udents of the money problem. It may be summed up thus:
other things being equal, the value of the monetary unit, expressed
in terms of all other commodities, falls as the quantity of money
increases, and _vice versa_. That is, prices rise and fall in
direct proportion to changes in the total quantity. This is a simple
explanation of a complex and difficult set of conditions. The phrase,
"other things being equal," betokens the statement of a tendency where
there are several factors. The quantity theory explains what happens
when there is a change in one of the factors--the number of pieces
of money. There are three large sets of facts to be brought into
relationship with each other in the quantity theory: (1) the amount
of business, or the number of trades effected; (2) the rapidity of
circulation, depending on the methods by which business is done; (3)
the amount of money available. According to the quantity theory we
must expect that, when conditions (1) and (2) remain fixed, the value
of money will vary inversely as its quantity. This quantity theory may
be expressed in the formula P = MR/N when P is the symbol for price,
or the general price level, N is (1) above, R is (2), and M is (3).
P, therefore, changes directly with either M or R, or inversely with
N.[6]

Sec. 11. #Interpretation of the quantity theory.# The quantity theory
must be carefully interpreted to avoid various misunderstandings of it
that have appeared again and again in economic discussion.

(1) It does not mean that the price level changes with the absolute
quantity of money, independently of growth of population and of the
corresponding growth in the volume of exchanges.

(2) It is not a mere per capita rule to be applied at a certain moment
to different countries. For example, Mexico may have $9 per capita and
the United States $35, while average prices may not differ in anything
like that proportion. But in these two countries not only the amounts
of exchanges per capita but the methods of exchange and the rapidity
of the circulation of money differ greatly.[7]

(3) It cannot be applied as a per capita rule to the same country
through a series of years, without taking account of the many changing
factors. It is estimated that in 1800 the money stock was about $5
per capita in the United States, and in 1914 about $35[8], but average
prices have not necessarily changed in the same ratio. In a period of
years a country may change in a multitud