in the theory of value and prices.
101
fK, B, ... MJ fA. B, ...I K, B a . . . M j A. B, ...
[ K„ B, ... M„ J [ A„ B„ . . . M„ J
in which obviously in general a change in A will produce a greaterinfluence on p a then an equal change in B, etc. But it shows clearlythat p a is not a function of A alone.
Usually n ]> m. Hence we may use the first m equations of thesecond set, or in fact any m equations. The resulting determinant-quotients must be equal and must equal also the several likedeterminates for production.
The corresponding values of p b , p„ etc., may be found and maybe substituted in the fourth set.
If wherever A, now occurs in the fourth set, we substituteK„ —A, — A 3 — . . . — A„ from the first set, and likewise for B„ etc.,the resulting fourth set is self-sufficient. We have thus eliminatedcl\J
the variables etc., p„ etc., A t , B„ etc., and have gotten rid of
the first, second and third set of equations. We can proceed nofurther, however, until the explicit forms of the functions F(A 1 ),etc., are given.
LIMITATIONS OF THE PRECEDING ANALYSIS.
No pretense is made that the preceding analysis is perfect or ex-haustive. There is no such analysis of any phenomena whateyereven in physics. The suppositious in Ch. II, § 2 of Part I, are ofcourse ideal. They only imperfectly apply to New York City orChicago . Ideal suppositions are unavoidable in any science. In factit is an evidence of progress when the distinction between the idealand the actual arises.* Even in hydrostatics the assumption of per-fect fluidity is never fully realized. The physicist has never fullyexplained a single fact in the universe. He approximates only.The economist cannot hope to do better. Some writers, especiallythose of the historical school are disposed to carp at the introduc-tion of a refined mathematical analysis. It is the old story of the
* See Prof. Simon Newcomb. The Method and Province of Pol. Econ. , N. Am.Rev., CCXI, IX.