24 Irmng Fisher — Mathematical investigations 



(6) 



/A dJJ 

 -=— . dA^ Total utility. 

 dA -^ 



'0 



(7) ^ • Ta — Utility-value. 



(8)f 



«/o 



dA 



'^d\J ,^ ^ dJJ 

 -=-r . dA—A . -7T = (jrain, 



dA dA 



dJJ _ 



Asswn2Jtio7i : -yr = Function of A 07ili/. 



a A. 



Gorrollaries : From (1) and (2) and postulate, when B is ex- 



changed for A 



dB TfA ' 



From (3) and assumption, in the equation : ut. of 

 dAjut. of dB=in, the value of n is independent 

 of the particular commodity and of its quantity 

 M used in the definition. 



CHAPTER II. 

 MECHANISM. 



Scarcely a writer on economics omits to make some comparison 

 between economics and mechanics. One speaks of a " rough cor- 

 respondence" between the play of "economic forces " and mechan- 

 ical equilibrium. Another compares uniformity of price to the level- 

 seeking of water. Another (Jevons) compares his law of exchange 

 to that of the lever. Another (Edge worth) figures his economic 

 " system " as that of connected lakes of various levels. Another 

 compares society to a plastic mass such that a " pressure " in one 

 region is dissipated in all " directions." In fact the economist bor- 

 rows much of his vocabulary from mechanics. Instances are : Equi- 

 librium, stability, elasticity, expansion, inflation, contraction, flow, 

 efliux, force, pressure, resistance, reaction, distribution (price), levels, 

 movement, friction. 



The student of economics thinks in terms of mechanics far more 

 than geometry, and a mechanical illustration corresponds more fully 

 to his antecedent notions than a graphical one. Yet so far as I know, 

 no one has undertaken a systematic representation in terms of me- 

 chanical interaction of that beautiful and intricate equilibrium which 

 manifests itself on the " exchanges " of a great city but of which the 

 causes and effects lie far outside. 



