in the theory of value and prices. 95 



Second. That the curve shall approach the axis of ordinates 

 asymptotically and in such a manner that the whole area between 

 it and the axis is finite, to express the fact that marginal utility 

 becomes infinitely ^ninus for consumption of, and infinitely plus for 

 production of finite li^niting quantities of commodity.^ 



Third. The curves begin (have commodity equal to zero) at a 

 finite vertical distance from the origin. (These assumptions are less 

 generally true of production than of consumption, but they have 

 been here employed throughout.) 



It is evident that in comparing the forms of curves for different 

 articles their differences and peculiarities are determined in a most 

 delicate fashion by the form of the curve . . . far more delicately 

 than, with our present statistical knowledge, is necessary. 



Observe, then, what the abscissa of our curve stands for. An 

 infinitely thin \2^jqv xdy is the amount additional demanded (or 

 supplied) in response to an infinitesimal decrease (or increase) dy in 

 marginal utilitj^ The abscissa x is the ratio of the infinitesimal 

 layer xdy to the infinitesimal change of price, dy. It is therefore 

 the rate of increase of quantity demanded\ (or supplied) in relation 

 to change of marginal utility. AM (figs. 2 and 3) is the initial rate. 

 Consulting II, § 2 of this appendix, we see that 



Xj=zfxdy 

 Hence, dxj z=z xdy 



But y = 2/y and dy = dy^ 



Hence — "^ = x. 



That is the abscissa of our curve is the tangential direction in 

 Jevons' curve, considered with respect to the axis of ordinates. 



Hence if Jevons' curve be subjected to the condition of being 

 convex, the new curve must have the simple condition that succes- 

 sive abscissas diminish, etc., etc. 



Hitherto nothing has been said as to the mode of representing 

 total utility and gain. 



If 2/j is the marginal utility (which may be figured in money) at 

 which a consumer actually ceases to buy, y,, that at which he would 



■•• Cf , Auspitz und Lieben. pp. 7 and 1 1 

 t Cf . foot note Ch. IV, § 8, div. 3. 



