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define perfect substitutes as such that this ratio is absolutely constant.The essential attribute of completing articles is that the ratio ofthe quantities actually produced and consumed tends to be constant(as many shoe-strings as shoes for instance, irrespective of cost).We may define perfect completing articles as such that this ratio isabsolutely constant.
If we suppose each set of competing and completing articles tobe “ perfect,” it is possible to arrange the cisterns so that the changeof form of some cisterns as due to change in the contents of othercisterns shall be small or nothing. Thus if four grades of flour be“perfect” competing, so that their marginal utilities are always inthe ratio 8, 9, 11, 17, we may form a joint cistern for individual Iwhose contents shall be “flour,” the quality unspecified. Eachcubic unit of liquid shall represent equivalent quantities of eachgrade, i. e. £ barrel of the first quality, £ of the second, of thethird or -fa of the fourth, while the ordinate shall represent the com-mon utility of any one of t hese equivalent quantities.
If four completing articles as the parts of a coat, sleeves, pockets,buttons, and coat proper are always produced and consumed in num-bers proportional respectively to 2, 4, 3 and 1, we may form a jointcistern for individual I whose contents shall be “ coats,” parts un-distinguished.
With such combinations as these, the cistern analysis of Part Iwill represent the economic relations fairly well and almost per-fectly if the deviations from equilibrium are not followed too far.
But few articles are absolutely perfect representatives of eitherthe competing or the completing group, and a member of one groupmay also belong to another. Thus butter is completing to breadand biscuit, and although a cheapening of bread directly increasesthe utility of butter it indireotly increases it by decreasing the useof biscuit.
It is readily seen that the interrelations of the shapes of the cis-terns—if we now treat each quality of meat, etc. and each part of autensil as a separate commodity—are too complicated even to bementally representable without some new mode of analysis.
§5.
The former analysis is incomplete, not incorrect. All the inter-dependence described in Part I exists, but there also exist otherconnections between the shapes of the cisterns which could not bemechanically exhibited. For any one position of equilibrium the