364 



NATURE 



[August 14, 1890 



machinery, we shall advert to some passages which seem 

 to us to contain things which some would rather have 

 expressed otherwise. In the first note of his " Mathe- 

 matical Appendix," Prof, Marshall, referring to the 

 weakened motive power of distant or deferred pleasures, 

 thus writes : — 



" Let -^ be a pleasure of which the probability is p, and 

 which will occur, if at all, at time /. Let r be the rate of 

 interest per unit which must be added to present pleasures 

 before comparing them to future, and let R = \-\- r ; then 

 the present value of the pleasure is/^R-;." 



Should it not be more clearly expressed here, or else- 

 where, that this formula holds only of marginal utility, 

 and that it is not a general psychological truth irrespec- 

 tive of conditions imposed by a money market ? For 

 instance, I anticipate a series of pleasant hours extended 

 over several weeks during which I shall be occupied in 

 mastering this stupendous work. But I do not observe 

 that the anticipated pleasure of the third week differs 

 from that of the first according to an exponential law of 

 variation. 



Another verbal modification is suggested by the fre- 

 quent use of the " law of substitution " ; which, as above 

 intimated, imports that producers will, as a rule, substitute 

 the less for the more expensive methods of production. 

 Might it not be well more often to substitute the simpler 

 statement that the producer will seek to maximize his 

 net advantages, considered as a function of different 

 variables, e.g. labour, capital borrowed, &c. ? From the 

 principle that the partial differential of this function with 

 respect to each of the variables is equated to zero follow, 

 more easily perhaps than by verbal exposition, proposi- 

 tions of the form that " wages tend to equal the net 

 produce of the worker's labour " (pp. 547-48)- No doubt 

 it is convenient to have a term which, as we understand, 

 covers two distinguishable cases : where the maximum of 

 advantage is pursued by varying the variable, or by 

 discontinuously passing from one function to another. 

 Indeed, this is a distinction on which Prof. Marshall, 

 true to his motto, Natura nil facit per saltutn, has, 

 probably for good reasons, not insisted as much as 

 might have been expected. 



The condition above mentioned, that the first term of 

 variation should be equated to zero, may of course in- 

 dicate a minimum, as well as maximum, of utility. Prof. 

 Marshall, following the analogy of physics, attributes to 



a minimum the property of equilibrium. For example, 

 in the case represented by the annexed figure, which 

 NO. T085, VOL. 42] 



corresponds to the author's Fig. 20 (p. 424)— SS' and dd' 

 being, as above explained, the supply and demand curves 

 — Prof. Marshall says, " H and L are points of stable 

 equilibrium, and K is a point of unstable equilibrium." 

 This interpretation may appear doubtful, when we con- 

 sider that the supply curve, when descending, is the locus 

 of minimum advantage for the producer. At any assigned 

 price, e.g. SH or bk, this locus represents the very worst 

 arrangement for the producer, the very bottom of the 

 trough, where he cannot, even theoretically, be supposed 

 content to stay. If this view be accepted, some doubt 

 will be thrown on the "theory of multiple positions of 

 equilibrium " {ibid.). A solution of these little difficulties, 

 consistent with the author's conclusions, will probably be 

 found by those who follow out the hints afforded by his 

 pregnant notes. 



A comparison with the eminent mathematical econo- 

 mists Messrs. Auspitz and Lieben suggests one more 

 scruple. Those theorists regard the demand curve as 

 the envelope of a series of discontinuous curves, each of 

 the sort contemplated by Prof. Marshall, corresponding 

 to different scales of living. This conception, if accepted 

 as important, might have some bearing on the theory of 

 " consumers' rent." 



But in dwelling on such technical points we should 

 run the risk of conveying an unfair impression of 

 the worth and accuracy of Prof Marshall's work. 

 The theoretical subtleties about which a difference 

 of opinion is possible "have a very narrow range of 

 practical bearing." Prof. Marshall is the first to admit 

 of his theory, "when pushed to its more remote and 

 intricate logical consequences, especially those con- 

 nected with multiple position of equilibrium, that it 

 slips away from the conditions of real life, and soon ceases 

 to be of much service in dealing with practical problems." 

 Besides, this is a subject on which, as Disraeli said, the 

 author is much more likely to be right than the critic. In 

 this sort of mixed mathematics the authority of one who 

 is, above all others, conversant with both ingredients of the 

 mixture is almost supreme. He, of all mathematical 

 economists, has best complied with his own maxim that 

 the economist, while he employs " systematic reasoning 

 as to the quantities of measurable motives, .... must 

 never lose sight of the real issues of life ; and these are 

 all, with scarcely any important exceptions, affected more 

 or less by motives that are not measurable." 



Of the two parts of the economist's work we have here 

 dwelt somewhat exclusively on that which best admits of 

 being [viewed synoptically, the more abstract side. We 

 must be 'content with recording, without illustrating, the 

 judgment that the moral and mathematical parts of Prof. 

 Marshall's work are on a level of excellence. He not only 

 applies the differential calculus to measure increments such 

 as "a shilling's worth of happiness," but he also brings a 

 higher faculty to judge of goods which cannot be measured 

 by money, such as " the fulness and nobility of human life," 

 "a pure heart, and a love towards God and man." He 

 renders to the queen of the sciences the things which 

 belong to her province, and to the spiritual side of 

 our nature things which transcend man's power of 



calculation. 



F. Y. E. 



