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MA THEMA TICAL APPENDIX to Principles of Economics by Alfred Marshall (http://www .econlib .org/library/Marshall/marPtoc.html) NOTE I. (p. 93). The law of diminution of marginal utility may be expressed thus:—If  u  be the total utility of an amount  x  of a commodity to a given person at a given time, then marginal utility is measured by d u d x · δx ; while d u d x measures the marginal degree  of uti lit y . Je vo ns and some other write rs use “Fi nal utility" to indicate what Jevons elsewhere calls Final degree of utili ty . There is room for doubt as to which mode of expressi on is the more conven ient: no question of princ iple is in vol ved in the decision. Subject to the qualications mentioned in the text d 2 u d x 2  is always negative. NOTE II. (p. 96). If  m is th e amount of mo ne y orgene ra l purc ha s- ing power at a person’s disposal at any time, and  µ  represents its total utility to him, then d µ d m represents the marginal degree of utility of money to him. If  p  is the price which he is just willing to pay for an amount x of the commo dity which give s him a total pleasu re u , then d µ d m p = u; and d µ d m dp d x = d u d x . If  p is the price which he is just willing to pay for an amount x of another commodity, which affords him a total pleasure u ,

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