90
APPENDIX I.
MISCELLANEOUS REMARKS ON PART I.
I. FAILURE OF EQUATIONS.
Jevons (p. 118) discusses the failure of equations for simple ex-change. It is clear that such failure must frequently occur in com-plex exchanges hut no one has apparently commented on it. It wouldseem at first sight that this would introduce an indeterminate elementinto our results. Such however is not the case unless we take accountof articles neither produced nor consumed ; fhen the highest pricewhich any consumer will pay for the first infinitesimal is less thanthe lowest price at which any one will produce it; there is no pro-duction nor consumption and the term price has no determinatemeaning. As soon as changes in industrial conditions, that is in theshape of the cisterns or their number makes this inequality into anequality, the article enters into our calculations.
Suppose A is produced by n n people, consumed by n K , and ex-changed or retailed by n t , where n n n K and n t are each less than n(the number of individuals.) Moreover from the nature of ourformer suppositions if any of the three are greater than zero allmust be, for anything once in the system is supposed to be produced,exchanged and consumed within the given period of time.
The number of people who do not
produce A is n—n^,exchange A is n — n t ,consume A is n — n K .
The number of unknowns dropped out of the equations in Ch. VI,§ 2, is
3?i-Kr + ^ + nJ of the type A liir , A„ e , A,,,, etc.,and 3n-{n 7t -{-n e -\-n K ) °* the type •
or 6?i —2(w v -J-» e -|-n i[ ) altogether.
The failing equations in the first set are none,
“ “ “ “ second “ none,.
“ “ “ “ third “ 3 n —(«„ + n t +*n K ),
“ “ “ “ fourth
“ “ “ “ fifth
or 6n— 2(n r + n, + n c ) altogether.
From the above agreement it appears that there can be no indeter-minate case under the suppositions which were first made. Let uslook at this somewhat more closely.
3 ”-K+ n « + w *)>
none,