Milton Friedman, the American Nobel Prize laureate in economics, famously stated, “Inflation is always and everywhere a monetary phenomenon.“

In this blog post, I’ll try to show why Milton Friedman was right, and why he is still right, using some simple math.

But first, the entire Friedman quote: “Inflation is always and everywhere a monetary phenomenon, in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in the quantity of output.”

Inflation, according to Friedman, occurs when the quantity of money increases faster than the rate of production (“output”).

By the way, you can always argue about what the money supply is (e.g., M1 or M2) and which measures of production we use, but Friedman usually refers to relatively broad measures of the money supply (e.g., M2 in the US or M3 in the Eurozone), and production is usually measured as real GDP.

If you asked Friedman what he really meant, he would answer that he begins by understanding the inflation process by using the so-called equation of exchange. So let us take a deeper look.

The exchange equation
Friedman began with the exchange equation, which was initially formulated mathematically in 1911 by fellow American economist, Irving Fisher, in his book The Purchasing Power of Money:

(1) M•V=P•T

Where M is the money supply, V denotes the velocity of the money supply in the economy during a certain time period, P denotes the price level, and T denotes the number of transactions in the economy.

We must keep in mind that “transactions” at Fisher can be converted into economic production, therefore we can also formulate the equation of exchange as follows:

(2) M•V=P•Y

Where Y represents real GDP (“output”). It also implies that the right side of the equation depicts nominal GDP, which is the price level (P) multiplied by real GDP (the number of commodities produced in the economy).

You can alternatively state that the left side (M•V) of the equation is the price of the entire economy.

At the same time, you can state that (2) is a definition, because it must apply absolutely that in an economy with money, everything we buy and sell is bought and sold with money.

(2), on the other hand, does not state definitively how money, pricing, and output are related. (2) says nothing about what decides what. Hence (2) is not telling us anything about causality.

But consider Friedman’s claim that inflation is always a monetary phenomenon.

We might begin by expressing (2) as growth rates rather than levels:

(3) m + v = p + y

Here, m is the rate of growth in the money supply (e.g. over a quarter or a year), v is the growth rate of velocity, y is the percentage growth in real GDP, and p is the percentage rise in the price level – i.e. what we commonly term inflation.

We obtain the following if we move (3) around a little:

(4) p = m + v – y

And here’s what Friedman says: if m (“the quantity of money”) grows faster than y (“output”), it follows that inflation (p) rises.

However, in the formulation above, Friedman does not mention velocity (v). However, this does not imply that Friedman is unaware of the existence of v or that it has no bearing on inflation. Of course, he knows that – afterall the basis for what he is saying is the equation of exchange.

As a result, one could argue that Friedman could have been more specific in stating that inflation (p) happens when the sum of the money supply (m) and the velocity (v) increases faster than production (y).

An alternate phrasing could have been that money’s purchasing power is determined by the supply of and demand for money.

If the supply of money (M) rises relative to the demand for money (V and Y), the value of money falls – in other words, you can buy less of the production for the same amount of money – and so the prices of goods rise (P).

Monetarists such as Milton Friedman (and myself) doesn’t argue that there is an one-to-one link between the rise of the money supply and inflation.

However, we can see from the preceding that this is not the case because it would require us to ignore what happens to Y (y) and V (v), and understanding the inflation process requires far more than just looking at the development of the money supply, but on the contrary, we see that understanding the money supply must be central to understanding why we get inflation (or deflation).

What about supply shocks?
When economists and others discuss inflation, they frequently state that rising oil costs, for example, have caused inflation to rise. But what role does it play in the quantity equation?

Does Friedman (and other monetarists) genuinely believe that rising gas prices (as in 2022) have no effect on inflation? No they don’t, but again it is more complicated that most commentators make it out to be.

The explanation is that if the price of a production input (for example energy prices) rises, it will naturally have a negative effect on production, causing Y to fall.

And, recalling equation (4) above:

p = m + v – y

Then, logically, for a given m and v, if y goes negative, then p must increase. In other words, a negative supply shock that cuts output will cause the economy’s price level to rise, but only if the central bank lets it.

The central bank will always be able to cut m correspondingly, and therefore the price level (and consequently inflation) is always determined by the central bank – even if there are negative supply shocks.

However, reducing m if a negative supply shock causes y to fall is not necessarily a good monetary policy response, and Friedman would certainly not argue for it.

However, this does not change the fact that the central bank has complete control over the price level through managing the amount of money in the economy.

It should be emphasized that while gas prices in Europe climbed in 2022, real GDP in fact also increased. This suggests that it was not simply a negative supply shock, since real GDP then would have declined. That however as we know did not happen. However, more on that in a later piece.

Finally, when we talk about inflation, we don’t mean individual months or quarters in which prices rise (or fall), but rather a continuous increase in the general price level, and in order for a supply shock to be able to trigger continuous price increases, we need a continuous negative supply shock, which historically hasn’t been happening for longer periods.

Rather, in modern market economies, productivity grows over time – that is, Y increases over time, and so the price level should fall over time. The reason that hasn’t happened in the Western world since WWII is that M (and V) have increased faster than Y.

Inflation is not caused by changes in RELATIVE prices
Above, we talk about production as if the economy only consists of one product, whereas in fact, what we’re looking at is the sum of different products’ production. However, where there are more items in the economy, we may easily re-formulate the equation of exchange.

Assume that the economy contains two goods: good A and good B. As a result, the quantity equation is as follows:

(5) M•V=P_a•Y_a + P_b•Y_b

Where P_a an is the price of good A, Y_a is the production (quantity) of good A, and P_b and Y_b are the price and production of good B, respectively.

Equation (5) can tell us more about a common error made by economists and laypeople when discussing inflation. In particular, a shift in a specific price, such as the price of food or energy, causes inflation.

In other words, can a price increase on good A increase the overall price level?

We get answer when we look at an economy that does not use money at all – a barter economy.

If there is no money in the economy, M equals 0, and (5) is rewritten as follows:

(6) 0•V = P_a•Y_a + P_b•Y_b <=>

(7) 0 = P_a•Y_a + P_b•Y_b <=>

(8) P_a•Y_a = -P_b•Y_b

Equation (8) states that I can “buy” item A if I have a quantity of item B. I can trade myself for an unit of B by exchanging a particular amount of good A.

When we normally discuss prices we usually represent them in monetary terms, such as euros or dollars.

However, in a barter economy, we discuss relative prices, such as how many bananas I must pay for a beer.

If we look at (8) and assume that the production of B declines for whatever reason (e.g., a poor harvest), then the price of good B (P_b) must rise compared to the price of good A (P_a).

But what about the pricing level? So what is the total price of the two goods? Nothing. This is due to the fact that the price is expressed as an exchange ratio rather than in euro or dollars. If the price of item A rises relative to the price of good B, the price of good B must decline relative to the price of item A.

This means that, similarly, we cannot discuss inflation in a barter economy, and thus it follows that we can only discuss inflation in a monetary economy.

In other words, inflation can only be defined as a monetary phenomenon. Price increases can be sustained and widespread only if the money supply (M) grows faster than the demand for money (1/V and Y).

As a result, while central banks around the world may be attempting to absolve themselves of responsibility for rising inflation in 2021-22, the fact, however, remains that the significant increase in inflation in the US and Europe would not be possible without the central banks’ expansion of the money supply in 2020-21.