in the theory of value and prices. Ill 



To pass in review all that has been done in expanding and apply- 

 ing the idea of marginal utility (and most of this expansion has 

 been purely mathematical) would not be possible here, nor would it 

 be possible to state all the other notions which have grown out of a 

 mathematical treatment. It has corrected numerous errors and con- 

 fusion of thought. This correcting function has really been the 

 chief mission of mathematics in the field of physics though few not 

 themselves physicists are aware of the fact. 



In fact the ideas of marginal utility and disutility may be re- 

 garded as corrections of two old and apparently inconsistent theories 

 of value — the utility theory and the cost of production theory. 

 Utility was first thought of as proportional to commodity. (That 

 this was never explicitly assumed is a splendid illustration of how 

 without a careful mathematical analysis in which every magnitude 

 has definite meaning, tacit assumptions creep in and confuse the 

 mind). It was next pointed out that utility could not explain price 

 since water was useful. So "utility" and "scarcity" were jointly 

 privileged to determine price. It was Jevons' clear and mathemat- 

 ical exposition of utility which showed the shallowness of the for- 

 mer discussion and brought to light the preposterous tacit assump- 

 tion, unchallenged because unseen, that each glass of water has an 

 inherent utility independent of the number of glasses already drunk. 



Jevons laid emphasis on demand. Many who accepted his work 

 were still applying the analogous errors to supply. Ricardo* had 

 indicated the idea of marginal cost. But even Mill did not perceive 

 its extension beyond agricultural produce. Considerable credit 

 belongs to Auspitz und Lieben for working out the legitimate con- 

 sequences and showing by a beautiful mathematical presentation 

 that the marginal utility theory and the marginal cost theory are 

 not opposed but supplementary. In fact the " margin " itself is 

 determined by the condition that the utility and the cost of final 

 increments shall be equal (when measured in money). 



Mathematical method is to be credited with the development of 

 the ideas of consumers' and producers' rent or gain so ingeniously 

 applied by Auspitz und Lieben and so conspicuous in the orig- 

 inal article of Prof. J. B. Clark on the law of the three rents.f 

 The intimate and mathematically necessary relation between the 

 equality of marginal utilities and disutilities and the maximum sum 

 of consumers' and producers' rent, a theorem emphasized by Auspitz 

 und Lieben, and Edgeworth, is of course due to the mathematical 

 instrument. ♦ • 



*Pol. Econ., Ch. 3. . f Quart. Jour. Econ., April, 1891, 



