## Monday, March 7, 2016

### What V is

Scott Sumner:
What does MV = PY actually mean?

It means V is PY/M.

And that’s all it means. But the textbook description of MV=PY is sometimes a bit confusing, as it seems to say two conflicting things:

1. V is the velocity of circulation, the average number of times a dollar is spent per year

2. MV = PY is an identity. But this suggests V is defined as PY/M

So which is it? It turns out that when MV= PY was first created, V was probably something like #1, but today #2 is the accepted definition.

"And that’s all it means." I swear, sometimes I think Sumner says things just to see if anyone will challenge him.

//

First of all, Sumner asks what the equation of exchange (MV=PY) actually means. Then he re-arranges the equation to get V by itself. And then he gives two definitions for what V may or may not mean. But his original question was not What does V actually mean? His original question was What does the equation of exchange actually mean?

Looks to me like a failure to focus.

But okay. Maybe Sumner wanted to talk about velocity, and he just bungled the opening. Maybe that's it. So let's look at his two meanings for velocity.

The two definitions Sumner offers are identical. Perhaps economists today don't use the phrase "the average number of times a dollar is spent per year". But that is precisely what the V = PY/M equation says. If PY is the spending and M is the quantity of money, then V is "spending per dollar" -- or, the average number of times a dollar is spent per year.

That's why they call it "velocity", for crying out loud.

//

Let's go again.

Velocity is GDP divided by M.  GDP is the size of the economy, and M is the size of the money supply. So velocity is the size of the economy divided by the size of the money supply. It measures how many times the entire quantity of money would have had to be spent, to buy the whole of GDP. So again, velocity is spending per dollar.

When you take miles traveled and divide by gallons consumed, you get miles per gallon. When you take spending and divide by the number of dollars in use, you get spending per dollar.

That's how it is. It can't be helped.