in the theory of value and prices. 



85 



CHAPTER HI. 

 MECHANICAL ANALOGIES. 



For each individual situated in the "economic world," suppose 

 a vector drawn along each axis to indicate the marginal utility in 

 that "direction." The marginal utility of consuming (a) is a vector 

 positive along the A axis, the marginal disutility of producing [ci) 

 (or the disutility of paying money for a) is an equal \'ector in the 

 opposite direction. In like manner the marginal utilities and 

 disutilities along all axes are equal and opposite. 



This corresponds to the mechanical equilibrium of a particle the 

 condition of which is that the component forces along all perpen- 

 dicular axes should be equal and opposite. 



Moreover we may combine all the marginal utilities and obtain a 

 vector whose direction signifies the direction in which an individual 

 would most increase his utility. The disutility vector which indi- 

 cates the direction in which an individual would most increase the 

 disutility of producing. These two vectors are (by evident geo- 

 metry) equal and opposite. 



The above is completely analogous to the laws of comj^osition and 

 resolution of forces. 



If marginal utilities and disutilities are thus in equilibrium "gain" 

 must be a maximum. This is the mere application of the calculus 

 and corresponds exactly to the physical application of the calculus 

 which shows that at equilibrium the balancing of forces implies that 

 energy is a maximum. Now energy is force times space, just as 

 gain is marginal utility times commodity. 



§2. 



In Mechanics. 





In Economics. 



A particle 



corresponds to 



An individual. 



Space 



a u 



Commodity. 



Force 



a a 



Marg. nt. or disutility 



Work 



a a 



Disutility. 



Energy 



a n 



Utility. 



Work or Energy = force x space. 

 Force is a vector (directed in space). 

 Forces are added by vector addition. 



(" parallelogram of forces.") 

 Work and Energy are scalars. 



Disut. or Ut. = marg. ut. x commod. 

 Marg. ut. is a vector (directed in com.) 

 Marg. ut. are added by vector addition. 



(parallelogram of marg. ut.) 

 Disut. and ut. are scalars. 



