626
THE. ECONOMIC JOURNAL
the expense of transportation per unit of commodity, and the
price in A being changed from pa to pa + δ, we have
∩a(pa ÷ 8) + ∩g(pa + δ + e)
= Fa(pa + ɛ) + Fb(pa + δ + e)
(Arts. 67 and 68.)1
We have now to enquire whether the quantity denoted by
either member of this equation is greater than the corresponding
quantity before the communication was opened ; whether the
following inequality holds :
Fa(pa + ɛ) + Fb(pa + δ + e)
>Fa(pa) + Fb(pb).
Cournot answers this question in the negative by showing that
the inequality does not hold in a particular case : namely, when
the original prices, pa pb, differ from each other, and also from the
new price in A, by only a small quantity, in which case also the
cost of transport, e, must be small, since otherwise exportation
from A to B would not take place on the removal of the barrier.
This reasoning, or that which is based on another particular
assumption, viz. δ and pb — (pa + e) small (Art. 68, Iastpar.), is
quite correct. But the assumption that e should be small leads to
an erroneous conclusion in a subsequent problem : to determine
the effect of a tax on exports or imports (Art. 70).
If p is the price of the article in the exporting country before
the imposition of the tax u, and p + δ the price after the tax, we
have, before the tax, ∩a(p) + ∩b(p + e) = Fa(p) + Fb(p + e).2
And after the tax u per unit of commodity has been imposed, we
have
Ω∙a(p + ɛ) + ʃɪb(p + δ + e + u)
= -^,a(P + δ) + Fb(p + δ + e + u).
Cournot now proceeds to draw conclusions from the last
equation by expanding and neglecting the powers, not only of δ
and u, but also e, above the first power. I submit that Cournot’s
ɪ For pa + δ being the price of the commodity in A, and accordingly the (net)
price which the producers in A obtain (not only for that portion of the product
which they sell in A, but also) for that portion of their product which they sell in
B at a price heightened by the cost of transport e, the quantity offered by the pro-
ducers resident in A at the (net) price pa + δ, together with the quantity offered by
the residents in B at the price pa + δ + e, is equal to the quantity demanded by
the residents in A at the price pa + δ, together with the quantity demanded by the
residents in B at the price pa + δ + e.
2 Compare the last note.
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