Why the line can keep going up

In July 1946, prices in Hungary doubled about every fifteen hours. The central bank issued a banknote for one hundred quintillion pengő — a one followed by twenty zeros — and printed one for a sextillion that never left the vault. On the first of August the forint arrived, at four hundred octillion pengő to the forint. Twenty-nine zeros, deleted in a morning.

It is the most extreme entry in the record books, and it is useful precisely because it is absurd. Nothing in Hungary became 10²⁹ times more valuable that summer. The ruler had broken, and someone replaced the ruler. Hold on to that distinction, because this is an essay about a question that sounds naive and is not: can an economy keep growing forever?

The previous essay argued that a stock market at a record high is a rising line doing what rising lines do. This one is about why the line rises in the first place, and whether there is any good reason to expect it to stop.

Two lines, not one

When someone says the economy is growing, they are describing two different lines that happen to point the same way. The first is nominal: output counted in today's money. The second is real: the same output with inflation taken out. Most of the confusion about "infinite growth" comes from mixing them up.

The nominal line goes up by design. Since 2012 the Federal Reserve has stated that two percent inflation is the goal. Norway set a target of 2.5 percent in 2001 and lowered it to 2 percent in 2018. A two percent target is a promise that prices will double roughly every 35 years and rise about sevenfold in a century. That is not the system failing; it is the system working as specified. So nominal GDP is supposed to keep setting records even if nothing real changes — and it does. Since 1947, US nominal GDP has hit a new all-time high in about nine quarters out of ten. In the last 75 years only two full years, 2009 and 2020, failed to set one.

Over a century this compounds into numbers that look alarming until you remember what they are. Since 1913 the dollar has lost about 97 percent of its purchasing power. What cost one krone in Norway in 1913 costs roughly seventy kroner today. Nobody is seventy times richer because of that. The ruler shrank.

Big numbers are a property of the ruler, not of the wealth.

The real line is the interesting one, and we will get to it. But the nominal line deserves a section of its own, because when it moves fast enough, something physical has to give.

When the numbers outgrow the ruler

Economists call it hyperinflation when prices rise more than fifty percent in a month. Steve Hanke and Nicholas Krus (2012, "World Hyperinflations") counted 56 episodes that met that bar; by 2020 the tally had reached 62. What they have in common is that the numbers stop fitting their containers. Prices outgrow the banknotes, the ledgers, the cash registers and eventually the software, and someone has to raise the ceiling. The usual way is to lop off zeros.

Germany did it first at scale. In 1914 a dollar cost 4.2 marks. By November 1923 it cost 4.2 trillion, the largest note was for a hundred trillion marks, and photographs in the Bundesarchiv show a wall being papered with money. (The wheelbarrow of cash is legend; the documented evidence shows suitcases and baskets.) The fix was the Rentenmark, at one trillion old marks to one — a rate chosen because it restored the pre-war 4.2 per dollar exactly. The only change was deleting twelve zeros.

Zimbabwe did it three times in three years: three zeros in 2006, ten in 2008 and twelve in 2009, twenty-five in all. The 2008 cut came with an unusually honest explanation: the Associated Press reported that the computers, calculators and cash machines at the country's banks could no longer handle basic transactions in billions and trillions. Six months later the central bank issued a hundred-trillion-dollar note, and two weeks after that it removed twelve more zeros. The note now sells to tourists for a few dollars, more than it was ever worth as money.

Venezuela has removed fourteen zeros since 2008, in steps of three, five and six, and the newest bolívar has already lost most of its value again. On New Year's Day 2005 Turkey removed six, and the 20-million-lira note became a 20-lira note. Between 1942 and 1994 Brazil went through eight currencies; one real is worth 2.75 quadrillion of the 1942 cruzeiros. Even Iceland cut two zeros, in 1981.

Software engineers will recognise the pattern, because we have our own version. In December 2014 a K-pop video approached 2,147,483,647 views, the largest number a signed 32-bit integer can hold, and YouTube remarked that it had never expected a view count that big. The counter moved to 64 bits, which raised the ceiling to about 9.2 quintillion. (In fairness, YouTube had quietly widened it months earlier; the glitching digits were a joke.) The same ceiling sits under every 32-bit Unix clock: at 03:14:07 UTC on 19 January 2038 the seconds-since-1970 counter overflows and wraps to December 1901. The fix is Hungary's, run in reverse. Instead of making the number smaller, you make the box bigger.

The United States has written one of these ceilings into law. The first general limit on federal debt, in 1939, was 45 billion dollars. Since July 2025 it has been 41.1 trillion. The Treasury counts 78 occasions between 1960 and the early 2020s on which Congress raised, extended or redefined the limit, and there have been more since. A fixed number of dollars in an economy whose dollar size is designed to grow every year will keep hitting its head. Each time it is reported as a crisis. It is better understood as a ruler being lengthened to fit the thing it measures.

Norway's version is quieter. The krone arrived in 1875, prices barely moved until 1913, and the climb that began with the First World War has never forced a redenomination. But the same pressure showed up at the bottom of the scale. The 1- and 2-øre coins lost legal status in 1975, the 5 and 25 øre in 1985, the 10 øre in 1993 and the 50 øre in 2012. A low-inflation economy does not raise the ceiling. It lets the floor fall away.

None of this is growth. Deleting zeros, widening a counter, raising a legal limit: each changes the unit and leaves the economy exactly where it was. Which brings us to the question that matters.

Where real growth comes from

Take the inflation out and the line still rises. The Maddison Project (Bolt and van Zanden, 2024) is the standard long-run reconstruction. For most of recorded history the average person lived on the equivalent of about a thousand dollars a year, in 2011 prices. In 1820 the world average was about 1,100. In 2022 it was about 16,700, nearly fifteen times higher, and almost all of that came in the last two centuries. Something changed.

The first good account of what did not change it came from Robert Solow (1956, "A Contribution to the Theory of Economic Growth"). Piling up machines cannot sustain growth by itself, because each extra machine adds less than the last. Saving more raises the level of income, not its long-run growth rate. A year later Solow did the accounting for the United States: output per hour roughly doubled between 1909 and 1949, and about seven-eighths of that came from the leftover he called technical change, not from more capital per worker. The engine was in the residual.

Paul Romer (1990, "Endogenous Technological Change") explained what the residual is made of. Ideas are non-rival. If I use a machine, you cannot use it at the same time. If I use a recipe, you can use it too, and so can everyone else, at no extra cost. That is why an economy built on ideas escapes the diminishing returns that bind an economy built on stuff. Romer's picture is a kitchen: valuable things are made by combining cheap ingredients according to a recipe, and growth comes from better recipes rather than more cooking. His back-of-the-envelope sum: with about a hundred elements in the periodic table there are roughly 94 million ways to choose four, and with a few thousand sets of proportions for each, about 330 billion recipes — before you allow more than four ingredients. In his words, "possibilities do not merely add up; they multiply." It won him the 2018 Nobel, shared with William Nordhaus. Michael Kremer (1993) added the corollary: if ideas are shared, more people means more ideas, so population growth should speed up as population grows — and across a million years of data, it did.

Nordhaus supplied the clearest single example of what a better recipe does to a price. In his history of lighting (1997) he estimated that in Babylon around 1750 BC, some 41 hours of labour bought a thousand lumen-hours of light. By 1992, with a compact fluorescent bulb, it took about half a second. An hour's work buys roughly 350,000 times as much light, and because price indexes track fuel and lamps rather than light, they miss most of that gain. Real growth is, if anything, understated.

It has also been fairly predictable. In 1930, at the start of the Depression, Keynes guessed that living standards in rich countries would be four to eight times higher a century later. By 2022, US GDP per person was about 5.5 times its 1930 level and the UK's about 4.4 times. He was right about the line and wrong about the fifteen-hour working week that was supposed to come with it: people took the gains as consumption, not leisure.

But the planet is finite

This objection deserves a fair hearing, so here is its strongest form.

The Limits to Growth (Meadows, Meadows, Randers and Behrens, 1972) is usually misremembered as a prediction of collapse by the year 2000. Its actual claim was conditional: if the growth trends of 1970 continued unchanged, planetary limits would be reached within a century, most likely followed by a sudden decline in population and industry. It also said the trends could be changed. Two later checks took it seriously. Graham Turner (2008) found the business-as-usual scenario fitted thirty years of data best. Gaya Herrington (2021) found the two best fits were a pollution-driven collapse scenario and a "comprehensive technology" scenario in which growth halts and declines without collapse. The scenarios only part ways after about 2020, so the data cannot yet pick between them.

Robert Gordon (2016, The Rise and Fall of American Growth) makes a different pessimistic case: the century from 1870 to 1970 — electricity, the engine, plumbing, chemistry — was a one-off, and the innovations since have been narrower. His projection for US output per person from 2015 to 2040 is about 0.8 percent a year. Note what that is: a rising line, just a flatter one. Even the leading pessimist is not forecasting a plateau.

Bloom, Jones, Van Reenen and Webb (2020, "Are Ideas Getting Harder to Find?") put numbers on the worry that the easy recipes are used up. Keeping Moore's law going now takes more than eighteen times as many researchers as in the early 1970s, and the United States has had to double its research effort roughly every thirteen years just to keep growth per person steady. Growth has held because effort has grown. Whether effort can keep growing is a real and open question.

Then there is the famous bet. In 1980 Julian Simon let Paul Ehrlich pick five metals and a thousand dollars' worth of them on paper; if their inflation-adjusted price was higher in 1990 Simon would pay the difference, and if lower, Ehrlich would. All five were cheaper, and Ehrlich mailed a cheque for 576.07 dollars. The honest footnote (Kiel, Matheson and Golembiewski, 2010) is that over rolling ten-year windows across the twentieth century, Ehrlich would have won about six times in ten; the 1980s were a lucky decade for Simon. The bet proves less than either side claimed. The quieter point is that a century of booming demand did not make the metals trend upward in real terms.

So what is the answer? It is that GDP measures value, not tonnes. The model behind The Limits to Growth tracks physical stocks with fixed or slowly improving technology, which is exactly the thing Solow and Romer say the growth is not made of. And the evidence that the two can come apart is now fairly direct. Andrew McAfee (2019, More from Less) went through the 72 materials the US Geological Survey tracks and found that American consumption of all but six had peaked and was falling, in absolute terms, while the economy kept growing. That is apparent consumption, so some material embedded in imports is missing, and global material use is still rising; the rich-country pattern is a proof of possibility, not a victory lap. Carbon tells the same story. Between 2005 and 2019, 32 countries grew their economies while cutting CO₂ emissions, even counting the emissions in what they import (Hausfather, 2021). The UK's fell by over a third while its real GDP rose by a fifth. Global emissions are not yet falling, but the link between growth and carbon is breakable, and in a few dozen countries it has already broken.

The planet is finite. The list of recipes is not.

Ecological limits are real. They constrain how we grow — what we burn, what we dig up, what we put in the air. They do not show that the line must flatten, because the line is not counting the things they constrain.

What this means for the line on a chart

An index is a claim on earnings, and earnings are a slice of the economy. If the economy grows, nominally by design and really by invention, the earnings grow, and so does the thing that is a claim on them.

Over the long run that is what the data show. Dimson, Marsh and Staunton, whose yearbook covers 35 markets from 1900, put world equities at about 5.2 percent a year after inflation through 2024, against 1.7 percent for bonds. For the United States the figure is around 6.5 percent; Jeremy Siegel (Stocks for the Long Run, 2022) gets about 6.7 percent real going back to 1802. Most of that is dividends plus earnings that grow with the economy — a little more slowly than GDP, because new companies capture a share of the growth that existing shareholders never see. Bernstein and Arnott (2003, "Earnings Growth: The Two Percent Dilution") put that gap at about two points a year.

That drift, nominal by construction and real by ideas, is the thing underneath the all-time highs in the previous essay. The records are not the market being clever. They are the line being a line.

The honest caveats

Growth is a tendency, not a promise. The S&P went from September 1929 to September 1954 without a new nominal high, and Japan's stock market spent most of three decades below a peak set at the end of the 1980s. Twenty-five years is longer than most people's patience and some people's retirement.
Real growth may well slow. Gordon's 0.8 percent and Bloom's doubling-every-thirteen-years are serious arguments, not strawmen. "The line keeps rising" says nothing about how steeply.
Ecological limits are real constraints on how we grow, and the decoupling so far is slow. The argument is that growth does not need more tonnes, not that the tonnes have stopped mattering.
Nominal growth is not wealth. Seventy kroner for a 1913 krone is a fact about the ruler. If your savings sit in cash, the ruler shrinking is the whole story.

So

Two lines. The nominal one rises because central banks have decided it should, and when it rises too fast the zeros get deleted, the counters get widened and the ceilings get raised, none of which makes anyone richer or poorer. The real one rises because people keep finding better recipes, and a recipe, unlike a tonne of copper, can be used by everyone at once.

Whether the planet can support infinite growth is the wrong question, because growth is not measured in planet. The right question is whether we keep finding recipes faster than the old ones run out. For two centuries the answer has been yes. That is not a guarantee. It is a very long streak with a mechanism behind it.

Sources

Solow, R. M. (1956). "A Contribution to the Theory of Economic Growth." Quarterly Journal of Economics. ideas.repec.org
Solow, R. M. (1957). "Technical Change and the Aggregate Production Function." Review of Economics and Statistics.
Romer, P. M. (1990). "Endogenous Technological Change." Journal of Political Economy. ideas.repec.org
Romer, P. M. (2008). "Economic Growth." The Concise Encyclopedia of Economics. econlib.org
Kremer, M. (1993). "Population Growth and Technological Change: One Million B.C. to 1990." Quarterly Journal of Economics. ideas.repec.org
Bloom, N., Jones, C. I., Van Reenen, J. and Webb, M. (2020). "Are Ideas Getting Harder to Find?" American Economic Review. aeaweb.org
Gordon, R. J. (2016). The Rise and Fall of American Growth. Princeton University Press. Forecasts from "Off Its Pinnacle", IMF Finance & Development, June 2016. imf.org
Meadows, D. H., Meadows, D. L., Randers, J. and Behrens, W. W. (1972). The Limits to Growth. Universe Books.
Turner, G. M. (2008). "A comparison of The Limits to Growth with 30 years of reality." Global Environmental Change. docs.niwa.co.nz
Herrington, G. (2021). "Update to limits to growth: Comparing the World3 model with empirical data." Journal of Industrial Ecology.
Kiel, K. A., Matheson, V. A. and Golembiewski, K. (2010). "Luck or skill? An examination of the Ehrlich–Simon bet." Ecological Economics.
Nordhaus, W. D. (1997). "Do Real-Output and Real-Wage Measures Capture Reality? The History of Lighting Suggests Not." In The Economics of New Goods, NBER. nber.org
McAfee, A. (2019). More from Less. Scribner.
Hausfather, Z. (2021). "Absolute Decoupling of Economic Growth and Emissions in 32 Countries." Breakthrough Institute. thebreakthrough.org
Keynes, J. M. (1930). "Economic Possibilities for our Grandchildren." Reprinted in Essays in Persuasion (1931).
Bolt, J. and van Zanden, J. L. (2024). "Maddison style estimates of the evolution of the world economy: A new 2023 update." Journal of Economic Surveys. rug.nl
Dimson, E., Marsh, P. and Staunton, M. (2025). UBS Global Investment Returns Yearbook 2025. ubs.com
Siegel, J. J. and Schwartz, J. (2022). Stocks for the Long Run, 6th ed. McGraw-Hill.
Bernstein, W. J. and Arnott, R. D. (2003). "Earnings Growth: The Two Percent Dilution." Financial Analysts Journal. cfainstitute.org
Hanke, S. H. and Krus, N. (2012). "World Hyperinflations." Cato Working Paper no. 8. cato.org
Federal Reserve (2012). Statement on Longer-Run Goals and Monetary Policy Strategy. federalreserve.gov
Finansdepartementet (2018). New regulation on monetary policy. regjeringen.no
Norges Bank. Withdrawn coins, 1957–2012. norges-bank.no
US Treasury. Debt Limit. home.treasury.gov
FRED. Gross Domestic Product, quarterly (GDP) and annual (GDPA). fred.stlouisfed.org
Statistisk sentralbyrå. Konsumprisindeksen, tabell 08184. ssb.no

Not investment advice. This is a piece about how a number behaves, written by a software developer, not a licensed adviser. The figures in the text are drawn from the sources listed above and rounded where the sources themselves are estimates.