The Equation of Exchange

The fact that economics is a complex subject is no secret. With things as they are in the world at present, analysing and breaking down what exactly is going on is fairly difficult.

At times like this, it is always handy to be able to delve into a theoretical toolkit to see if there are any age-old concepts that can help us understand situations. On that note, I sure have a delight for you…


A wonderfully simple, and yet very meaningful equation – this is the Equation of Exchange. It is actually a fundamental identity in the world of economics.

An identity?

Yep. An identity is different from an equation in that it is always holds true. A simple example of this is the equation:

x2 = x

This is an equation, because the relationship can be satisfied in some cases, but the statement that x2=x is not at all true in general. In fact, this equation only holds true when x=0 or x=1. Compare this to the trivial (and extreme) case of

x = x

Obviously x=x is true for any value of x, and so this statement is actually an identity. Therefore, we could actually write this by replacing the equals sign with the ‘identically equal to’ sign – the one with 3 lines instead of 2, as I have used for the Equation of Exchange above.

What the letters mean

First off, let me define what each of the letters stands for:

M is the nominal money supply – i.e the amount of the money in the economy. Generally, this is controlled by the central bank (Bank of England in the UK, Federal Reserve in the US and so on).

V is the velocity of circulation. This tells us how much money actually changes hands (on average) in a given period of time.

Imagine that you and your friend Bob (hi Bob) are the only people in the country and you are the only one with any money – just £1 unfortunately.Suppose you buy Bob’s flea collection for a pound and subsequently Bob buys your prized dancing hamster for the pound that he just earned. Then the money has changed hands twice, so the velocity of money is 2 for that time period. If you bought 50 things from Bob and Bob bought 50 things from you over the course of a year, each time exchanging the same pound, then the velocity would be 100 per year.

P is the average price level of goods and services in the economy.

Y is the real output of the economy (usually measured in GDP – Gross Domestic Product). ‘Real’ means that it is not measured in currency, so that changes in price do not affect Y.

Real variables are important in economics because they indicate the true value of something. If you made £1 last year selling daisy chains (not a greatly profitable business, obviously) but made £2 this year, you may think that your profits are doubling and your marketing skills are capable of putting Saatchi and Saatchi out of business. But if the value of the pound fell by 4 times in that year (meaning that £1 last year was worth the same as £4 this year), then unfortunately you’ve halved your real profit. Turns out daisy chains are not the new iPod or Wii then. What a bummer.

What the Equation means

If we go back to yourself, Bob and your £1 economy we can see that this equation is an identity  because each side of the equation is essentially a different way of measuring the same thing.

The money supply in the economy is the lonely £1, and the velocity is 100 per year. Therefore the left side of the equation MV = 1 x 100 = 100.

The average price of a transaction in our mini economy is also £1 (since we said that every transaction costs £1), and the output is 100 (since output is essentially the number of transactions made). So the right side of the equation PY = 1 x 100 = 100. Hence we can see how MV=PY is satisfied here.

Should I be excited by this?

Probably not, as it stands. But because we now have a concrete relationship between 4 different variables, we can manipulate the equation and try to use it to see how things in the economy might work.

The most famous direct theory to come from this equation is the Quantity Theory of Money. If we assume V and Y are constant, then M is proportional to P. This means that changing the money supply changes the price level proportionally. According to this, we can see that all the billions and trillions that central banks are trying to pour into the economy should cause a rise in the average price level. Of course, if they pour money in at a faster rate, then the price will go up at a faster rate. The rate that the price level goes up is defined as inflation, and so we expect an increased inflation rate as a result of all the money pouring.

The great thing about the equation is that it is very easy to form some sort of hypothesis as to what might or what should happen in a given circumstance. Based on our observations, we can then look at what actually happened, and go deeper into other factors that might be involved in the monetary mechanism.

As with any tools, the beauty of having them is that it gives us a starting point for looking at the world and analysing a situation. You can then proceed to go in as deep or as far as you want to. This is value of the Equation of Exchange, and you probably should be excited by this fact.


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