In my similar but much cruder analysis (https://www.lesswrong.com/posts/rQxrSRPJGmksGjK8z/it-s-time-for-a-self-reproducing-machine) I got a much smaller doubling time. My capital doubling time was also about a year for a self-duplicating human-staffed machine shop. Then I got improvements for 24/7 operation and the shorter-lived capital adjustment. But my largest single gain was caused by making everything physically smaller. Most industrial processes run N times faster if they are N times smaller. Of course the individual finished goods are N^3 times less massive. Some don't scale like this-- ovens, heat diffusion and electric motors are cases I thought of. After considering the scaling laws of all the processes I was imagining, I settled on N=5. That gave me a doubling time of about five weeks.
Of course that is the doubling time for a diminutive economy, and it might be objected that teeny-weeny finished goods have no economic value. But it is always feasible to use the tiny economy to produce a larger one, until we have scaled back to normality. Assume that we can vary the scaling parameter N per generation, and assume the scaling properties described in the last paragraph. Then we're best off setting N to the optimal (fastest) value, and let it run, keeping only a small fraction of tiny productive capacity working to produce full-sized goods. This will rapidly beat a full-sized self-reproducing economy. Figuring out the optimal allocation of tiny versus full-sized production is beyond me, because I'm an engineer, not an economist. But you do not have this handicap!
What happens when you physically scale down the economy by a factor N? Resources scale differently with N. We can look at a few resources whose costs scale differently:
So different parts of construction scale as different powers of N, ranging from N^0 to N^3, What a mess!
In Part 1, I found that a fully automated economy using today's production methods could double roughly every year. In Part 2, I modeled the transition from today's economy to that maximum-growth composition and found that energy production could double within about four years. Both parts held production methods fixed: each sector continues using exactly the recipes it uses today, with robots replacing human workers.
That assumption is too conservative. Today's production recipes were chosen at very different factor prices from what a post-AGI economy would face. Labor is expensive today, so recipes minimize labor use. Humans must also be physically present, so recipes are built around them. Interest rates are low, so recipes lean on durable equipment that lasts for decades. Post-AGI, labor becomes nearly free and capital reproduces fast enough that effective interest rates rise sharply.
This part asks how much faster the economy could grow when recipes are reoptimized for post-AGI factor prices, using only existing or historically-observed technology rather than novel improvements. The first section starts from the US 2017 input-output tables and applies four channels: stripping out the capital and services that exist only to accommodate human workers, closing the productivity gap between average and frontier plants, building cheaper short-lived capital, and shifting recipes toward more labor-intensive production. I also revisit Part 1's construction-lag treatment, as lags become increasingly important at higher growth rates. The second section turns to historical US input-output tables going back to 1947, and asks how much further the rate rises when each commodity can be produced using the cheapest recipe from any era.
This part is a grab bag of different effects, each with its own uncertainties, but that largely stack together. My central estimate is that the economy's maximum self-reproduction rate is between 1 yr⁻¹ and 2 yr⁻¹, corresponding to doubling times of four to eight months. This is roughly twice as fast as Part 1's one-year doubling time. Part 1's savings-rate adjustment applies unchanged. I have not recomputed resource-depletion adjustments on the reoptimized recipe mix; Part 1 shows these are unlikely to overturn the qualitative result, but the exact adjustment may differ because reoptimized recipes draw on a different resource bundle.
Existing or historically-observed methods of production cannot push the rate much higher than this. In Part 4 we will ask: how much faster could production go with better technology?
This series grew out of a project initiated by Holden Karnofsky, with substantial earlier work by Constantin Arnscheidt and Adin Richards. I’m grateful for comments on this post and/or earlier iterations of the project from Holden, Constantin, Adin, Paul Christiano, and Tom Davidson. Thanks also to Claude Opus 4.6 and 4.7 for help with all aspects of this project; in particular, the appendices were written with heavy AI assistance and are less polished than the main text.
Improvements absent technological change
Construction lags become more severe at high growth rates
Part 1 modeled construction lags with two uniform values — one for structures, one for equipment — and found that they reduced the growth rate modestly unless structure lags ran to multiple years. Here we give each sector its own construction lag drawn from industry data on actual build durations, and add a separate deployment lag for heavy-process industries, such as semiconductors, that require substantial post-build commissioning time. We also lag flow inputs through the intermediate matrix, capturing transport and production-cycle times for these goods. We model AGI as eliminating regulatory time entirely and compressing physical durations to the fastest currently-demonstrable benchmarks. Details are in Appendix E.
Why do lags matter more at the higher growth rates we compute in this part? Consider a toy single-sector economy where capital
Substituting an exponential solution
This has two regimes. When the lag is short compared to the doubling time, the growth rate approaches
dominated by the lag
Applying per-sector lags to the full IO model at emergency utilization with priced labor:
Part 1's two-bucket lag model gives 0.63 yr⁻¹ at a 6-month structure lag and 1.2-month equipment lag, close to the 0.68 yr⁻¹ here. Resolving lags per-sector does not substantially change the headline.
Production without humans needs less capital and fewer service inputs
Part 1's Von Neumann calculation already excludes consumer goods, because they do not enter as intermediates in manufacturing; the maximum-growth economy does not invest in them. But human workers also drive costs inside production sectors. For example, if a mining company buys lunch for its workers, this shows up as an intermediate input to mineral ore production. The same firm may need to build office space for its management, use vehicles with driver cabs, and develop HR systems for payroll. All of these capital goods and service expenditures exist only because humans are employed by the company, and once labor is automated, none of it is needed.
In Appendix F.2 we work through every row of the IO system on both channels —
The biggest capital savings come from office and commercial structures that currently house white-collar and retail workers, and are no longer needed once these workers are automated. The biggest intermediate savings are also from office space — when firms lease rather than own, rent appears as a flow through
Closing within-industry productivity gaps modestly speeds up growth
The Von Neumann calculation in Part 1 takes each sector's production recipe to be what the average plant does. But the average plant is not the best plant. Within a typical manufacturing industry, the BLS Dispersion Statistics on Productivity finds that the 90th-percentile plant produces roughly 50% more output per unit of input as the average. AGI plausibly closes most of the real gap by managing every plant at frontier quality and rebuilding capital at the best available vintage.
Not all of the 90-10 spread reflects closeable productivity differences. Bloom et al. (2019) decompose within-industry variation in total factor productivity into contributions from four factors: management practices, R&D intensity, ICT spending, and worker education. AGI plausibly substitutes for each of these. These factors account for about a third of the raw 90-10 spread, with the rest reflecting pricing strategy, location, and measurement noise rather than closeable differences. We apply this third to each manufacturing sector, and a uniform 10% uplift across non-manufacturing. Details are in Appendix F.3.
The harder question is what the productivity gap actually means. A more productive plant might use labor more efficiently, capital more efficiently, or get more output from the same materials. The literature has not directly decomposed cross-sectional plant productivity dispersion into factor-augmenting components. The closest evidence — Doraszelski and Jaumandreu (2018) on the bias of technological change over time — suggests roughly equal labor-augmenting and Hicks-neutral contributions. We adopt a 50/50 split as our central case, noting the uncertainty by reporting bounding cases in both directions.
Computing growth rates under each decomposition, we find:
The growth effects of labor-augmenting productivity gains are small. Post-AGI, labor is already cheap, so saving more of it adds little. The Hicks-neutral half of the productivity gap drives most of the modest central-case uplift.
Cheaper, shorter-lived capital can substantially increase growth
Capital wears out as you use it. At today's real interest rate of about 5%, durable capital makes sense because the cost of tying up funds is small relative to the savings from not replacing equipment frequently. At doubling times of around a year, the opportunity cost of capital is much higher. A 30-year machine will see the economy grow more than a billion-fold over its lifetime. Almost all of its useful life falls in a period when it is a negligible fraction of the capital stock. The optimal response is to build cheaper, shorter-lived capital.
Reducing capital requirements per unit of output also increases depreciation, because cheaper or less durable equipment wears out faster. At modest reductions (10–20%), the depreciation penalty is small. At larger reductions it grows, and eventually each capital good hits a physical ceiling. We model this tradeoff using a power-law wear function calibrated to BEA depreciation rates, and estimate per-good engineering ceilings for each capital category. The formalism and ceiling values are in Appendix F.4.
At emergency utilization with priced labor:
I think the 10% uniform scenario is probably conservative, but the per-good engineering ceilings are more aggressive and I'm not sure they can be realized. The unconstrained optimum extrapolates far outside calibrated ranges and is probably very unrealistic. This channel is more uncertain than the previous two. How far each capital good can be compressed is a component-level engineering question, and the aggregate is hard to pin down without detailed analysis of individual goods.
Cheap labor shifts recipes toward labor-intensive production
Every sector can trade capital for labor to some extent, producing with larger workforces rather than investing in labor-saving equipment. Today's recipes are optimized for current US wages and are capital-heavy as a result. Post-AGI, robots and compute replace a human worker at roughly 8% of their current wage, and the optimal recipe in every sector shifts back toward labor.
How much it shifts depends on how easily each sector can substitute labor for capital. Economists usually model this using the constant-elasticity-of-substitution (CES) production function:
where
Labor service is supplied by robot and compute capital with fixed engineering coefficients, but the rental cost of that capital depends on the growth rate
These numbers should not be taken too seriously. The literature estimates of
Summary
Three of the channels above — management, human presence, and durability — modify independent parts of the IO matrix and compose cleanly. CES labor substitution is harder to compose because it rebuilds the system at different factor prices. Of the four, human presence is the one I'm most confident in, as things like office space and corporate services are clearly unneeded in work sites where humans have been automated. Management, durability, and CES labor substitution each depend on parameters with more uncertainty.
The table below stacks each less-certain channel on top of the Part-1-plus-presence baseline, and shows the all-four-combined row at both the central durability setting (
At AGI-lag, baseline plus human presence reaches 0.88 yr⁻¹ on its own. The all-four-combined row pushes this to 1.28 yr⁻¹ at the central durability setting and 1.41 yr⁻¹ at engineering ceilings.
Older recipes support faster growth
Previous iterations of the US economy had faster growth rates
The US has published input-output tables going back to 1947. Figure 1 shows the free-labor Von Neumann growth rate at several points in time. Over the past seven decades the rate has more than halved, both on the raw matrices and after applying the F.2 human-presence cut to each year's IO matrix.
Figure 1. Free-labor
The dominant form of technological progress in manufacturing has been labor-saving capital deepening: replacing workers with more and better machines. This raises output per worker but increases the capital required per unit of output; the Von Neumann growth rate is determined by the latter. The historical labor-intensive recipes use less capital, and at post-AGI factor prices that makes them the cheaper option. A 1947 steel mill that employs fifty workers and ties up less capital per ton of steel is a better deal than a 2017 mill that employs five workers but requires far more machinery.
We could also consider adding input-output data from other countries into the mixture. As we already saw in Part 1's Appendix B, OECD countries have Von Neumann growth rates comparable to the present-day US, and when I considered them alongside the US historical tables, they did not add much. Developing countries might be more labor-intensive and therefore have faster Von Neumann rates, but I was not able to find sufficiently granular IO tables for this to be a useful analysis.
Older recipes can lift the growth rate substantially
Older US economies used more labor and less capital per unit of output. Post-AGI, labor is cheap, and those older production methods could become cheaper options. But we cannot simply swap in 1947 methods wholesale. Older economies have no recipes for robots or compute, and most goods have changed too much across decades to be meaningfully compared. An accountant in 1947 and an accountant in 2017 are doing very different work, despite sharing a job title.
Picture each year's economy as its own island, running its own input-output recipes locally. Robots and compute are supplied from the 2017 island — the only one that can build them — and shipped elsewhere to automate labor. Some commodities — for example electricity or aluminum — are similar enough between islands that we can freely allow exchange. Others, like construction or business services, have changed so much across decades that it is not meaningful to ship them between islands, and so they must be produced locally.
Of the 398 sectors in the 2017 input-output tables, we identify 97 that can be meaningfully compared to at least some of the historical tables. These fall into three confidence tiers:
Other sectors are excluded either because they have no equivalent in the older tables, or because of data quality issues. For example, the 2017 tables lump precious metals mining with iron mining, but earlier tables lump precious metals with copper mining; this makes meaningful comparison impossible even though the underlying goods are physical.
For each comparable commodity, a linear program picks the cheapest production method from any of the five source years (1947, 1963, 1972, 1987, and 2017). Picking a year's column commits to that year's full input structure; a 1972 aluminum smelter uses 1972 construction and 1972 law firms. Formulation and data sources are in Appendix G.
At emergency utilization with priced labor, solving the linear program on progressively wider subsets of comparable commodities:
Each tier of comparable goods substantially increases the growth rate. Our confidence that the calculation reflects physically achievable manufacturing falls as we move to higher tiers, since the comparison shifts from like-for-like physical units to inflation-adjusted shipment values. On the other hand, the different years are only able to trade a limited number of goods, and within each sector must use entirely the methods of that year. This exercise also understates the available advantages, since there are intra-sector productivity improvements to be gained.
By looking at which years provide these goods, we can get a sense of where these improvements come from. Under the AGI-lag condition:
The goods are distributed across a range of years. Heavy industrial commodities go to the oldest years, where capital deepening since has been steepest. The 1987 table takes most of the machinery rows because manufacturing methods between 1987 and 2017 are similar enough for the deflator-based comparison to be meaningful, while earlier tables either lack these categories or have changed too much.
We can see how economic activity is distributed between each year's tables through the fraction of robots, compute, and electricity they consume:
Production is mostly split between four of the five years, with 1972 contributing only a small share. We tested additional years (1967, 1977, and 1997) as sources but each received effectively zero weight and is dropped from the analysis.
Stacking channels on the merger further accelerates growth
Three of the section 1 channels can be applied to each year's columns before the merger picks recipes; CES labor substitution is excluded because the merger already captures that channel empirically. At emergency utilization with priced labor, growth rates
Of the three channels applied here, management is the most uncertain extrapolation: the within-industry productivity gap is estimated from modern BLS data, and we do not know whether it was larger or smaller in earlier decades. Human presence and durability are less sensitive to the source year — human presence is mostly a binary classification done per vintage, and the durability ceilings are rough enough to apply similarly across eras. At AGI-compressed lags, the Tier 1 merger with human presence alone gives 1.12 yr⁻¹, resting on physical-unit comparisons and the most well-grounded channel. The full merger with all three channels reaches 1.69–1.84 yr⁻¹ depending on durability assumptions.
Appendix E: Lags revisited
E.1 The lag-shifted eigenvalue problem
Part 1's Appendix A.3 modeled construction lags with a single per-commodity delay
In general, every input flow in the economy carries its own lag: the time between when the input is committed and when it contributes to useful output. Each entry
This is a matrix of
This reduces the problem from
The same lag operators multiply the depreciation-replacement flow
On the maximum-growth path
As in Part 1,
E.2 Data sources
Two principles govern how lag values are set. First, lags are anchored to fabrication-cycle and construction durations, not order-to-delivery lead times. Multi-year backlogs for aircraft, turbines, and transformers reflect queue depth, not build time, and do not enter the eigenvalue. Second, the AGI scenario strips all regulatory and administrative time and compresses physical durations to the fastest demonstrated benchmarks, assuming 24/7 robot crews and aggressive prefabrication. The compression is bounded by physics floors that cannot be eliminated: refractory cures, fab yield curves, catalyst conditioning, concrete hydration, and biological growth cycles.
IP, intangibles, services, utilities, and the robot/compute extensions are held at zero lag.
Structures (NAICS 23). Three rows — manufacturing, other nonresidential, and office/commercial — carry roughly 36% of total
Equipment (NAICS 33). Anchored on fabrication-cycle durations: aircraft at 9–12 months for the airframe assembly cycle, power transformers at 3 months for the fab cycle behind a multi-year lead time, ships at 12 months for hull build behind multi-year backlogs. Minor rows fall through to NAICS-3 prefix defaults.
Nineteen industries have non-zero deployment lags, concentrated in heavy-process metals, mining, refining, chemicals, cement, semiconductor fabs, aircraft, and electric power. AGI compression is on the order of 3×. Anchors:
Production cycles. Most manufacturing sits at one to three weeks. Continuous-flow sectors (petroleum refining, petrochemicals, nitrogenous fertilizers) at hours to one day, anchored on Ullmann's. Advanced-node semiconductors at 90 days for the wafer cycle, anchored on TSMC/Intel references. Iron and steel at 3 days, aluminum at 1 week, cement at 1 week. Agriculture at 60 days, forestry at 90 days (harvest-and-mill of existing stocks; a 365-day biological-cycle sensitivity shifts the merger headlines by 0.15–0.45 yr⁻¹). AGI compresses production cycles by 3× outside agriculture and forestry, which compress by only 20%.
Ship times. Dominant transport mode per commodity from the BTS Commodity Flow Survey, mapped to seven modes (bulk rail/road, local truck, ocean, air, pipeline, bulk grain, precision air cargo) with per-good overrides. AGI compresses shipping 1.3–3× by mode.
At-plant curing and processing. Non-zero for concrete products (1 day for ready-mix transit, 2 weeks for precast curing) and biologic pharmaceuticals (30–60 days for cell-culture cycles). Physics-bound; held at current values in the AGI scenario.
Appendix F: Channel-by-channel perturbation analysis
F.1 First-order eigenvalue perturbation
Several Part 3 channels modify the IO triple
The unperturbed problem is
where
This vector has an economic interpretation as the shadow-price for which every sector earns the same rate of profit
Differentiating both sides under perturbations
The numerator is a value-weighted sum of the perturbations; the denominator is the equilibrium value of the capital stock.
The four lag matrices reshape the eigenvalue problem. As derived in Appendix E.1, with
Define the lag-effective matrices
and analogously the sandwiched perturbations
which has the same form as the lag-free version with
where
is the lag-adjusted capital stock. The terms beyond
F.2 Capital and services sized for human presence
Each row
Both
A-side changes
For most A-matrix inputs we can classify each row cleanly as either wholly human-consumed (cut entirely,
A handful of A-side rows don't fit this clean dichotomy and we treat them separately:
The sector 531ORE (Other real estate) aggregates rent paid for office space (cut) and rent paid for warehouse and industrial space (kept). We resolve the row per user-industry: each consumer
Legal services, accounting, management consulting, and management of companies are in part required to deal with human management and labor (employment law, payroll, HR, in-house benefits administration), and in part required for cognitive decisions that an AGI-run firm still has to make (audit, strategy, treasury, capital allocation). It is hard to know precisely what fraction is human-management overhead;
B-side changes
As with A-matrix inputs, most physical capital can be split into things that exist only for humans (cut entirely,
The Office and commercial structures sector aggregates office buildings (cut entirely), warehouses (kept with the 10% comfort cut), and retail / lodging / other commercial space (cut entirely, but consumer-facing tenant industries have
F.3 Within-industry productivity dispersion
For each four-digit NAICS manufacturing industry, BLS publishes the activity-weighted log 90/10 productivity spread, averaging about 0.8 across manufacturing over 2015–2019. The relevant quantity for our purposes is the gap from the activity-weighted mean to the 90th percentile, which under log-normality with the implied
Bloom et al. (2019, Table 4) report a joint spread share of
BLS does not publish dispersion statistics outside manufacturing. The sector-specific frontier-gap literature gives a similar range:
We use a uniform default of 1.10 outside manufacturing. Using sector-specific values instead does not meaningfully change the headline rate.
Each sector's
F.4 Capital redesign and the depreciation–intensity tradeoff
Consider a sector with physical capital
where
Minimizing over
Assuming current designs are firm-optimal at today's interest rate (
At
We compute
The redesign factor varies more across capital goods than across users, so we apply a single
The optimality condition gives the slope of the wear curve at
The per-row ceilings
The capital-redesign perturbation cuts both
The resulting ceilings, with each row's
The
F.5 CES labor-capital substitution
Each sector
Each sector chooses a recipe
to produce one unit of output via the CES production function,
The full problem maximizes
The factor prices that drive each sector's recipe come from the maximum-growth path itself. The capital price for sector
The labor price is the rental and flow cost of the robot and compute capital that delivers sector
where
Holding the factor prices fixed, cost-minimization gives the closed-form recipe
and the CES constraint at equality gives the magnitudes,
By construction,
Ten of the 398 sectors have one factor essentially absent, and the CES does not apply to them. Two have no labor reference, including owner-occupied housing and the secondhand goods adjustment, so
Across the remaining sectors at
Appendix G: Cross-year merger
Stack
Let
by bisection on
For lag-adjusted scenarios, production and deployment lags enter via row/column multipliers
The five source years and their IO resolution are:
The 1947 entry uses the original 192-industry Evans-Hoffenberg "Interindustry Relations Study" rather than the BEA-reworked 85-sector version, because higher resolution unlocks separate attribution to specific 1947 commodities that collapse into too-coarse industries at BEA resolution. The 1987 BEA-IO benchmark inherits its 6-digit SIC code scheme from 1972, with sector overrides where the BEA classification changed. All five years are at emergency utilization, with the 2017 QPC multipliers applied uniformly.
Capital matrices for all years are built from BEA detailed nonresidential fixed assets, which provides per-industry asset composition for each year back to 1947. The 1947 capital column uses 1963 asset-composition shares applied to 1947 K/Y intensity levels at the BEA-83 parent level, with each Evans-Hoffenberg child sector inheriting from its parent.
We systematically worked through all 398 sectors in the 2017 IO tables and excluded those that could not be meaningfully compared to at least some of the older years. The main categories of exclusion were:
The 97 sectors that survive this screening are split into three confidence tiers as described in the body text. Tier 1 goods are compared in physical units (tonnages, kWh, BTUs) with no capability-factor rescaling. Tier 2 goods use physical units but with known product drift that the unit conventions only partly absorb. Tier 3 goods are compared using inflation-adjusted real shipment values from the NBER-CES Manufacturing Industry Database, restricted to sectors and years where the deflator approach is reasonable. This is generally 1987-vs-2017 comparisons, where manufacturing methods are similar enough that a deflator comparison is defensible.
The linear program balances physical robots in 2017-robot-dollar units. Each year