in the theory of value and prices.

67

cistern mechanism may represent accurately the quantities, utilities,and prices, but the shape of each cistern is a function of the wholestate of equilibrium and differs as soon as that differs. However ingeneral the interdependence in the shapes of the cisterns is veryslight. That is, the utility of a commodity usually varies so muchmore under a variation in the quantity of that commodity thanunder variations of other commodities that the relations, discussedin Part I may be regarded as good first approximations. Especiallyis this true if the interdependent commodities are grouped a s in § 4,so as to eliminate all the really important influences of commoditieson each other.* It will subsequently appeal that the analysis ofPart II is also incomplete and so will it ever be. Neither economicsnor any other science can expect an exhaustive analysis.

§6.

Recurring to the definitions of utility as a quantity (Part I, Ch. 1),it will be noted that the third definition which indicated the ratio oftwo utilities was based on the assumption that the utility of eachcommpdity was independent 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). Toabandon this assumption aB we have now done is to forego the useof 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 amountof some one article as our unit of utility. Of course if we shoulduse some other marginal utility as a unit, the measurements will notnow agree. This, however, is no calamity. It will presently appearthat the meaning of the phrase “ one utility is twice another ” is ofno real importance for the subject in hand.

Confine attention first to two commodities (a) and (6) consumed by.One individual. Let- this individual first arrange his whole consump-ekinjcoinbination to suit himself. Then in order to partially analyzethis equilibrium of choice let us 'metaphorically experiment on him

* Marshall, Prin. Econ. , Math, note xii, p. 756, says: “Prof. Edgeworth’s planof representing U and V as general functions of x and y [see preface to thismemoir] has great attractions to the mathematician; hut it seems less adaptedto.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.’’