THE LIMIT CASE · ECONOMIST ARC — PART 2 · RISING ACTION
Economics lists land, labor, and capital. It left off the factor that was always doing the work — and it is the one with a floor.
Part 1 ended with an engine running and a gap opening. For two hundred and fifty years the rich world has grown roughly one and a half to two percent richer per person per year, and that number has two faces: every year the economy learns to make last year's output with fewer hands, and the freed hands make the new things. Getting richer and shedding labor are the same event measured twice. The system's genius was never that it avoided displacement — it displaced relentlessly, for centuries — but that creation kept pace with freeing, so the gap between the two rates stayed near zero through the whole industrial era. Part 1's diagnosis is that AI breaks the pace-keeping: it is the first automation aimed at the layer that builds automation, so the freeing rate accelerates off its historical anchor while the absorption machinery, calibrated across centuries to that anchor, has nothing that scales with it.
And the diagnosis ends by naming a destination — the Limit Case, in which capital and energy do everything traditionally productive, and frontier work absorbs at most a fifth of the people.
That sentence smuggles in a claim, and this essay exists to earn it. Open any economics textbook and the factors of production are land, labor, and capital. Energy is not on the list — not demoted, not footnoted; absent. Part 1 drove one of the listed factors toward zero. The claim that what remains is "capital plus energy" quietly seated at the table a factor the textbook never invited. Where did it come from? Why was it never listed? And why should it — rather than capital, the factor that actually is on the list — be the unit in which everything downstream gets measured?
The answers, in order: it was always there; because it was cheap; and because of what waits at the bottom of two falling curves. Start with the curves, because the strongest version of this argument is not conceptual at all. It has been running in the national accounts for fifty years.
Take the American economy, 1975 to 2024, and ask the same question of each factor: how much of it does a unit of output require, compared to what it required in 1975?
| input per unit of real output, 1975→2024 ✦ | change | %/yr (log) |
|---|---|---|
| energy (quads per $T of real output) | −65% (11.5 → 4.0) | −2.13 |
| labor (workers per $T of real output) | −51% | −1.45 |
Both fell. For labor that is expected — falling labor content per unit of output is Part 1's entire subject, the two-faces identity at work. The surprise is the other line: we have automated out energy faster than labor ✦. Energy input per unit of real output fell sixty-five percent over the window, against labor's fifty-one.
The reason is that the same engineering function works on both factors. The gear from Part 1's panels — capital and energy applied to replace an input — does not care which input it is pointed at. Point it at labor and you get the assembly line, the spreadsheet, the language model. Point it at energy and you get the LED, delivering roughly ten times the light per watt of the incandescent bulb it replaced ◦; the variable-frequency motor controller, which stopped industrial motors from running flat-out against a throttle; the electric drivetrain, three to four times the tank-to-wheels efficiency of combustion ◦; the doubling of fleet fuel economy under CAFE ◦; the heat pump, which moves three or four units of heat for every unit of work it consumes ◦. Efficiency is a pursuit as old as engineering, and the data shows it responding to exactly the incentives you would expect: the energy curve's steepest dive follows the price shocks of the 1970s — price finds efficiency — and Part 4 will argue that a deliberate energy tax makes that signal permanent rather than episodic.
The aggregate version of the same story: the economy ran on 69.8 quads of primary energy in 1975 and 94.6 in 2024 — 1.36×, or 0.63%/yr ✦ — while real output grew 3.85× ✦ and population 1.57× ✦. Divide through by people and the result deserves a sentence of its own: the average American today runs on about fourteen percent less primary energy than in 1975 ✦, while consuming roughly two and a half times the real output ✦. And since 2000, total US primary energy consumption has not grown at all ✦ — a quarter-century in which efficiency gains paid for the entirety of economic growth.
So the two factors were never distinguished by their slopes. Both fall, and energy falls faster. The difference — and the rest of this essay — is the destination. Labor's curve is headed to zero. Energy's is not. Before we can say why that asymmetry decides everything, we need to be precise about who these factors are.
The classical triple — land, labor, capital — dates to the founding generation of the discipline, and two centuries of institutional architecture hangs off it. Taxation falls overwhelmingly on labor income. Social insurance is keyed to employment. The national accounts decompose value added into wages and profits. Money sits underneath as the neutral measuring stick. The triple is not a modeling convenience; it is the load-bearing frame of the modern state.
Two amendments produce the true list. The first is old news: fold land into capital. Land has behaved like capital for a century — bought, sold, improved, collateralized, depreciated everywhere but the tax code — and the classical rent distinction, whatever work it did in 1817, does none in an accounting of production at the limit.
The second amendment is the one this essay is for: add the input that was always doing the work. Every act of production — every transformation of matter from a less useful arrangement to a more useful one — is powered. Nothing in an economy moves, forms, heats, cools, computes, or assembles except by the expenditure of energy. The engine was never labor plus capital. It was labor plus capital plus energy, with the third term left off the ledger because its price was small. Its role never was.
Now run Part 1 through the corrected list. Automation drives the labor term toward zero, and what remains is not capital alone — it is capital plus energy. The factor that was never on the list becomes half of what remains. Section 8 will argue the stronger claim: closer to all of it.
The dimensional version of the argument belongs to the economist Steve Keen and the physicists Robert Ayres and Russell Standish: a production function that omits energy is not simplified, it is incoherent — output is a flow of transformed matter, transformation is work, and work requires free energy. Their formulation is the best sentence in the literature: capital without energy is a statue; labor without energy is a corpse. A factory with the power cut produces nothing. A worker without calories produces nothing, and then stops being a worker. Every output ever made, from the first cooked meal to a frontier training run, took energy to make — the cooking fire and the gigawatt data center are endpoints of one continuous line, and the whole line is the economy.
An engineer's corollary comes from Robert Miller, in a 2017 exchange on basic income that this project has carried with it since: because the economy is a physical process — the application of energy to the transformation of raw materials into goods and services — economic proposals can be screened the way you screen claims about physical systems. Does this conserve? Where does the energy come from? Is this an economic perpetual-motion machine? The test never tells you which policies are good; it tells you which are impossible, and that is a shorter list to argue about. It is also the discipline this arc tries to hold itself to — when Part 3 anchors money, it anchors it to meters, not to models — and it is the deepest reason energy keeps forcing itself back into the frame: of all the factors, it is the one with a conservation law.
To be fair to the discipline: economics has not ignored energy so much as filed it under intermediate inputs. Growth accounting knows the joules are there; it prices them at their cost share — a few percent of GDP ◦ — and concludes they are minor. That conclusion, and exactly why it fails at the limit, is Section 6's subject. First, the honest question: if energy was always fundamental, how did a model that omitted it work so well for so long?
Because mis-specifying a structure only costs you when the missing term binds.
In 1900 the bill for almost anything was mostly labor. Wages dominated cost; energy ran a few percent; and prices, being labor-mediated, tracked real value well enough for every practical purpose. A model that omits a small, stable term is roughly right, and roughly right for two centuries is a better empirical record than most models ever assemble. Economists were not being obtuse when they left energy off the list. They were reading the bill, and the bill said labor.
Two conditions kept the omission harmless. Labor dominated the cost of everything, so labor was both the binding constraint and the natural unit. And energy was cheap and elastically supplied — there was always more coal, then more oil, so its price carried no information a model needed.
The record even stamps the exceptions for us. The two brief periods when the second condition failed — 1973 and 1979 — produced precisely the macroeconomic chaos an omitted-but-suddenly-binding factor should produce: stagflation, the joint movement of prices and output that the labor-and-capital toolkit of the day could neither predict nor explain. There is an entire empirical literature on oil shocks preceding postwar recessions ◦, and it is best read as the residue of the omission: when the missing term moves, the model breaks, and the profession files the breakage under a special topic rather than amending the list.
Both conditions are now ending at once. Part 1's mechanism removes the first: the labor term is being driven toward zero, taking with it labor's claim to be the natural unit. And the AI build-out strains the second: for the first time in decades, the marginal unit of growth arrives asking for power before it asks for people.
Here is the limit argument proper, and it is the hinge of the essay.
Labor's asymptote is zero. Nothing in physics reserves any step of production for human hands; every task is a transformation, and transformations can be powered and directed by capital. Whatever work humans retain at the limit — the frontier fifth, the chosen crafts — they retain by preference and by comparative advantage at the frontier, not by physical necessity.
This is not a thought experiment; one sector already ran it to near-completion. Around 1800, farming took roughly nine in ten American workers; today it takes fewer than two in a hundred, and each of them feeds well over a hundred people ◦ — the largest labor-elimination in economic history, and the food supply did not merely survive it, it multiplied. The residue is as instructive as the collapse: a growing share of the agricultural labor that remains has migrated to the bespoke — organic, heirloom, non-GMO, small-batch — work kept not because a commodity calorie needs a human hand but because some buyers prefer one on it. Agriculture is the whole argument in miniature: labor driven toward zero by capital and energy, with the remainder drifting to the frontier by preference. The groceries in the price record below are the output of exactly that automation.
The claim still invites two objections. The first mistakes preference for necessity — the hand-thrown pot, the boutique tomato, valued because a person made them; but as agriculture shows, that is demand for human-madeness, not a physical requirement of production, and it is where the frontier crafts live. The second is the substantive one: the labor hardest to automate is not cognitive but sensorimotor — Moravec's paradox — the plumber in the crawlspace, the picker of soft fruit. That is a genuine moat, but one of engineering difficulty, not of physics; it governs the timeline to zero, not whether zero is reachable, and it is the moat that foundation-model robotics has begun to drain. And the argument needs less than literal zero in any case: only that labor's floor is zero while energy's sits above it — which factor dominates the bill does not turn on whether the last hands ever leave.
Energy's asymptote is not zero. Converting materials into goods has a minimum energy bill that physics sets: the free-energy difference between the starting arrangement and the finished one, the Carnot bound on every heat engine in the chain, and — for the economy's newest sector — Landauer's floor under every erased bit. Engineering approaches these floors; nothing crosses them. The fifty-year efficiency march of Section 2 is a march toward a wall, and the wall's position is set by thermodynamics, not by ingenuity.
Now the arithmetic. The unit cost of anything decomposes into labor, energy, capital, and materials — and materials are upstream capital and energy, because extraction is itself capital and energy applied to the earth. The one input that does not reduce to energy is land — or more precisely space to build — and at the limit, for goods at least, it is negligible. That leaves labor, energy, and capital. Let the labor term go to zero. Let the energy term fall to its floor and stop. Capital does not vanish — it is the machinery still doing the producing — but capital is itself made by capital and energy, so its cost recurses toward energy on a longer timescale, the reduction Section 8 completes. So the share of the remaining bill that is energy is forced upward — not by any forecast about demand or technology, but by division: a shrinking numerator's neighbor going to zero while it holds at a floor, and the other neighbor resolving into the same joules given time. Dominance at the limit is arithmetic. We do not need to know when the curves bottom out, only which of them has a hard stop above zero.
This is also where the standard objection answers itself. The objection: energy is two to four percent of GDP by cost share ◦ — how can a rounding error be "the" factor? Answer: cost shares are labor-era observations. Energy's share is small today because labor still dominates the bill and because fifty years of the efficiency march kept it small. The claim was never that energy is the biggest line item now. The claim is that energy is the irreducible remainder — the one term with a floor — and shares at the limit are set by floors, not by today's invoice. Quoting today's cost share against the limit argument is quoting the very number whose trajectory is the argument.
All of this is visible in the price record, if you measure prices in the right unit. Dollars conflate a good's real cost with the dollar's own decay; price a thing instead in hours of work — how long the typical wage must labor to buy it — and the dollar drops out, leaving the real labor-cost of the thing. Do that across fifty years and the basket splits exactly as the limit argument predicts (the chart below). The goods the machine reached fell, some steeply: a television that cost the better part of a work-week in 1974 costs an afternoon today. The labor-locked services rose roughly in proportion to how much irreducible human time they still contain — healthcare, schooling, childcare. And one line runs flat across the whole half-century: gasoline. A gallon of fuel costs about what it always did in work-minutes, because it is nearly pure energy, and energy holds its value while labor is automated out around it. The chart is the essay's three claims in one image — goods heading to zero, services resting on their labor floor, energy resting on its own floor above zero.
Two corroborating trends deserve mention with their evidentiary weight stated plainly: they are corroboration, not load-bearing. Labor's share of national income has been falling for decades across the rich world ◦ — the bill drifting away from the factor the institutions are built on. And data-center electricity has inflected — a few percent of US load today, with every serious forecast bending upward ◦ — the first major industry whose output is almost dimensionally energy. Both point the direction the floor argument predicts. Neither is the proof. The proof is the floor.
Part 3 carries a section like this one, and it buys more credibility than anything it hedges. Four entries.
Jevons. Efficiency does not historically reduce energy consumption; it finances growth — Jevons watched it happen to British coal in 1865, and the rebound literature has confirmed the pattern ever since. Our own window is a clean specimen: US consumption flat since 2000 while output grew ✦ means efficiency gains were consumed by growth almost exactly, a rebound running near a hundred percent. At the take-off, demanded computation and production may outrun efficiency outright — that is what the data-center inflection is. None of this troubles the argument, because the argument is about energy content per unit and its floor, not about the aggregate. But the error to avoid is implying that efficiency shrinks the machine. It does the opposite — efficiency grows the machine — and Part 3 will lean on that.
Offshoring. Part of the measured US intensity decline is structural rather than technical: energy-intensive production moved offshore, and the intensity of US consumption fell more slowly than the intensity of US production ◦. The −2.13%/yr is not pure engineering. The world's number is the honest denominator at the limit, and its slope is shallower — same direction, less flattering. The consumption-based series belongs in the chart dossier before this publishes (draft debt, below).
The floors arrive at different dates. "The thermodynamic floor" is a family of floors. In materials they are near: steel takes roughly 18–20 GJ per tonne in practice against a theoretical minimum around 6–7, with the best plants near 14 ◦ — call it one more doubling of efficiency and then physics. In computation the floor is far: Landauer's bound sits orders of magnitude below current practice ◦, which is why compute keeps riding its efficiency curve while the materials economy hits the wall first. Exactly where each floor sits is another of this arc's deliberately unpinned dials — like the take-off exponent and the i-term to come, it sets the timeline, not the conclusion. The conclusion needs only what thermodynamics guarantees: the floors exist, and they are above zero.
The labor line is per worker, not per hour. Hours per worker have declined secularly, so on an hours basis labor content fell somewhat faster than the −51% in Section 2's table ◦ — not enough to reorder the curves, but the per-hour series is the stricter denominator, and the chart dossier should eventually carry it.
One reduction remains, and it is the deep cut of the essay.
What is capital, physically? A machine is matter arranged usefully. The matter was extracted by capital and energy. The arranging was done by capital and energy, with a garnish of labor that Part 1's mechanism is shrinking toward zero. Recurse on the capital in that sentence and the regress terminates in the same place every time: at the limit, capital is embodied energy — energy spent earlier, stored in the form of useful structure. The term is not ours; industrial ecology prices buildings, machines, and materials in embodied joules as a matter of routine accounting ◦.
So the two-factor economy of Section 3 reduces once more. Capital plus energy is energy-spent-earlier plus energy-now. The economy at the limit is a machine that turns energy into output, built from components that are themselves prior energy expenditure — energy all the way down, current joules and amortized ones. This is the sentence Part 3 will take as its premise, so it is stated here at full strength, with its provenance shown.
Two everyday objects show the reduction in motion. A car is embodied energy you can see: tons of smelted steel, cast aluminum, formed glass — energy spent earlier and stored as structure. Its labor content has fallen for a century, but its material content cannot fall far, because a car is fundamentally a large mass of shaped metal; its embodied-energy floor sits high. A television has a floor too — every object does — but a far lower one, and it has moved most of the way to it in a way the car cannot. The 1974 set was mostly mass and labor: a leaded-glass vacuum tube and a steel chassis, hand-wired and hand-assembled. The 2026 panel is a different object built a different way — two thin sheets of glass, some plastic, an LED backlight, and a little driver silicon — a fraction of the old mass, and therefore a fraction of the embodied energy. And the display itself is patterned across its glass by the same family of lithographic, batch-integration processes that make chips: very-large-scale integration, spread over an area rather than a fingernail. That is what drove the labor out and the mass down at once. This is why, priced in hours of work, the television fell to an afternoon while the car did not: the television could be re-founded on a process that trivializes both labor and material; the car is stuck in the mass of the thing. Capital is yesterday's energy — and which capital gets cheap is decided by whether its embodied energy can be re-founded or is locked in matter. (That fork, and where it sends the automobile next, is its own argument.)
The reduction is less exotic than it sounds; two working disciplines already keep their books this way. Industrial ecology runs life-cycle energy accounting on exactly this logic. And energy economics evaluates energy sources by energy return on energy invested ◦ — not dollars returned on dollars — precisely because at the system level the money accounting obscures the physics that decides viability.
One number from the fifty-year record should be named now, because Part 3 will hang a great deal on it. The efficiency march of Section 2 has a clean measure: output per joule grew about 2.1%/yr on the window ✦. Strip out population growth and the residual — output per person-joule, the rate at which the economy learned to wring more from the same people and the same energy — ran 1.21%/yr ✦. Hold that number. When Part 3 decomposes real growth into a metered population term, a metered energy term, and a technology residual, the residual is this march. And this essay's central fact — that the march approaches a thermodynamic floor while labor exits the bill — is what gives that residual a known long-run destination: zero. The monetary architecture of the next essay and the physical argument of this one are a single claim viewed from two sides.
Suppose the argument lands: production at the limit is energy-mediated, and the joule is the honest unit of analysis. The institutional stack of Section 3 was built on the old list, one hook per factor — and each hook wants re-anchoring. Stated here as directions only; the later parts do the engineering.
Taxation wants the base that cannot dodge. Good tax theory asks for something inelastic, unavoidable, and cheaply metered. Labor income at the limit is the opposite — a vanishing base. Corporate income is a definition that reorganizes away under exactly the pressure this arc describes — and so, for the same reason, would any attempt to tax the robots or the AI directly. Energy is metered at a countable set of points, and every form of automated production — hosted, subscribed, self-run, or not yet invented — draws it. Part 4 builds the stack.
Trade wants energy content. Border adjustment math needs a physical quantity that survives re-invoicing and transshipment, and the world has already started keeping the relevant books — the EU's carbon border mechanism prices embodied energy content at the frontier today ◦. The accounting exists; the arc extends it.
Redistribution wants a per-capita share of the base. If the productive base is capital plus energy, and the labor→income→consumption chain no longer reaches everyone, then the distributive question becomes: what is a person's share of the energy-denominated machine? Parts 3 and 4 give that question two instruments — one monetary, one fiscal.
And money — the measuring stick itself. Not the claim that money always was energy in disguise: money is a general claim on everything, and that generality is real and worth keeping. But at the limit, what money buys is energy-arranged matter — so money becomes, in effect, a proxy for energy, and the two converge to nearly the same thing. That is what makes the joule the honest unit of analysis for production. Whether the unit of account should follow it is a separate question, with a century and a half of hard-won monetary history bearing on it.
Strip the essay to its spine. The production function was never labor plus capital — it was labor plus capital plus energy, with energy omitted because it was cheap and labor dominated the bill, an omission that was a statement about prices, never about physics. For fifty years the same engineering that automates out labor has automated out energy faster — sixty-five percent against fifty-one ✦ — and the two curves differ not in slope but in destination: labor's ends at zero, energy's at a floor that thermodynamics sets and no amount of ingenuity crosses. Whatever the economy costs at the limit, it costs in energy — and the capital that does the producing is itself yesterday's energy, spent and stored as structure.
Part 1 diagnosed the break: the freeing of labor is about to outrun every mechanism built to absorb it. This essay named the regime on the far side: an economy that is, physically and at last visibly, a machine that turns energy into output.
If energy is becoming the right unit of analysis — the unit in which production and trade are most honestly measured — then a question follows, and it deserves an essay's worth of skepticism rather than a paragraph's worth of enthusiasm. Should the unit of account follow the unit of analysis? Should the dollar itself be pegged to the engine of the economy?
Part 3 proposes exactly that — and then spends most of its length trying to break the proposal against fifty years of data.