Is money a conserved quantity?

Question

Excuse the naïve question, but I have a rather limited understanding of economics, and this question has been bothering me since my school economics teacher couldn't answer it satisfactorily many years ago. It is also a question that is a prerequisite to many others I have.

Is money a conserved quantity, in the same sense as we have conserved quantities in physics (e.g. energy)?

In daily transactions that I have experience with, it obviously is. If I buy something from Joe, and give him \$10, I will have \$10 less and he will have \$10 more. But the total amount we have together has not changed.

Does this apply to all transactions? If not, when is it violated? In what situations is money created, and when does it disappear (other than physically destroying paper based money)?

This then leads to a closely related question: Where can I find out how much is there of a given currency? How much USD exists in total, if we combine the dollars owned by everyone in the world?

If this question is considered too basic, I would appreciate suggestion about where a mathematically minded person might read up on this topic.

Answer 1

Νominal money could be seen as a "conserved quantity" in a similar/analogous sense that we have in physics, under some qualifications and restrictions.

I stress that we are talking about the nominal value of money, which is an indisputable quantity and legal tender (the concept of "real" value is an estimated value and hence subject to disagreements etc.)

Then if we exclude
1) The central bank/government with the authority of the law
2) The commercial banking system as regards Transactions that have to do with taking or repaying loans
3) Actions that just destroy the physical carrier (say, burn the paper bill)

...then transactions do not alter the amount of nominal money, and in that sense, the nominal value/amount of money is conserved.

We exclude 1) because the central bank / government have the power by law to create new money (and destroy existing money, for example "cutting zeros" after a hyperinflation episode).

We exclude 2) because commercial banks create money under the "fractional reserve banking" system, while money is destroyed whenever a loan is repaid (the part that has to do with the principal, not the interest). The OP should ask a different question if the OP wants to know about that.

We exclude 3) because we can argue that these are not "normal economic transactions".

So the system in which nominal money can be considered a "conserved quantity" is a subset of a real world economic system.

Answer 2

Is money a conserved quantity, in the same sense as we have conserved quantities in physics (e.g. energy)?

It should be noted that "money" has a technical definition in economics. There are different definitions of money supply (often with labels like M0, M1, M2, M3) that include different instruments.

One important component of the money supply is "currency in circulation" (such as dollar bills and coins). As you observed in your question, most transactions in currency will result in the amount of currency being unchanged: when I hand someone a 10 dollar bill, the amount of 10 dollar bills in circulation is unchanged. From the perspective of individuals, we have to do something silly, like light cigars with \$50 bills, to reduce the amount of money in circulation.

However, the amount of currency in circulation changes. Banks receive currency from the central bank (and distribute it to their clients), and also return currency (such as worn out bills) to the same place. The banks exchange other components of the money supply (as discussed next) to get currency from the central bank.

The next major component of money supply definitions is deposits at banks. (This includes deposits at the central bank, which are called reserves in the United States.) Once again, people can have transactions that shuffle amounts of money between bank accounts, leaving the amount unchanged.

Does this apply to all transactions? If not, when is it violated? In what situations is money created, and when does it disappear (other than physically destroying paper based money)?

Turning to bank deposits, they are created by the act of bank lending. This is discussed in this article from Bank of England researchers.

Therefore, the amount of (bank) money goes up and down with the amount of loans outstanding, which varies across the cycle.

This then leads to a closely related question: Where can I find out how much is there of a given currency? How much USD exists in total, if we combine the dollars owned by everyone in the world?

Central banks generally publish statistics with money supply numbers, with the various components.

The St. Louis Federal Reserve has a statistical page called FRED. This is a link to the series for monetary aggregates (over 1000 series!)

Since it may be difficult to browse all of those series, you could look at the H.6 Release link to latest release, which lists the components of the money supply, and their values.

If this question is considered too basic, I would appreciate suggestion about where a mathematically minded person might read up on this topic.

As you can see, the amount of money changes as a result of some transactions. However, there are some accounting laws that do limit the relationships between monetary values in economies: accounting identities. These relationships are weaker than energy conservation laws, but they do limit what outcomes are possible.

For example, if we use simplified national accounting, the government deficit during a year will equal the increase in the amount of government-issued money and debt (bonds and bills). This has to hold, as otherwise someone has made an accounting error. (Once again, there are complicating factors in the real world, which will add more terms to the accounting identity.) An interesting accounting identity is the relationship S=I (national savings = national investment); link to a question related to that identity.

There is a non-mainstream school of thought within economics that uses what are called "stock-flow consistent models" (or SFC models), that underline the importance of accounting identities in framing models. I was trained as an applied mathematician, and I found the book "Monetary Economics: An Integrated Approach to Credit, Money, Income, Production, and Wealth" to be the introduction that best suited my background. There is an excellent treatment of all of these accounting issues.

Answer 3

Answer: no.

In our fractional reserve monetary system, money (in particular in the form of demand deposits) is being created and destroyed all the time. It is created when loans are made by commercial banks and destroyed when the principal on those loans is repaid.

Re: "In daily transactions that I have experience with, it obviously is. If I buy something from Joe, and give him \$10 dollars, I will have \$10 less and he will have \$10 more. But the total amount we have together has not changed." - indeed true. It would only not be true if you borrowed the \$10, from a bank in which case a fresh \$10 will have come into existence at that moment.

Re: "when does it disappear"... if you had previously borrowed \$100 form a bank and you now repay them that \$100, that money disappears out of existence. If you had additionally to give them say \$5 of interest for that loan, then that $5 does not disappear - the bank gets to keep it.

With regard the total quantity - that question is complicated by the fact that there are a variety of forms of money. I'm afraid that's a bit of a minefield. But that is just the kind of data that is published in FRED.

Answer 4

I guess that, if you have a rather limited understanding of economics, what you need is getting some intuitions.

Also, in this first part, I only deal with commercial banks. Note however, that only commercial banks create money while central banks emit/issue money (more about this difference in the last part). But how does creation of money work, is this creation real in the physical sense ?

Say I have a bike (money) and because I am not using it, I park it somewhere (commercial bank) someone can borrow it. However, if I need my bike, it must be where I left it. This is what the liquidity risk is about. In this case my bicycle is a conserved quantity, and the "parker" (banker) has a book, in which she writes that she has my bicycle:

bike1 ............................................ date-infos-etc

Thus the parker lends my bike and hopes that I am not about to come back to use it. But the borrower will also have to park the bike somewhere, because she will not use it permanently. And she parks it in the same parking. So the parker henceforth has what follows written in her book

bike1 ............................................ name1-date1-infos1-etc1

bike1'............................................ name2-date2-infos2-etc2

So the second bike, i.e. bike1' (actually the same as bike1), is scriptural. Thus quantities are scripturally not conserved.

But the effects on economic activities is anything but scriptural: me, I still enjoy the fact of having this bike, in term of solvency and so on. The borrower can use this bike to go faster (leverage effect to increase her income) than before.

When the borrower does not need the bike anymore, she informs the parker, who erases the second line in her book, which destroys the scruptural bike refered to as bike1'.

Thus money is an object whose quantity is conserved, but an object that commercial banks can duplicate/create scripturally until the liquidity risk becomes unbearable, i.e., until the probability that everybody wants to use the scriptural money at the same time becomes to high, which would be equivalent to the so-called bank run.

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Following @Anasta's comments

To address the first comment. Creation of money by commercial banks is what I describe above. Briefly but strictly speaking, emission is the physical increase of money supply and this is the exclusive prerogative of Central Banks. Creation of money (thus what I am talking about in the first part of my answer), consists of duplicating scripturally this supplied money.

To address the second comment. In practice, the risk of liquidity is (semi-) unobservable, and cannot be managed perfectly. That is why there are standards on banks' minimum capital ratios: using my simplifying/intuiting example above, this capital ratio would be something like [ the amount associated to the first line written in the book ] divided by [ the total written amount (corresponding to the sum of all amounts reported in the book) ]. Also, as just outlined, the first asset (bike) is actually owned by the shareholders of the bank, which subsequently shifts the liquidity risk from the first line to the following lines. But theoretically, the process of scriptural creation can be infinite as soon as the book (above) contains one line (shareholders' equity), used to generate a second one, which could in turn be used to generate a third one, and so on. Indeed the capital ratio can converge asymptotically towards $0$. Theoretically (i.e. if the liquidity risk is perfectly managed) there is no hard constraint. Finally on this point, the constraint is only regulatory, and without it, banks would have the right to rush, soon or later, headlong into disaster. And as you mention, this minimum capital ratio is subjectively determined, and we should expect it to be upward pressured as centuries goes by.

To address the third comment. Printed money is nothing more than the emanation of a record, written somewhere. This is even more visible when you use your credit card: does the amount you type when buying something on internet have any sort of physical representation ? Physically not but scripturally it does. And, actually, if you were under the impression that there is no detectable difference between these two kinds of money (bikes), this is because the the "first" bike is also borrowed from someone else.

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To go further

But who is the first/primordial lender ? First of all, note that it is impossible to go further without clearing up the prevailing confusion regarding the two following terms: creation versus emission, since expressed as such, the two underlying notions are incompletely rendered for people. Strictly speaking creation in the economical sense means scriptural creation -- and this is the core subject of my answer --, while emission in the economical sense means ex nihilo creation of central bank money in the common sense. So, as you can see, these two terms are deceptive cognates of their everyday-life usage.

Briefly (and still giving some intuitions), the first lender, historically, is a central-bank-like institution. And this institution, when printing money, appears as doing it ex nihilo. But in reality, these institutions turn human conceptions/psychology/beliefs into value. So saying that this generation of value is done ex nihilo is not correct strictly thinking. A (caricatured but not so far from reality) example is:

On the one hand, assume the existence of a country whose name is Gouzlouk. This nation has no installed capital, no infrastructure, no army, no productive system, no school, no no.

On the other hand, assume the existence of a country whose name is ASUK. This nation has a highly capitalized economic system, gold reserves, a powerful army, a highly productive system which produces things that everybody wants, and, specially, a currency that many other nations use as unit of value of their own monetary system.

It is obvious that, if Gouzlouk nation prints money from what is said to be nothing, it will really be nihilo, since nobody in the world economy will buy what they produce, since they produce nothing, and even if they produce something and sell it in their own currency, nobody will wants to buy their production since they would first have to buy Gouzlouk's currency, which even if almost free, gives access to nothing desirable. A contrario, if ASUK nation prints money, it won't be ex nihilo at all ! And given that every nation in the world have their pockets full of ASUK's currency, which gives access to anything you want, they will have no interest to undermine it. Furthermore ASUK's army owns missiles everywhere and the nation is headed by a trigger man.

Pablo Picasso was often found drawing on the paper tablecloths at his favorite restaurants. Restaurateurs would often ask him to leave the drawings instead of paying the bill.

Picasso was a central bank of his own.

Answer 5

No, because money can be destroyed and counterfeited. For example, I have a shop, and you buy something from me. I could burn the money. The number of goods have not changed, but money has. Similarly, evildoers can counterfait money, adding it to circulation, without changing the amount of goods available in the economy.

Answer 6

The general balance equation is the proper context for answering the question of whether money is or is not a conserved quantity in the same sense as a physical quantity.

https://chemeng.queensu.ca/courses/CHEE221/files/Week%207%202014.pdf

The question is whether money is conserved in the same sense as a physical quantity. Note first there is no natural or moral law which specifies conservation of money. Money in the form of elastic bank deposits is generated by social customs known as debtor-creditor relations. The bank issues new money, an increase in the elastic money supply, and takes a loan note which is the promise to repay money in the future. When the loan is repaid the bank reduces (consumes) money that had previously been generated in the elastic money supply. There is no physical or natural law or rule which specifies how society must generate, consume, or conserve money during transactions. Natural laws, by contrast, always hold that certain quantities are conserved during every physical process.

Conservation laws are natural laws, which are statements in classical physics, which specify conservation of electric charge, mass, momentum (linear and angular), and energy. These laws state in general that the total quantity of electric charge, mass, momentum, or energy remains constant during a physical process, where a physical process is a natural interaction between a system and its surroundings.

The General Balance Equation is given as:

Accumulation = (Generation - Consumption) + (Input - Output)

where accumulation in the system at the end of a process is the quantity generated minus the quantity consumed plus the transfer as input across the boundary minus the transfer as output across the boundary. The conserved quantities in physics are not transformed via a process of generation or consumption so these terms are zero for the quantities designated electric charge, mass, momentum, and energy.

Balance equation for a Conserved Physical Quantity:

Accumulation in System = Input - Output

where there is the possibility of either transport or transfer of the physical quantity across the boundary during a natural process and the total amount of quantity in the system and the surroundings must remain constant during the process. The numbers we assign to these quantities are arbitrary but whatever number gets assigned for example the energy states then energy must be conserved or remain constant as measured in the system and its surroundings. Therefore the net accumulation of the system is a loss in the surroundings.

Money is a human accounting record and there is no natural unit of money. There are no money units in the laws of nature. This means we discount nature to transform resources to human use and we generate money before it can be "conserved" or transfer ownership during a transaction. This is true whether gold or silver or paper notes or bank records are evidence of the money unit which is just a name and symbol. So money is not conserved in the same sense as a physical quantity. However money as a moral accounting record may be conserved, that is, neither generated nor consumed during a social custom, in a transaction where title to previously existing money transfers from one party to another.