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rightly formulated. The price being raised from P to P + pɪ,
and the amount consumed being diminished from D to D—d,
Hagen puts for the loss of the consumers p (D—d). If he had
added ⅜ p × d, this would have been an intelligible measure of
the loss of consumers’ rent ; being, in fact, the expression
which Dupuit—with as much accuracy perhaps as the subject
admits of-—has put for what is now called consumers’ rent.1
From this formula Hagen concludes that export trade may or
may not be disadvantageous (p. 14). By parity of reasoning he
finds that importation must always be advantageous (p. 16). A
small bounty may be attended with a slight gain. It may be
questioned whether, in view of the unsoundness of the premises,
any value attaches to these deductions.
In conclusion, Hagen joins issue with Cournot on two points
corresponding to the second and third term of Hagen’s exporta-
tion-formula (above). On the question whether the productive
factors which are displaced by exportation or importation should
be taken into account, Hagen seems to have the better of Cour-
not.2 In the matter of consumers’ rent it is not easy to say
which is most in the wrong, Cournot who ignores, or Hagen who
falsifies the theory. Indeed, a similar difficulty affects the com-
parison between the two authors’ whole treatment of International
Trade.
(3) MangoldtI—This author leads up to the subject of Inter-
national Trade by some sections on Exchange (§§ 62-—74, 1st
edition), in which he represents Demand and Supply by curves
very similar to those which are now in vogue. In virtue of these
constructions Mangoldt, writing without reference to his prede-
cessors, Cournot, Dupuit, and Gossen, may claim to be one
of the independent discoverers of the mathematical theory of
Demand and Supply.
In his Appendix (Anmerkung) On the Equation of Interna-
tional Trade Mangoldt begins by following Mill’s supplementary
sections,4 dividing the subject according as the demand for a
commodity is, or is not, inversely proportional to its price. Under
the first head Mangoldt considers first the case of two variables,
and deduces conclusions substantially identical with those of
Mill, in usefully varied language. Mangoldt then goes on to the
, 1 See article on Dupuit in Palgrave’s Dictionary.
2 Cournot has replied in his Principes of 1863, Art. 185. Hagen speaks of review-
ing Cournot’s work as a whole. Does such a review exist ?
3 Grundriss der Vollcswirthschaftslehre, 1st edition, 1863. 2nd edition (posthu-
mous, edited by F. Kleinwachter), 1871.
4 Above, p. 609 note.