84 Irving Fisher — Mathematical investigations 



no need for the substitution of joint utilities for single ones. As a 

 matter of fact the number of really perfectly completing articles is 

 relatively small. 



If two articles are " perfect " substitutes for consumption and the 

 ratio of their marginal utilities is the same for all consumers, while 

 from a producer's standpoint they are not " perfect" substitutes, the 

 consumers fix the ratio of their prices (viz: that of their marg. ut.) 

 and the producers produce quantities accordingly. But the quan- 

 tities of each consumed by different individuals is entirely indeter- 

 minate. Thus the milk from each cow may be regarded as a sep- 

 arate commodity. The consumer is indifferent to which milk he 

 drinks, and purely accidental causes determine how much of each he 

 gets ; the producer, however, milks determinate amounts from each 

 cow. 



If two articles are perfect substitutes both for production and 

 consumption and the ratio of their marginal utilities and of their 

 marginal disutilities are all alike their prices will have this ratio, but 

 the relative quantities of each produced and consumed is entirely 

 indeterminate ; (e. g. the colors in the binding of a book). 



If two articles are perfect substitutes and the ratio of their mar- 

 ginal utility of the first to the second is for every consumer greater 

 than the ratio of their marginal disutilities to all producers, the 

 first commodity alone will be produced and consumed and its price 

 will be determined as for any commodit}^ 



In general if two articles are perfect substitutes, but the ratio of 

 their marginal utilities and the ratio of their marginal disutilities is 

 different for different individuals, those to whom the ratio of mar- 

 ginal utilities of the first to the second is greater than the ratio of 

 their prices will consume only the first, those whose utility ratio is 

 less than the ^^rice ratio will consume only the second, those whose 

 disutility ratio is greater than the price ratio will produce only the 

 second ; those for whom it is less, only the first.* In this case the 

 price of each article is determined just as usual, but for each indi" 

 vidualVho does not consume or produce one or the other, its mar- 

 ginal utility or disutility simph^- fails to have meaning and drops 

 out of the equations ; just as in Part I, occasionally a cistern may 

 be entirely out of the tank water. 



* If some producers and consumers should have their utility or disutility ratio 

 identical with the price ratio the relative amounts produced and consumed are 

 indeterminate to the extent of this coincidence. 



