# John Stuart Mill and the Quantity Theory of Money

Mostly for aficionados of the finer points of economics and its history. From John Stuart Mill’s Principles:

If we assume the quantity of goods on sale, and the number of times those goods are resold, to be fixed quantities, the value of money will depend upon its quantity, together with the average number of times that each piece changes hands in the process . The whole of the goods sold (counting each resale of the same goods as so much added to the goods) have been exchanged for the whole of the money, multiplied by the number of purchases made on the average by each piece. Consequently, the amount of goods and of transactions being the same, the value of money is inversely as its quantity multiplied by what is called the rapidity of circulation. And the quantity of money in circulation [M] is equal to the money value of all the goods sold [PQ], divided by the number which expresses the rapidity of circulation [V]. (Mill [1848] 1871: 494 – letters in parentheses inserted into the text)

As an equation:

M = PQ/V

Or as more commonly stated:

MV = PQ

Following that para are a number of considerations that help make additional sense of the point and also make it more comprehensible in relation to the operation of an economy.

This entry was posted in Classical Economics. Bookmark the permalink.

### 50 Responses to John Stuart Mill and the Quantity Theory of Money

1. Arky

If we assume the quantity of goods on sale, and the number of times those goods are resold, to be fixed quantities

..
That’s stupid.
It isn’t ever a fixed quantity.

2. Bruce of Newcastle

M = amount of money in a bucket of money
P = no. of politicians
V = average velocity of a politician towards a bucket of money
Q = quantity of votes they risk losing by taking the bucket of money

3. Arky

This post encompasses simultaneously the two stupidest fields in human endeavour: economics and libertarianism.

4. 2dogs

Since the GFC, it’s really hard to know what M actually is, given how much the balance sheets of the central banks have expanded.

5. Arky

So this evolved into:
MV=PT
where:
M=Money Supply
V=Velocity of Circulation
P=Average Price Level
T=Volume of Transactions of Goods and Services

6. Arky

What happens when people start buying shitloads of stuff with various cryptos?

7. Entropy

Sinc writes another paper about how crypto is the future.

8. Dogs

M is what it’s always been and will continue to be irrespective of their balance sheets’ size.

9. Frank Walker from National Tiles

Sinc writes another paper about how crypto is the future.

An interesting theory put out there by BTC spruikers: it may be undergoing it’s own “Nixon Shock”.

What happens when people start buying shitloads of stuff with various cryptos?

To what? With cards like TenX and CoinJar, you can use crypto like cash. I’m not sure there will be any change fundamentally different to the bank deposit base shrinking and also stabilising monetary growth, deflated by output growth.

Arky
#3142127, posted on August 27, 2019 at 6:09 pm

This post encompasses simultaneously the two stupidest fields in human endeavour: economics and libertarianism.

I can’t help that you love government gibs and you are a low achiever.

10. Fat Tony

Arky
#3142127, posted on August 27, 2019 at 6:09 pm
This post encompasses simultaneously the two stupidest fields in human endeavour: economics and libertarianism.

Arky – add the third stupidest – doing up old cars to original condition.
You shoulda made up a spaceframe with a big blown V8 and grafted the panels onto it.

How’s that going? I’ve only been on here a bit occasionally for the last few months – working – so I’ve missed any updates.

I agree though – if economics was any good, the world’s economy would be going great.

11. Arky

and you are a low achiever.

..
I would achieve more but it would cut into my rest.

12. Put simply, if you increase the quantity of money (M) buy just printing the stuff, then ipso facto you inflate the value of products (PQ).
See Venezuela, Zimbabwe et al.

13. Arky

You shoulda made up a spaceframe with a big blown V8 and grafted the panels onto it.

..
Noooooooooooooo.

14. Arky

then ipso facto you inflate the value of products (PQ).

..
You ignored V.
There has to be a panic factor of people wanting rid of money for goods.

15. Frank Walker from National Tiles

Get back on the car stuff. Great to watch.

16. Arky

No.
Wrong.
I have mixed V up with T?

17. Arky

Stop being a prick and define V, Dot.

18. Frank Walker from National Tiles

The velocity of money. You were correct. It is the measure of transactions made.

I think you mixed up Q and T, BTW.

19. Arky

What is the Velocity of Money
The velocity of money is the rate at which money is exchanged in an economy. It is the number of times that money moves from one transaction to another. It also refers to how much a unit of currency is used in a given period of time. Simply put, it’s the rate at which people spend money. The velocity of money is usually measured as a ratio of gross national product (GNP) to a country’s total supply of money.
– Investopedia.

20. Here you go. Steve Kates would be interested in this.

Richard D. Wolff is Professor of Economics Emeritus, University of Massachusetts, Amherst where he taught economics from 1973 to 2008. He is currently a Visiting Professor in the Graduate Program in International Affairs of the New School University, New York City.
Earlier he taught economics at Yale University (1967-1969) and at the City College of the City University of New York (1969-1973). In 1994, he was a Visiting Professor of Economics at the University of Paris (France), I (Sorbonne)…

BA in History from Harvard College (1963);
MA in Economics from Stanford University (1964);
MA in History from Yale University (1967); and a
PhD in Economics from Yale University (1969)

Wow! Look how long he’s spent in classrooms.
And what does this “perfesser” have to say?

Redistribution tears societies apart, it’s— here’s the parallel: you’re going into the park on a Sunday afternoon, you’re a married couple, you have two children. One is six and one is seven, and you stop because there’s [a] man selling ice cream cones. And you give one of your children an ice cream cone, it’s got four scoops. And the other one, an ice cream cone with one scoop. And you continue walking. Those children are going to murder each other. They’re gonna struggle. What are you doing? And don’t then come up — ‘okay, you’ve had — you’ve eaten this part of your scoop, so give the other part of your scoop to your sister, or your brother,’ — stop. The resentment of the one who hose [???] his ice cream or her ice cream — you see where I’m going?

Yeah yeah, we see where you’re going you commie bastard.

https://www.thenewneo.com/2019/08/24/a-sample-of-utopian-leftist-thought-today-part-ii-richard-d-wolff-and-the-ice-cream-cones/

21. Arky

I need to think further on this.

06/26/2017Frank Shostak
For most financial commentators an important factor that either reinforces or weakens the effect of changes in money supply on economic activity and prices is a velocity of money.

It is alleged that when the velocity of money rises, all other thing being equal, the buying power of money declines (i.e., the prices of goods and services rise). The opposite occurs when velocity declines.

If, for example, it was found that the quantity of money had increased by 10% in a given year, — while the price level as measured by the consumer price index has remained unchanged — it would mean that there must have been a slowing down of about 10% in the velocity of circulation.

The mainstream view of money velocity
According to popular thinking the idea of velocity is straightforward. It is held that over any interval of time, such as a year, a given amount of money can be used again and again to finance people’s purchases of goods and services. The money one person spends for goods and services at any given moment can be used later by the recipient of that money to purchase yet other goods and services.

For example, during a year a particular ten-dollar bill might have been used as following: a baker John pays the ten-dollars to a tomato farmer, George. The tomato farmer uses the ten-dollar bill to buy potatoes from Bob who uses the ten dollar bill to buy sugar from Tom. The ten-dollars here served in three transactions. This means that the ten-dollar bill was used 3 times during the year, its velocity is therefore 3.

A \$10 bill, which is circulating with a velocity of ‘3’ financed \$30 worth of transactions in that year. Consequently, if there are \$3000 billion worth of transactions in an economy during a particular year and there is an average money stock of \$500 billion during that year, then each dollar of money is used on average 6 times during the year (since 6*\$500 billion =\$3000).

The \$500 billion of money is boosted by means of a velocity factor to become effectively \$3000 billion. From this it is established that

Velocity = Value of transactions / supply of money

This expression can be summarized as

V = P*T/M

Where V stands for velocity, P stands for average prices, T stands for volume of transactions and M stands for the supply of money. This expression can be further rearranged by multiplying both sides of the equation by M. This in turn will give the famous equation of exchange

M*V = P*T

This equation states that money times velocity equals value of transactions. Many economists employ GDP instead of P*T thereby concluding that

M*V = GDP = P*(real GDP)

The equation of exchange appears to offer a wealth of information regarding the state of the economy. For instance, if one were to assume a stable velocity, then for a given stock of money one can establish the value of GDP. Furthermore, information regarding the average price or the price level allows economists to establish the state of real output and its rate of growth.

Most economists take the equation of exchange very seriously. The debates that economists have are predominantly with respect to the stability of velocity. Thus if velocity is stable then money becomes a very powerful tool in tracking the economy. The importance of money as an economic indicator however diminishes once velocity becomes less stable and hence less predictable. It is held an unstable velocity implies an unstable demand for money, which makes it so much harder for the central bank to navigate the economy along the path of economic stability.

Why velocity has nothing to do with the purchasing power of money
But does velocity have anything to do with the prices of goods? Prices are the outcome of individuals’ purposeful actions. Thus the baker John believes that he will raise his living standard by exchanging his ten loaves of bread for \$10 which will enable him to purchase five kg of potatoes from Bob the potato farmer. Likewise, Bob has concluded that by means of \$10 he will be able to secure the purchase of ten kg of sugar, which he believes will raise his living standard.

By entering an exchange, both John and Bob are able to realize their goals and thus promote their respective well-being. John had agreed that it is a good deal to exchange 10 loaves of bread for \$10 for it will enable him to procure 5kg of potatoes. Likewise Bob had concluded that \$10 for his 5kg of potatoes is a good price for it will enable him to secure 10kg of sugar. Observe that price is the outcome of different ends, and hence the different importance that both parties to a trade assign to means.

It is individuals’ purposeful actions that determine the prices of goods and not some mythical velocity.

Indeed, according to Mises in Human Action, the whole concept of velocity is hollow;

In analyzing the equation of exchange one assumes that one of its elements — total supply of money, volume of trade, velocity of circulation — changes, without asking how such changes occur. It is not recognized that changes in these magnitudes do not emerge in the Volkswirtschaft [political economy, or more loosely‘economy’] as such, but in the individual actors’ conditions, and that it is the interplay of the reactions of these actors that results in alterations of the price structure. The mathematical economists refuse to start from the various individuals’ demand for and supply of money. They introduce instead the spurious notion of velocity of circulation fashioned according to the patterns of mechanics.

Furthermore, money never circulates as such;

Money can be in the process of transportation, it can travel in trains, ships, or planes from one place to another. But it is in this case, too, always subject to somebody’s control, is somebody’s property.

Consequently, the fact that so-called velocity is ‘3’ or any other number has nothing to do with average prices and the average purchasing power of money as such. Moreover, the average purchasing power of money cannot even be established. For instance, in a transaction the price of one dollar was established as one loaf of bread. In another transaction the price of one dollar was established as 0.5kg of potatoes, while in the third transaction the price is one kg of sugar. Observe that since bread, potatoes and sugar are not commensurable no average price of money can be established.

Now, if the average price of money can’t be established it means that the average price of goods can’t be established either. Consequently, the entire equation of exchange falls apart. Conceptually the whole thing is not a tenable proposition and covering a fallacy in mathematical clothing cannot make it less fallacious.

According to Rothbard in Man, Economy, and State:

The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. Mathematics can at best only translate our previous knowledge into relatively unintelligible form.

Even if we were to accept that the essential service of money is its speed of circulation there is no way that this characteristic of money could explain the purchasing power of money. On this Mises explains in Human Action:

Even if this were true, it would still be faulty to explain the purchasing power — the price — of the monetary unit on the basis of its services. The services rendered by water, whisky, and coffee do not explain the prices paid for these things. What they explain is only why people, as far as they recognize these services, under certain further conditions demand definite quantities of these things.

22. You ignored V.
There has to be a panic factor of people wanting rid of money for goods.

That’s not how equations work. There are things called constants.
There doesn’t have to be an increase or decrease in the velocity of money. Just print ink on paper and inject into the economy, get inflation.
But this does have knock on effects (positive feedback loop).
The effect is that of INCREASING the velocity of money. People tend to spend ASAP when inflation is high.
Therefore……if you increase M artificially, you also inevitably increase V after inflation has already appeared, making it a double whammy on PQ.

23. Arky

That’s not how equations work. There are things called constants.

..
That seems to be the point in debate. Whether it is valid to assume that the V and the T are constant.

24. The Pugilist

Baa Humbug, don’t get an identity confused with an equation. The MV=PT is an identity and therefore is always and everywhere true but tells nothing about behavioural relationships.

25. That seems to be the point in debate. Whether it is valid to assume that the V and the T are constant.

No no, they don’t have to be constants Arky. But for the sake of answering the question “what happens if governments just print money?”, the equation says inflation must result. It’s a given.

As far as V is concerned, think of it this way. If people horde their money under a mattress (slow V), then traders need to coax them into spending that money. Usually some sort of offers and or discounts. DEFLATION.
If however people are spending like drunken sailors (fast V) as happens during a gold rush, then traders KNOW they’ll get more for their goods and services. They raise prices…inflation.

26. Arky

But this does have knock on effects (positive feedback loop).
The effect is that of INCREASING the velocity of money. People tend to spend ASAP when inflation is high.

..
That sounds right to me.
Also that there would be a lag effect.
I still think the driving force for all of it is demographics.
And in a lot of ways predetermined by very long term changes in populations on a generational basis.
You may think that a central bank doing x or y has some effect on prices, but I put it to you that the decisions they make are from a limited number of possible actions in response to demographically driven changes and are therefore mostly inevitable.

27. The Pugilist

V is related to the demand for money. M is the (in our case, central bank determined) supply of money. Butbthere is nothing in the identity that illuminates us on how M or V is determined. And whether P (ie average price) exists is another matter. The concept of an average price makes about as much sense as a global average temperature.

28. The Pugilist

As far as V is concerned, think of it this way. If people horde their money under a mattress (slow V), then traders need to coax them into spending that money

A low (high) V represents an increase (decrease) in the demand for money. Because money affects virtually every market, an increase in demand for money, corresponds to a relative decrease in demand for all other transactions. Also, ‘transactions’ should.include assets as well as goods and services.

29. The Pugilist

And in a lot of ways predetermined by very long term changes in populations on a generational basis.

Yes, desire to save versus borrow changes throughout your lifetime. But using the broad definition of transactions, an increase in the money supply, which lowers the price of money (interest rates), leads people to rid themselves of that excess supply of money. We see people borrowing more to buy goods, services and assets, companies pay out more dividends, etc.
It is all much easier to understand if you think about demand for, and supply of, money rather than macroeconomic voodoo aggregates, like velocity or the average price. That is the point Mises was making.

30. The Pugilist

In essence, my suggestion is to think about monetary economics in terms of real, tangible, observable quantities, like interest rates, the supply of money, quantities and prices of goods/services/assets bought and sold.
Velocity of circulation and the average price are abstract at best

31. Arky

A low (high) V represents an increase (decrease) in the demand for money. Because money affects virtually every market, an increase in demand for money, corresponds to a relative decrease in demand for all other transactions. Also, ‘transactions’ should.include assets as well as goods and services.

..
Interesting.
Thank you Pugilist.

32. Fat Tony

My money has a velocity (V) of c
And that speed is constant. V = c

(c = speed of light)

33. Frank Walker from National Tiles

Whether it is valid to assume that the V and the T are constant.

Velocity certainly can vary. There is no reason to assume it is constant. The volatility of velocity is why monetarism before inflation targeting *failed*. It only targeted Q, roughly speaking.

PS

Good explanations Pgulist.

PPS

Arky

You are on the right path. You’re also figuring this out on your own and I reckon you’re getting it. This is a big compliment because heaps of people do not understand this at all.

34. The Pugilist

My pleasure Arky. I should add that the definition of ‘money’ vs ‘assets’ is a real complication. As an example, in my view, Bitcoin and other cryptocurrencies are essentially ‘money’ but the ATO defines it as an asset. That means you have pay capital gains tax on the change in value, which is a deliberate attempt to invalidate its use as money and keep us all using fiat currency. And when I say currency, I mean an ever increasing share of our balances spent through electronic payment systems.

35. Frank Walker from National Tiles

Money is, ‘the most sought after commodity’. What is money can only ever be defined at a static point in time. It might/can change dynamically.

36. The Pugilist

Agreed Frank. And there can be more than one type of money present in an economy. Of course, governments as monopoly issuers of a currency will always try to force out alternatives. Forcing citizens to pay their taxes in their own monopoly issued currency is the bedrock of so-called ‘modern’ monetary theory

37. Arky

Thanks Frank.

38. Rex Mango

How did JS Mill go at the races?

39. an increase in demand for money, corresponds to a relative decrease in demand for all other transactions.

That of course would assume a recession or a crisis.

————–

On a related topic.

The Bank of Japan owns about 50% of the government bond issuance. The ECB, about 30%. I would argue the debt could literally be expunged… eliminated. This would apply more so in Japan, which is a unitary political system.. more so than the EU.

The market has essentially accepted currency issuance which is perpetual in place of debt. The bonds on the BOJ’s account could simply be retired.

40. The problem, as I see it is that the BOJ’s balance sheet, is well, a balance sheet and it is supposed to balance. If the government retired the debt, which is the asset side, it would have to be replaced with something in order to balance. Perhaps the government could simply issue perpetual bonds at zero interest, or plug the hole with a large equity infusion. I have to really think about this though as I’m not sure.

If the government posts equity in place of the retiring bonds, it wouldn’t impact the markets with a massive infusion of currency as it would never leave the BOJ’s books. It would simply be a book entry.

The point is that the markets have allowed the BOJ to increase the money supply without the action impacting with hyper-inflation because no one believes the BOJ would allow high inflation. This indicates massive.. absolutely massive confidence in the central bank.

And there a people here telling what a sinister thing it is even though markets are perfectly fine with it. Large Western central banks are hugely influential and trusted. It’s really incredible.

41. The Pugilist

That of course would assume a recession or a crisis.

Not necessarily. Depends on how large the increase was, how temporary it was and what caused it. Sure, a large, persistent spike would imply a recession. But a sharp change in the demand for money does not just come out of thin air. It has to be caused by something, hence the reason it was often thought of as an intensifying factor but never the direct cause of a downturn.

42. The Pugilist

If the government posts equity in place of the retiring bonds, it wouldn’t impact the markets with a massive infusion of currency as it would never leave the BOJ’s books. It would simply be a book entry.

This is true, but then what happens to liquidity, prices and yields in the bond market?

43. but then what happens to liquidity, prices and yields in the bond market?

P, for all intents those bonds are out of the market. Sure, the market expects the equivalent to make its way back, but the adjustment wouldn’t be problematic because those assets wouldn’t have to be repriced. The only problem, as I see it would be that if was a permanent expungement, perhaps the market would not be so agreeable if the CB tried QE later on. People would see the additional increase in the money supply as permanent and not temporary ( which is how QE is looked at/sold now). A permanent increase may not be treated so benignly.

44. Pyrmonter

Why money, and not the sum of the total amount of credit extended? Few transactions settle in cash: why is M relevant?

45. Mark A

I wonder, was it possible to have a GFC before the markets and derivatives and money an such?
And did the ancient peeps have central banks, and how on earth did they manage their wealth without banks and super funds?

All too confusing.

46. Mark A

Also, how did the useless parasites and layabouts who exploit the system now make their fortunes?
For I’m sure they were about even in those times.

47. JC
#3142311, posted on August 27, 2019 at 10:25 pm

The problem, as I see it is that the BOJ’s balance sheet, is well, a balance sheet and it is supposed to balance. If the government retired the debt, which is the asset side, it would have to be replaced with something in order to balance. Perhaps the government could simply issue perpetual bonds at zero interest, or plug the hole with a large equity infusion. I have to really think about this though as I’m not sure.

I once read a boffin say why not just mint \$Trillion coin or two and keep it at the Central Bank vault and voila’, you have your books “balanced.”

They’re piss farting around too much with currencies. Once these blockchain type things take a solid hold (they’re doing a fine job at mo), these dick heads are going to burn everyone.

48. Colonel Crispin Berka

Last minute question for anyone still lurking.
If the V has increased, you can decrease the M without any reduction to the sum of products P x Q.
Is this equation the macro-economic justification for the ATO’s war on the \$100 note?

49. The Pugilist

If the V has increased, you can decrease the M without any reduction to the sum of products P x Q.

That is fundamentally true because it is an identity. But it doesn’t help much because V is an unobservable, theoretical construct. You certainly can’t observe it in real time, so you can’t change the money supply quickly enough to bompensate for movements in V. As I outlined earlier, movements in V are a function of other things – essentially anything that affects the demand for money.

Is this equation the macro-economic justification for the ATO’s war on the \$100 note?

I think that is more an attempt to shift more and more transactions into (teachable and therefore more easily taxed) electronic payment systems. It is being done under the pretext of stopping criminal transactions.

50. max

Copernicus also became the first person to set forth clearly the “quantity theory of money,” the theory that prices vary directly with the supply of money in the society. He did so 30 years before Azpilcueta Navarrus, and without the stimulus of an inflationary influx of specie from the New World to stimulate his thinking on the subject. Copernicus was still being a theorist par excellence. The causal chain began with debasement, which raised the quantity of the money supply, which in turn raised prices. The supply of money, he pointed out, is the major determinant of prices. “We in our sluggishness,” he maintained, “do not realize that the dearness of everything is the result of the cheapness of money. For prices increase and decrease according to the condition of the money.”

“An excessive quantity of money,” he opined, “should be avoided.”

https://mises.org/library/copernicus-and-quantity-theory-money

This site uses Akismet to reduce spam. Learn how your comment data is processed.