in the theory of value and prices. 10] 



Pa =^ \ r — \ \ 



fK. 



B 



=r- 



B 



M. 1 



fA. 



B 



M, 1 _ 



.J^' 



B 



K,. B„ ... M, 



B. . . . M, 



j^ K„ i3„ ... M„ J 1^ /\„ 1^„ . . . iVJ„ J 



in which obviously in general a change in A will produce a greater 

 influence on p^, then an equal change in B, etc. But it shows clearly 

 that p^ is not a function of A alone. 



Usually n ^ m. Hence we may use the first m equations of the 

 second set, or in fact any m equations. The resulting determinant- 

 quotients must be equal and must equal also the several like 

 determinates for production. 



The corresponding values of p^^ p^^ etc., may be found and may 

 be substituted in the fourth set. 



If wherever A^ now occurs in the fourth set, we substitute 

 K„ — A^ — Ag — . . . —An from the first set, and likewise for B^, etc., 

 the resulting fourth set is self-suflicient. We have thus eliminated 



the variables y^ , etc., p„, etc., A^, B^, etc., and have gotten rid of 



a A. 



the first, second and third set of equations. We can proceed no 

 further, however, until the explicit forms of the functions F(Aj), 

 etc., are given. 



APPENDIX II. 

 LIMITATIONS OF THE PRECEDING ANALYSIS. 



§ 1- 

 No pretense is made that the preceding analysis is perfect or ex- 

 haustive. There is no such analysis of any phenomena whatever 

 even in physics. The suppositions in Ch. II, § 2 of Part I, are of 

 course ideal. They only imperfectly apply to New York Citj?- or 

 Chicago. Ideal suppositions are unavoidable in any science. In fact 

 it is an evidence of progress when the distinction between the ideal 

 and the actual arises.* Even in hydrostatics the assumption of per- 

 fect fluidity is never full}^ realized. The physicist has never fully 

 explained a single fact in the universe. He approximates only. 

 The economist cannot hope to do better. Some writers, especially 

 those of the historical school are disposed to carp at the introduc- 

 tion of a refined mathematical ancdysis. It is the old stor}' of the 



* See Prof. Simon Newcomb. The Method and Province of Pol. Econ., N. Am. 

 Rev., CCXI, IX. 



