1. Money
  2. Production and consumption
  3. Capital
  4. Interest and capital
  5. The laws of macroeconomics
  6. Inflation and unemployment
  7. The solution to inflation and unemployment as caused by the pathological process of capital growth



It is often implicitly assumed that economic events can be understood through direct observation. This may be one of the reasons economic analysis is mainly carried out in microeconomic terms. Monetary analysis is no exception. Even though concepts such as income, saving, investment, interest, capital are mostly considered at the national level, they are almost inevitably arrived at through a process of aggregation of their microeconomic components. If, as is widely believed, macroeconomics were simply the result of such an aggregative process, microeconomic variables would be the only relevant object of enquiry of economic analysis. This would not imply, however, that economists are to limit their analysis to direct observation. In particular, this would not allow them to define money irrespective of its peculiar, immaterial nature. Even at the microeconomic level, money remains a numerical form issued by the banking system. One important point of our analysis is therefore the fact that monetary economics requires a thorough investigation over and above mere factual observation and centred on a clear understanding of the banking nature of modern money.

Another central point is the substantial distinction between economics and mathematics. Following Walras’ endeavour to establish economics as a psychico-mathematical science, most economists have been developing oversophisticated models with no bearing on the real world. Despite their increasing mathematical complexity, all these models suffer from the same shortcomings, since they all stem from the same basic assumption, i.e. that economic theory is intrinsically axiomatic. The procedure proper to mathematics, and so often fruitfully applied to physics and other ‘exact’ sciences, has been extended to economics on the arbitrary assumption that economic events can be analysed in the same way as physical events. Now, contrary to what happens in physics, the economic system is entirely a man-made entity. This means that not even a single element of this system may be taken as an axiom. But if everything must be explained starting from scratch, then economic analysis cannot result from the combination of a given number of assumptions according to a series of axiomatic relationships.

Mathematics is seen as a necessary requirement for rigour and seriousness, and its use is thought to be essential to economic theory even at the expense of its faithfulness to reality. However, economics is a science in itself, capable of being as rigorous as any other exact science, and it is not through the systematic use of mathematics and through axiomatization that this end will be reached. As innovative as mainstream attempts at modelling the economy may appear, they still rely on an old-fashioned conception of money. In particular, they seem unable or unwilling to recognize the totally immaterial nature of bank money. The reason for their anachronistic choice of commodity money is that it pares away the risk to be forced to abandon the safe harbour of the neoclassical paradigm of general equilibrium. Yet, the hope of safeguarding the principles of the axiomatic approach, as advocated by Walras and his followers, is jeopardized by the actual working of our economies. From prices to profits, from capital to interest, from saving to investment, economic concepts and magnitudes are clearly of a monetary nature. Moreover – as bankers well know – money does certainly not pertain directly to the world of real goods and services, so that any attempt at explaining economics in pure real terms is doomed to failure. Unless one uncritically accepts Debreu’s axiom that real goods are numbers, one has to admit that Walras’ relative exchange is unsuited to solving the problem for which it was conceived: the determination of numerical prices.

It is only money – conceived of as a purely numerical form – that can allow for the solution to this key problem. But this implies a radical change affecting the whole body of theoretical economics, and, in particular, the relationship between micro- and macroeconomics. This is what Keynes’s theory was intended to do: provide a synthesis between classical and neoclassical analyses transcending the traditional opposition of micro- and macroeconomics. As economists know, this aim has been scorned and neglected given the attempt by general equilibrium theorists to subsume Keynes’s contribution under a neoclassical synthesis and also because of Keynes’s own inability to found macroeconomics on consistent and autonomous macroeconomic principles. Quantum macroeconomics builds up the macroeconomic foundations for macroeconomics while allowing for the dialectical synthesis of the classical, neoclassical, and Keynesian analyses into a new monetary theory of production and circulation. From a monetary point of view, economics is a science with its own logical laws. The aim of economic theory is to determine what these laws are and to show how they can be implemented


  1. Money

Money is a very peculiar ‘object’, which has too often been mistaken for a real good. As recent developments in banking theory have confirmed, it would be both anachronistic and wrong to take money as a material thing. This makes things clearer if not easier: money is an immaterial entity issued by banks every time they carry out a payment on behalf of their clients. Referring to the famous economic distinction between stocks and flows, we would say that money is a flow whose instantaneous circulation has a stock of income (or capital) as its object. Banks create the flow but not its object, which is closely related to production. This is to say that money and credit are not one and the same thing. In order to provide their clients with credit, banks need to back it with a positive deposit, that is, with a positive amount of income or capital. Contrary to what happens for the creation of a simple flow (a numerical vehicle with no positive value), the income banks lend is not of their making. Correctly used, double-entry book-keeping does not allow for the creation of income independently of production. Thus, by creating money banks simply provide the economy with a numerical means of payment, the object of the payment being derived from the association of money with current output.

The very nature of bank money is numerical. If money were a positive asset, banks would benefit from the extraordinary power to create riches out of nothing, as it were, which is plain nonsense. In reality, banks act as monetary intermediaries, which means that money is issued as a flow any time banks carry out a payment on behalf of their clients. Every payment is a ‘tripolar’ transaction involving a bank and two of its clients, in which each of the three agents involved is simultaneously a purchaser and a seller on the labour, commodity, and financial markets. As a purely numerical form money never enters a net sale or a net purchase and must therefore be clearly distinguished from bank deposits, net assets and liabilities entered as stocks in the bank’s balance sheet and that can only result from the association between money proper and real output established by production. Knapp’s idea that money is essentially state money is thus contradicted by the fact that, like any other economic agent, the state cannot finance its spending through money creation, that is, by issuing its own acknowledgment of debt. In a logical (as opposed to pathological) system, public spending is constrained by the amount of income the government can obtain through taxation, private loans, and the sale of public goods and services, which simply means that, again like any other agent, the state can finance its purchases only by simultaneous and equivalent sales on the commodity and financial markets.

What lies behind the confusion between money and income is the concept of credit money and the wrong belief that when banks create money they grant a positive credit to the economy. This is particularly clear in the monetary analysis of production proposed by the members of the so-called ‘theory of the circuit’. Apparently unaware of the absurdity implicit in maintaining that banks can create positive financial assets out of nothing, these economists claim that production is financed by newly created credit-money that firms spend to cover their costs. What has been entirely missed by the theorists of the circuit is the ‘vehicular’ nature of money. Its understanding requires entering the world of purely numerical magnitudes and of double-entry book-keeping. What ‘circuitists’ and post-Keynesian economists have clearly seen is that money is bank money. What they have failed to see is that banks create a purely numerical magnitude that is simultaneously positive and negative, and that this magnitude exists only instantaneously, as a circular flow..


1.1 Money and value

Since the Classics, the problem of value has been considered to be fundamental to the very existence of economics. If produced goods and services were to remain heterogeneous (as they are when considered merely from a physical point of view), economics would have no status as a science, since it would lack a proper object of enquiry. In order to become homogeneous and be transformed into commodities, physical goods and services must be measurable by a common unit or standard of value. Money has traditionally played this function. Yet, there is still little agreement as to how money (particularly modern bank money) may become the standard of value. According to a widespread interpretation, classical and neoclassical authors share the belief that money is essentially a commodity chosen among other commodities to act as a general equivalent. Now, this material conception of money is far from being unanimously adhered to by the great classical and neoclassical economists. Marx’s concept of form of value, for example, is close to Walras’ concept of numéraire, and they both refer to money as to a non-material entity, a numerical form whose fundamental role is to act as a numerical unit of account. The age-long debate on the existence and the nature of value in economics originates from lack of consensus as to whether value should be considered as a substance, a peculiar dimension of commodities (absolute value), or resulting from the measurement of commodities in terms of commodities (relative value). The analysis of bank money shows, however, that neither alternative is the right one. Instead, it is the combined intuition of Marx and Walras that leads to the correct definition of value.


1.2 Money, prices and exchange

Although economists are unanimous in considering money as a means of exchange, most theories still lack a satisfactory explanation of the way money may become the general equivalent of produced output. Mainstream economics is based on the concept of relative exchange. In their most rigorous expression, neoclassical theories consider money as being perfectly neutral. Yet, the assumption of money neutrality is seriously challenged by the over-determination in the demand for commodities. The smooth functioning underlying the traditional Arrow-Debreu Walrasian model is hindered by a series of restrictions (Jevons’s double coincidence of wants, budget balance constraint, monotone excess demand diminution, excess demand fulfilment). To overcome these difficulties some economists have pleaded for the effective introduction of money and the financial market into general equilibrium theory. Their attempts fails, mainly because of the old-fashioned conception of money to which they are still anchored. The same conclusion applies to the traditional version of the quantity theory of money and to its determination of prices. Quantum monetary analysis provides an alternative solution. As soon as money is conceived of as a pure numerical form, it becomes possible to move from the world of relative exchanges to the world of absolute exchanges. It is the nature of bank money that leads us towards this new conception of monetary transactions. Whereas the concept of relative exchanges subsumes a world in which money is essentially a commodity, the concept of absolute exchanges applies to a world in which money is a numerical standard issued by the banking system as a simple IOU.


1.3 Money and credit

Money and credit have long been confused, partly because of the net-asset definition of money and partly because money creation implies indeed a financial intermediation by banks. It is not easy, thus, to avoid considering the creation of money as a creation of credit. The analysis of the way money is issued by banks and integrated with physical output is once again fundamental in clarifying the relationship between monetary and financial intermediations. Although they take place simultaneously, these two operations are distinct; and so are their results. While money is a simple numerical vehicle allowing the flow of payments, credit implies a financial transfer of income. While money has no value of its own and can indeed be created, income derives from production and defines an absolute exchange between a real and a monetary deposit. Credit is concerned with the lending of such a deposit. It appears, thus, that the supply of credit must be kept distinct from that of money.

The monetarist concept of money supply is ill-founded since, assuming money to be a positive asset, it confuses money with income. In fact, it is income that is a positive asset. The supply of credit is the supply of a positive amount of income and requires the existence of a bank deposit (a stock), whereas the supply of money refers to the capacity of banks to convey payments (flows) on behalf of their clients. By failing to distinguish clearly between these two functions (monetary and financial intermediations) carried out by banks, economists have been led to develop an anachronistic conception of money, inconsistent with its book-keeping nature and incapable to explain the working of our monetary economies of production. As the recent evolution of banking and applied technology shows, it is no longer possible to conceive of money as a material medium of exchange. If money is a general equivalent it is because it gives a numerical form to current output, and not because it has a positive value equal to that of the goods it is exchanged with. Money and output enter an absolute, not a relative, exchange, and banks are the intermediaries through which the result of this absolute exchange is lent, spent or invested.


  1. Production and consumption

It is no mystery that economists have not reached agreement as to the way the economic process of production must be conceived. Important differences remain, for example, between Keynesian and neoclassical authors, between those who consider production as a one-way process and those who analyse it as a circular flow. The role of money within this process has been thoroughly investigated in the past, and is still one of the most debated arguments of economic theory. French and Italian economists have recently animated a fruitful debate about the way money may be associated with current production. Thanks to these efforts it has become clearer that, when considered as an economic process, production is a monetary (as well as a physical) phenomenon. Leaving the study of the physical properties of output to other experts, economists must centre their investigation on the monetary aspect of production. It is only by doing so that they can determine whether production is merely a physical process of transformation or it is also a process of creation, i.e. whether output is only a transformed input or a net product. Once again the analysis of bank money makes it possible to reconsider the whole problem afresh, clearing the way for a new conception of production as an instantaneous process in which money and physical output become one and the same thing.

A truly macroeconomic analysis of production is possible only if human labour is recognized a different conceptual status from the other factors, and money is no longer identified with a positive asset. According to a modern interpretation of Keynes’s monetary analysis, production is thus an economic process resulting from labour alone and giving rise to an economic output defined in wage units. Since it is through the association of money with produced output that income is formed, and since income is the specific result of production, it follows that, from a purely economic viewpoint, production is the instantaneous event (the payment of wages) through which produced output is issued as a positive amount of money income. In its most rigorous definition, production is then an absolute exchange since it is the very transaction through which output is changed into a sum of money income, that is, through which output becomes the object of a bank deposit. The macroeconomic nature of production follows immediately from the fact that each single payment of wages increases the amount of national income currently formed.


As far as consumption is concerned, its macroeconomic nature appears clearly as soon as it is related to the final expenditure of income, that is, to Keynes’s identity between total supply and total demand. In contrast with the notions of consumption function and equilibrium advocated by mainstream economists, quantum macroeconomics shows that, like production, consumption concerns the absolute exchange between money and output. Interpreted as the expenditure carried out for the final purchase of produced output, consumption is an instantaneous, macroeconomic event defining the destruction of a positive income.


  1. Capital

All the concepts elaborated in the analysis of monetary production converge here to provide a theory of capital in keeping with the laws of bank money. If we start by considering the classical concept of capital and the main contributions provided by the economists who have analysed it, particular attention must be paid to the works of the Austrian school. According to the Austrian vision, capital is time and it involves command over current output. This view has been in part taken over by some neoclassical economists, who have come to consider capitalistic production as a process stretching over time. The concept of intertemporal prices is fundamental in the neoclassical approach; so is capital aggregation. However, the difficulties inherent in the problem of aggregation and in the need to derive the prices of capital goods from their own costs of production seriously undermine this approach. As Hicks clearly put it, capital is a twofold entity, monetary and real. To reduce capital to a collection of capital goods is seriously misleading. The Austrian view must be reassessed starting from a rigorous analysis of bank money and its relationship with time and current output.

In its first and simplest form, capital is related only to the flow of time and defines a reversible transformation of income. No income can ever be found in the interval shared by the instant income is formed and the instant it is finally spent. It is here that capital enters the picture: saved the very instant it is formed, income is immediately replaced with a financial claim and henceforth transformed into capital-time. Although it is correct to relate capital to time, this relation is not the same with respect to circulating or fixed capital. The passage from one form of capital to the other implies the investment of profit and involves the definitive transformation of savings into a social capital. Fixed capital results from the productive investment of part of society’s income saved-up in the form of profits. This process has been analysed by Schmitt, and is the core of quantum monetary macroeconomics.


  1. Interest and capital

Firmly built on Keynes’s identity between macroeconomic saving and investment, the analysis of fixed capital is a necessary step towards the understanding of interest. Wrongly conceived of as the price of money or as the price equilibrating supply of and demand for liquidity, interest would still remain an arbitrary magnitude if it were not related to capital accumulation. In fact, even the existence of a positive interest on consumption loans would be difficult to justify if it were not backed by a positive interest derived from macroeconomic investment (saving). Being simultaneously positive for an agent and negative for another, the payment of interest on consumption loans is a zero sum transaction, which leaves the amount of social income unaltered. In clear contrast with the microeconomic nature of interest on consumption loans, interest on fixed capital is a macroeconomic income. Through the investment of profits (that is, the ‘capitalist’ form of social saving), part of current income escapes consumption and is transformed into fixed capital. Hence, the accumulation of fixed capital implies a sacrifice by society taken as a whole (macroeconomic saving), and interest is nothing more than the compensation for this sacrifice. The investment of saving (profits) and its transformation into macroeconomic capital defines a final loss of income – which will no longer be available on the financial and commodity markets – and interest becomes the compensation for this loss, an income that, period after period, replaces the saving initially absorbed in the production of fixed capital goods.


  1. The laws of macroeconomics

Macroeconomic laws are not empirical laws derived from constant sequences of events and influenced by economic agents’ behaviour. Independent of individual or collective behaviour, these laws derive from the flow nature of money and are concerned with the logical structure of payments relating to production and exchange. The first and fundamental law of macroeconomics establishes the necessary equality – or the identity – between macroeconomic supply and demand. Since it is through the payment of the macroeconomic costs of production that physical output is transformed into economic output, the measure of macroeconomic supply coincides with the numerical expression of these costs. Once it is established that labour is the sole macroeconomic factor of production, it necessarily follows that macroeconomic supply is expressed by the total amount of direct and indirect wages paid to workers: money wages are the standard through which physical output acquires its (economic) numerical form. As for macroeconomic demand, it can easily be shown that it is determined by the amount of income available in a given economy. Since it is through production that macroeconomic income is formed, it immediately appears that wages define both global supply and global demand: macroeconomic supply and macroeconomic demand are the two terms of an identity, the two aspects of one and the same reality.

The second macroeconomic law is as strict as the first, for it establishes the identity between each single agent’s sales and purchases. Once again it is because money is a simple flow that it cannot finance any net purchase. The instantaneous and circular flow of money necessarily implies, in fact, that both buyer and seller are simultaneously credited and debited for the same amount of money, which means that they are both and to the same extent sellers and buyers. Whether we consider the transactions carried out between residents of the same country or between countries, the law applies, since money does not change its nature when moving from the national to the international level. No single agent, resident or country, can therefore be a purchaser without simultaneously being a seller on the labour, commodity, or financial markets.

The third macroeconomic law establishes the identity between saving and investment. Macroeconomic saving and macroeconomic investment form a unity. In fact, macroeconomic saving is precisely that part of macroeconomic income that is invested in the production of fixed capital goods. If an economy is to produce capital goods, it has to save part of its current income and invest it in this new production. Defined as the production of fixed capital goods, macroeconomic investment is therefore necessarily equal to macroeconomic saving. It is thanks to its macroeconomic saving that an economy can build up its fixed capital, and it is through macroeconomic investment that it transforms part of its income into fixed capital. Finally, the three macroeconomic laws mentioned here can be derived from the unique principle of absolute exchange established by Schmitt’s quantum theoretical approach.


  1. Inflation and unemployment

According to the majority of economists, inflation is due to an unexpected rise in money supply. Prices are both real and monetary. Inflation is identified with a process of continuously rising monetary prices caused by an increase in the quantity of money affecting aggregate demand. Now, a rapid growth in the money supply increases aggregate demand only if money has a positive value, that is, if it is issued as a positive asset. But the value of money is identified to the inverse of the price level. The vicious circularity of the traditional approach is thus patent: it is simultaneously maintained that money is issued already endorsed with a positive value and that this value depends on a price level that is itself dependent on the aggregate demand exerted by money. Another common feature of orthodox analyses is the widespread use of the price index as a standard of inflation. Yet, there are increases in market prices that simply lead to a new distribution of income without modifying money’s purchasing power, which clearly shows how unreliable it is to measure inflation by a persistent rise in microeconomic prices.

The quantum theoretical approach to inflation implies a radical change with respect to traditional analysis. Starting from Keynes’s identity between global supply (S) and global demand (D), it is shown that a numerical difference between these two terms arises when capital accumulation and amortization are carried out within a system of payments in which no distinction is made between money, income, and fixed capital. It is thus not inconsistent to have a situation in which S and D are identical despite the fact that D is numerically greater than S. The nominal rise in global demand leaves its value unaltered, but decreases the value of each single unit charged to carry it over. Each monetary wage-unit loses part of its initial value or purchasing power, which indicated that inflation is the altering of the initial relationship between produced output and its monetary form.


Today’s pathological process of capital accumulation and amortization is also the cause of a worrying growth in involuntary unemployment, that is, of a situation in which unemployment rises ‘whatever the behaviour of all economic agents’ (Bradley 2003: 399). As suggested by Wicksell, pathological capital accumulation and over-accumulation leads to a fall in the natural rate of interest. When the natural rate is very close or equal to the market rate of interest, deflation sets in, and the economy starts suffering both from an inflationary increase in prices and from a deflationary rise in unemployment. The coexistence of inflation (D > S) and deflation (D < S) is a mark of today’s monetary disorder. Traditional analysis cannot account for it, nor can it reconcile these two disequilibria with Keynes’s logical identity (D ≡ S). Yet this is precisely what has to be done. Schmitt’s quantum theoretical approach leads to this dialectical reconciliation within a truly macroeconomic analysis of inflation and unemployment.


  1. The solution to inflation and unemployment as caused by the pathological process of capital growth

An important topic of quantum macroeconomics concerns the role of positive analysis in setting the principles of the reform needed to fulfil the goal set by normative analysis, that is, the creation of an economic system free of any monetary pathology. In particular, one should look both at the measures suggested so far by mainstream economists in order to achieve monetary stability at the national level, and at the changes advocated by macroeconomic quantum analysis, in order to adapt the accounting structure of the banking system to the very nature of money, income, and capital. The development of double-entry book-keeping – made possible by the discovery of negative numbers – is at the origin of bank money, and represents the cornerstone of today’s system of payments. Ricardo and Keynes are among the economists who have mostly contributed to the understanding of bank money. It is to Ricardo, for example, that we owe the distinction between money creation and financial intermediation. Taking over Smith’s concepts of nominal and real money, Ricardo was able to show that, whereas nominal money is literally created, real money (income) derives from production, which is why credit must be backed by a financial intermediation instead of being wrongly identified with money creation. Keynes’s monetary theory of production further contributed to improve monetary analysis, while bankers should be acknowledged the merit of radically ameliorating the workings of the monetary system by implementing an inter-bank clearing structure to settle inter-bank payments.

The monetarist approach to monetary policy is inadequate to deal with monetary disorders. A rigorous analysis of the way money is issued by banks and associated to physical output through production shows, in fact, that Friedman’s microeconomic conception of money and of the way it interacts with the real world is highly unrealistic and misleading. By defining money as a positive asset, Friedman misses the distinction between money and income and fails to grasp the monetary nature of economic production. It thus follows that the price stability advocated by Friedman is neither a necessary nor a desirable requirement of economic growth. What really matters is not to grant only ‘a limited amount of flexibility in prices and wages’ by controlling the money supply, but to provide a sound monetary structure in which money plays its role in conformity with its own (banking) nature. At a national level, monetary disorders can be properly eradicated only through a reform of the banking system based on the structural distinction between monetary, financial, and fixed capital departments.