Questa pagina è stata trascritta e formattata, ma deve essere riletta. |

on the use of the differential calculus etc. | 85 |

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:Δ*x*. 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:Δ*x*. 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

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