 In Jeff Hummel’s Monetary Theory and Policy class recently, he assigned an interesting computational problem that shed light on the main factors driving the drop in the U.S. money supply between 1929 and 1933. He used a problem from Greg Mankiw’s Intermediate Macro text. The problem didn’t give magnitudes but I assume everything was in billions of dollars.

The money supply was \$26.5 billion in 1929 and \$19.0 billion in 1933. That’s a drop of 28 percent.

Here was the first question. What would have happened to the money supply in 1933 if the currency-deposit ratio had risen the way it did but the reserve-deposit ratio had remained constant? (The c/d ratio rose because people tried to convert their demand deposits to currency; the r/d ratio rose because banks were trying to have reserves available for people trying to convert their demand deposits to currency. Both factors caused the money supply to fall.)

M = (cr + 1)/(cr + rr) times B,

where M is the money supply,

B is the monetary base = currency held by the public (C) plus bank reserves (R)

cr is C/D, where D is demand deposits

rr is R/D.

In August 1929,

C = \$3.9 billion

D = \$22.6 billion

B = \$7.1 billion

R = \$3.2 billion.

To make sure the formula worked, I plugged the numbers in for August 1929.

cr = C/R = 3.9/22.6 = of 0.17

rr = R/D = 3.2/22.6 = 0.14.

So plug and chug.

M = (0.17 + 1)/(0.17 + 0.14) times 7.1

= 1.17/0.31 times 7.1

= 3.8 * 7.1

= 27.0 (close enough)

By 1933, cr had risen to 0.41 and rr had risen to 0.21.

So if rr had stayed at 0.14, the only other thing we need to know is B in 1933. That was \$8.4 billion.

So M would have been (0.41 + 1)/(0.41 + 0.14) times 8.4

= 1.41/0.55 times 8.4

= \$21.5 billion.

In other words, rather than falling from 26.5 to 19, the money supply would have fallen to 21.5.

Next question:

What would have happened to the money supply if the reserve–deposit ratio had risen but the currency–deposit ratio had remained the same?

R/D rose to 0.21. Assume C/D stays at 0.17.

Then M = (0.17 + 1)/(0.17 + 0.21) times 8.4

= 1.17/0.38 times 8.4

= 3.08 * 8.4

= \$25.9 billion.

So the money supply would have fallen from 26.5 to 25.9, a drop of only 2.3 percent.

In part (c), which mattered more? The increase in the currency/deposit ratio.