in the theory of value and prices.

95

Second. That the curve shall approach the axis of ordinatesasymptotically and in such a manner that the whole area betweenit and the axis is finite, to express the fact that marginal utilitybecomes infinitely minus for consumption of, and infinitely plus forproduction of finite limiting quantities of commodity .*

Third. The curves begin (hive commodity equal to zero) at afinite vertical distance from the origin. (These assumptions are lessgenerally true of production than of consumption, but they havebeen here employed throughout.)

§ 6 .

It is evident that in comparing the forms of curves for differentarticles their differences and peculiarities are determined in a mostdelicate fashion by the form of the curve . . . far more delicatelythan, with our present statistical knowledge, is necessary.

Observe, then, what the abscissa of our curve stands for. Aninfinitely thin layer xdy is the amount additional demanded (orsupplied) in response to an infinitesimal decrease (or increase) dy inmarginal utility. The abscissa x is the ratio of the infinitesimallayer xdy to the infinitesimal change of price, dy. It is thereforethe rate of increase of quantity demanded f (or supplied) in relationto change of marginal utility. AM (figs^ 2 and 3) is the initial rate.Consulting II, § 2 of this appendix, we see that

x j = / xd v

Hence,

dxj = xdy

But

V — Vs and dy = dy }

Hence

dXj

= x.

That is the abscissa of our curve is the tangential direction inJevons’ curve, considered with respect to the axis of ordinates.

Hence if Jevons’ curve be subjected to the condition of beingconvex, the new curve must have the simple condition that succes-sive abscissas diminish, etc., etc.

§ 7 -

Hitherto nothing has been said as to the mode of representingtotal utility and gain.

If y , is the marginal utility (which may be figured in money) atwhich a consumer actually ceases to buy, y k that at which he would

* Cf. Auspitz und Lieben. pp. 7 and 11.t Cf. foot note Cb. IV, § 8, div. 3.