Reader questions, answered with the arithmetic shown

No. The Bank for International Settlements (the BIS, a bank owned by the world's central banks) uses the IMF's grouping. It splits the world into advanced economies and emerging market economies, and China is in the second group, as its largest member. The report's own text discusses China's growth under the emerging-market heading, and every one of its cross-country charts lists China on that side. The advanced bloc is the United States, the euro area, Japan, the United Kingdom, Canada, Korea, Australia and the other rich economies, 43 in all. Together they produced $69.6T of GDP in 2025, the IMF’s figure. The Growth Saviour lists every one, with its output since 2016 and its share of the total.

That matters for every number on the main page built from this baseline. The $42T pool of wages (all the pay earned by the bloc's workers), the white-collar wage pool on the §4 slider, and the growth dial in §6 all describe the advanced bloc only. Chinese wages are not in the pool that AI revenue would have to draw from, and Chinese growth does not move the dial.

A little under half of the advanced bloc's GDP is American: $30.9T of $69.6T in 2025 at market exchange rates, or 44%. Weighted by purchasing power (what money buys locally), as the BIS does when it adds countries up, the US share is lower, about 37% (both IMF figures; the economies page has every country). So the bloc's growth rate leans on the US without being set by it. Any target for the bloc as a whole quietly sets a target for US growth. The rule of thumb: each extra percentage point of US growth moves the bloc's growth rate by between a third and a half of a point, depending on which weights you use.

A worked example: if the rest of the bloc grows at 2.25% and the whole bloc is to reach 2.5%, the US must grow at roughly 2.9%. That is about two-thirds of a point faster than the others, and about 43% of all the bloc's growth. Drag the sliders to change the assumptions:

This has an uncomfortable consequence for the main page's §6 dial, whose horizontal axis is this same bloc-wide growth rate. At the default settings, the 3.4% at which growth pays for the whole bet needs US growth of roughly 5.4% a year until 2030. The 2.9% at which total pay grows as fast as it used to needs the US near 4.0%. Apart from the rebound after Covid, the US last grew faster than the first rate in 1984, and last grew near the second in the boom of the late 1990s. The dial treats the bloc as one economy. Split it into its parts, and its better zones assume America carries everyone else.

Where the numbers stand (as of 22 October 2026). The IMF's October 2026 outlook puts advanced-economy growth at 2.1% for 2026: the US at 2.3%, the euro area at 1.1%. In the latest quarter, the US grew +2.2% at an annual rate in Q2 2026 (after +2.5% in Q1), and the euro area grew +0.6% on the previous quarter (+1.2% on a year earlier). Set that against the dial: today's bloc-wide rate is where the dial starts, the point at which growth pays for none of the bet. Set the sliders to today's mix, with the rest of the bloc near 2.0%, and paying for the bet out of growth needs the US to sustain roughly 6% a year until 2030, against the 2.2% it last reported. The main page's §6 carries a decade-long reality-check chart of exactly this split.

Yes, in principle, and it is the hopeful reading. The front page’s §3 shows that the revenue the spending needs is larger than the world’s business-software budgets, so most of the money has to come from somewhere else. There are two candidates. One is wages: AI does work that people were paid for. The other is growth: AI helps people produce more, and the revenue is paid out of output that would not otherwise exist. In that case nobody’s wage has to go, and workers’ share of income need not fall. The BIS’s report includes this case and calls it a productivity boost.

The arithmetic is the same either way. If AI sellers keep a quarter of the value they create, their customers must gain $5.2T a year by 2030 for the builders to receive their $1.3T floor. Found entirely from wages, that is 65 million jobs’ worth of pay. Found entirely from growth, it takes the advanced economies growing by an average of about 3.4% a year to the end of 2030, against 2.1% today; after that, growth could return to its old pace. Any mix works: each extra tenth of a point of growth a year spares about 4.7 million jobs’ worth of wages.

How likely is it? The studies the BIS surveys put AI’s lift to economy-wide productivity growth at less than 1%, where the floor needs 1.3 points, and the BIS notes that a lasting rise in trend growth has not happened since the Industrial Revolution. So it is possible, and on the evidence so far it is not the likely case. The Growth Saviour lets you try every mix.

The date matters as much as the rate. The spending’s bill falls due by the end of 2030, because the chips bought now are worn out by then. If the same growth arrived over ten years it would need only 2.7% a year, which is within the range of those studies, but by 2030 it would supply under half of what the spending needs. Growth that comes late can spare workers and still leave the first investors unpaid. The Growth Saviour sets out the cases.

This is also where the site’s reading differs from the starkest version of the argument. The historian Adam Tooze describes the bet as two-sided: either the investment is vindicated because AI replaces a great deal of work, or it is not and investors take the losses. Growth is the third outcome. The size of the growth it would take is the reason it is easy to leave out.

The capture rate is the share of a customer’s gain that the AI seller receives as revenue. A firm that replaces an $80,000 job will not pay $80,000 for the AI that does it, or there would be no reason to switch. At a capture rate of 25% it pays $20,000 and keeps $60,000. The rate matters because it multiplies everything after it: at 25%, each dollar of AI revenue needs four dollars of saved wages or of new output.

The 25% is this site’s assumption. Two kinds of evidence suggest it is generous to the AI sellers. The first is prices where AI is sold by the job done, so that the price can be set against what a person costs. Salesforce launched its AI service agent in September 2024 at $2 a conversation, and Intercom charges $0.99 for each customer query its agent resolves. A customer contact handled by a person cost $8.01 on average in a 2019 Gartner survey. That puts the AI price at about 25% and 12% of the human cost. The comparison is rough: the cost figure is from 2019, a contact is not quite the same thing as a resolved query, and Salesforce has since added other ways to pay.

The second is history. The economist William Nordhaus estimated that American innovators kept about 7% of the value of their innovations in the first year, and about 2% in the long run, between 1948 and 2001. Competition passes the rest on to customers as lower prices. The St. Louis Fed economist on the reading page describes AI’s productivity gains the same way: passed on to buyers and workers, not kept by the seller.

A lower rate makes the bet harder to pay for, not easier. At 10%, the floor needs $13T a year of saved wages or new output, not $5.2T. So the figures on this site that rest on 25% are more likely to understate what the bet needs than to overstate it. The slider in §4 runs from 10% to 60%.

The dial in §6 takes one figure from §4: the $5.2T a year that AI must be worth to its customers by 2030 for the builders to earn their floor. It then asks where that money comes from. Growth above today’s pace pays for part of it. The rest comes out of wages. At today’s 2.1% growth, all of it comes out of wages: workers’ share of income falls from 60% to 53% and total pay shrinks. From about 2.2% a year, total pay stops falling. From about 2.9% it grows as fast as it used to, though workers’ share still falls. At about 3.4%, growth pays for all of it.

It stops in 2030 because that is when the spending falls due: the chips bought now are worn out by then. What matters is the level of output the economy has reached by that date, not how long the faster growth lasts. For the long run the front page shows the BIS’s own forty-year scenario beside the dial, and that rests on a much stronger assumption: that AI keeps taking over new tasks, year after year.

Every input is a figure the rest of the site already uses: the floor from §2, the capture rate from §4, the IMF’s figures for output and for today’s growth, and a 60% share of income for workers. The Growth Saviour runs the same sums with the capture rate on a slider, and shows what happens if the growth comes late.

The reference model is the Bank for International Settlements' Annual Economic Report 2026. Chapter I ("Progress and peril") documents the trillion-dollar building programme of the five biggest AI builders the BIS names (Alphabet, Amazon, Meta, Microsoft and Oracle) and how it is paid for. Box C ("Transformative AI, long-term growth and r-star") models what the economy looks like if the bet pays off and AI does the work that people used to be paid for. The framing, the bet as a wager on replacing white-collar wages, follows Adam Tooze's Chartbook 456, which read the BIS report the way this site does.

The site began with a simple frustration. The arithmetic that links the headlines about capital spending (money spent on things that last for years: chips, buildings, power) to what is at stake for jobs and wages rarely appears on one screen. So this site walks through it from end to end: from capital spending to the revenue it must earn every year to pay for itself, from that revenue to the wage pool it would have to come out of, from the wage pool to jobs, and from jobs to growth and to workers' share of income. Every assumption a reader might dispute is on a slider, and every number that carries weight is traced in a published ledger of derivations, which a script checks each time the site is published. Reported results come from public filings, captured by the pipeline behind Geo-V.eu, a sister project. Built and maintained by RAAK.work. The page is updated after each set of results on the watch list, and every revision is dated in the revision history on the main page.

The revenue floor is the revenue the five builders must take in every year for their AI spending to pay for itself. It adds three costs: the chips wearing out, because they last only a few years; the running costs, mostly electricity; and the profit investors require for putting up the money. At the front page’s starting values that comes to $1.30T a year. It is this site’s arithmetic, not the BIS’s, though it asks the BIS’s question: can the revenue justify the spending? The glossary shows the sum.

The floor is what the builders must receive, and their customers must pay more. Most computing reaches the final customer through firms in between, such as Anthropic, which rent it from the builders, add their own costs and profit, and sell AI products. Working that through, with a method taken from a Goldman Sachs note, gives what this site calls the buyers’ bill: $1.82T a year at its starting values. It has its own page, which also reruns the jobs arithmetic on it.

The front page keeps to the floor for two reasons. It is the measure the BIS model tests, and it can be checked each quarter against the builders’ own published results, which is what the tracking page does. The bill rests on assumptions nobody can yet check. So wherever the front page sets the floor against what customers spend, in §3 and §4, it says the comparison is kind to the bet.

Some are. Most, deliberately, are not, and the ledger says which is which. Taken directly from the BIS: the five companies, the trillion dollars spent in 2025–26, the window and range of capital spending the companies have committed to, the dating of the boom from 2023, the Box C scenarios (including the share of national income that goes to workers as pay falling toward 20% by 2060), and the twist in which demand runs out because workers who lose wages stop buying. Built by this page: the §2 revenue floor (the revenue the AI spending must earn every year to pay for itself) and the buyers’ bill built on it (what final customers must pay for the builders to reach the floor, once the firms that sell AI products have added their costs and profit; it has its own page, and the front page keeps to the floor), the §4 capture-rate arithmetic (the AI company's share of the wage saving it produces for a customer), the §6 dial showing how much of the bet growth pays for and how much comes out of wages, the same trade-off in more detail on The Growth Saviour, the charts on the tracking page, and §5's diagram of the loop. The BIS tests something different from the floor: net economic surplus, meaning revenue minus capital spending and interest on debt, inside a calibrated model that includes how the spending is financed. And the BIS defines the loop (firms in the boom investing in, buying from and selling to each other, so one firm's spending is another's revenue) but draws no picture of it. The arrows in §5's diagram are put together from disclosed and press-reported figures, each labelled as one or the other.

Where a construction departs from the report, the departure is named on the page and justified in the ledger. That includes the floor's biggest limitation: it is static, while the BIS models a financed system in which a shortfall makes itself worse. One boundary is worth stating plainly: the model is the BIS's five and stays that way. SpaceX listed on the stock market in June and, in its first quarter as a listed company, spent $2.35 of capital for every dollar of revenue. It appears beside the five as evidence and never inside the required revenue ramp, the gap chart’s five-way split or the capital spending total.

The results figures come from company filings and press releases: 8-K filings to the US securities regulator, quarterly results releases, and the companies' own guidances. An automated pipeline captures them within hours of each set of results. Nothing comes from memory or from estimates. When a figure is not published, the page says so rather than filling the blank. Microsoft no longer states its AI revenue at an annual rate; Meta reports no AI revenue line at all. Every constant that carries weight, every model input, and every known bias is documented in the derivations ledger. The ledger classifies each number as taken from the BIS, built by the page (arithmetic shown), or a named departure from the BIS (with the reason given). A script compares the ledger's register of constants with the page each time the site is published. A number that drifts from its documentation cannot go live.

Every figure needs two independent sources that agree before it reaches the site. The pipeline’s capture is only ever one of them. The other is the company’s own filing or results release, and where the two disagree, the filing wins. Figures reported in the press rather than filed are labelled as such every time they appear. One exception is named: Anthropic has so far filed only a confidential draft of its prospectus, and its figures reached this site through a single news report. Each of them carries the label “From Anthropic’s draft prospectus, as reported by Reuters on 28 Sept 2026. Not an official filing.” They will be replaced when the public filing appears. A second exception was added on 8 October 2026: a figure reported by the Financial Times, Bloomberg or Reuters stands on that one report. It is still labelled press-reported, and the ledger still names the report.

Because no company reports "AI revenue" in dollars that can be audited, and inventing a split would break the site's first rule. So the chart shows two honest extremes and lets you switch between them. The upper-limit reading counts all revenue growth since 2023 (the low point from which the BIS dates the boom) as AI revenue. That overstates it, because it includes growth in retail, advertising and ordinary cloud business. The trend-adjusted reading subtracts each company's own growth pace from before the boom and keeps only what is left over. That understates it, because the years the trend is taken from were themselves lifted by rebounds and acquisitions. The true figure, which no one can observe, sits between the two readings, and the verdict sentence under the chart changes to match.

The model's five companies are the five the BIS names as the spenders: Alphabet, Amazon, Meta, Microsoft and Oracle. Apple is left out on purpose. Its capital spending of roughly $11B a year is a rounding error beside the roughly $840B the five have said they will spend in 2026, and that makes Apple the bet's control group: it sells into the same economy, but has made no wager. Nvidia is the supplier the five's capital spending flows to, so its results are a thermometer for the spending side, not a bet of its own. SpaceX, which listed in June, is a sixth builder that the BIS did not count, and it is tracked as the extreme case of spending ahead of revenue. The AI labs (Anthropic, OpenAI) appear as evidence about future revenue. Every row outside the model says so in the row itself, and none of them feeds the charts. The glossary calls all of these beside the model.

The page's sharpest test is a gap opening between two sets of records: company revenue and payroll data. If AI revenue is truly substitution revenue, money that used to be paid as wages, it must eventually show up in the payroll data. Run the §4 arithmetic backwards: if today's AI revenue were drawn from wages, tens of millions of jobs' worth of pay would already be visibly missing from the employment statistics. They are not, which proves that today's revenue still comes from IT budgets and the loop (firms in the boom buying from and investing in each other). The tracking page’s jobs chart draws US payrolls month by month from January 2023, the year the revenue is measured from, so the two can be read side by side. Around 2027–28 the required revenue ramp passes what software budgets can plausibly supply. From that point, revenue staying on schedule and payrolls staying quiet cannot both go on. One of them gives. Meanwhile the depreciation wall (most of the hardware must be replaced within roughly five years) forces the funding question by about 2028 whatever else happens. Failure looks like the revenue line breaking first; "success" looks like the jobs column breaking instead. The watch list dates every reading.

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No. Every model here is deliberately simple and built to get the order of magnitude right, so that its assumptions can be inspected. It is the opposite of a forecast. The site exists so that a reader can disagree with a specific number, drag it, and see what follows. Nothing on these pages is a recommendation to buy or sell anything.