in the theory of value and prices. 83 



The last two members of this equation are new and require a 

 word of explanation. The next to the last is an obvious conse- 

 quence of the principles of composition and division. Its denom- 

 inator represents the marginal utility of Gun and Trigger combined 



and is written ttts-tttu' ^^ ^^^^ ^^^^ member. 



But the quantities which are starred are those which can under 

 our supposition no longer be said to exist. Hence all members of 

 the equation containing a star drop out and we have left the first, 

 second and last members. In other words, if two articles are 

 perfectly completing their joint marginal utility is in the ratio to 

 their joint price as the marginal disutility of producing either 

 article is to its price (negatively) or as every other marginal utility 

 is to its price. 



■ In like manner if two articles are perfect completing articles from 

 the producer's standpoint, as beef -hides and beef -meat, their joint 

 marginal disutility is to their joint price as the marginal utility of 

 either is to its price (negatively) or as any marginal utility is to its 

 price. 



If two articles are such that thej^ are perfect completing both as 

 to production and consumption and in the same ratios, they not 

 only have no separate utilities or disutilities but they can have no 

 separate prices. Thus, the head, limbs, tail and other parts of a 

 horse are produced together and consumed (used) together ; they 

 have no separate price. 



It is impossible for articles to exist which are perfect completing 

 articles both for consumption and production but are produced in 

 one ratio and consumed in another. 



Suppose two articles are such that the production of one is per- 

 fectly completing to the consumption of the other. Suppose, for 

 instance, that the production of a ton of iron involves the consump- 

 tion of a ton of coal, and that the consumption of the ton of coal 

 also implies the production of a ton of iron. The iron producer in 

 this case could not be said to have utility for more coal so long as 

 he does not produce more iron, nor can he be said to have disutility 

 of producing more iron without consuming more coal. What 

 utilities or disutilities then does he have ? He may be said to have 

 a joint marginal disutility of producing iron and consuming coal. 

 This " joint " disutility is to the difference of the prices of iron and 

 coal as the marginal utility of any commodity to him is to its price. 



Like i)rinciples a])ply to three or more perfectly completing 

 articles. As long as articles are not perfectJy completing there is 



