# What exactly is "quantity of money per unit of output"?

When making the case about inflation being monetary phenomena, Milton Friedman shows a graph where "quantity of money per unit of output" move together with CPI. What is "quantity of money per unit of output"? Is it real GDP?

Update:

– 1muflon1
Commented Mar 3, 2021 at 18:58
• @1muflon1 added link to the presentation. Commented Mar 3, 2021 at 19:01
• Do you know what quantity of money is, and what output is? Commented Mar 4, 2021 at 14:13

It is the quantity of money, measured by money supply of 'near money', divided by the real GDP. You can see that from reproduction of those tables in the:

The Collected Works of Milton Friedman, compiled and edited by Robert Leeson and Charles G. Palm.

Here is a link to chapter from that book which reproduces the lecture and the figure from the lecture. You can see the picture also below (the note under the table makes it explicitly clear Friedman is talking about quantity of money per real GDP.

• I googled this question while watching video on inflation where was measured the ratio of QoMpUoO to CPI and if GDP calculated by adding up all of the money spent by consumers, then these lines will ALWAYS match which renders such plots pointless: QoMpUoO = money / ( GDP / units); CPI = money / goods; GDP = goods * price; => QoMpUoO = money / (goods * price / units) == money / goods => QoMpUoO == CPI. Thus stating like "quantity of apples == apples" Commented Feb 25, 2022 at 9:26
• @Slaus those equations are not correct Money/Goods =/= CPI also real GDP is not GDP/units but GDP/deflator. Real GDP is still expressed in \\$ terms i.e. real GDP could be 1 million dollars. Real GDP is not unitless. Also nominal GDP = Real GDP * Price level where price lvl is estimated using CPI (from which you can construct deflator by dividing CPI by 100) so QoMpUoO = Money/ real GDP or Money / (GDP/(CPI/100)) so if you wanna express it in terms of CPI QoMpUoO = (Money * CPI)/(GDP*100)
– 1muflon1
Commented Feb 25, 2022 at 9:35
• Thank you for your comment! Especially for such quick response on 1-year-old topic. What seems weird to me (putting aside specific nuances) is that there is a way of expressing QoMpUoO as a function of CPI. The whole point of collecting any stats (plot on this video is stats) is an attempt to reveal any hidden correlation of presumably unrelated phenomena, but it doesn't make any sense of working with such data if QoMpUoO IS a function of CPI - of course there will be some correlation. Commented Feb 25, 2022 at 10:19
• @Slaus 1. the graph above is not there to show correlation (for that scatterplot is better) it shows the two variables move together. Although that usually does imply high correlation it’s not shown directly. 2. Friedman was monetarist. Monetarists believed that money market can be reasonably well described by MV=PY. Further they believed (although now we know erroneously) that V tends to be constant. In that case it makes sense to plot M/Y against P as a time series line graph since if MV=PY holds and V is constant then precisely M/Y should move in a lockstep with P. That’s the point of graph
– 1muflon1
Commented Feb 25, 2022 at 10:26

From Money Mischief chapter 8, in a footnote: "For the United States and the United Kingdom, the price index is the deflator implicit in computing real national income... For all the countries except Brazil, money is defined as the counterpart of the total designated M2 in the United States... For the U.S. and the U.K., output is real national income; for the other countries, real gross national product. For the U.S. and the U.K., the data come from Friedman and Schwartz (1982, tables 4.8 and 4.9), extrapolated after 1975 by official data..."

Money Mischief is from the early 1990s. My impression is that older sources would use a narrower money measure, but I never saw evidence of it.

The numerator is nominal; the denominator is real. That's the arithmetic that makes "money relative to output" similar to the price index.