[[Categoria:Pagine che usano RigaIntestazione|Scientia - Vol. VII.djvu{{padleft:93|3|0]] conditions of equilibrium which have been already established, all the economic particles are disposed at points such that no indefinitely small change of the system is possible; the final step which any one X can be induced to make in conjunction with one Y having the same slope for all, corresponding to a rate of exchange for small quantities Δη:Δx. Now by the assumption introduced in this paragraph, it is open to any individual on either side of the market, say X_r (or, mutatis mutandis, Y_r) to supply himself by exchanging small quantities with a great number of dealers. In other words, his whole course from zero to the point (x_r, η_r) may be made up of steps taken in conjunction with different Y_s, each small step in the direction of the common slope Δη:Δx. If now X_r by multiplying steps of this kind can reach a point, say (x'_r, η'_r) which represents greater advantage to him than the point at which he was just now supposed to be at (x_r, η_r), he will tend to proceed to that point. He cannot do so, it may seem, because there will not be increments of y forthcoming on the terms offered to proceed to the new point; since they are as advantageously employed by their owners in dealing with other Xs. But it will be worth the while of X_r to offer rather better terms (with respect to short terminal steps), to a number of Ys than those which are represented by the given slope; since if it is advantageous for X_r to move from (x_r, η_r) to (x'_r, η'_r) it will in general^[1] be advantageous for him to move to some point in the neighbourhood of (x'_r, η'_r). Thus the system cannot be in equilibrium unless any individual dealer X_r (and similarly each Y) whose dealing consists of η_r received in return for x_r given, obtains as much y as he is willing to take at the rate of exchange defined by the ratio η_r:x_r. In other words, the point (x_r, η_r) is on the demand-curve of the individual X_r, and accordingly the point of equilibrium for the system is on the collective demand curve which represents the total demand (on the part of the Xs) for y at each compared rate of exchange between x and y. Likewise the point of equilibrium is on the collective demand-curve which represents the total demand on the part of the Ys for x; or in other words, the curve representing the supply of y. Therefore

1. ↑ In the absence of singularities; the usual continuity in the functions with which we are concerned may postulate.