American unemployment is rising. Corporate profit margins are at a record. The math that makes both true at once.
For most of the last century, the stock market and the job market moved together. Since 2023 they don’t. This piece is the math that explains why, the dashboard that lets you test it, and the limits of what it can tell you.
| metric at end of 2028 | if AI plateaus today | if AI grows linearly | if AI keeps doubling |
|---|---|---|---|
| AI task horizon what a job takes a human vs what AI can finish | 4 hrs | ~1 day | ~3 months |
| GDP, cumulative change model output at t=36mo from Cobb-Douglas | +13.0% | +22.8% | +30.9% |
| Labor share of income fraction of output going to workers | 60% → 58% | 60% → 43% | 60% → 30% |
| Median consumption (welfare) consumption-equivalent change for a median worker | +9.2% | −5.8% | −21.0% |
| …with non-substitutable labor floor (25% of jobs) GDP gain capped by L_non factor (Economy/JobSwapping.lean) | +9.6% | +16.6% | +22.4% |
| …with average recession risk GDP minus expected Poisson drag (Economy/RecessionShock.lean) | +11.7% | +21.4% | +29.5% |
| …with capex bubble pop at t=18 months gK collapses to maintenance (Economy/CapexBubble.lean) | +6.1% | +15.3% | +22.9% |
Economists have a recipe for how a country makes stuff. It fits on one line, it’s almost a hundred years old, and once you see it the paradox collapses into arithmetic.
Y = A · K0.4 · L0.6
Y is output. A is productivity (how good we are at our jobs). K is capital (the machines and server farms). L is labor (workers). The 0.6 next to L means workers contribute about 60 percent of what the country produces. The 0.4 says capital and productivity do the other 40.
The sneaky part: the exponents are less than 1, so the formula is concave in each input. Halve the workforce and output only drops by about a third. Cut it to a tenth and output is still a quarter of what it was. Try the knobs below.
Pull labor down slowly. Watch what output does. This is the same formula above, live. Cut workers in half and output barely budges. Cut them to a tenth and output is still a quarter of where it started. The line is curved, not straight.
That curve is the whole story in miniature. Half the workers, two thirds the output. A tenth of the workers, a quarter of the output. The economy holds itself together, mostly, as long as some workers are still in it. Then, one day, the last of them walks off, and the whole thing goes at once. Hold that shape in your head. You’re going to need it in a minute.
GDP up about 2.8 percent with flat hiring. Finance calls this Ghost GDP: growth on paper without anyone on the ground feeling richer. No magic, just the formula.
Five companies (Microsoft, Google, Amazon, Meta, Oracle) are pouring over $700 billion into servers, GPUs, and datacenters this year. That’s 2.5 percent of US GDP, and it’s a larger share of capital formation than any single industry has claimed in the post-war data.
METR measures one honest number: how long a task has to be before the best AI chokes. In 2019 that was seven seconds. This year it’s about twelve hours, with about 1.5x uncertainty either direction from modeling choices. The spread between the three curves above is the honest width of what we don’t know about the next three years.
Six sliders. Three charts. Three preset buttons. Drag anything. The charts redraw live. Teal dots are proved values; lines between are the formula interpolating. Presets snap to a canonical calibration. The growth-shape toggle picks whether AI plateaus, grows linearly, or keeps doubling.
Every dot on these charts is computed from a formula in an open repository. Hover any number in the post above to see the file and line. press ? for keyboard shortcuts
Here’s the uncomfortable part. In the same AI-exposed jobs, the younger workers are losing their footing and the older ones are gaining it. That isn’t a story about AI replacing labor in general. It’s a story about AI replacing the bottom rung of the ladder. The internships. The first jobs. The “we’ll train you up” roles that used to turn twenty-two-year-olds into thirty-year-olds with a career.
Run the machine forward three and a half years and here’s what you get. By the end of 2029:
pipeline_metr_horizon_36mo proves intelligenceLevel 36 (log 2 / metrFastSlope) = 512 exactly.This isn’t a prediction of an unemployment number. It’s a prediction of a shape. The first-job market doesn’t recover by itself, on this trajectory, unless something in the formula changes. The next section is the list of things that could.
The model is simple on purpose. Simple things are easier to audit, and easier to break. The five cracks below aren’t hand-waves: three of them are kernel-verified theorems with concrete numbers, two are honest unknowns. Any one would turn most of this page into wallpaper. Click to open each one.
Nothing doubles forever. If the pace slips from four months back to seven, the whole model slows down with it, and we get a few more years to figure things out. You can watch this happen: drag the doubling-time slider to the right and watch the teal line in the dashboard bend downward. That version of the future is slower and kinder. Or it stops doubling at all, and grows linearly. Or it plateaus today. Try the growth-shape toggle in the dashboard above to see what each of those looks like.
None of that is in the model. If Congress passes a basic income, or taxes AI-driven work, or sets a floor on how much of the economy has to go to workers, the lines move. A labor-share floor in particular would directly break the trajectory chart above. That’s the whole point of one: to stop that line from falling.
The five companies spending all that money aren’t quite earning enough to cover it. They’re borrowing roughly $400B against $1.7T in market cap. The kernel says: if debt service ever exceeds cash-flow growth, the capital growth rate drops from about 6 percent a year to about 1.5 percent — maintenance only. Plug that into the model and the 36-month GDP gain falls from +30.9% to +22.9%, an eight-point haircut. The theorem is CapexBubble.bubble_pop_ghost_gdp_loss: the loss equals (1−α)·(g_hyper − g_maint), no multiplier or feedback assumed.
The formula quietly assumes a worker and a machine are swappable. They aren’t. Childcare is 1.5% of US payroll, nursing is 2.0%, skilled trades 4.6%, personal care 2.8% — about 25% of jobs sit in a bucket no GPU can substitute for. The kernel models this as a Cobb-Douglas nest over (capital + AI) and the non-substitutable bucket: output bottoms out at L_non^(1−α), which AI literally cannot grow. With α = 0.6 and a 25% floor, the 36-month GDP gain falls from +30.9% to +22.4%. The theorem is JobSwapping.jobSwap_cobbDouglas_zero_Lnon_limit: as L_non goes to zero, output goes to zero, regardless of how much capital or AI you stack.
The smooth-growth assumption is a useful fiction most of the time and a terrible one during a downturn. NBER says the post-1950 US has had a recession about once every five and a half years, lasting roughly ten months on average, with a peak-to-trough GDP hit around 2.5%. The kernel encodes this as a Poisson hazard of 0.015 per month against a per-month shock of 0.0025. Expected drag over 36 months: 1.35% off cumulative GDP, dropping the headline +30.9% to +29.5%. Sahm’s rule (3-month-average unemployment up 0.5pp from its trailing 12-month minimum) is the early-warning bell. As of March 2026 the FRED real-time reading is 0.20, up from near zero a year ago but still below the 0.50 trigger. It hasn’t rung. It’s rising. Worth watching. The theorem is RecessionShock.recession_expected_loss.
The stock market and the job market did something they’re not supposed to do. A ninety-year-old formula explains it. The formula has three ingredients: productivity, capital, and labor. Two of them are growing fast. The one called labor isn’t. The math says output keeps climbing. It doesn’t say anything about who gets paid.
Every number on this page traces to a theorem in an open repository. 202 theorems, zero sorries, zero unchecked axioms. The model isn’t a forecast. It’s a lens. It shows you why the thing you’re seeing isn’t a contradiction, what the three most honest guesses about the next three years look like, and where the cracks are when those guesses go wrong.
You can argue with the calibration. You can change the sliders. You can toggle the growth shape. What you can’t do is look at 4.3% unemployment, 13.3% record profit margins, and $700 billion in AI capex from five firms at the same time and call it a paradox. It isn’t one. It’s the formula, doing exactly what the formula does.
The math fits the world you’re living in. Believe your eyes.