Social Market Economy 2.0: Made in Germany not by Marx

Marx was wrong with his answer to the important question: "Where does profit come from?" We answer it not ideologically, but as an engineering problem — Made in Germany. The answer is not: "Profit comes from the exploitation of workers," as Marx thought, but "Profit arises as remuneration for bearing the risk of production and sale." But remuneration is not one-sided: With the profit, the loss case must also be borne when production or sale fails. Engineering problem means: We also prove our answer and do not merely assert it, as unscientific communism does. And we supply the architecture of the software that implements this system. We should also emphasise: Our answer needs no theory of behaviour or rationality, no special ability to calculate the future. We need no theory of behaviour, only the arithmetic of accounting: Plus and minus with the natural numbers 0, 1, 2, 3 and so on as euro-cent amounts. We do, however, need so-called quadruple-entry accounting, where two connected double-entry books always record one business transaction. That is precisely why it is called quadruple-entry accounting. By the end of the article it will be clear why this is necessary.

Double-entry accounting always works — no matter which price theory, investment theory or other optimising theories of behaviour underlie the recorded decisions. It is always consistent, i.e. the balance sheet always balances, when in booking from debit to credit one actually respects debit = credit. One must always book the same amount on the debit and credit sides of T-accounts; that is all there is to observe. That is the secret of double-entry accounting, since 1494, when Pacioli first wrote down the principles. A number is booked twice; in quadruple-entry accounting, four times. The constructions that ensure that quadruple-entry accounting is consistent yield the theory of money and the distribution of what is produced jointly. That is the foundation of what is, in our view, the first consistent theory of money. We call it MoMaT — Monetary Macroeconomics Accounting Theory, a theory of national accounting. It needs no theory of behaviour; it must always hold, for all behavioural — that is, economic — theories. That is why we also call MoMaT the axiomatics of economics. Without accounting consistency at the national accounting level there is no economics. As hitherto.

MoMaT is the result of 70 years of work on a theory of money that now exists. Renée has worked on it since about 1989, since his dissertation and really a few years of study before that. Viktor since 1996, when he heard the diagnosis from Martin Hellwig: Economics has no theory of what money is. As economists we did not want to tell ourselves that we operate in a science that does not understand its core. So much for the history; the rest is legend, one might think.

This article is the hopefully generally understandable version of the mathematised MoMaT theory of money. It begins with the addition and subtraction of natural numbers in accounts, T-accounts, profit-and-loss statements and balance sheets. And it ends in the sophisticated mathematics with which we today understand and design programming languages to describe computations, that is, software. With this approach our theory of money can even compute the software of monetary systems, provably correct, from its specification. Out of the theory arises the model, the software that reproduces the monetary systems of this theory. But here we are already in very deep water. Anyone who wants to and is interested can read everything in our material on the subject right here on this site, including a 700-page book. And money interests everyone. Because it is about our division of labour, our division of risk and — with our system — also a computable division of what is produced jointly.

So now from the beginning. What exactly was Marx's question? Where does profit come from? Where is the problem? The problem begins in the following situation. An entrepreneur wants to make a product. For that he needs, let us say, labour and resources. Capital such as machines we think of for now as resources, like land for example. The entrepreneur has to pay these factors of production, labour and resources, because they do not want to share in the risk of production. They want to see money immediately, and rightly so. The risk is that production fails, that no one wants the product, or that it is replaced by another. This risk of consuming resources without a return is borne by the entrepreneur, not by the employee and not by the landowner either. That is the problem.

And what did Marx overlook? The following: The entrepreneur receives from a bank an initial financial endowment, a balance on a current account against a loan, let us say 100 euros. In return he commits to repaying the loan, let us say in three annual tranches of 33 euros. If we now also grant the entrepreneur a profit mark-up of 7 euros, to 40 euros — for good reason, as we will see later —, then a problem arises in a so-called closed economy. A closed economy is one in which consumers and resource suppliers are the same group of people. Which people do we have in our example? The resource owners, the labour suppliers and the capitalist. The capitalist skims off the profits of the firm and consumes. The firm does not consume. It only produces the consumer goods, here out of labour and resources. The bank, for simplicity, does not consume either, makes no profits and is free of charge — a kind of beer mat, who owes whom what. The firm owes the bank the repayment of the loan, the consumers owe the firm the purchase price. That's it. We do not even need interest at first to explain what happens.

So we have three households — labour, resources, capitalist — that consume what production makes with the help of the initial loan. Note: We are talking here about sectors of an economy, not about individual households or producers, but about the totality of households, producers and banks, even though we often say agent or household. So far, so clear. Now the real problem: The 100 euros are paid by the firm to the labour and resource household. The firm wants to earn 40 euros each year, with the profit mark-up, from selling the products. The concrete problem: The 100 euros at labour and resources are used up after 2.5 years. So where do the remaining 20 euros come from (= 3 x 40 - 100)? That is what is meant by "Where does profit come from?"

Marx had no answer to this, or rather thought it came from the exploitation of labour. We have now proven, by all the rules of the art, that the answer is in principle simple. Although we will see later that concretely it is not so simple at all — only in principle. Which also explains why it is only now, with the most modern mathematics, possible to identify the principle and solve it concretely.

So what is the simple explanation of the problem? After one year, in which the first investment project runs, a second begins. Likewise, let us say, for three years. After two years a third begins. After three years the first project is finished and another begins. So we are dealing with overlapping projects that begin and end at different points in time. And with that, in the second year new demand deposits arise that can be used to pay for consumption and profit — above all precisely the 20 euros that were "missing" in Marx and that do NOT result from the exploitation of employees. That is, employees can be, but need not be, exploited for capitalism to work.

The overlapping investment projects in different firms are what necessarily follows from the division-of-labour organisation of our economies. It is the organisational form of modern economies. Noticing this was Adam Smith's great achievement and marks the beginning of economics. Whereas the question of household management already begins with Aristotle, in the concept of the household and its management: Oikos and Oikonomia. Adam Smith asked one further question: How is what is produced jointly distributed among the people?

To answer this we must clarify more precisely what risk is and how it is borne. Risk does not disappear, it must be borne and distributed. That is what banks are for. And profit. Employees bear no risk, they are paid immediately. What does the risk consist of? In the unprofitable use of resources and labour. It costs but brings no returns when the risk materialises — that is, when production and sale do not succeed. The consequence: The consumption of resources has to be written off as consumption, precisely as use that brings no return. Out of the return the entrepreneur pays the loan with which he remunerated the risk-averse factors. They are rightly risk-averse: In a division-of-labour economy it makes no sense that the workers regularly bear the risk of the firm in which they are employed. If they want to, they can still participate, or found a competing firm themselves and do it better and cheaper. As the standard case, the supplier of the factors of production must be remunerated immediately. That is the stage for a mostly misunderstood actor in the economy.

Interest. No villain, but a risk premium. As with insurance. The investors in Silicon Valley work exactly this way: invest in 10 startups. 9 go bankrupt, the investment is gone, but 1 startup goes through the roof. This risk of default has to be covered by interest. The investor's profit. So far, so simple.

However, there is also here a problem thousands of years old: money that earns money, or put differently, compound interest. When one earns money merely by waiting, without taking on risk, something is wrong in economic logic and above all in the incentive systems. One earns money through money when one can also lose it. That is: when one takes on risk. Not merely by sitting back and drinking tea. On the seat of power. That is unfair. Whoever, as is customary in economics, regards interest as compensation for patience is already standing with one foot in the hell of financial crises and social collapse: waiting then multiplies money. That makes no sense when no risk is taken on in the process. Then it is indeed a bad capitalist. Although here too it must be noted: A good game does not consist of good players, but of good rules. Who can blame others for exploiting bad rules. We must change the rules and not demonise the players who exploit them. That makes no sense. On the contrary, exploiting the rules is necessary in order to reveal the problem, which should then, however, be followed by a change of rules. That is what MoMaT is for.

That a capitalist makes profits is nothing indecent. It has to be so, because the entrepreneur or capitalist, as owner of the firm, is the first layer of the risk-absorption hierarchy. First entrepreneurs take in profits. And when they misinvest, build wrong products that are not in demand, the profit shrinks again, as a write-off. Quite normal. So far, so good.

If the firm has too few retained earnings, for instance because it is only just being founded, then the bank has to provide the means, the money. If the bank miscalculates, invests only in unsuccessful firms, or gets its insurance premium — interest as a risk premium — wrong, then it goes bankrupt. If it does not have enough equity, that is, retained earnings, then the central bank has to step in and rescue or wind down the bank. That is then the function of the lender of last resort, or, in a pure paper-money system, of the provider of first liquidity. This makes the matter of bearing risk not quite as simple as indicated above. The banking hierarchy from the entrepreneur through the banks to the central bank is a hierarchical system of risk absorption. First the entrepreneur himself is called upon, then the banks, then the central bank. The central bank in turn cannot go bankrupt; it is the ultimate risk-absorption layer of society, or of the currency area. It prints the means with which one finally discharges one's debts. That is what makes the clearing of risks, payments and repayments so difficult. We are dealing with a hierarchy of risk absorption.

A current account contains no money. It is only a reference, a document, a digital account balance. It shows how much cash the account holder can dispose of at most. Either as a withdrawal in banknotes at the cash machine. Or as a transfer with which he can pass this right to dispose of cash to another business partner. The banks in turn also have current accounts, at the central bank. This is usually called reserves. That too is a right to dispose of cash. The banks can hold it as cash on hand in the vault, as bundles of money. Or they can themselves transfer it via the central bank, that is, rights to dispose of cash, to another bank. This distinction is very important, because it ultimately grounds the cascades of risk absorption. Only cash discharges debt finally. If my bank goes bankrupt before the transfer, then my business partner will rightly demand cash or a right to dispose of cash by another route. That is the mathematical problem, the modelling and implementation problem: to understand and implement these processes of incurring and discharging debt through payments, and to keep them consistent.

Which debts do we mean? Not only debts from a loan. In every (two-sided) business transaction debts arise: in a bicycle purchase the debt of the bicycle owner to deliver the bicycle, and in return that of the buyer, usually to deliver money — cash or rights to dispose as current-account balances. So in practically all purchase, rental, labour and similar contracts debts arise that are cancelled again, by fulfilment, upon the conclusion of the exchange. In investment and loan contracts cash debts arise between today and tomorrow.

At this point one has to make clear a further surprise of our theory of money: Only paper-money systems are stable. Gold-backed ones are not. Why is that? We are used to answering this question with: "Yes, but only gold is worth something, paper is worth nothing." That may have been correct in times before functioning legal systems, but today we have enforceable rights, and anyone who has ever had the bailiff at the door knows what this is about. Moreover, at this point one must once again make clear what we do with cash: We discharge ourselves finally from the debt contracts of our exchange-based economy. So when there is much to exchange, much activity in the economy, that is good, and we need a lot of money. If the underlying of the cash, gold, is limited, we have a problem when the required volume rises. That is the reason why only cash that can be produced without limit is speculation-resistant. Only then is it not worth speculating on an end to cash creation. Draghi, with his "Whatever it takes", ended the speculative waves against the ECB in 2012 through that remark alone. Stable. For that the central bank simply has to print it. Since the process of printing money and booking the new cash is the only (!!!) process that concerns only a single double-entry accounting system, namely that of the central bank, one also sees that this does not make the central bank infinitely rich. Together with the understanding that interest is a risk premium and that the central bank should be able to print an unlimited amount of it, a new understanding arises of what the tasks of a central bank are. Not steering the business cycle by changing an interest rate, but only setting the creditworthiness standard to be met for investments, and ensuring the payment system. No more than that. That, by the way, is also how they came into being, as pure clearing and settlement places between banks, not as omnipotent business-cycle-steering authorities. And there they will return, once it is generally understood what money and hence interest is.

At the hierarchical banking system it also becomes clear: The winding-down and liquidation of a bank is incomparably more difficult than that of a bankrupt firm. In the case of a firm, someone has to write off an amount of money equal to the failed, unrepaid investment. With that it is also clear: Debts are not to be repaid unconditionally. That is what insurance is for. Whoever demands unconditional repayment demands a modern form of slavery. In the case of a bank that goes bankrupt, there must also be a write-off, but in addition the non-problematic loans are redistributed to other banks or risk bearers — firms can do this too. This is because firms are, so to speak, the leaves of the debt tree of the economy, and banks the branch forks. When the branches disappear, their leaves have to be hung on other branches — the green, intact leaves; some disappear with them, the dried-up ones, the bankrupt investment projects.

From this architecture there arises yet another insight that further complicates the theory of money. The only closed economy that exists is the world economy. All others are in fact open. Some goods come from abroad, some go abroad. Investments too cross borders. What remains is the central quantity of economics: the sum of all creditors (of their lent amounts) and the sum of all debtors (of their debts). These two sums must be equal. The world as a whole is NOT in debt — to whom, after all? Not because of some particular assumption about behaviour or rationality, but as an arithmetic certainty. For every debtor there is a creditor. That is logically not conceivable otherwise. Astonishingly, the Venetians already knew this when, around 1400, they developed accounting. They spoke of "for every debtor a creditor". In our concepts they were thus speaking of quadruple-entry accounting; only there does this quantity appear. Between the double-entry accounts.

What is astonishing is not that they knew it, but that until our theory of money no one had grasped it mathematically. As double-entry accounting — of an entrepreneur, of a household — it has hardly been formalised. In a few scholarly publications, yes, but not the so-called quadruple-entry accounting that must stand behind any theory of money. What is quadruple-entry accounting? Simply a system of double-entry accounts that are connected with one another. That is, the national accounting systems. The connections consist of shared accounts. How so? The current account of a firm appears in its accounting as a T-account, as a bank balance on the asset side. It is a balance. The same T-account, or the same figure, appears at the account-keeping bank as a liability account. The same figure, but on the liability side at the bank. That is a liability of the bank towards the firm.

The same holds for the loan accounts: a liability at the borrowing firm, an asset at the lending bank. The banks too are connected with one another through current accounts: a balance of one bank at another against a liability on the other side. Likewise the reserves, that is, the balances of the banks at the central bank. These balances now, when one sets up a theory of money, have to be netted against one another and also programmed. The specification must ensure that the software which handles the payment and booking business preserves these invariants — that is, the arithmetic equalities. When booking, it must not happen that they hold beforehand and not afterwards. This is not trivial. For one has to observe the hierarchies and distinguish which account belongs to which counter-account and which hierarchy level we are talking about — with millions of households, thousands of banks and hundreds of thousands of firms. A firm has, in part, tens of thousands of T-accounts per double-entry set of books, a holding a quadruple-entry set with the double-entry books of its subsidiaries, an entire economy a quadruple-entry accounting. Not to mention the entire quadruple-entry accounting of the world economy. One can imagine that here one no longer gets by with linear algebra — even though accounting is really only linear algebra. Plus and minus of natural numbers, rarely once a multiplication. For structuring and securing consistency one then needs the most abstract and therefore most powerful mathematics: the modularisation mathematics of mathematics itself, the mathematics of programming-language design and its compilers, which in MoMaT now becomes the mathematics of economics. This is complicated, but the principles, we think, everyone can understand. And everyone must understand them. That is what this article is for. After all, it is about our labour, our risk and our joint production output, to be distributed. In one economy. And in the end the whole world.

The central banks control money creation, and can therefore print as much cash as they like. With that they control the distribution of what is produced jointly. If they let this be taken out of their hands, the modern form of exploitation arises: of nations by other nations. This happens through contracts denominated in foreign monetary units, so that the central bank is only occupied with procuring these foreign monetary units by printing its own monetary units. Understanding these mechanisms is the second part of the work of our theory of money, which now follows the first part of the work. This will not take another 70 years. Since now essentially everything is clear and the quadruple-entry accounting and monetary policy of central banks only have to be applied to this question.

Because a theory of money was so far lacking, it was easy to keep these processes of redistribution within and between economies hidden — for those who understood them. Our work thus stands in the tradition of the Enlightenment: an exit from self-incurred immaturity, or rather from the loss of sovereignty of central banks. Here as a demand upon the central banks that organise the division of labour through money as well as through the distribution of risk and profit.

In summary, we plead for an understanding of the architecture of our monetary systems — it is sophisticated, but not yet perfectly implemented and built out, because not yet fully understood. It is easy to rail against it and want to abolish capitalism. To understand and improve it is incomparably harder. Here is our attempt and contribution to that. The rest is man-made — no deterministic course of history, no automatism that overcomes capitalism into socialism. Although: if one wants to call a perfect capitalism, one that sensibly produces private goods (rivalrous and excludable: toothpaste, cars etc.) and public goods (non-rivalrous, non-excludable: security, environmental protection), socialism — so be it. We should on no account play the two sides off against each other: the entrepreneurs who bear risk, work 24/7, can go bankrupt and have social ruin before their eyes, and the employees who justifiably have no appetite for risk but can likewise become entrepreneurs. Neither capitalism, as an invention of the preceding generations, nor the people within it has deserved that. Whoever chants "Death to capitalism" should bear in mind that they thereby also mean "Death to the capitalist". But who is then to take on the risk? In the jungle too it is risky. The risk of life and survival does not disappear. That is the deal in this world and not in paradise — how boring that would be.

Further reading​

Further reading