Talk:Quantity theory of money

Restructuring

I've restructured the article significantly. I am still not comfortable with it in-so-far as it presents a Friedmanite theory as the modern quantity theory, and in-so-far as the “Principles” subsection over-simplifies even that Friedmanite take. Also, I have not really gone over the criticism section, to ensure that it is logically well-grouped. Glancing at it, it seems to be padded by inefficiencies. —SlamDiego 16:31, 19 February 2007 (UTC)

a rudimentary theory

$P={\frac {M\cdot V}{Q}}$

If $V$ and $Q$ were constant, then:

$\Delta P=\Delta M\,$

Can this be correct? If it is, can it be better explained? As calculus, it's not true. It would be true if dP and dM were expressed as percentages ie dP/P = dM/M. I'll add a note or make a change if no one disagrees. JBel 22:53, 8 April 2007 (UTC)

Good catch! —SlamDiego 04:15, 11 April 2007 (UTC)

Yes. It's correct if one held velocity and output constant, but holding output constant when M changes is not an assumption Monetarists hold or would be willing to defend.

When we differentiate the quantity equation with respect to time t and held velocity constant, we get:

${\frac {dP/dt}{P}}={\frac {dM/dt}{M}}-{\frac {dY/dt}{Y}}$

Multiplying both sides by dt will yield a familiar equation:

${\frac {dP}{P}}={\frac {dM}{M}}-{\frac {dY}{Y}}$

Or:

$\pi _{t}=g_{t}^{M}-g_{t}^{Y}$

As Milton Friedman put it in 1970:

"...inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output." Viespe0 (talk) 23:37, 8 December 2024 (UTC)

inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output. This is too reductive. A big part of, e.g. hyperinflation is not just an increase in the amount of money (the quantity), but also in the velocity of money, because of inflationary expectations, which cause people to buy more instantly and save less, so more money is in circulation. TucanHolmes (talk) 16:23, 9 December 2024 (UTC)

Exactly If people anticipate prices to increase significantly then they will buy now rather than later. While velocity exists in the equations I presented, the velocity of money is treated as constant because velocity is assumed to be relatively stable and predictable — an assumption that was challenged as the velocity of money has been generally volatile and unpredictable. Monetarists could not explain this so their approaches were abandoned in the 1900s-2000s. Viespe0 (talk) 17:46, 19 December 2024 (UTC)

Confusing article

The criticism section needs some editing. Several different criticisms are all written together in one paragraph, and they are not clear to begin with. Also there should be an explanation of the difference between the old quantity theory of money and the modern one pionered by Milton Friedman.

How's this for a leftist slant: "For instance recent disinflation is less due to monetarist policies than to free trade and anti labor policies which boost profits while depriving labor of their pricing power."

Also the criticism section seems to mostly address Friedmenesque monetarism and/or money supply targeting by central banks rather then the Quantity Theory per se. It's perfectly feasible for someone to believe in the Quantity Theory but oppose monetarism. I tried to clean it up a bit, but it could definetly use a re-write.radek 21:06, 11 April 2007 (UTC)

Please don't place comment sections out of order!

Anyway, yeah, there's plent of room for improvement. Note my comment on restructuring above. Things used to be worse. —SlamDiego 21:12, 11 April 2007 (UTC)

I don t see any leftist slant, in the sentence you comment (and I wrote) it is a rather objective one. the money supply has barely changed, M3 continues to rise some 8-10% each year passing in Europe and USA (and that does not change if you take M1, M2 or any agregate), yet consumption goods prices used to grow some 6-10% before 1980 and rise now some 2-4%. Disinflation hence has nothing to do with monetary policies and all to do with anti labor policies. Inflation has simply be redirected from inflation in consumption goods prices to inflation in capital goods prices (see how housing and stocks have risen way beyond their fundamental value) Panache 11:34, 7 June 2007 (UTC) I edited the critics section, it now follows the 5 hypotheses above. I just had trouble developping the source of demand for money. the part written about stocks seemed counter intuitive to me (when stocks increase demand for money increase so one should expect deflation all things being equal, but usually when that happens theres is inflation, as production is forced to increase, and when they unload stocks in fact it creates deflation because more goods come in the market, producers are driven into bankrupcies etc. So its not a good line of critic and if anyone has another idea about the demand for money, please go for it. adide from that the article should I think include the recognition by friedman himself that his theory was proven a failure in explaining the recent desinflation Panache 11:34, 7 June 2007 (UTC)

It is evident that English is not your first language, and that your English reach somewhat exceeds your grasp. It is hard to read your edits, and hard to read your comments here. —SlamDiego_←T 23:00, 7 June 2007 (UTC)

thanks slam diego, your contribution is very helpful Panache I made the critics section clearer. ANd left a blank, one for the demand of money.

money demand

The quantity theory is the basis for the Keynesian Liquidity Preferance theory of money demand, so I put it in because I think it's relevant and important. In fact I'd like to see this section a expanded a bit (not too much though). If the fact that QT is a basis for a theory of inflation is relevant so is, IMO, this other aspect. Currently there's no article in wiki on Money Demand (at least none that I can find, the closest is this Transactions demand), which is a shame. But if and when this article is created we could perhaps just link to it, rather then have the statement here, if someone really really objects.radek 21:16, 11 April 2007 (UTC)

You seem to be treating the equation of exchange as identical to the quantity theory of money. But the quantity theory hold that there is a positive relationship between $P$ and $M$, whereas some economists have believed that all of the response (long-term as well as short-term) to $\Delta M$ will be in $Q$; that belief (albeït certainly not one that I hold) is compatible with the equation of exchange but contrary to the quantity theory of money.

Certainly $M_{D}$ is very important to economic theory, but I think that the discussion may be misplaced. —SlamDiego 21:24, 11 April 2007 (UTC)

I guess you have a point - both the quantity theory and liquidity preferance are based on the equation of exchange but there's no necessary relationship between them. Still, seeing as there's no article on money demand, nor a separate article on 'equation of exchange' (and I don't think there should be) I think the edit, short as it is, provided one is careful with the wording, should stay. But if you feel very strongly about it then go ahead and remove it.radek 21:32, 11 April 2007 (UTC)

Well, why don't you leave it but begin working on an article in which it would be better located, move the equation there soon, and make sure that each article includes the other in its “See also”? —SlamDiego 00:22, 12 April 2007 (UTC)

Sure, I've been meaning to write the money demand article for awhile anyway. Gimme the weekend. radek 21:31, 12 April 2007 (UTC)

I just fleshed-out the article on the equation of exchange. Please look at it and see what edits you want to make, especially to the subsection on $M_{D}$. —SlamDiego 19:26, 14 April 2007 (UTC)

Looks good. Thanks, I'll take the ref here. radek 23:38, 14 April 2007 (UTC)

Objections

Recent unsigned Edit moved to below as per Wikipedia:Talk page guidelines#Layout. --Thomasmeeks 19:47, 26 August 2007 (UTC)

There a number of incorrect ideas and an almost complete lack of logical flow to this article, suggesting no one who has contributed is an economist (as recognized by the profession). I am not interested in writing it, but came across this page in a link from the real bills doctrine, which is a mess.

Even the note on Friedman's restatement of the quantity theory of money does not follow his paper, which treats velocity (not money) as a function of several variables, most of which are assumed stable over very long periods (he does provide some empirical support for this). In this case, velocity is fairly constant, allowing for the pass-through of % changes in the money supply to % changes in prices, if transactions are constant. The argument about differential changes versus discrete changes in the discussion page is true, but ignored by economists, particularly Greenspan, who used a version of this equation assess money policy. —Preceding unsigned comment added by 63.168.131.24 (talk) 20:31, August 24, 2007 (UTC)

Criticism Section

There are no citations at all, and the entire section needs to be written. —Preceding unsigned comment added by 67.189.176.236 (talk) 16:26, 13 February 2008 (UTC)

Yup. —SlamDiego_←T 16:36, 13 February 2008 (UTC)

Since there has been a little confusion, let me make it clear that I didn't write that section. A long time ago, I did a little clean-up on it, then someone else came along and made it truly awful. The other people have done more clean-up. But mostly people seem to do as I — stare, go “Bleh!”, and then depart. —SlamDiego_←T 17:09, 13 February 2008 (UTC)

Rothbard?

Is there, in fact, a good reason to have Rothbard's book amongst the references for this article? —SlamDiego_←T 00:05, 15 June 2008 (UTC)

Yes, I believe so. While the 1963 book focuses on the 1930s depression, its thesis rests on monetary policy and the quantities of money issued by central banks. Using that theory he rather extensively explains why the most significant economic event in American history (to date) resulted from an abuse of the monetary mechanism. (Here is Chapter 6, as an example: http://www.mises.org/rothbard/agd/chapter6.asp ) The monetary function is central to everything in the Austrian School. A case could be made that others of Rothbard's books could be included as well. Perhaps there is another book that could serve as an even better reference? --RayBirks (talk) 01:48, 15 June 2008 (UTC)

To say that monetary theory is important to Austrian School economics and vice versa doesn't say that this book by Rothbard is here an appropriate reference. This article is not about general monetary theory; it's about a family of propositions concerning the relationship between changes in over-all prices and changes in the money supply. Rothbard's book is about “business cycles”, and very much focussed on one particular business cycle.

(If Rothbard provides a more accessible version of the explanation of inflation provided by v. Mises in Theorie des Geldes und der Umlaufsmittel, then I could see directing the reader to the pages or chapter in which he does that much.) —SlamDiego_←T 08:27, 15 June 2008 (UTC)

I haven't seen any good reason to keep th eRothbard reference, and have removed it. I have, however, added a reference to the relevant section of Mises's Human Action. —SlamDiego_←T 06:32, 23 July 2008 (UTC)

Archive Panache

I have moved the discussion with and about Panache to Talk:Quantity theory of money/Archive 1. (I thought about deleting it altogether, as it can be found in the history of this page. But I figured that, if I did so, then the discussion would surely be resurrected.) —SlamDiego_←T 06:30, 23 July 2008 (UTC)

Fisher's equation of exchange and money in practice

I'm reading Money by John Kenneth Galbraith, and on page 208 he puts Fisher's equation in a footnote. He says it looked like:

$P={\frac {MV+M'V'}{T}}$

where P is the level of prices, M is the circulating currency, V is the velocity of currency, M' is the volume of bank deposits 'subject to check', V' is the rate at which these deposits turn over and T the volume of trade. That's basically what is on this page, except that here both have been lumped together. In the article it mentions briefly, as an example, that M could be currency + checking + savings. But I'm curious as to what the general thoughts among economists are as to what is appropriate to use as money in this equation?

Also, in the first equation of this article, it shows $\mathbf {p^{T}}$. Why is the superscript T necessary? II | (t - c) 04:30, 9 December 2008 (UTC)

The appropriate thing to use as money in the equation is a superset of the set of things used as money in the relevant transactions. If, for example, checkable deposits were used to make some of the purchases, then checkable deposits must be in the set, but needn't be included if checkable deposits were not employed. If the set used is a proper superset of the the things used as money, so that something is included that wasn't actually used in the transactions, that is automatically offset because its velocity is zero, and the average velocity of the set is thus reduced correspondingly; the equation then still works. However, its usefulness may be reduced.

As savings accounts became more liquid (both because of formal changes in intermediation and because of social change), consensus moved towards regarding them as immediately important components to the use of the equation of exchange. Previously, “$M_{1}$” basically referred to circulating currency plus checkable deposits, and “$M_{2}$” referred to that plus savings; then $M_{1}$ was renamed to “$M_{1a}$” and $M_{2}$ to “$M_{1b}$”. Then they stopped talking about $M_{1a}$. Then $M_{1b}$ was renamed to “$M_{1}$”. Thus, $M_{1}$ was almost utterly displaced by $M_{2}$.

The superscript “$T$” indicates that the transpose of the vector is used. This is simply a matter of “dotting the ais and crossing the tees”. Amongst economists, it probably wouldn't hurt to suppress that bit of notation, but this article isn't written primarily for economists. And anyone confused by the “$T$” can fall back in the sigma operator expression. —SlamDiego_←T 06:51, 9 December 2008 (UTC)

Ah, yeah. It looks fine. I see why the vector is transposed (linear algebra flashback). II | (t - c) 08:11, 9 December 2008 (UTC)

Basically this is a whole another can of worms with lots of debates over the years in the economic literature as to what the proper measurement of 'money' is. There's some of that discussion in the article on Money supply. Essentially it depends on the research question you're asking.radek (talk) 07:12, 9 December 2008 (UTC)

J.H. McCulloch once jocularly suggested that there be some measurement that included luggage. What should be appreciated is that this would be somewhat frivolous, yet not actually nonsense. Luggage could be, and almost certainly has been used as a medium of exchange in some transaction. —SlamDiego_←T 07:44, 16 December 2008 (UTC)

$V$

I keep finding rot like this

This equation, like the previous one, holds, because $V$ is constructed to make the two sides equal.

insinuated into the article. In point of fact, since there is a ratio between any two quantities (including the number of hairs on George Bush's head and the Dow Jones Industrial average) the equations would all be vacuous tautologies if $V$ were constructed to make the two sides equal.

Economists were discussing monetary velocity before “the price level” was more than an incoherent gleam in anyone's eye. $V$ is the frequency with which, on average, a unit of money is used to make a purchase.

In a small, simple economy, $V$ is independently observable, without knowing prices or quantities. One could simply watch each quantity of currency, see how often it changed hands, query whether the transfer involved a purchase (without asking how much was purchased or at what price) and then average the frequency with which a unit of money changed hands. In a modern economy, such tracking is no longer practical, but that doesn't mean that the velocity has somehow become unreal or constructed as a ratio of $\left(P\cdot T\right)/M$.

$V$ is logically and mathematically (though not definitionally) equal to $\left(\mathbf {p} ^{\mathrm {T} }\cdot \mathbf {q} \right)/M$ because each turn-over of the monetary unit in the act of purchasing involves exchanging a sum of monetary equal to the quantity purchased times the unit price of the good or service.

$V$ is approximated by — not constructed as — $\left(P\cdot T\right)/M$, based on the notion that $\mathbf {p} ^{\mathrm {T} }\cdot \mathbf {q}$ may be approximated by $P\cdot T$. The equation of exchange stands or falls based upon that approximation, not upon some alleged construction of $V$. —SlamDiego_←T 18:05, 23 February 2009 (UTC)

Not just “original”, but bad

This set of insertions

• [1]

is mistaken. In the absence of further constraint(s), an increase in the money supply can have three possible effects that leave two values unchanged:

1. an increase in over-all prices
2. an increase in the over-all level of economic activity
3. a decrease in the velocity of money

Nor should these possible effects be labored in the lede; the lede is supposed to succinctly summarize the quantity of theory, not to attack it. —SlamDiego_←T 19:08, 27 May 2009 (UTC)

Okay now, for pushy amateurs:

$M\cdot V=P\cdot T$

So

$V={\frac {P\cdot T}{M}}$

So if $M$ increases, and $P\cdot T$ remain unchanged, what happens? $V$ decreases. That's just basic algebra. If you've found a source that claims that an increase in $M$ must mean an increase in $P$ or in $T$ or in both. Then you've found a source that is sloppy or mathematically ignorant or both. Stop putting nonsense in the lede.

Also stop putting material that wouldn't belong in the lede that isn't proper to a lede even where it's not incorrect.

And stop treating Keynesianism as a single school with a unified position on quantity theories. There are certainly critics of the quantity theory, but this article is better with no “Criticism” section than with a cartoon version. —SlamDiego_←T 05:55, 28 May 2009 (UTC)

As to the recurring claim about “the Keynesian school”, Keynes is not a school, he was a single economist. There are a multitude of schools that draw their beliefs or inspiration from interpretations of Keynes, and they have varying attitudes towards the quantity theory. Stop putting a cartoon version of criticism in the article. —SlamDiego_←T 21:32, 29 May 2009 (UTC)

Historically, the velocity of money flow doesn't change much. (See the data from US Department of Commerce, from 1960-2010, V of whole US differed no more than 3%) So we can regard V as a constant. --LunarShaddowღIvy (talk) 08:17, 15 March 2012 (UTC)

Example is misleading

The example "If $V$ and $Q$ were constant, then..." is misleading. It first sets up a correlation, and then goes on to declare that there is a correlation. I'm going to give as clear an example as I can, which requires no more than fractions and rudimentary algebra.

You and me are the only two people in the universe, and we each have 10 dollars. You sell stuff, and I sell things. Today you came over and traded 10 bucks for some of my things, and later on I came over and bought 20 bucks of your stuff. So even though there was only ever 20 dollars, we still traded 30 dollars in activity. Let's call it A for activity:

$A=30dollarsSpent$

$M=20dollarsInCirculation$

$Q=2transactions$

We can then calculate the average money spent per transaction:

$P={\frac {30dollarsSpent}{2transactions}}=15{\frac {dollarsSpent}{transaction}}$

And we can get the average dollarsSpent/buck in circulation:

$V={\frac {30dollarsSpent}{20dollarsInCirculation}}=1.5{\frac {dollarsSpent}{dollarInCirculation}}$

It should then make sense that the main equation holds true:

$P{\frac {dollarsSpent}{transaction}}={\frac {MdollarsInCirculation{\frac {VdollarsSpent}{dollarInCirculation}}}{Qtransactions}}={\frac {MVdollarsSpent}{Qtransactions}}$

Any changes to M dollarsInCirculation will alter V dollarsSpent/dollarInCirculation. The only exception is the subset of answers where dollarsSpent and transactions change in exactly the right proportions to produce an identical result. That subset of answers is a plane in a volume of possible answers -- literally infintesmally small in comparison.

To suggest that the dollarsSpent/dollarInCirculation can be held constant while changing the dollarsInCirculation displays either a lack of understanding or intentional misdirection. So if there are no valid counter-arguments, next month I'm going to alter the page.AngleWyrm (talk) 21:58, 19 September 2009 (UTC)

First of all, Do not jump the queue by placing a new section of comments ahead of other sections. Entirely new sections go at bottom of the page. Entirely new comments within a section go after previous comments in that section. Newer replies to previous comments go after previous replies to that comment.

Second, what you call an “example” is not an example in anything other than a misleading sense of “example”. It is — and is plainly labelled — a rudimentary theory.

Third, You are confusing the equation of exchange with the quantity theory of money. Your example (which is indeed an example) does not explain the quantity theory at all. The quantity theory of money is a theory that changes in the quantity of money are a significant cause of changes in the price level. The way that we explain the effects of changing one variable ($M$) on another ($P$) is by holding everything constant that conceptually can be held constant. This is no different in principle from explaining the law of conservation of momentum by presuming a lack of external forces. —SlamDiego_←T 00:22, 20 September 2009 (UTC)

The attempt to describe a causal relationship between money supply and average price is not supported by the variables at hand. A change in M changes the denominator of V=A/M. The restriction that V remain constant requires that we examine only those answers where A has also changed, and furthermore that the change in A matches the change in M so that the new V'= V. Not only is that, from this small subgroup we then go on to cherry pick only the answers where Q has also not changed. This is an extraordinarily small fraction of the possible outcomes, and not representative of the full set of answers.

I see that you are the author of this page, but not the author of the misrepresentation. It is probably a good idea to place a note at the top of the page, stating that the validity of the information presented through the links and summarized here on the wiki is contested. AngleWyrm (talk) 23:38, 20 September 2009 (UTC)

No arithmetic equation could establish a causal relationship.

The model is overtly labelled “rudimentary” — imperfect, incomplete, in the earliest stages of development.

Immediately before presenting the rudimentary theory, the article explains

But there are questions of the extent to which each of these variables is dependent upon the others. Without further restrictions, it does not require that change in the money supply would change the value of any or all of $P$, $Q$, or $P\cdot Q$. For example, a 10% increase in $M$ could be accompanied by a 10% decrease in $V$, leaving $P\cdot Q$ unchanged.

The fact that someone doesn't agree with the theory doesn't imply that the theory shouldn't be presented, nor that it shouldn't be presented in the most accessible form. And that is exactly and only what the section that you propose to clutter-up does.

There are no cases in the real world in which a body is not subjected to external forces; physicists are not simply “cherry picking” when they pretend otherwise. Yet we would not be so absurd as to flag an article as disputed because it discussed how a body behaved if it were not subjected to external forces.

There is no single author to this page, though I've edited it more extensively than have other editors. —SlamDiego_←T 11:10, 21 September 2009 (UTC)

I do not just 'disagree' with you. The equation has three degrees of freedom: CurrencyInCirculation, DollarsSpent and numTransactions. The situation is identical to holding the width and height of a box 'constant' while changing it's length. If I tell you my box is 4' long, what does that say about it's volume? It could be the box my fluorescent bulb came in. It cannot even be said that 'in general' or 'most of the time'. There are infinitely many more boxes with the same length but different volume.

Your responses seem to be those of an author whose project has been seen to be a hoax. If you didn't write it, then maybe you could look into the history and determine who did, and more importantly why they did. My guess is it was someone who stood to make a fortune if the right government officials were convinced to print up more money. AngleWyrm (talk) 02:19, 22 September 2009 (UTC)

Uhm, no. You are now actively refusing to get the point. I'll not feed the trolls, and I will see to it that any vandal here is blocked. —SlamDiego_←T 04:13, 22 September 2009 (UTC)

Do not remove a comment after a reply has been made to it, falsifying the context of the reply. If you wish to withdraw a remark after a reply has been made to it, then strike through it. —SlamDiego_←T 23:32, 24 September 2009 (UTC)

My Quantity Theory of Geese I'm going to prove via null hypothesis that gallons of gas consumed during a vacation trip has a "direct, positive relationship" with the density of geese/mile witnessed during that trip.

$P{\frac {geeseSeen}{mileDriven}}\times QmilesDriven=MgallonsGasUsed\times V{\frac {geeseSeen}{gallonGasUsed}}$

Dividing both sides by Q milesDriven:

$P{\frac {geeseSeen}{mileDriven}}={\frac {MgallonsGasUsedV{\frac {geeseSeen}{gallonGasUsed}}}{QmilesDriven}}={\frac {M\times V}{Q}}{\frac {geeseSeen}{mileDriven}}$

If we hold V geese/gallon and Q milesDriven constant, then the total quantity of gas used effects the density of geese/mile. AngleWyrm (talk) 21:35, 13 October 2009 (UTC)

This is not the place for your “original research” on geese, just as it would not be the place for your “original research” on monetary theory. —SlamDiego_←T 03:38, 14 October 2009 (UTC)

Equation of exchange v. quantity theory

This edit entails a significant theoretical mistake.

One can subscribe to the equation of exchange without accepting the quantity theory; the equation of exchange does not affirm that velocity is stable nor even that it is exogenous. Opponents of the quantity theory who accept the classical dichotomy are simply committed to the proposition that $V$ or $Q$ will rise to offset an increase in $M$. The edit apparently soguht to convey a sense that $V$ or $Q$ were relatively constant with overscores, but that notation is not transparent, and does not in any case address the next point:

Some proponents of the quantity theory do no accept the classic dichotomy; they do not accept that a price level and real values of transactions can be disentangled one from another.

Hence, I have removed that part of the lede that confused the equation of exhange with the quantity theory.

I am further concerned about the remaining effect of the edit. It seems to classify and caricature pre-Keynesian economics as did Keynes. The term “classical” might be best avoided altogether, and certainly shouldn't be used as Keynesians peculiarly used it (just as it should not be used as Marxists peculiarly used it); and there was much division over the quantity theory in the pre-Keynesian era. —SlamDiego_←T 23:37, 8 October 2009 (UTC)

I have removed the reference to “classical” economics, but done nothing more to the passage beyond tightening-up the wording a bit. —SlamDiego_←T 03:38, 14 October 2009 (UTC)

Cambridge version of equation of exchange

Unless it's explained how the Cambridge version of the equation of exchange was used to criticize the quantity theory, I think that a section on it is misplaced in this article. Meanwhile, I think that a discussion of the Cambridge version should be in the article on the equation, so I am going to clone it there. (I won't remove it from this article before there's been some opportunity for discussion.) —SlamDiego_←T 06:18, 25 November 2009 (UTC)

I was working from one reference on this that referred to the Cambridge equation as its own brand of the quantity theory, not just the equation of exchange. I'll try to find some more sources and clarify that issue and make the importance of the Cambridge equation a little clearer. Thanks for cleaning up my equations.--Bkwillwm (talk) 13:23, 25 November 2009 (UTC)

I think the Cambridge approach to quantity theory probably deserves its own article. From what I've scrapped together, most people seem to view the Cambridge approach as an alternative quantity theory of money. I think the best thing to do would be to give the Cambridge its own article. It deserves some mention on this page, but, hopefully, there's enough material to warrant an article and this article shouldn't devout too much space to Cambridge. I'm going to start Cambridge cash-balance theory. "Cambridge equation" apparently can also refer to a Post-Keynesian growth theory, so I think an alternative title would useful and the New School's Economic history site uses this term. I'll get this article going and we can keep some of the most relevant articles here.--Bkwillwm (talk) 00:11, 26 November 2009 (UTC)

Well, it would probably be good to have a separate article. As for this article, I think that it could use a discussion of the Cambridge approach (though briefer than that which would be in any separate article), but that it should be as part of an explanation of a criticism, and in the criticism section. —SlamDiego_←T 12:27, 26 November 2009 (UTC)

‘The theory was challenged by Keynesian economics’

I think that's putting it too strongly. IIRC the main dispute is that according to Keynesians it's broadly true, but that the relation between money supply and prices isn't so simple or direct because it must operate through a market mechanism, which involves the labour market, consumer spending power and other factors. I wouldn't claim to be an expert though. — Preceding unsigned comment added by 80.114.146.117 (talk) 21:04, 9 July 2016 (UTC)

It might be relevant to note that Keynes famous statement "in the long run we're all dead" was in reference to the monetary theory. Basically, money supply will eventually have an impact, and if a one-off change occurs it will probably eventually result in price changes. But probably it'll be after many intervening processes, many economic factors that will be more significant. By the time the money supply impact could be assessed, it'll have lost its thread of logical consequence. So, yes, in the long run supply matters. It's a long run in which we here are all dead. — Preceding unsigned comment added by 208.80.117.214 (talk) 09:11, 3 May 2017 (UTC)

Evidence?

The section titled evidence provides nothing but Friedman's general claims. This hardly qualifies as evidence in the scientific method sense - as something that can be used to disprove an idea. In fact, probably the best evidence I can think of is Volker's experience in the late 1970s and early 1980s at the Fed. Under Friedman's influence, they initially targeted money supply, at least as best as they could. It didn't have an impact. So they switched to interest rates, which did. While the details are interesting, the broad results were clear evidence, and showed that in a very major case monetary theory was disconfirmed. This matters more than assumption-driven equations.

In general, economics gets away with weak definitions of evidence, and the quantity theory of money is a good example. Friedman's work is riddled with cherry picked examples, poor quality data, and other fact problems. Monetarism is saddled with true-believers, the worst circumstance for science. Inflation has winners and losers, and monetarists fought for those who stood to lose - lenders. They fixated on money supply because it appears in hyperinflation. But an extreme case is poor evidence for complex reality. — Preceding unsigned comment added by 208.80.117.214 (talk) 08:59, 3 May 2017 (UTC)

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"Quantity equation" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect Quantity equation. Please participate in the redirect discussion if you wish to do so. _signed, Rosguill ^talk 22:11, 13 November 2019 (UTC)

This money supply comment

This isn't correct: "In mainstream macroeconomic theory, changes in the money supply play no role in determining the inflation rate as it is measured by the CPI." 2601:152:301:443E:A092:1608:952D:AA3B (talk) 00:07, 27 May 2022 (UTC)

Theologian and Economist Martín de Azpilcuet

The page for Martín de Azpilcueta states that he independently discovered QTM. I would not be surprised if several mathematicians independently reached similar conclusions about economics during the renaissance, so a rewording of the introduction on this page may be in order. That being said, the citation for this claim on Azpilcueta’s page is not digital, and so I cannot vet it.

Does anyone have any good sources they can link in? Azpilcueta seems to be comparatively obscure, especially relative to a name like Copernicus who's contributions to science have had incredibly dramatic effect. His own page needs a good deal of citation and general research. However, I would like some general help clearing this up for the sake of this article. I have memories of reading this page a few years ago and Copernicus was not mentioned. HistorianFromSyracuse (talk) 05:15, 31 January 2023 (UTC)

Maybe to sequence Criticism

In accordance to "credit mechanics" bank money expansion or destruction (or not changing) depends on payment flows.

Maybe that table beside could be interesting to notice within sequence "criticism" - feel free to put it in. Thx! CGB 62.240.134.35 (talk) 13:43, 4 April 2023 (UTC)

References

A Mathematical Formulation of Friedman's Restatement of QTM. Original Research?

This all may constitute original research since I have no sources, but I conducted a basic mathematical analysis on the quantity equation and here's what I got:

Milton Friedman famously wrote:

"It follows from the propositions I have so far stated that inflation is always and everywhere a monetary phenomenon, in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output." – Friedman, Milton. The Counter-Revolution in Monetary Theory. Institute of Economic Affairs, 1970.

This conclusion can be derived through a straightforward analysis of the quantity equation:

$MV=PY$

Where $M$ is the nominal supply of M1 money, $V$ is the velocity of money, $P$ is the aggregate price index, and $Y$ is real income (output).

Differentiate both sides with respect to time $t$:

${\frac {d}{dt}}(MV)={\frac {d}{dt}}(PY)$

Apply the product rule to both sides:

$M{\frac {dV}{dt}}+V{\frac {dM}{dt}}=P{\frac {dY}{dt}}+Y{\frac {dP}{dt}}$

The Monetarist tradition treats velocity as constant $dV/dt=0$, so we will do the same. Consequently, the differential equation becomes:

$V{\frac {dM}{dt}}=P{\frac {dY}{dt}}+Y{\frac {dP}{dt}}$

We can normalize velocity $V$ using $V=(PY)/M$. Thus:

${\frac {PY}{M}}{\frac {dM}{dt}}=P{\frac {dY}{dt}}+Y{\frac {dP}{dt}}$

To simplify the algebra, let’s apply Newton's notation to the temporal derivatives so that:

${\frac {PY}{M}}{\dot {M}}=P{\dot {Y}}+Y{\dot {P}}$

Multiply both sides by $M$ (distribute for the RHS):

$PY{\dot {M}}=MP{\dot {Y}}+MY{\dot {P}}$

Divide both sides by $PY$:

${\dot {M}}={\frac {MP{\dot {Y}}}{PY}}+{\frac {MY{\dot {P}}}{PY}}$

Simplify:

${\dot {M}}={\frac {M{\dot {Y}}}{Y}}+{\frac {M{\dot {P}}}{P}}$

Bring the common term $M$ outside the fractions and combine like-terms:

${\dot {M}}=M\left({\frac {\dot {Y}}{Y}}+{\frac {\dot {P}}{P}}\right)$

Divide both sides by $M$:

${\frac {\dot {M}}{M}}={\frac {\dot {Y}}{Y}}+{\frac {\dot {P}}{P}}$

Switch back to Leibniz's notation:

${\frac {dM/dt}{M}}={\frac {dY/dt}{Y}}+{\frac {dP/dt}{P}}$

Multiply both sides by $dt$:

${\frac {dM}{M}}={\frac {dY}{Y}}+{\frac {dP}{P}}$

Define terms:

$g_{t}^{M}=g_{t}^{Y}+\pi _{t}$

Where $g_{t}$ are percentage increase of the superscript at time $t$ (so that $g_{t}^{M}=dM/M$ and $g_{t}^{Y}=dY/Y$) and $\pi _{t}=dP/P$ is the rate of inflation.

Solve for the inflation rate:

$\pi _{t}=g_{t}^{M}-g_{t}^{Y}$

This is precisely what Friedman wrote in 1970 but in mathematical form. This derivation serves as a clear mathematical statement and reinforcement of Friedman’s QTM while acknowledging its dependency on its underlying assumptions. Phenomena!

It says that inflation as a percentage increase can be expressed as the excess of the percentage increase in the money supply over the percentage increase in output.

To put it more intuitively, inflation occurs when too much money is ‘chasing’ too few goods, so prices increase to absorb the surplus in aggregate demand (financed by money) as a rationing mechanism.

However, while the assumptions explicitly stated (constant velocity) are well known and attributed to the QTM, I think this constitutes "original research" since I can't find a similar system of differential equations in the literature, but maybe someone may find the evidence I need to dispel my belief.

Viespe0 (talk) 23:11, 8 December 2024 (UTC)