The important magnitude, called the velocity of circulation, or rapidity of turnover, is simply the quotient obtained by dividing the total money payments for goods in the course of a year by the average amount of money in circulation by which those payments are effected. This velocity of circulation for an entire community is a sort of average of the rates of turnover of money for different persons. Each person has his own rate of turnover which he can readily calculate by dividing the amount of money he expends per year by the average amount he carries.

Note: he’s dividing the total flow of money exchanged for goods (and not the nominal value of output) by the money stock.

Let us denote the total circulation of money, i.e. the amount of money expended for goods in a given community during a given year, by E (expenditure); and the average amount of money in circulation in the community during the year by M (money). M will be the simple arithmetical average of the amounts of money existing at successive instants separated from each other by equal intervals of time indefinitely small. If we divide the year’s expenditures, E, by the average amount of money, M, we shall obtain what is called the average rate of turnover of money in its exchange for goods, E/M, that is, the velocity of circulation of money.*16 This velocity may be denoted by V, so that E/M = V; then E may be expressed as MV. In words: the total circulation of money in the sense of money expended is equal to the total money in circulation multiplied by its velocity of circulation or turnover.

Also relevant is this quote:

An algebraic statement is usually a good safeguard against loose reasoning; and loose reasoning is chiefly responsible for the suspicion under which economic theories have frequently fallen. If it is worth while in geometry to demonstrate carefully, at the start, propositions which are almost self-evident, it is a hundredfold more worth while to demonstrate with care the propositions relating to price levels, which are less self-evident; which, indeed, while confidently assumed by many, are contemptuously rejected by others.

Of course, I’ve been quoting from Irving Fisher, “The Purchasing Power of Money”, Chapter 2, “PURCHASING POWER OF MONEY AS RELATED TO THE EQUATION OF EXCHANGE”

]]>“If that happened often, then we wouldn’t call MV “nominal spending [on output]”. Not unless we violated your premise that V is the ratio of [some] M to nominal output.”

I have to disagree. Nominal spending refers to the use of dollars as the unit of account. It says nothing about whether money changed hands. If I buy a car and pay with T-bills, the transaction is a part of NGDP, but no money changed hands. The ratio of M to NGDP is V regardless of what assumptions you use about transactions technology, it’s just a definition, and hence can never be vioted by real world facts.

]]>*“There are different types of money, etc.”*

My argument is “for a given type of money”.

*“Lots of final goods transactions occur without money being transacted”*

If that happened often, then we wouldn’t call MV “nominal spending [on output]”. Not unless we violated your premise that V is the ratio of [some] M to nominal output. Furthermore, if barter was common then drops in spending wouldn’t cause such large increases in unemployment. As Nick Rowe will happily explain to you.

More broadly, you need to accept that money matters as the medium of exchange as well as the unit of account. Because money is the unit of account, supply and demand for money determines nominal spending. And because money is the medium of exchange, nominal spending determines nominal output (the circular flow of income). (Sticky nominal wages only matter because we have to pay workers *with money*.)

nanute, we can make numbers smaller by multiplying them by fractions less than 1, as well as negative numbers.

]]>Nanute, Yes, of course it’s positive.

Saturos, That’s a different argument, but I’m still not buying. Lots of final goods transactions occur without money being transacted. Barter, or financial assets may be exchanged. There are different types of money, etc.

]]>*Since you have once again decided to revert to acting like a 10 year old and resort to name calling, this conversation is over.*

Again, as I noted here, I call you Full Unemployment Hawk because I find your self-given name ironic. You call yourself a full employment hawk, yet I am convinced your ideas if/when practiced actually exacerbate unemployment.

]]>Since you have once again decided to revert to acting like a 10 year old and resort to name calling, this conversation is over.

]]>Since you have once again decided to revert to acting like a 10 year old and resort to name calling, this conversation is over.

]]>*“I cannot for example say something like “I desire to change my actualized velocity to a new desired velocity in the future.”*

*That shows a complete misunderstanding of the concepts.*

If the “concepts” cannot be interpreted in that way, then they are simply not related to economic science.

What you are saying is not desired velocity, but a desired ratio between spending and cash balances. If that is what desired velocity means, then we already have a name for that. It’s called cash preference.

*Actual or realized velocity IS a residual equal to (P x Y)/M, and is determined by them. This is not a decsion variable for people. But desired velocity is a decision variable that individuals control.*

*I, you, and everybody else, at any GIVEN level of P and Y, can decide I want to REDUCE the amount of money I have in my cookie jar or checking account. To do this I increase my spending at that level of P and Y. This increases desired velocity.*

No, you can only do so by purchasing more goods or the same goods at higher prices, because spending more money more often means there has to be more production. You cannot simply demand to spend more of your money on more goods and then poof the goods are there and thus you achieve your desired additional velocity. If the supply of goods does not increase, then a higher demand that is represented by your additional desire to spend more money, will simply raise prices, which means you cannot hold P constant.

*Similarly I can decide I want to INCREASE the amount of money I have in my cookie jar or checking account. As a result, at any given P and Y, I reduce my spending. This reduces velocity.*

The same principle applies as above, but in reverse.

*In other words people, by decreasing or increasing the money balances they have at any given level of nominal income, increase of decrease desired velocity. Both monetarism and Keynesian economics agrees with this.*

They both fail to take into account production, which is why they both treat velocity as exogenous.

*Decisions by people to decrease or increase their money balances, that is, increase or decrease their desired velocity, result in increases or decreases, respectively, in expenditures, (either directly, or indirectly working through expenditures on financial assets and therefore interest rates), and the increased/decreased expenditures increase/ decrease P and Y at any given money supply.*

Yes, THAT is something I can agree with. Now P*Y is changing.

*Using the equation of exchange M x V = P x Y, with V being DESIRED income velocity, implies that with given M, if V goes up, P and/or Y increases to make the equation hold. Similarly, if V goes down with a given M, P and/or Y goes down.*

But that is not the direction of causality. That’s the problem you are having by treating the equation like a physics equation. It is not true that a person changing their desired velocity will make Y or P increase. The direction of causality is that people desire to spend more money relative to their cash balances, at that will affect P*Y from one direction, and production will affect P*Y from the other direction.

I cannot increase productivity by merely desiring to spend my money more often, that is, spending more quickly after each paycheck or product sales receipt. You cannot say that if desired spending increases, then Y “must” increase to “balance the equation.” Remember, the equation ONLY says money spent is equal to money received. If a person desires to spend more money, then others will of course receive more money. This doesn’t mean production goes up. Production goes up apart from velocity. Prices are in part affected apart from velocity since prices are in part a function of supply.

]]>Actual or realized velocity IS a residual equal to (P x Y)/M, and is determined by them. This is not a decsion variable for people. But desired velocity is a decision variable that individuals control.

I, you, and everybody else, at any GIVEN level of P and Y, can decide I want to REDUCE the amount of money I have in my cookie jar or checking account. To do this I increase my spending at that level of P and Y. This increases desired velocity. Similarly I can decide I want to INCREASE the amount of money I have in my cookie jar or checking account. As a result, at any given P and Y, I reduce my spending. This reduces velocity.

In other words people, by decreasing or increasing the money balances they have at any given level of nominal income, increase of decrease desired velocity. Both monetarism and Keynesian economics agrees with this.

Decisions by people to decrease or increase their money balances, that is, increase or decrease their desired velocity, result in increases or decreases, respectively, in expenditures, (either directly, or indirectly working through expenditures on financial assets and therefore interest rates), and the increased/decreased expenditures increase/ decrease P and Y at any given money supply.

Using the equation of exchange M x V = P x Y, with V being DESIRED income velocity, implies that with given M, if V goes up, P and/or Y increases to make the equation hold. Similarly, if V goes down with a given M, P and/or Y goes down.

]]>