Mat 16, 1913] 



SCIENCE 



759 



Fisher starts from the obvious identity that 

 what is spent per annum is equal to what is 

 spent. If E be expenditure in cash and E' ex- 

 penditure by check, we have 



E + E'={E + E'). 



Now if M be the amount of money in circula- 

 tion, the average velocity V of circulation or 

 rate of turnover of this money per annum may 

 be defined by the equation 

 E = MV; 



and if M' be the amount of deposits subject to 

 check, the average velocity V of turnover of 

 deposits may be defined by 

 E' = M'F'. 



Further, if (?{ be the quantity of a substance i 

 which is bought and Pi the price, PiQi will be 

 the amount spent in this transaction. Total 

 expenditure (E -\- E') during the year will be 

 the sum 'S,PiQi of the various products PiQt 

 for the transactions of the year; or 

 (E + E')=-SpiQi. 



This equation may be modified by the intro- 

 duction of the total trade T for the year and 

 the average price P. Then 



and the fundamental identity becomes 



MV + M'V'=zPT, (1) 



which is the equation of exchange'' (Chaps. 



i.-ni.). 



Such a mathematical identity is, as every 

 one knows, a mere truism whose validity no- 

 body should be rash enough to dispute. It 

 might therefore be thought, and it is appar- 

 ently the idea of many, that, being a truism, 

 the equation is worthless, that nothing more 

 can be obtained from it than has been put into 

 it. This opinion has been somewhat of a 



' This simple form of the equation applies only 

 to self-contained communities where each transac- 

 tion is settled during the year. The author, how- 

 ever, discusses (p. 370 ff.) the modifications neces- 

 sary when unsettled accounts and intercommunal 

 trade are present, and comes to the conclusion that 

 the changes are insignificant in the case of the 

 United States. 



stumbling block relative to all mathematics, 

 and even such a prince of mathematicians as 

 Poincare did not think it beneath him, in his 

 philosophizing moments, to try to explain why 

 mathematics can really amount to something, 

 why it does give results which are valuable, 

 why it is really creative. We need not enter 

 upon that question here; we may admit that 

 by proper discussion and transformation 

 mathematical identities do reveal important 

 relations not obvious in the original form of 

 the identity. Let us admit the same in re- 

 gard to the identity (1). 



We now have under our eyes six separate 

 elements, M, M', V, V, P, T, entering into 

 the equation of exchange, and we may focus 

 our attention upon the effects produced upon 

 certain of these elements by supposed varia- 

 tions in the others. For instance, if the 

 amount of trade T and the velocities Y, 

 V of circulation of money and deposits 

 remain constant from year to year while 

 the amounts of money M and of deposits M' 

 increase, it follows indubitably that the gen- 

 eral price level P must rise. On the other 

 hand, if M, M', V, V remain constant while 

 trade increases, the level of prices must be 

 lowered. As a matter of fact the statistics for 

 the United States for 1896 and 1912 are as 

 follows : 



M 31' r V T P 



1896 ... 0.88 2.71 18.8 36.6 191 60.3 

 1912 ... 1.70 8.15 21.0 53.0 435 107.6 



If we regard the price level P as the passive 

 element, the effect, and the other elements as 

 causes,^ we shall attribute the rise in the price 

 level chiefly to the great increases in deposits 

 subject to check and in their velocity; for the 

 product MV has about kept pace with the in- 

 crease in trade, whereas M'V has greatly out- 

 stripped it. 



When it is a question of such actual fig- 

 ures as these, we have reached a stage some- 

 what remote from the equation (1) in the 

 sense in which it was originally set up. Orig- 

 inally MY stood merely for the expenditures 



= The author gives reasons to justify this as- 

 sumption. 



