130 Dr. WHEWELL, ON THE MATHEMATICAL EXPOSITION OF 



11,1 . , , 13, 4 



Since x is in these cases = -, — , and - respectively, and mx = 0, -, — , we nave m = 0, m = -, 



5 10 2 r ; 8 8 5 



3 

 m = — in the three cases respectively. 



4 



7- Which of these classes of cases is likely to exist in practice ? 



It will be apparent, on consideration, that one or other will occur according to the nature of 

 commodity, and thus, that m has different values for different commodities. We shall 

 endeavour to indicate certain classes of commodities according to this relation. 



8. (A) There may be some commodities on which, in a given society, the same sum is 

 expended whatever be the price of the article (per unit) ; a smaller quantity being bought 

 exactly in proportion as the price is higher. Such would be the case with ornamental attire, 

 for instance, if each person, or if persons on an average, were to spend upon it a determinate sum 

 every year ; — an allowance for dress, as it might be termed. In this case, when p becomes 

 p (1 + x), p'q', the money demand, remains unaltered, whence pq (1 + mx) = pq. Here m = 0. 



9. (-B) There may be other commodities of which the quantity bought is the same 

 whatever be the price : such, for example, may be articles which are looked upon as necessary 

 by rich persons ; as, for instance, official dresses, and conventional appendages of persons in office, 

 and the like. Here, when p becomes p (1 + x), q remains unaltered. Therefore pq (l + mx) 

 = pq (l + x). Here m = 1. 



10. (C) There are other commodities of which the price increases more rapidly than the 



quantity supplied diminishes : for instance, the general necessaries of life. It has been supposed 



that a deficiency of one-fifth in the supply of corn will raise the price four-fifths. Supposing 



4 9 36 11 .4 11 



this true, the money demand becomes = -x- = — = 1 -\ — . And since x = - and mx = — , 

 ' 5 5 25 25 5 25 



11 

 m = — . 

 20 



11. The more we suppose prices to rise for a given diminution of supply, the more will m 

 approach to 1. If we suppose that a diminution of one-fifth in the supply will treble the 



4 12 7 . 7 



price, we have the money demand =-x3= — = 1+-. And since mx = - and x = 2, 



5 5 5 5 



7 14 

 m = — = — . 

 10 20 



In all these cases m is between and 1. 



12. (D) There may be other commodities of which the price increases in a less pro- 

 portion than the supply diminishes : or, as the case is perhaps more evident, there may be com- 

 modities, of which, when the price diminishes, the demand increases, and in so great a proportion 

 that the whole sum expended on them is greater than before. This may be the case with 



