THEORY OF INTERNATIONAL VALUES
631
case of three or more variables. He discerns the general propo-
sition that—cost of production being supposed constant irrespec-
tive of quantity, and abstraction being made of cost of transport
—if trade is opened between two countries, the commodities
previously produced in both countries will now fall into two
groups, each produced altogether in one country; the
rate of exchange between the members of each group
inter se corresponding to the cost of production of each
commodity (in the country in which it continues to be
produced), and the relation between the two groups
being determined by the rate of exchange between the
produce of a unit, of productive force in one country and
that of a similarly defined unit in the other country.1
This simple truth Mangoldt complicates by positing a
commodity as it were intermediate between the two
groups, which may serve as a. measure whereby to ascer-
tain from which of the countries any particular' com-
modity will be exported. '
The following construction of our own seems to give
the substance of Mangoldfs expositions ; it being under-
stood that the substance, as the metaphysicians say, is
not a copy of its manifestations. Let us figure the
relation between the costs of production of the set of
commodities in Country No. I. by a series of points
a, b, c, <⅛c., on a right line, any one of which a is obtained
by measuring from a fixed origin o, a distance equal
to the logarithm of the number of units of productive
force which go to the production of a unit of that com-
modity in Country No. I. Let the natural values of
the commodities in Country No. II. be similarly de-
signated by the points a', bz, c', &c., measured from
o' ; o' being taken so that о o' is the logarithm of
the number of units of productive force in Country
-o'
Fig. 7.
No. II. of which the produce is equivalent in the international
market to the produce of a unit of productive force in Country
No. I. (log. v, or log. ɪ in our notation2 ). It appears at once
from the figure that, when trade has been established, it is
cheaper for Country No. I. to import a', b', and c' than to
produce them ; and to produce d and e than to export them.
The measure or standard which Mangoldt desiderates
would be afforded by the commodity, if the distance between c
ɪ The V of our formula ante.
2 Ante, p. 441.