in the theory of imlue and prices. 67 



cistern mechanism may represent accurately the quantities, utilities 

 and prices, but the shape of each cistern is a function of the whole 

 state of equilibrium and differs as soon as that differs. However in 

 general the interdependence in the shapes of the cisterns is very 

 slight. That is, the utility of a commodity usually varies so much 

 more under a variation in the quantity of that commodity than 

 under variations of other commodities that the relations discussed 

 in Part I may be regarded as good first approximations. Especially 

 is this true if the interdependent commodities are grouped as in § 4, 

 so as to eliminate all the really important influences of commodities 

 on each other.* It will subsequently appear that the analysis of 

 Part II is also incomplete and so will it ever be. Neither economics 

 nor any other science can expect an exhaustive analysis. 



§8. 

 Recurring to the definitions of utility as a quantity (Part I, Ch. 1), 

 it will %)e noted that the third definition which indicated the ratio of 

 two utilities was based on the assumption that the utility of each 

 commodity was indej)endent of the quantity of any other com- 

 modity. This assumption was necessary to prove that two applica- 

 tions of def. (3) led to harmonious results (Part I, Ch. I, § 4). To 

 abandon this assumption as we have now done is to forego the use 

 of that third definition. At the close of Part II a further discus- 

 sion of " utility as a quantity " will be given. At present we con- 

 tent ourselves by assuming the marginal utility of a given amount 

 of some one article as our unit of utilit}^ Of course if we should 

 use some other marginal utility as a unit, the measurements will not 

 now agree. This, however, is no calamity. It will presently appear 

 that the meaning of the phrase " one utility is twice another " is of 

 no real importance for the subject in hand. 



Confine attention first to two commodities (a) and (b) consumed by 

 one individual. Let this individual first arrange his whole consump- 

 tion combination to suit himself. Then in order to partially analyze 

 this equilibrium of choice let us metaphorically experiment on him 



* Marshall, Prin. Econ., Math, note xii, p. 756, says: "Prof. Edgeworth's plan 

 of representing U and V as general functions of x and ]/ [see preface to this 

 memoir] has great attractions to the mathematician; but it seems less adapted 

 to express the every day facts of economic life than of regarding, as Jevons did, 

 the marginal utilities of apples as functions of x [the quantity of apples] simply.'' 



