Frederick Soddy’s Debt Dynamics

In the field of ecological economics, Frederick Soddy looms large. Born in 1877, Soddy became a chemist and eventually won a Nobel prize for work on radioactive decay. Then he turned his attention to economics.

Between 1921 and 1934, Soddy wrote four books that looked at how money relates to the physical economy. For his ground-breaking work, Soddy was rewarded with deafening silence. Here’s how ecological economist Eric Zencey puts it:

… Soddy carried on a quixotic campaign for a radical restructuring of global monetary relationships. He was roundly dismissed as a crank.

Although ignored during his life, Soddy’s work would become a central part of ecological economics. Let’s have a look at Soddy’s thinking.

Wealth vs. virtual wealth

Like a good natural scientist, Soddy insisted that human society is constrained by the laws of physics. Humans survive, he noted, by consuming natural resources. Exhaust these resources and we’re done for.

Think of humans (and our economy), says Soddy, like a machine. We transform energy into physical work. Like all machines, we’re bound by the laws of thermodynamics, which say that you can’t get something for nothing. Energy output requires energy input. That means humans are forever dependent on natural resources.

Now comes the problem. Our biophysical stock of resources — what Soddy called ‘wealth’ — is bound by the laws of thermodynamics. But money — which Soddy called ‘virtual wealth’ — is bound only by the laws of mathematics. Money can grow forever. Natural resource extraction cannot. This mismatch, Soddy claimed, is the root of most economic problems.

Cows and virtual cows

Here’s an example of Soddy’s thinking. Suppose that Alice is a would-be cattle farmer. She inherited some land and wants to use it to farm cattle. The problem is she has no money.

Not to worry. Alice goes to the bank and gets a $100,000 loan. With this money, Alice buys 100 cows. She’s now a cattle farmer — her dream is fulfilled!

Wait, says Soddy. Alice has a problem. She’s invested her ‘virtual wealth’ (money) in ‘real wealth’ (cows). But her ‘virtual wealth’ came from interest-bearing debt. That means the amount she owes the bank grows with time. Let’s have a look at this dynamic.

Banks usually require that you make regular payments on your debt. But to simplify the math, let’s assume Alice’s bank operates differently. It requires no regular payments. Instead, after t years, the bank demands full repayment (with interest). The amount Alice owes depends on three things:

  1. The size of her loan (the principal, P)
  2. The interest rate (r)
  3. The time (t, in years) since her initial loan

Assuming interest accrues annually, here’s the formula for the amount (A) that Alice owes:

A = P(1+r)t

Suppose the bank charges 5% interest (r = 0.05). Here’s how much Alice will owe for various call-in times:

Call-in time Amount owed
5 years $127,628
10 years $162,889
20 years $265,330
30 years $432,194

What’s important are the dynamics of Alice’s loan. As the call-in time increases, the amount she owes grows exponentially. This exponential dynamic, says Soddy, is a problem. Here’s why.

Alice used her $100,000 loan to buy 100 cows. If the bank calls in her loan after 10 years, she owes $163,000. That’s the equivalent of 163 cows. If Alice wants to avoid bankruptcy it seems she has only one choice. To repay her loan, Alice must breed more cows.

So here is the problem with interest-bearing debt. It comes with a baked-in need for economic growth. Or so it seems …

Inflating away debt

Repaying interest-bearing debt doesn’t necessarily require economic growth. There’s a second option. Interest-bearing debt can be paid back with inflation.

To see how, let’s return to farmer Alice. With her $100,000 loan, Alice bought 100 cows. After 10 years, the bank calls in her loan at $163,000. If cow prices don’t change, Alice needs to sell 163 cows to pay her debt. At first glance, it seems like her only option is to breed more cows. But there is an alternative. She could raise the price of cows.

Alice bought her cows at $1,000 per head. If she sells them for $1,630 per head, she can repay her loan without breeding more cows. So repaying interest-bearing debt doesn’t necessarily require economic growth. It can also be financed with inflation.

Breadth and depth

Our toy model of debt (based on Soddy’s reasoning) leads to a simple conclusion. If interest-bearing debt is to be repaid (en masse), there are only two options:

  1. The economy must grow
  2. Prices must grow

Jonathan Nitzan and Shimshon Bichler call these two scenarios breadth (economic growth) and depth (inflation). Although it’s theoretically possible to pursue both strategies at once, Nitzan and Bichler find that real-world societies tend to be single minded. They cycle between rapid growth with slow inflation (breadth), and slow growth with rapid inflation (depth). (For details, see Chapters 15 and 16 of Capital as Power.)

Both scenarios allow societies to pay off debt en masse. Yet both have problems. Let’s start with breadth. It’s simply suicidal (and impossible) to pursue economic growth forever. At some point we’ll either exhaust our resources and/or pollute the environment so badly that growth will cease. So paying off debt with perpetual growth is not an option.

What about depth? At first glance, it seems like inflating prices is a sustainable way to deal with debt. After all, the environment doesn’t care if prices grow exponentially. But humans do seem to care. Few people want inflation. Why?

The answer can’t be found on paper. That’s because in theory, inflation is a uniform increase in prices. But in practice, it never works this way. Real-world inflation is always differential. Some people are able to raise prices faster than others. This means that inflation always redistributes income. Unfortunately, the winners tend to be the powerful. (For details, see Jonathan Nitzan’s thesis Inflation As Restructuring.)

So based on Soddy’s reasoning, we find that interest-bearing debt comes with a fundamental problem. There is no fool-proof way to pay it back. Perpetually economic growth isn’t an option. And if we try to inflate away debt, the accompanying income redistribution creates instability. It seems there’s no way out of debt.

Debt default

Actually, there is a way out of debt, and it’s surprisingly simple. We wipe the slate clean. We debt default.

In his book Debt: The First 5,000 Years, David Graeber argues that throughout history, default was the most common way of dealing with debt. Often this happened on a large scale in something called a ‘debt jubilee’. Unpayable debts were wiped off the books, allowing debtors to start fresh. Of course, this wasn’t a long-term solution. Eventually debts would accrue again, requiring another jubilee. But as long as debt loads remained reasonably small, the cycle could repeat without too much trauma.

This debt cycle is a good example of a wider phenomenon found everywhere in nature — stability through fluctuation. Natural systems are stable not through stasis, but through small-scale fluctuations. These fluctuations are a way of mitigating the exponential dynamics that would otherwise be catastrophic.

As an example of such fluctuation, take population growth. If left unchecked, populations (of any organism) tend to grow exponentially. But they never grow forever. Eventually resources are depleted and the population declines. When the population is again small enough that resources are plentiful, exponential growth resumes. The result is a boom-bust cycle — stability through fluctuation.

Of course, if the fluctuations are huge, we can hardly call this ‘stability’. But in most healthy ecosystems, population fluctuations are small. The key to dampening boom-bust cycles appears to be diversity. When there are many species in an ecosystem, each keeps the population of others in check. Prolonged exponential growth never gets a foothold.

Debt monoculture

In nature, the surest way to provoke exponential growth is to destroy diversity. This is something that industrial farmers know well. Here’s their recipe. Cut down a forest, plant a single crop, and wait … for the exponential growth of pests. In nature, monoculture is the enemy of stability. The same is probably true among humans.

Back to Soddy’s debt dynamics. Soddy thought that the exponential dynamics of interest-bearing debt were a problem. Looking at nature, however, and we realize that exponential dynamics are everywhere. So it’s not the dynamics themselves that are the problem. The trouble starts when these dynamics go unchecked. In nature, exponential growth goes unchecked when we plant monoculture crops. In human societies, exponential growth goes unchecked when we have debt monoculture.

The term ‘monoculture’ is especially apt, because debt is literally a culture. Debt is an idea — a convention of quantifying property rights, and then applying exponential dynamics to these rights. The dynamics themselves are not the problem. The trouble starts when the idea of interest-bearing debt becomes a monoculture.

Interestingly, throughout most of human history the use of debt was limited. And when it was used, many people were skeptical that debt should accrue interest. Hence the ban, in many medieval societies, on interest-bearing debt (dubbed usury). Think of this skepticism of debt as a sign of cultural diversity.

Debt, anthropologist David Graeber argues, is just one particular way of solving a fundamental social problem. All societies function by keeping track of a web of social obligations. Throughout most of human history, these obligations were tracked loosely and qualitatively. Alice helps Bob catch a fish. Bob returns the favor by helping Alice cook. Different cultures (and even different sub-cultures) had different ways of conceiving and tracking these obligations. Cultural diversity.

Then came capitalism.

There are many ways that capitalism is different from other forms of culture. But perhaps the most important is the use of quantification. In capitalism, the web of social obligations (that have always existed) suddenly became quantitative. Bob doesn’t owe Alice a favor. He owes Alice $10. And if he doesn’t pay, that amount grows exponentially with time.

The idea of interest-bearing debt is an old one. But it’s only with capitalism that this idea became widespread. In other words, capitalism is the first debt monoculture. Capitalism takes the diverse ways of thinking about social obligations and replaces them with one. Interest-bearing debt.

As with any monoculture, we expect boom-bust dynamics to be amplified. And so they have been. But here’s the terrifying truth. For the last 200 years we’ve been riding one long boom. For two centuries, debt has grown continuously. We’ve achieved this by perpetually consuming more resources and by perpetually raising prices.

Eventually there will be a reckoning. Societies like the United States are now plumbing the depths of income inequality (i.e. income redistribution). And humans are pushing the limits of the Earth’s carrying capacity. So what’s worked for the past 200 years won’t work for the next 200.

It seems clear that debt monoculture is doomed to fail. So in a way, Frederick Soddy was right. The dynamics of interest-bearing debt are a problem. But only because we’ve allowed them to become the dominant human culture.

Support this blog

Economics from the Top Down is where I share my ideas for how to create a better economics. If you liked this post, consider becoming a patron. You’ll help me continue my research, and continue to share it with readers like you.


Stay updated

Sign up to get email updates from this blog.

This work is licensed under a Creative Commons Attribution 4.0 License. You can use/share it anyway you want, provided you attribute it to me (Blair Fix) and link to Economics from the Top Down.

[Cover image: Linda Hall Library]

Further reading

Graeber, D. (2010). Debt: The first 5,000 years. New York: Melville House Pub.

Nitzan, J. (1992). Inflation as restructuring. A theoretical and empirical account of the US experience (PhD thesis). McGill University.

Nitzan, J., & Bichler, S. (2009). Capital as power: A study of order and creorder. New York: Routledge.

Soddy, F. (1926). Virtual wealth and debt: The solution of the economic paradox. London: George Allen & Unwin.

Soddy, F. (1934). The role of money: What it should be, contrasted with what it has become. London: George Routledge & Sons.

Zencey, E. (2009). Mr. Soddy’s ecological economy. The New York Times.


  1. Ha! I almost asked if you had read Sody on an earlier post! Though I don’t know if I agree entirely with your characterization of him here. When he first started talking about econ he was fresh off his chemistry nobel for his work with radiation and and could see nuclear weapons and power in the pipeline. He had a sort of early ‘energy will be too cheap to meter’ take in Cartesian Economics and Aberdeen lectures.
    He had the credit creation theory of money nailed down, but he was outraged at the fact that society gave banks licence to print money. So you could say he was really the main intellectual force behind positive money. Of course Positive Money, while getting the objective ‘this is how the economy works’ part mostly right wanted to implement this insane QTM type system.

  2. Hi, Blair. I haven’t read the article yet (I will, of course), but I couldn’t wait to ask you this: what’s your opinion on the sovereign money proposal? It’s heavily inspired on Soddy’s 100% reserves idea, so I think the question it’s not too out of place. Thanks

    • Hi Asier,

      About sovereign money. I think that money is the quintessential public good. It’s how we regulate our activity. As such, the creation of money should be controlled democratically. So yes, I’m in a favor of the state having the sole right to create money … as long as the state is democratically controlled. The problem is that in places like the US, democracy seems to be eroding. But that’s a wider problem for another day …

      • Thanks for the reply. I agree with everything you said, especially the eroding democracy part. I was going to joke saying that if you think democracy is in bad shape in the US watch out for Spain (a colony of a colony, as I like to think of my country), but thinking again maybe being the center of the Empire makes it more difficult, with so much Power at stake.
        I especially liked two points in the article: usury being banned in feudal times; and capitalism quantification being a cultural process or ritual (which answers Wolf1 comment below: the abandonment of the Ancient Jubilees isn’t caused by some mischievous neoliberal conspiracy; it’s a question of culture –i.e. morality– and timing –we are still in the 200 years long boom; watch out for the next 200– instead).

      • “As such, the creation of money should be controlled democratically. So yes, I’m in a favor of the state having the sole right to create money … as long as the state is democratically controlled.”

        Prof. R,A,Werners agrees that ‘the creation of money should be controlled democratically’, but not directly by ‘the state’?


        is someone who offers evidence that the ‘right’ type of credit creation is the key to a ‘superior economic performance’?
        “Economies that manage to focus credit creation on productive and sustainable use – i.e. not for consumption and asset transactions – are likely to achieve superior economic performance (high nominal GDP growth and comparatively low inflation, without asset price cycles and with financial system stability). As the World Bank (1993) indicated, and others have also found (Patrick, 1962; Wade, 1990; Werner, 2000a, b; Werner, 2003), at the heart of the East Asian economic miracle has been a process of guiding credit towards productive use and suppressing unproductive and unsustainable (hence systemically risky) use of credit. . . .

        Importantly for our disaggregated quantity equation, credit creation can be disaggregated, as we can obtain and analyse information about who obtains loans and what use they are put to. Sectoral loan data provide us with information about the direction of purchasing power – something deposit aggregates cannot tell us. By institutional analysis and the use of such disaggregated credit data it can be determined, at least approximately, what share of purchasing power is primarily spent on ‘real’ transactions that are part of GDP and which part is primarily used for financial transactions. Further, transactions contributing to GDP can be divided into ‘productive’ ones that have a lower risk, as they generate income streams to service them (they can thus be referred to as sustainable or productive), and those that do not increase productivity or the stock of goods and services. Data availability is dependent on central bank publication of such data. The identification of transactions that are part of GDP and those that are not is more straight-forward, simply following the NIA rules.”

      • Excellent article Blair, thank you. I having been working with a great friend on this subject for many years and he has been an inspiration to me about many things to do with money and wrote the Foreword to my book.

        I think he has a wonderful proposition about managing debt; he calls it ‘Quantitative Boosting’ and describes it in his recent posting on his own blog:

        I should love to have your opinion on this, and of course, you can communicate directly with him.

  3. Thank you for bringing up another early, reality based economic thinker.
    A couple of notes:
    First: cow analogy is terrible.
    Among other things: a typical 100 cow breeding herd will yield 80+ more cows every year (breeding herds are skewed female). Even a “normal” herd will yield 40+ more cows every year. So repayment of 163 cows in 10 years is trivial.
    Secondly, the notion of exponential interest (sic) outgrowing the economic ability to pay – again, not new. A 5% interest rate per year isn’t exponential, but that’s a quibble. More importantly: if, in fact, the Sumerian, Babylonian and other ancient societies understood this, then the reason such knowledge isn’t more widespread is due to something other than ignorance.
    I would suggest reading Dr. Michael Hudson’s work, in particular – the ways by which neoliberals have funded economists from Clark to Friedman and Hayek to understand why this past “common” knowledge isn’t common.

    • In the good old days with 100 cows you would need two bulls, four horses at least two men. Your income would come from dairy and selling off young calves. If a cow/calf operation you would need two horses and one man and your income would come from selling off yearlings. The constraint would be crop production, grass, hay, mangels, turnip, potatoes, oats, barley. I grew up on such a farm in Ireland, we were quite mixed with pigs, turkeys and geese added to the mix. This was in 1940s’ and 1950s’ we were quite well off compared to the rest of Europe and particularly Great Britain which is only 60% food sufficient. Todays industrial scale farming is quite destructive and wasteful and will suffer greatly as foosil fuel becomes scarce.

    • Wolf,

      I think you missed the point of the cow analogy. It’s not about whether it’s possible (or even difficult) to breed more cows. It’s about the very idea that you should have to do it to repay a loan.

      Not sure I understand your ‘quibble’ with ‘exponential interest’. Any interest rate is, by definition, exponential. It has nothing to do with the rate, but from the mathematical formula for compounding interest (an exponential function).

      I’m not arguing that the arguments here are new. They were not new when Soddy wrote them a century ago. But as you say, they’ve been suppressed.

  4. My Grandfather homesteaded in Canada . The WW2 was an expensive period for CDN as much of England’s resources were supplied by CDN at little or no cost.
    The Banks needed capital so they offered to CDN farmers a repayment plan on their mortgages, by simply paying 50 cents on the dollar..
    This allowed my Grandfather to finally get out of debt.

  5. Good article as always and glad to see you’ve read Graeber.

    I know you’re also familiar with MMT, so I’d like to refer you to the most advanced stuff on money and debt I know of. Perry Mehrling is one of the smartest men in the world when it comes to the economics of money, debt, and banking.

    We don’t exactly have an interest rate monoculture. Chequing accounts have no interest, their price is at par with the dollar and they are a form of debt.The amount of different forms of debt is really bewildering!

    Something I wish you took more from MMT is the position that debt isn’t a bad thing. And these fluctations you’re talking about already happen in the “monoculture” of different debt instruments. You actually reference it in this article, the business cycle.

    You’re very close to what I think the real problem is. The distinction I like to draw between economy and ecology is that economy is about money. Animals use tools and produce stuff just like many economists like to talk about, heck they even might be “rational actors”. But what distinguishes economy from ecology is money, and money is entirely human. The monoculture you’re looking for is humans and there is nothing keeping us in check. Money only accounts human relations like property rights or tax payments. It inherently places humans in power above other species and that leads to a poor ecosystem.

    In some sense I’m splitting hairs here, you say the issue is a quality of debt, I’m saying the quality at issue is that it’s human-centric. But the ecology/economy distinction is nice to have, its like the industry/business distinction Veblen makes.

    • Hi James,

      The main thing I take from MMT is that money could, if the government wanted to, be issue without debt in the form of deficit spending. And to respond, I don’t think debt is necessarily bad. Like an IOU, it’s just an accounting device. However, interest-bearing dynamics add an instability that needs to be checked. But I do think we agree on many things.

    • Yes, but MMT has no real political path forward. It merely states that the governnment, “could always” spend money into existence. There’s a heck of a lot glossed over in “could always”. Kucinich, on the other hand, with his 2011 bill, HR2990 lays out a legislative blueprint to transform our current bank-created money system to a democratically created money system.

      In addition MMT is splintered where one proponent will contradict another. The constructs that MMT uses to make a point are also non-intuitive and contrived – completely inaccessible to the public. The only takeaway that people latch onto is the false claim that government now is not constrained on spending.

  6. Soddy understands the true nature of money. One aspect I ponder though is it’s not clear he is taking the money multiplier effect into account. Alice can pay the interest and principal for those cows not by selling them but by using the income they generate – like we do for a house now. I see the real problem with interest is not so much that it’s not payable, but that it is non-productive income that steals virtual wealth from the economy to access “unearned” real wealth.

Leave a Reply