•50 Irving Fisher —Mathematical investigations

is therefore not even roughly proportioned to his benefaction. Ifthe exact shares among I, II, III, etc. in the old and new produc-tion of A are known, the proper combination of stopper-positionsmay be made and the reactions, now exceedingly complicated, maybe watched.

6. Depress each stopper A, B, C, etc. There will be a general fallin prices. But it will not be true that if the quantity of each com-modity is doubled its price will be halved, and the price of onecommodity in terms of another unaltered as Mill* * * § apparentlythought, for the ratios of exchange are not the ratios of the con-tents of the cisterns but of their ordinates. Nor will the ratios ofdistribution of commodities remain the same. If however all cis-terns in each front and back row are geometrically similar and theirfilled portions also similar (a most unreal condition), the ratios ofdistribution of commodities will be unaffectedf and if furthermoreall cisterns are similar, the ratios of prices will be unaltered.|

In the actual world aside from differences in the shapes of cisternsthere are more important differences in the way in which they arefilled. Those for necessaries are relatively full as compared withthose for luxuries and those for the rich as compared with those forthe poor. Hence the effect of a proportionate increase of produc-tion in all commodities will depress the price of necessaries muchmore than of luxuries.

The effects on the valuation or marginal utility of money will bemore complicated. If we suppose the depression of the stoppers tobegin when they are far extended, the effects may be roughlydescribed as follows. At first the valuation of money increasessince the prices decrease faster§ than the marginal utilities, reachesa maximum (which is different for each individual and depends onthe 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. HI, Ch. XIV, §2.

f For proportional increase of the contents of the cisterns in the same frontand back row will reduce their ordinates proportionally and Bhrink the back com-partments alike, thus restoring equilibrium.

| For in addition to the above consideration the reduction of ordinates in allrows 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 materiallycontracts the back compartment.