-behaved, but there would still be various ways in which our published real GDP statistics fail to measure it properly. Many of the issues people identify with real GDP do not engage with the deep issue posed by heterogeneity and non-homotheticity in particular, and so are merely measurement issues. The corresponding proposed improvements to real GDP, or to real GDP measurement, are thus proposals for the improved “measurement” of a quantity that does not exist, namely the CRS utility representation of our common preferences.

Even in an economy of common, homothetic preferences, real GDP statistics would be imperfect measures of welfare because of:

1. Periodic measurements. GDP growth tracks utility growth perfectly only if our consumption of every good grows continuously, its price changes continuously, and the quantities and prices are tracked in continuous time. This allows us to “integrate along the demand curve”, as in the example of Section 2.1. When quantities and prices are tracked only periodically, say by the quarter or year, we have to weigh the growth of each good’s quantity from one period to the next by its share in the first period, its share in the second period, or some interpolation of the two. Or equivalently, we have to use goods’ first-period, second-period, or interpolated relative prices.

   

   The study of price and quantity indices concerns how exactly to do this interpolation, given some information about the shape of demand.

2. New goods. The first issue is bigger the more a good’s price and quantity change between periods. An especially extreme change occurs when a good i is first introduced at t*—i.e. its price falls at t from “infinite” (or equivalently, any finite price at which demand would have been zero)—and the price at which it is introduced is low enough to make its initial demand x_it* non-negligible. The issue is biggest of all when i is introduced for free (p_it* = 0), as software products often are.

   

   Free or not, this is the issue people are usually referring to when they talk about the challenge of accounting for new goods in GDP. It would be perfectly dealt with (in an economy of common, homothetic preferences) if we knew how much each consumer would be willing to pay for those first x_it* units. The “GDP-B” project (Brynjolfsson et al., 2025; “B” for “benefits”) aims to fill this gap by periodically surveying people about how much they would be willing to accept to forego the use of various new products, especially free software products.⁶

3. Home production. Often, the goods we actually consume are not the goods we buy, but the goods we (or our families and friends) produce from the bought ingredients. The value added by cooking a meal, for example, appears in measured GDP when the meal is cooked in a restaurant but not when it’s cooked at home. Hulten and Nakamura (2017, 2020) explore how to fill this gap with a home-production-inclusive measure they call “EGDP” (“E” for “expanded”).

4. Market power. If a consumer has some market power in the market for some good i, the price she pays for i will generally be lower than her marginal utility in i. (More precisely, the ratio between price and her marginal utility will be lower than the ratio for some good j over which she does not have market power.) A modification to GDP that better tracks welfare would weight the growth of each good not by its actual GDP share—its share in “quantities times prices”—but by its share in “quantities times marginal utilities”.

5. Non-market goods. Just as new goods are sometimes introduced for free, many “goods” that have been free all along may change over time in quantity or quality. Suppose the weather slightly improves somehow, making life more enjoyable without affecting how much we work or what we produce. If we have common, homothetic preferences over the extended list of goods that includes market goods and weather quality, we can “price” the benefit of the better weather like any other good, by asking how much we would have been willing to pay for the improvement—or how much we would be willing to accept to undo the improvement, which will be the same if the improvement is small. We can do something similar for other unpriced goods, like leisure, health (insofar as it varies over time for reasons other than better or worse medicine), or even freedom.

Perfectly dealing with all these issues, and all others in a similar vein, could expand real GDP into a perfect measure of prosperity in an economy of common, homothetic preferences. But they would not touch the “deep issue” that, outside these conditions, the two come apart.

3. Faster growth can easily be undesirable

3.1 The irrelevance of the three strong positive correlations

To summarize the previous section, it is an important and unfixable fact that real GDP (and its cousins) are not even well-behaved quantities, and so don’t have any necessary connection to anything we could possibly mean by welfare, prosperity, the “size of an economy”, or anything else. Why then do they seem to be useful constructs? Why do they correlate with other measures of prosperity so closely?

An example. Suppose we lived in a world with a long list of potential goods—first food, growing at 5%/year; then string quartets, growing at (5/2)%/year; then haircuts, growing at (5/3)%/year; and so on—each of which would, on being introduced, grow more slowly than all the previous goods. Suppose the only open question about the future of technological development were how many of the goods we would invent: we will invent goods #1–n for some n. If n is higher, we are better off, but real GDP (and consumption, productivity, etc.) and their growth rates are lower. If we invent up to good n, the long-term annual growth rate is (5/n)%. (The same is true if what grow at 5%, (5/2)%, and so on are not the goods’ quantities but our productivities at producing them, i.e. their maximum feasible quantities.)

In this case, at every point in time, prosperity and real GDP would be perfectly anticorrelated across future technology paths. We could invent 0 more goods, 1 more, 2 more, and so on, and inventing more would always deliver more prosperity and less real GDP.

But even in this pathological case,

1. At each time t, the countries with larger GDPs will be those that can afford larger quantities of the goods available at t. The higher-GDP countries will be the more prosperous ones.

2. Suppose our production of every good is hit by a negative 10% shock roughly every other year, due to the mysteries of the business cycle (or the weather). Then over any short horizon, the years with higher real GDP will be the more prosperous years.

3. Suppose real GDP has been growing over the long run, and technology has been improving over the long run as well, as new goods have been introduced and the quantities of the old goods have grown. Then the long-term trends will be pointing in the same direction, so the decades or centuries with higher real GDP will be the more prosperous ones.

So even though positive correlations along these axes are obvious and well documented (e.g. by Jones and Klenow (2016)), we can’t infer from this that in a choice among technology paths, we should aim for the path with the faster GDP growth.

3.2 More goods, less “growth”?

The example above may seem rigged. Why would higher-indexed, later-invented goods systematically grow more slowly than lower-indexed, earlier-invented ones? Many recently-invented goods, like semiconductors, grow (in quantity or productivity) more quickly than many old goods, like musical performances.

This is true, but there are at least two reasons why technology paths in which the variety of goods grows more quickly could yield slower real GDP growth than less desirable technology paths in which variety grows more slowly.

First, when there are more goods, R&D effort must be divided more thinly across them. Suppose for simplicity that

• there are fixed populations of researchers and workers, and

• there are no R&D spillovers across goods: if the researchers all focus on increasing output per worker of n goods, each good gets 1/n of the researchers, and productivity on that good grows by (5/n)%/year.

This would precisely reproduce the long-term logic of the example above. In fact, this mechanism is precisely how “second-generation endogenous” growth models explain the fact that growth has not accelerated in recent history despite a large increase in the number of researchers.⁷ The drag on growth in output per good imposed by an expanding range of goods may not have to be large for this to be an important effect, since variety is expanding so rapidly.⁸

Second, while new goods are still expensive, they are produced in smaller quantities. In cases where productivity grows mainly via learning by doing, therefore, the rate at which we can ramp up production of a new good might tend to be slower than the rate at which we can accelerate the production of an existing good that has already gotten beyond the prototype stage. Introducing new goods will then tend to “dilute real GDP growth” with goods that are, at least initially, slower-growing than average.

An example. This model is similar in some ways to that of Oberfield (2023) and the other “flying geese” models cited on p.1. The spirit of the extreme version presented here is that, for each good, we get a singularity—it’s eventually free, so we can consume it in unlimited quantity—but by the time of its singularity, its GDP share is zero, and we’ve shifted our spending over to the goods that haven’t yet exploded. You might think of it as a model of media, like books. We’ve already effectively had a singularity in (digital) copies of the Canterbury Tales: we can pull it up for free in as many browser windows as we could ever want. If all we consumed were old stories like the Canterbury Tales, the growth rate of every good would already have exploded. But instead of spending on cranking out as many copies of the Canterbury Tales as we possibly can, we’ve shifted our spending over to new books, which remain scarce and slow-growing while they’re new and dominate our spending.

Preferences and constraints: The population is constant, normalized to 1. There is a continuum of goods n = 0 to ∞. Each person has the same nominal budget, and the same non-homothetic utility function

\(u(x) = \int_0^\infty \big(1-e^{-x_n}\big)dn.\)

So as in the example of Section 2.2, there is a limit (of 1) on the utility we can derive from each good, which we approach by consuming an unlimited quantity of it, and total utility is additive across goods.

Productivity at producing good n at time t is denoted A_nt.

A_nt = ∞ if n ≤ t. A_nt = 1/(n–t) if n > t.

So each good’s productivity grows hyperbolically, but higher-indexed goods have later singularities: the number of units of good n we can produce by t blows up at time t = n.

I’m defining the productivity paths to be exogenous, but we could get the same result in a learning-by-doing model, where A_nt is some function of cumulative production of n up to t.

Normalize total expenditures at each time to ¼. So at t, we have

\(\int_0^\infty \frac{x_{nt}}{A_{nt}} dn = \frac{1}{4}.\)

Optimal purchases: An infinite quantity of goods n ≤ t will be consumed for free, giving the consumer t “utils”. As for how to allocate the budget of ¼ across goods n > t, differentiating U(·) gives the first order condition that, for some constant 𝜆, any good consumed in positive quantity must, when purchases are optimal (at the quantity denoted x*_nt), satisfy

\(\frac{e^{-x^*_{nt}}}{n-t} = \lambda \quad \implies \quad x^*_{nt} = -\log\big(\lambda(n-t)\big).\)

If it’s desirable to buy a positive quantity of good n, it’s desirable to buy a positive quantity of good m < n, since A_m > A_n and the utility function is symmetric. Conjecture that the chosen budget constraint of ¼ makes it so that it is desirable to buy positive quantities only of goods whose index is less than t+1.

Fixing the time, let i ≡ n – t denote a good’s index above the highest-indexed good in infinite supply (which is good t). So x_i* = –log(𝜆i). Substitute this into the budget constraint:

\(\int_0^1-\log(\lambda i)i\,di = \frac{1}{4} \quad \implies \quad \lambda = 1.\)

So x_i^* = –log(i). This verifies the conjecture.

GDP shares and the share-weighted growth rate: The GDP share of good i is its quantity times its “price” times 4. So 4x_i/A_i; or, –4i log(i). Note that this is independent of time; the good that is indexed i, at each time, always has the same GDP share.

The index of good i (i.e. n–t) falls by one unit per unit of time that passes, so the absolute growth rate of the quantity of good i can be found by differentiating –log(i) with respect to i and then negating: 1/i. For the proportional growth rate of good i, divide by the quantity to get –1/(i log(i)).

Productivity A, consumption x, and GDP share σ by good at t look like this:

So the real GDP growth rate is constant at

\(\int_0^1 4 di = 4 = 400\%.\)

Technological advances cause us to shift our spending to ever higher-indexed goods, but the share-weighted average of the goods’ growth rates is unchanging.

My tentative guess is that a model of roughly this form helps to explain the near-constancy of frontier growth since the demographic transition, when the primary source of “world GDP growth” shifted from cranking out ever more copies of the same object (the human body) to improving living standards per person via new kinds of goods. As e.g. Bessen (2018) documents, the GDP shares of various important good-categories have historically initially increased as they’ve grown more abundant, and then fallen as they’ve grown so abundant that we’re near-saturated in them and we’ve shifted to new things.

Hopefully it’s clear that the constant GDP growth in this example is not an artifact of the fact that the production of goods n ≤ t “stops growing”. I chose hyperbolic good-level growth to have as extreme an example as possible, but the more general point is that, with this utility function, the fact that growth proceeds ever more quickly for the lower-indexed goods can be canceled out or outweighed (in terms of contribution to GDP growth) by the fact that the share of the lower-indexed goods gets ever smaller. If we made productivity growth, say, double-exponential, this qualitative relationship would remain.

3.3 Goods and growth after AGI

In the homothetic world, predicting the path of real GDP in the event that the production of all goods has been fully automated is, to my mind, straightforward. If at t we have K_t robots that can produce everything, including new robots, and their productivity (how many robots a robot can build in a year) is A_t, then output is A_tK_t. Even in the absence of technological development—even fixing A—a constant saving rate s > 0 lets output grow exponentially: the number of new robots we build at t is sAK_t, so in proportional terms the robot growth rate is sAK_t/K_t = sA,⁹ which is also the real GDP growth rate. If technology also advances over time—if A rises, so that each robot can produce ever more—then output grows superexponentially. The growth rate itself rises, until it equals sĀ, where Ā is the maximum feasible rate of robot reproduction. Since some intelligent animals, such as octopuses, can reproduce at a rate of 250,000x/year, we know that Ā is extremely high. 250,000 is a lower bound on it: and probably a very loose lower bound, both because we have no reason to believe that the biology is optimized on this front, and because robots in an automated world could be constructed across a long, hyper-specialized supply chain, whereas each octopus egg has to build a new octopus all “in-house”.¹⁰

I think this is a powerful argument, and it is entirely possible that real GDP growth ultimately gets this high. The argument relies on homotheticity, as we have seen, but that does not mean that we should reject it as a central case. Non-homotheticities could make growth slower or faster, because we shift our spending over time to the kinds of goods produced by slower- or faster-replicating machines.

A second argument for wildly explosive real GDP growth in an automated world is that, once robots can do all we can but much more quickly, they could simply do whatever we would have done without them, in less time. Whatever scientific breakthroughs, new products, or social reorganizations would have arrived over the next thousand years in the absence of the bots could be implemented, by bots doing everything at 100x speed, over the next ten.¹¹

This argument is also not quite watertight, in two ways. First, some kinds of technological development may be highly non-parallelizable, and if they’re important enough in the relevant sense, economic history in some sense has a speed limit.¹² Second, the bots of an automated world could change the “direction of economic history”, not just the speed. By accelerating the introduction of new goods by more than aggregate R&D effort, for instance, they could even deliver more prosperity and a slower growth rate, as we have seen. Still, the first-order fact that general-purpose machines could speed all economic activity (including invention) does again strike me as a powerful argument.

Where does this leave us? I learned long ago that I’m better at generating insights than at weighing and synthesizing them. But from where I sit, if you don’t object to attempts to quantify such imprecise uncertainty,

• If we really do bring about a world in which everything is automated, the growth rate suggested by the octopus thought experiment—s × [something over 250,000x/year]; say, 6 or 7 orders of magnitude (OOMs) higher than today—is a natural central case. But real GDP growth could be radically faster or slower, including even slower than today! How do we extrapolate the logic of growth accounting so far from historical experience? Though I’m thinking about the long run, it seems entirely plausible to me that diffusion frictions and internationally coordinated regulatory frictions slow things down a lot for two or three decades. And after 25 years at 30%/year growth, “real GDP” has grown by three OOMs: an even larger “gap”, in some sense, than the gap between a middle-class life today and subsistence. I have no idea what our preferences for variety vs. quantity will look like on those margins. So my interquartile range for the peak¹³ growth rate is huge: something like [1 OOM, 12 OOMs] higher than today.

• All of the above only applies to a world in which we fully automate everything (or, a set of goods that remains, over the relevant timespan, a gross substitute for everything else). I think this will probably happen. But I think it’s also possible that, before GDP growth has managed to rise by more than an order of magnitude, GDP gets permanently bottlenecked by a good in fixed supply, such as

  • natural resources for use in production;

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

  • historical artifacts;

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

  • various aspects of governance; or

  • the human touch.

  I give this around a 1 in 3 chance. Note that other than “natural resources for use in production” and “various aspects of governance”, these bottlenecks aren’t necessary. We could eliminate them by banning labor or the renting of beaches and historical artifacts. This ban would be undesirable, but it would make real GDP explode again, just as real GDP would grow more quickly if we banned the string quartets.

This leaves a ⅓ + ¼(⅔) = ½ chance that “real GDP growth” peaks at no more (or no less) than an order of magnitude higher than its current rate. So I’ll say that is currently my median case, though I also take the slower and more “GDP-singularitarian” scenarios very seriously.

4. Conclusion

It’s a bit of a trope that when someone makes the straightforward “AK” argument for why truly general-purpose robots would deliver explosive growth, economists often object that they wouldn’t because of a vague reference to “bottlenecks”, no matter how emphatically it was insisted that we’re considering the scenario in which the bots can do literally everything we do rapidly and at scale.

I don’t think most of the purported caps on the long-term global growth rate withstand scrutiny. Occupational licensing might slow things down for a while, for instance, but once the bots can do every job better than a human can, I expect it’s only a matter of time before some jurisdiction somewhere lets them rip. At the same time, the intuition economists often have that bottlenecks are everywhere might have something to it. Ironically, the bottlenecking mechanism that most stands out to me—new goods—is one economists almost always fail to notice, since the (all too few) economists thinking about long-term growth so overwhelmingly assume common, homothetic preferences in their models, so that the object of their study (“real growth”) is well-behaved. But it’s a mechanism that can generate new bottlenecks forever.

It would be absurd to take the case in which real GDP growth gets “bottlenecked by new goods” as a case of bottlenecks preventing radical impacts from AGI. We would get explosive growth in everything humans can do and more, as the human-substituting bot swarms reproduce blisteringly quickly—an outcome that would yield explosive real GDP growth on its own—yet, because the bots’ versatility also delivers an explosion of new and (in some cases, at some margins) slower-growing varieties, real GDP growth is contained. This reveals that real GDP is probably not what we were interested in all along, and raises the question of what we should track instead.

The answer is certainly not to just abandon chain-weighting and weigh goods’ growth rates at some base year’s GDP shares. If Papa Monzano had turned the oceans into orange juice instead of ice-nine, that would just be a weird world of free orange juice, at least for people on the beach, not one in which our economy had meaningfully exploded.

I expect there’s no general-purpose answer. For an index of how quickly we “spend the cosmic endowment”, track energy consumption. For an index of how well-off people are getting, track (some improvement of) my and Chad’s nifty composition of interest rates and the value of statistical life. If what we want is just an index of how crazy fast it will feel like the world is changing, and if a good’s share of our spending is a decent proxy for its share of our attention, I’ll tentatively grant that real GDP growth might not be such a bad proxy. “Felt rates of change” can certainly be path-dependent; if the world is going to move from state A to state C, an intermediate stop in state B could make the journey feel more or less wild. But on the whole, I’d say many important questions about the “speed of the future” are answered by many distinct variables, most of which are only tenuously associated with each other, or with real GDP, across the vast space of possible technology paths.

1. This essay is a compendium of an old hobby-horse of mine. Most of the content is taken from things I’ve already written, but some is new, and hopefully what is old benefits from the new context and framing.

2. And unchanging. I’ll also assume that they’re representable by a utility function that is continuously differentiable and increasing in each good.

3. Two features of these preferences combine to break homotheticity. The first is that preferences saturate, and the second is that at least one good is unnecessary (in fact both are unnecessary). To see why, consider the case where ū_i is the same for all goods and equal to ū. As the consumption of N goods goes to infinity, utility approaches Nū—it is determined by how many goods are consumed, not by the consumption of any one good. This leads to reversals. Consider two bundles, where x consumes a tiny amount of each of two goods, while y involves 0 units of some unnecessary good and 1 unit of the other good. Clearly we can set this up so that y ≻ x if the consumption in x is sufficiently small. But now consider blowing up consumption in each bundle by the factor α and let α → ∞. Then x ≻ y because the bundle x features two goods while the bundle y features only one.

4. In particular, c̄_i = [ū_i(θ–1)]^1/(1–θ).

5. This path-dependence issue has long been understood among economists doing index number theory (see Samuelson and Swamy (1974) for a review), but has been forgotten by all too many more. Given arbitrary paths of the production technology, path-dependence is avoided only by common, homothetic preferences. See Bellaïche (2010) for weaker joint conditions on preferences and technology that rule out path-dependence.

6. It seems it’s not always appreciated that a perfect survey of this kind really would fix the standard “new goods” issue.

7. The way these models are usually written, the goods are highly substitutable, so it would actually be better if we got faster growth of fewer goods: the ongoing, growth-depleting expansion in variety is a gigantic market failure. The same logic applies, however, if we work with a more realistic utility function like the one in Section 2.2, so that there is a real tradeoff between real GDP growth and welfare.

8. Or exhibiting so much turnover; see e.g. Broda and Weinstein (2010).

9. Or if the robots depreciate at rate d, net robot production is (sA–d)K_t, so the robot growth rate is sA–d.

10. Of course, the octopuses can only reproduce this quickly in practice if they have enough natural resources. But Davidson and Hadshar (2025) argue that a superintelligent robot population directed to self-replicate ever more quickly probably would be multiplying something like this quickly before running into natural resource constraints.

11. This implies a literal 100x acceleration to today’s real GDP growth only if, absent the all-purpose bots, we would have sustained the current growth rate for a millennium. Something like this seems to be an assumption in the background of a lot of conventional theorizing about long-term economic growth, e.g. by Jones (2022), but it’s not obvious.

12. I expect that technological development would still accelerate over time (again, see here), but if we manage to fill the world with “bot n” before our hordes of bot n’s invent “bot n+1”, natural resource constraints could start binding before growth on this “horizontal dimension” is proceeding blisteringly quickly.

13. Say, sustained over at least one “OOM of growth”.