in the theory of value and prices.

83

The last two members of this equation are new and require aword 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 combinedd IT

and is written

in the last member.

d( G&T) k

But the quantities which are starred are those which can underour supposition no longer be said to exist. Hence all members ofthe equation containing a star drop out and we have left the first,second and last members. In other words, if two articles areperfectly completing their joint marginal utility is in the ratio totheir joint price as the marginal disutility of producing eitherarticle is to its price (negatively) or as every other marginal utilityis to its price.

In like manner if two articles are perfect completing articles fromthe producer’s standpoint, as beef-hides and beef-meat, their jointmarginal disutility is to their joint piice as the marginal utility ofeither is to its price (negatively) or as any marginal utility is to itsprice.

If two articles are such that they are perfect completing both asto production and consumption and in the same ratios, they notonly have no separate utilities or disutilities but they can have noseparate prices. Thus, the head, limbs, tail and other parts of ahorse are produced together and consumed (used) together ; theyhave no separate price.

It is impossible for articles to exist which are perfect completingarticles both for consumption and production but are produced inone 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, forinstance, 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 coalalso implies the production of a ton of iron. The iron producer inthis case could not be said to have utility for more coal so long ashe does not produce more iron, nor can he be said to have disutilityof producing more iron without consuming more coal. Whatutilities or disutilities then does he have ? He may be said to havea joint marginal disutility of producing iron and consuming coal.This “ joint ” disutility is to the difference of the prices of iron andcoal as the marginal utility of any commodity to him is to its prioe.

Like principles apply to three or more perfectly completingarticles. As long as articles are not perfectly completing there is