December 12, 2018

## Monetary Freedom: Caplan on Velocity and Money Demand

### Caplan on Velocity and Money Demand Bryan Caplan gave an nice discussion of velocity on Econlog.

He explains that velocity is defined to be V = Y/M, where Y is nominal income and M is the quantity of money.

He then argues that it is better understood as the reciprocal of the amount of money people keep relative to their nominal incomes.

He states:

Velocity is therefore essentially a measure of income-adjusted money demanded. The only thing I would add is that Alfred Marshall came up with this idea, and called it “k” and in monetary economics we call it the “Cambridge k.”

Caplan makes the interesting point that if there were no real output and income, nominal income would be zero and so would velocity. He says that money would still be spent multiple times on whatever assets or remaining goods existed.

Caplan makes a great point that the demand for money (adjusted for income or not) is something about which individuals can make a choice. And it is possible to add up individual money demands to get an aggregate demand to hold money. It isn’t obvious how this can be managed for velocity understood as number of times a dollar is spent.

Finally, Caplan brings up the tautology canard:
Economists occasionally dismiss MV=PY as a mere tautology. Whenever I’ve
taught macroeconomics, however, I’ve found that it’s an immensely useful
tautology.

Caplan is saying that it is useful even if it is a tautology, but I think that it isn’t a tautology, and that this can be understood using Caplan’s approach.

The equation of exchange follows from the equilibrium condition that the quantity of money is equal to the demand to hold money: Ms = Md.

As Caplan notes,

Md = kY

Where k is the income-adjusted demand for money.

Add the equilibrium condition Ms = Md

And solve for: Ms = kY

k = 1/V (definition)

MsV = Y

Y = Py (definition, nominal income equals the price level multiplied by real income)

M = Ms (convention to drop the “s” on the quantity of money)

And the result is the equation of exchange, MV = Py

So what’s up with this notion that it is a tautology? Well, Ms = Md can be understood in two ways.

It is a tautology because all existing money is held by someone. In this sense, to hold money is to “demand” it.

What is the equilibrium condition? It is that actual money balances must be equal to desired money balances. That is, people hold the money and they want to hold it.

The equilibrium condition is Ms = Md because people will adjust their spending until desired balances equal actual balances.

As Caplan notes, this only holds in the aggregate if nominal income adjusts, and it is certainly plausible that changes in aggregate expenditure will impact both the levels of production and prices, and so y and P.

But don’t forget, there is this “liquidity effect” by which attempts to spend away excess money can impact the difference between the nominal yields on other assets and money, causing “k” to adjust. (Think about how a given increase in demand for a good raises its relative price and reduces its quantity demanded.)

In fact, I find it doubtful whether k or V are terribly useful.

Still, these ideas are the fundamental ideas of monetary theory.

It would be nice if all introductory macroeconomics students were as well grounded in these relationships as they are in basic supply and demand.