Summary: Analysis claiming that automating X% of the economy can only boost GDP by 1/(1-X) assumes all sectors must scale proportionally. The economy is a graph of processes, not a pipeline. Subgraphs can grow independently if they don't bottleneck on inputs from non-growing sectors. AI-driven automation of physical production could create a nearly self-contained subgraph that grows at rates bounded only by raw material availability and speed of production equipment.
Amdahl's Law for economics: Automating a sector that represents X% of GDP can boost output by at most 1/(1-X). Automating software (2% of GDP) gives ~2% boost; automating all cognitive labor (30% of GDP) gives ~42%.
Bottleneck tasks determine growth rate: "Suppose there are three stages in the production process for making a cheese sandwich: make the bread, make the cheese, combine the two together. If the first two stages are automated and can proceed much more quickly, the third stage can still bottleneck the speed of sandwich production." (Davidson 2021)
Baumol effects bind: "If bottlenecks persist—and I believe strongly that they will—we will have Baumol issues... 100% is a really big number. It's radically bigger than 80%, 95%, or 99%." (Twitter thread quoted on LW)
These framings share an implicit assumption: the economy is a single integrated production function where unautomated sectors constrain growth of automated sectors. I argue this assumption breaks when an automatable subgraph can grow without requiring inputs from non-automated sectors.
There's no rule in economics that says if you grow a sector of your economy by 10x, farm fields, lawyers and doctors must then produce 10x more corn, lawsuits and medical care respectively. The industrial revolution was a shift from mostly growing food to mostly making industrial goods.
For small growth rates, and small changes, the model is mostly true in much the same way that linear approximations to a function are locally true. But large shifts break this assumption as the economy routes around industries that resist growth.
During the industrial revolution, Factories needed more workers but were competing with agriculture. Without innovation, there could have been a hard limit on free labor available to allocate to factories without cutting into food production. Instead innovations like combine harvesters and other agricultural machinery freed up farm workers for factory jobs. There's economic pressure to route around blockages to enable growth.
A better model
The economy is a graph
processes are nodes in the graph that consume inputs and produce outputs
Subgraphs of the overall graph can grow, limited only by ability to buy inputs at the edges where they interact with the parent graph.
during the industrial revolution:
more mines were built to increase supply of metals (self contained growth)
innovations to freed up workers from agriculture jobs to move to the cities (interaction with the larger graph)
Structural changes to the economy can route around bottleneck to enable growth.
An illustrative case
Consider automating mining and manufacturing. We build the following:
Robots that can move materials and set up machines/factories
machines that can build:
more robots
more machines/factories
As inputs, the factories take metal ores, coal and solar power
Some things are purchased from the broader economy:
semiconductors
lubricants
anything it can't produce (EG:metals not available locally)
services of lawyers/engineers/etc.
Set this up in Australia sited on coal/iron deposits with some rail links connecting west/east for iron/coal.
This self contained economic core can then grow limited only by raw materials, speed of the underlying machinery and whatever it cannot produce that it has to trade for with broader economy like semiconductors or rare earths.
AI and robots don't take vacations, go to the doctor, put their kids in daycare or school. They needs chips, electricity and raw materials to grow. There will be some engineers, lawyers and lobbyists employed but not much relative to similar industrial production in the legacy economy. The system doesn't need much in the way of non-self-produced "vitamins" per unit of production.
It doesn't matter that this system hasn't replaced doctors in hospitals or convinced San Francisco to build housing. It can grow independently.
A hypothetical timeline
Starts with software:
AI agents start automating production planning
AI interfaces with industrial machinery
AI suggests production improvements
Bespoke software → bespoke hardware
Machinery raw material costs <<10% sticker price; eliminating labor drops prices by 1+ orders of magnitude[1]
Capital pours in similar to AI buildouts today
Manufacturing capacity grows very fast without needing to close power/resources loop yet
Electricity prices spike
Price of other things the growing industrial base needs spike:
raw steel, sheet metal, fasteners, copper, magnets, plastic
Shortages as outputs redirected towards growth
similar to DRAM/flash memory price hikes happening now due to AI demand
Early loop closure could avoid shortages (e.g. Western Australia industrial buildup geared towards self-replication)
Eventually there's pressure, loops close, semiconductor perhaps closes last.
Optimisation for doubling times yields >50% yearly growth, perhaps much more than that.
Full automation has the potential to massively increase productivity/growth. Right now most manufacturing output is consumer goods. Only a small fraction is machinery to replace/expand production. That machinery is often badly designed.
AI raising the floor on competence and automation would usher in absurd productivity gains. Full integration happens fast once AI replaces/convinces non-engineering trained MBAs of the stakes. Full automation/integration drops the capital cost to upgrade or build new production capacity. Things go insane.
Timelines and trajectories are hard to predict; ASI could compress everything, AI wall would stop it, AI capabilities might not generalize to optimizing manufacturing, but I think they will. Broadly, this doesn't happen or happens much slower if:
AI can't raise the competence floor in industry (AI winter, lack of generalisation, etc)
The growing self-contained sector can't buy the external inputs it needs
voters object to electricity prices spikes making air conditioning unaffordable
Some critical industry resists AI efficiency/integration
My own experience in industry and interactions with AI make me think 1) is wrong. 2) isn't an issue so long as there aren't political barriers in all countries. 3) is possible if some critical patents don't get licensed out, but lower tech out of patent technologies can usually be substituted albeit with some efficiency penalty.
Future posts I plan on writing supporting sub-points of this:
How bad things really are in industry
Industrial processes are very productive
existing proven industrial tech grow at >100% yearly based on simple production mass ratio calculations
(speculative technologies for very large economic scale-up)(multiple posts?)
this stuff enables much faster growth (100% --> 5000% yearly growth). Mostly making parts of the system cheaper/simpler:
I've seen examples of in-house-produced equipment that cost orders of magnitude less than comparable equipment from vendors while being simpler, more reliable, etc.
Right now, most of the graph ties back to a single node very strongly. That node is labor.
Modern labor is highly specialized, so this isn't a single node. A science fiction writer couldn't become a programmer overnight, despite both spending their days typing at a computer. Similarly, a commercial airline pilot couldn't retrain as a pediatrician in a single day, nor could a steelworker instantly become a linguist-translator. Moreover, the ability to switch careers declines with age—I myself changed professions at 30, and it was extremely difficult. Therefore, it would be wise to proactively identify workers in which professions will need retraining most urgently and potentially make this a central goal of social programs.
Summary: Analysis claiming that automating X% of the economy can only boost GDP by 1/(1-X) assumes all sectors must scale proportionally. The economy is a graph of processes, not a pipeline. Subgraphs can grow independently if they don't bottleneck on inputs from non-growing sectors. AI-driven automation of physical production could create a nearly self-contained subgraph that grows at rates bounded only by raw material availability and speed of production equipment.
Models being challenged:
This post is a response to Thoughts (by a non-economist) on AI and economics and the broader framing it represents. Related claims appear across LessWrong discussions of AI economic impact:
These framings share an implicit assumption: the economy is a single integrated production function where unautomated sectors constrain growth of automated sectors. I argue this assumption breaks when an automatable subgraph can grow without requiring inputs from non-automated sectors.
There's no rule in economics that says if you grow a sector of your economy by 10x, farm fields, lawyers and doctors must then produce 10x more corn, lawsuits and medical care respectively. The industrial revolution was a shift from mostly growing food to mostly making industrial goods.
For small growth rates, and small changes, the model is mostly true in much the same way that linear approximations to a function are locally true. But large shifts break this assumption as the economy routes around industries that resist growth.
During the industrial revolution, Factories needed more workers but were competing with agriculture. Without innovation, there could have been a hard limit on free labor available to allocate to factories without cutting into food production. Instead innovations like combine harvesters and other agricultural machinery freed up farm workers for factory jobs. There's economic pressure to route around blockages to enable growth.
A better model
The economy is a graph
Structural changes to the economy can route around bottleneck to enable growth.
An illustrative case
Consider automating mining and manufacturing. We build the following:
This self contained economic core can then grow limited only by raw materials, speed of the underlying machinery and whatever it cannot produce that it has to trade for with broader economy like semiconductors or rare earths.
AI and robots don't take vacations, go to the doctor, put their kids in daycare or school. They needs chips, electricity and raw materials to grow. There will be some engineers, lawyers and lobbyists employed but not much relative to similar industrial production in the legacy economy. The system doesn't need much in the way of non-self-produced "vitamins" per unit of production.
It doesn't matter that this system hasn't replaced doctors in hospitals or convinced San Francisco to build housing. It can grow independently.
A hypothetical timeline
Full automation has the potential to massively increase productivity/growth. Right now most manufacturing output is consumer goods. Only a small fraction is machinery to replace/expand production. That machinery is often badly designed.
AI raising the floor on competence and automation would usher in absurd productivity gains. Full integration happens fast once AI replaces/convinces non-engineering trained MBAs of the stakes. Full automation/integration drops the capital cost to upgrade or build new production capacity. Things go insane.
Timelines and trajectories are hard to predict; ASI could compress everything, AI wall would stop it, AI capabilities might not generalize to optimizing manufacturing, but I think they will. Broadly, this doesn't happen or happens much slower if:
My own experience in industry and interactions with AI make me think 1) is wrong. 2) isn't an issue so long as there aren't political barriers in all countries. 3) is possible if some critical patents don't get licensed out, but lower tech out of patent technologies can usually be substituted albeit with some efficiency penalty.
Future posts I plan on writing supporting sub-points of this:
I've seen examples of in-house-produced equipment that cost orders of magnitude less than comparable equipment from vendors while being simpler, more reliable, etc.