50 Irving Fisher — MatJiematical investigations 



is therefore not even roiighh^ proportioned to bis benefaction. If 

 tbe exact sbares among I, II, III, etc. in tbe old and new produc- 

 tion of A are known, the proper combination of stopper-positions 

 may be made and the reactions, now exceedingly complicated, may 

 be watched. 



6. Depress each stopper A, B, C, etc, There will be a general fall 

 in prices. But it will not be true that if the quantity of each com- 

 moditj^ is doubled its price will be halved, and the price of one 

 commodity in terms of another unaltered as Mill* apparently 

 thought, for the ratios of exchange are not the ratios of the con- 

 tents of the cisterns but of their ordinates. Nor will the ratios of 

 distribution of commodities remain the same. If however all cis- 

 terns in each front and back row are geometrically similar and their 

 filled portions also similar (a most unreal condition), the ratios of 

 distribution of commodities will be unaffectedf and if furthermore 

 all cisterns are similar, the ratios of prices will be unaltered. ;[ 



In the actual world aside from differences in the shapes of cisterns 

 there are more important differences in the way in w^hich they are 

 filled. Those for necessaries are relatively full as compared with 

 those for luxuries and those for the rich as compared with those for 

 the poor. Hence the effect of a proportionate increase of produc- 

 tion in all commodities will depress the price of necessaries much 

 more than of luxuries. 



The effects on the valuation or marginal utility of money will be 

 more complicated. If we suppose the depression of the stoppers to 

 begin w^hen they are far extended, the effects may be roughly 

 described as fo-llows. At first the valuation of money increases 

 since the prices decrease faster§ than the marginal utilities, reaches 

 a maximum (which is different for each individual and depends on 

 the initial distribution), and decreases when the decrease of ordin- 

 ates is faster than that of the thickness of the back cisterns. These 



* Pol. Econ., Bk. Ill, Ch. XIV, §2. 



f For proportional increase of the contents of the cisterns in the same front 

 and back row mil reduce their ordinates proportionally and shrink the back com- 

 partments alike, thus restoring equilibrium. 



X For in addition to the above consideration the reduction of ordinates in all 

 rows will be alike. 



^ Because when a cistern is relatively empty, a rise in the surface of its con- 

 tents diminishes the long ordinate by only a slight percentage but very materially 

 contracts the back compartment. 



