Growth theory · machine economy · artificial intelligence
Solow After
the Machine
In his 1956 growth model, Robert Solow separated accumulation from technical change. Seventy years later, that distinction is the cleanest way to understand why an AI investment boom is not yet an AI productivity regime.
AI does not add a new letter to Solow. It changes the quality, price, depreciation, and interaction of several letters we already have.
The old letters · new objects
The notation survives. The production system moves beneath it.
Hover, focus, or select a factor. The point is not to add “AI” to the equation, but to reopen what each existing term contains.
Capital becomes layered
Structures, accelerators, model weights, evaluations, and workflows accumulate and depreciate on different clocks.
Figure · economic classification
The machine is a production chain, not a new letter.
Structures
Data centres, cooling, grid connections
Capital stock
Compute
Accelerators, memory, networks, software
Capital service
Energy
Electricity and cooling consumed in use
Intermediate flow
Data + evaluations
Coverage, permissions, tests, feedback
Produced complement
Quality-adjusted machine service
Attempts × task value × success × acceptance × durability
Raw tokens sit inside attempts. Reliability, human verification, and downstream acceptance determine whether an attempt becomes a service.
Economic outcome
A release shipped. A case resolved. A decision improved.
The meaningful unit appears at the end of the production system, after review, integration, recovery, and demand.
A proposed heuristic
The Bottleneck-Migration Law
I call this the Bottleneck-Migration Law: every successful automation raises the shadow price of the remaining human, physical, and institutional constraints. The model becomes faster; review, integration, trust, and accountable judgment become relatively scarce. Productivity therefore begins where capability benchmarks end.
Figure · observed evidence
Writing code is not shipping code.
Across more than 100,000 developers, autonomous coding tools produced large local gains, which attenuated as work moved from commits through projects to releases.
Interactive model · simulated evidence
Build capital. Then confront the weak links.
The model separates AI accumulation from the organizational, verification, and energy constraints that determine whether machine potential becomes economic output.
Figure 1 · output per worker
Transition path, index at year 0 = 100
Assumptions
Output reinvested in compute, models, and AI equipment.
Share of machine capability surviving review, integration, and demand.
Economic obsolescence of hardware, models, and embedded workflows.
Evaluations, permissions, process redesign, skills, and decision rights.
Normalized capacity for power, cooling, networks, and grid access.
Annual quality gain in machine services at a fixed AI capital stock.
32.1%
50-year output lift
against conventional path
1.7%
Final annual growth
level and technical progress
20.1%
Machine potential realized
quality-adjusted service
Organization
Tightest complement
51.1%
Model assumptions and text fallback
Output combines conventional capital with quality-adjusted machine service. AI and organizational stocks accumulate through investment and depreciate independently. Population and labor-augmenting technology dilute capital per effective worker. The simulation deliberately omits prices, strategic competition, distribution, and general equilibrium, so it is a mechanism demonstrator rather than a calibrated forecast.
| Year | Output index | AI capital | Realized service | Translation gap |
|---|---|---|---|---|
| 0 | 100.0 | 0.20 | 0.09 | 0.55 |
| 10 | 129.4 | 0.51 | 0.27 | 0.79 |
| 20 | 163.0 | 0.58 | 0.40 | 1.00 |
| 30 | 205.3 | 0.63 | 0.57 | 1.27 |
| 40 | 247.1 | 0.66 | 0.61 | 1.79 |
| 50 | 292.8 | 0.68 | 0.62 | 2.47 |
Continue into the full argument
The Token Is Not the Factor
The long-form essay follows the argument from growth accounting and layered depreciation through task complementarities, energy constraints, adoption depth, over-investment, and a measurement programme for the firm.