theory Ofhnternational values
627
procedure is inelegant and leads him to an erroneous conclusion.
The simpler procedure is first to treat δ and u only as small, δ
being the dependent, u the independent variable. Thus,
δ(∩'a(p) + ∩'b(p + e) - F'a(p) - F'b(p + e) ∖
= - u(Ω'b(p + e) — F'b(p + e) ). /
If now e be small, we may expand both sides of this equation in
powers of e, and neglect terms involving powers of e above the
first, or rather neglect e altogether. Whether e be small or not,
it follows—the law of diminishing returns, as well as that of
diminishing utility, prevailing—that δ is negative, and less than
u ; or that the price falls in the exporting country and rises in the
importing one, contrary to the statement of Cournot (§ 21, par. 1).
I am confirmed in this view by Mr. A. Berry and Mr. C. P.
Sanger, who have independently made a similar correction. Mr.
Berry writes to me of the corrected reasoning : ‘ This may be
confirmed by the fact à priori evident that the disturbance of
price, δ, must vanish when the tax itself, u, vanishes. This is
the case in our equation, not in Cournot’s.’
It is certainly curious to find a wrong belief as to a matter
of fact in business resulting from a slip in mathematical analysis !
Mr. Berry has pointed out to me another slip in Art. 90,
pp. 183, 184. There a certain advantage which the author
ascribes to domestic as compared with foreign trade does not
follow from his own premises.
To this I have to add that those premises are very doubtful.
I allude to the theory of ‘ real ’ as distinguished from ‘ nominal ’
revenue. To collate here all the passages in all Cournot’s versions
which bear on this distinction would occupy too much space. It
must suffice to submit as the result of such an examination very
carefully performed the opinion that, while Cournot’s ‘ nominal
revenue ’ is much the same as what would now be called the money
measure of national wealth, his ‘ real revenue ’ signifies, if indeed it
is significant, such a measure as that which Mr. Giffen, Mr.
Bourne, and others have employed in determining the growth of
the quantity of a nation’s ‘ capital,’ or foreign trade. Such a
measure is obtained by multiplying the quantities of each com-
modity at the two compared epochs by its price at one of them,
the same price being combined with the two quantities, the one
at the initial and the one at the final epoch. Consistently with
this view Cournot says that if the price of a commodity rises
from po to p1, corresponding to a diminution of the quantity from