Equation of Exchange

Last week, the question was raised if the Equation of Exchange could be part of a 21st century economics education. Since I learned this equation when I was at school, you could ask yourself if it is not outdated. 

The equation, however, is of a simplicity that allows for many lessons about the economy. So, I would say: “Why not?”.

Let us have a closer look at the equation:


Where M is the money supply, V the velocity of circulation, P the price level and T the number of transactions in the period considered. The claim is, that with the number of transactions at the level of natural unemployment and the velocity a constant, an increase in the money supply will lead to an increase in the price level. Now, that makes sense. After all, when V and T do not, or cannot, change, the only thing that can change to keep the equation in balance is the price level, when the money supply is increased.

The thing I find most interesting about this equation is its assumptions. You may think I refer to the number of transactions. Obviously, when we are in a situation of under-utilisation of our productive capacity, the above will not fly, and the number of transactions can increase up to our productive capacity and the price level does not need to change. Needless to say the price level can change, since a change in the money supply is not the only change that can cause inflation.

The most interesting however is the velocity of circulation. Do you ever consider it when discussing the equation of exchange? Recently, I read an article about a classroom experiment on the equation of exchange. The designer intended the velocity to remain constant, but in the course of the experiment it constantly changed. Moreover, the velocity was lower than one, which does not make sense as far as a real world example goes.

I calculated the velocity, by the way, by rewriting the equation for V:

V = PT / M

In practice GDP or National Income is used to calculate PT.

Now, the interesting thing is, if we accept that the velocity of circulation changes, what will the outcome of the equation of exchange be? In the experiment, there were some students who decided to consume less, which is, from the perspective of the planetary boundaries, something to applaud. From the perspective of the equation of exchange it is interesting too, since this must have decreased the velocity of circulation – which was supposed to be a constant.

I was curious how the velocity of circulation has developed in the Netherlands, where I come from. I found some data on the site of the Central Bureau of Statistics, which were outdated, but it did give some insight:

Irving Fisher’s book The Purchasing Power of Money was first published in 1911, therefore these data seem recent by comparison.

The equation of exchange does also allow for the application of the thinking skill distinction. What is meant by the money supply in the context of the equation? Do we only consider cash and current accounts? Or do we also take the balance on direct savings accounts into account? If the direct savings are not taken into account, can I, as a savings account holder, change the money supply by withdrawing money from my savings account, and vice versa?

Who else can increase the money supply? Can the government? The Central Bank? Private banks? How do they do this? By printing money? Issuing government bonds? Fluctuating the interest rate? Adjusting liquidity requirements? How is it done in your country? What legislation applies? Do the contents of the security van in the picture increase the money supply?

Money supply is a stock, but when we apply the equation of exchange we do not refer to the money supply on that date, neither do we refer to the money supply at the end of the year under consideration. Which value do we refer to?

Transactions on the other hand, is a flow. We measure for example the number of transactions over a year. Do we then multiply it by the general price level? No, we do not, we multiply each product by its price and count up the products to arrive at the total of P times T. Are all transactions included? Or only real transactions, not counting financial transactions like trading securities?

Another question that came to mind was: “Does it matter why the money supply is increased?” Was it to increase government expenditures? Will this increase have an impact on the productive capacity? Did companies take out loans to increase their productive capacity or to improve productivity, or maybe to launch a new product line? Or is the increase in the money supply used to buy consumer goods?

What I intend to say here, is that an increase in the supply of money could very well imply an increase in the productive capacity, or the possible number of transactions T. This means that we cannot make a definitive statement what an increase of the money supply will do to the price level.

And this is what students should understand: that we make assumptions and under these assumptions we see certain ‘natural laws’. But when we let go of our assumptions, it turns out these natural laws do not exist at all. And that is a lesson that needs to be taught in a 21st century economics education.

henny@21steconomics.org – You can also find me on LinkedIn

Image by OSX on Wikimedia