106 Irving Fisher —Mathematical investigations
§ 10 .
It has been assumed throughout this investigation that marginalutility decreases as quantity of commodity increases. This is notalways true, e. g. it is obviously not true of intoxicating liquors.A study of the liquor traffic would require a somewhat differenttreatment from that of most other commodities. Still less is italways true that marginal cost of production always increases as thequantity produced increases. It is clearly not true that it costsmore in a shoe factory to produce the second shoe than it costs toproduce the first. Yet it is probably quite generally true that atthe actual margin reached in business the disutility of extending thebusiness grows greater. When this is not true and when it is nottrue that marginal utility decreases as quantity of commodity in-creasess an instability is the result. The matter of instability is oneelement at the bottom of the present industrial tendency towardtrusts and pools.
§ II-
There is no isolated market. Not only this but a “market” itselfis an ideal thing. The stalls in the same city meat market may befar enough apart to prevent a purchaser from behaving precisely asif he stood before two counters at once. The relation of the countersten feet apart differs in degree rather than in kind from the relationof London to New York .
THE UTILITY AND HISTORY OF MATHEMATICAL METHOD
IN ECONOMICS.
Mathematics possesses the same kind though not the same degreeof value in every inquiry. Prof. B. Peirce, * in his memorableLinear Associative Algebra , says : “ Mathematics is the sciencewhich draws necessary conclusions. ***** Mathematics is notthe discoverer of laws, for it is not induction, neither is it theframer of theories for it is not hypothesis, but it is the judge overboth. ***** it deduces from a law all its consequences.
Mathematics under this definition belongs to every inquiry, moralas well as physical. Even the rules of logic by which it is rigidlybound could not be deduced without its aid. The laws of argu-
* Amer. Jour. Math. } IV., p. 97.