 When I was in the UCLA Ph.D. program, one of the readings in my Monetary Theory course with Ben Klein, if I recall correctly, was Milton Friedman’s 1953 classic, “Commodity-Reserve Currency.” It was a chapter in his Essays in Positive Economics but originally appeared in the Journal of Political Economy in 1951.

It was that article, more than any other, that convinced me that a gold standard was too expensive. Friedman had shown that the annual cost of maintaining a gold standard would be 2.5 percent of GDP. That’s huge.

I now know that Friedman was wildly wrong. He greatly exaggerated the resource cost of a gold standard. I learned that in my Monetary Theory and Policy course, taught by Jeff Hummel at San Jose State University.

In his 1999 book, The Theory of Monetary Institutions, the main textbook for the course, Lawrence H. White goes through the math. The important point, though, before we get to the math, is that Friedman got his estimate by assuming that banks would hold 100 percent reserves of gold against demand deposits and time deposits. That assumption is wildly unrealistic and so his estimate of the resource cost of the gold standard is way too high.

Friedman gets his estimate as follows:

Delta G/Y = Delta G/Delta M * Delta M/M * M/Y

where Delta G is the dollar value of the annual change in the stock of gold,

Y is annual national income,

M is the size of the money stock M2, and

Delta M is the annual change in M2.

For M/Y Friedman took M2/NNP (where NNP is net national product). That was 0.625, which White says is roughly right today.

What is Delta M/M? White and Friedman assume that the purchasing power of gold remains constant as money demand grows. So the money stock must grow to maintain a constant price level (zero inflation).

Using the dynamic equation of exchange (which I used to call the “quantity equation” until Jeff said the “equation of exchange” is more precise),

Delta M/M + Delta V/V = Delta P/P + Delta y/y,

Where V is velocity,

P is price level, and

y is real income.

Friedman estimated Delta V/V to be -1% annually and Delta y/y, the growth rate of real income, to be 3% annually.

With a zero inflation rate, therefore, Delta M/M =4% annually (0 + 3 -(-1))

With Friedman’s earlier mentioned 100 percent reserve requirement, Delta G/Delta M = 1.

So now plug into: Delta G/Y = Delta G/Delta M * Delta M/M * M/Y

Delta G/Y = 1(0.04)(0.625)

= 0.025.

In short, the annual cost of maintaining a gold standard is a whopping 2.5% of GDP.

But White considers the actual history of reserves against deposits under the gold standard and gets a very different answer for the ratio of gold to money, G/M.

G/M = (R + Cp)/M,

where R = bank reserves,

Cp is gold coins held by the public, and

M is M2.

(R + Cp)/M can be rewritten as

R/(N +D) * (N + D)/M + Cp/M.

R/(N + D) is the ratio banks maintain between their gold reserves and their demand liabilities, which are N (currency notes) and D (demand deposits.)

In 19th century Scotland, which had a gold-based banking system and no legal reserve requirements, R/(N +D), was 2% or 0.02.

(N +D)/M is the ratio of M1 to M2.

Coins in 1999 United States were 8 percent of currency, currency was about 51% of M1, and M1 was about 32% of M2.

So Cp/M = 0.08 * 0.51* 0.32 = 0.013

Since M1 is 32% of M2, and coins (Cp) are 1.3% of M2, currency notes and demand deposits must equal 32% – 1.3% = 30.7% of M2

Therefore, R/(N +D) * (N + D)/M = 0.02 * 0.307 = 0.00614

So (R + Cp)/M  = 0.00614 + 0.013 = 0.01914.

The ratio of gold to the money stock is therefore about 2%, which is 1/50th of Friedman’s estimate.

So the annual resource cost of the gold standard, as a fraction of GDP, equals: 0.02 * 0.04 * 0.625 = 0.0005.

So that’s 0.05 percent of GDP.  QED.