Front Page Titles (by Subject) Competition in Exchange. - The Theory of Political Economy
The Online Library of Liberty
A project of Liberty Fund, Inc.
Competition in Exchange. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
About Liberty Fund:
The text is in the public domain.
Fair use statement:
Competition in Exchange.
One case of the Theory of Exchange is of considerable importance, and arises when two parties compete together in supplying a third party with a certain commodity. Thus, suppose that A, with the quantity of one commodity denoted by a, purchases another kind of commodity both from B and from C, who respectively possess b and c of it. All the quantities concerned are as follows—
A gives x1 of a to B and x2 to C,
B gives y1 of b to A,
C gives y2 of c to A.
As each commodity may be supposed to be perfectly homogeneous, the ratio of exchange must be the same in one case as in the other, so that we have one equation thus furnished—
Now, provided that A gets the right commodity in the proper quantity, he does not care whence it comes, so that we need not, in his equation, distinguish the source or destination of the quantities; he simply gives x1 + x2, and receives in exchange y1 + y2. Observing, then, that by (1)
we have the usual equation of exchange—
But B and C must both be separately satisfied with their shares in the transaction. Thus
There are altogether four unknown quantities—x1, x2, y1, y2; and we have four equations by which to determine them. Various suppositions might be made as to the comparative magnitudes of the quantities b and c, or the character of the functions concerned; and conclusions could then be drawn as to the effect upon the trade. The general result would be, that the smaller holder must more or less conform to the prices of the larger holder.