SOME SPECIAL PROBLEMS OF VALUATION 67

question of whether it is worth while from the point of view
of whether the increase of expenses is worth incurring, the
direct comparison of the increased cost of securing the
richer milk with the value of it when secured yields the
answer. The extra richness of the milk is secured at a
definite price, that is, the separate cost of an addition to the
butter yielded is observable, and thus, though the butter is
a product necessarily associated with others in its processes
of production, its marginal expenses of production admit
of separate examination. Such a separation of the specific
marginal expenses of joint products is possible in numerous
cases, and thus the resort to the preceding mode of treatment
 is not essential, at any rate when the conditions are
not those mentioned in discussing increasing returns. When
the marginal cost, as thus determined, corresponds to what
was there discussed under the name “prime cost,” the
distribution of the supplementary costs, among the various
joint products, necessitates a recurrence to the considerations
to which attention was directed in connection with the
assumption of invariability of, proportion between the
quantities of the different joint products. The point of
view now presented, of an effective separation of the costs
of the different products, does not lead to results contradictory
to those previously presented. Where both methods can
be applied, they will lead to the same result. In general,
the case of joint products more numerous than two can be
treated by similar principles, We shall give some further
consideration to the case later in the present chapter in
some brief remarks on the railway rate problem.
Corresponding to the case of joint production is the case
of joint use or consumption. A carriage needs horses or a
motor, a steel knife-blade needs a handle, and many useful
commodities are made from two or more different raw
materials. The demand which expresses consumers’ desires
is a demand for a combination of materials, and the demand
for the separate materials, by the producers of the commodities,
 is derived from the consumers’ demand for the
combinations, The problem before us is to determine the
separate marginal utilities of the components, a necessary