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 hasbeen purely mathematical) would not be possible here, nor would itbe possible to state all the other notions which have grown out of amathematical treatment. It has corrected numerous errors and con-fusion of thotight. This correcting function has really been thechief mission of mathematics in the field of physics though few notthemselves 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 theoriesof value—the utility theory and the cost of production theory.Utility was first thought of as proportional to commodity. (Thatthis was never explicitly assumed is a splendid illustration of bowwithout a careful mathematical analysis in which every magnitudehas definite meaning, tacit assumptions creep in and confuse themind). It was next pointed out that utility could not explain pricesince water was useful. So “ utility ” and “ scarcity ” were jointlyprivileged 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 aninherent utility independent of the number of glasses already drunk.
Jevons laid emphasis on demand. Many who 4 accepted his workwere still applying the analogous errors to supply. Ricardo* hadindicated the idea of marginal cost. But even Mill did not perceiveits extension beyond agricultural produce. Considerable creditbelongs to Auspitz und Lieben for working out the legitimate con-sequences and showing by a beautiful mathematical presentationthat the marginal utility theory and the marginal cost theory arenot opposed but supplementary. In fact the “margin” itself isdetermined by the condition that the utility and the cost of finalincrements shall be equal (when measured in money).
Mathematical method is to be credited with the development ofthe ideas of consumers’ and producers’ rent or gain so ingeniouslyapplied by Auspitz und Lieben and so conspicuous in the orig-inal article of Prof. J. B. Clark on the law of the three rents.fThe intimate and mathematically necessary relation between theequality of marginal utilities and disutilities and the maximum sumof consumers’ and producers’ rent, a theorem emphasized by Auspitzund Lieben, and Edgeworth, is of course due to the mathematicalinstrument. %
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