106 Irving Fisher — 3Iathematical investigations 



§10. 



It has been assumed throughout this investigation that marginal 

 utility decreases as quantity of commodity increases. This is not 

 always true, e. g. it is obviously not true of intoxicating liquors. 

 ii study of the liquor traffic would require a somewhat different 

 treatment from that of most other commodities. Still less is it 

 always true that marginal cost of production alwaj^s increases as the 

 quantity produced increases. It is clearly not true that it costs 

 more in a shoe factory to produce the second shoe than it costs to 

 produce the first. Yet it is probably quite generally true that at 

 the actual margin reached in business the disutilit}^ of extending the 

 business grows greater. When this is not true and when it is not 

 true that marginal utility decreases as quantity of commoditj^ in- 

 creasess an instabilitj^ is the result. The matter of instability is one 

 element at the bottom of the present industrial tendency toward 

 trusts and pools. 



There is no isolated market. Not only this but a "market" itself 

 is an ideal thing. The stalls in the same city meat market may be 

 far enough apart to prevent a purchaser from behaving precisely as 

 if he stood before two counters at once. The relation of the counters 

 ten feet apart differs in degree rather than in kind from the relation 

 of London to New York. 



APPENDIX III. 



THE UTILITY AND HISTORY OF MATHEMATICAL METHOD 



IN ECONOMICS. 



§1- 



Mathematics possesses the same hind though not the same degree 

 of value in every inqu.iry. Prof. B. Peirce,* in his memorable 

 Linear Associative Algebra^ says: "Mathematics is the science 

 which draws necessary conclusions. ***** Mathematics is not 

 the discoverer of laws, for it is not induction, neither is it the 

 framer of theories for it is not hypothesis, but it is the judge over 

 both. ***** It deduces from a law all its consequences. 



Mathematics under this definition belongs to every inquiry', moral 

 as well as physical. Even the rules of logic by which it is rigidly 

 bound could not be deduced without its aid. The laws of argu- 



Ainer. Jour. Math IV., p. 97. 



