Monetary Policy During the 1921 Recovery

Robert Murphy went after Barkley arguing in part:

The economy had clearly bottomed out and was recovering before the Fed loosened up the monetary spigots, looking at various criteria. (I should admit that the argument for monetary stimulus does have some support if we look at interest rates, rather than monetary growth. I will elaborate on this in a future blog post.)

Barkley had to respond to a barrage of other attacks but let’s focus on his main point:

My post argued that there was monetary stimulus in 1921 and noted that even though there was downward stickiness of wages in 1945-46 and also in 1982, there were rapid bouncebacks with monetary policy in particular being stimulative during those episodes (and fiscal policy also being so in the 1982 one under Reagan).

The alleged evidence Murphy refers to was a drop in the nominal level of the M2 money supply from mid-1920 to mid-1921 as if the nominal money supply was the right criteria even during a period when the consumer price index (1982 = 100) dropped from 20.9 (June 1920) to 17.6 (June 1921). A balanced discussion of monetary policy during this period can be found here:

To return to monetary policy, while the broad US monetary aggregates M1 and M2 did fall in late 1920 and 1921, they clearly did not suffer a disastrous collapse to the same extent as money supply from 1929 to 1933. For example, the broad money supply as measured by M2 fell by about 6.37% from Q3 1920 to Q2 1921, but began growing again in Q3 1921

Can we do a little simple arithmetic? If the nominal money supply drops from say $47 billion to say $44 billion during a 12-month period when the price deflator dropped from 0.209 to 0.176, does that not mean that the real money supply rose from about $225 billion (in 1982$) to $250 billion? Can I simply ask what part of the real money supply do these Austrians not understand?