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Mathematical investigations in the theory of value and prices / by Irving Fisher
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in the theory of value and prices.

45

the character of the cisterns. If all the A cisterns are alike andalso all B cisterns, all C cisterns, etc., then each commodity will bedistributed in equal parts among the individuals.

2. Press stopper I. This amounts to increasing the income of IIt does not increase the amount of commodities in the market butgives a larger share to I. The total money value of the same aggre-gate commodities in the whole market has increased by the amountof liquid added by depressing the stopper.

The added water in the back cisterns of the I row will make theback compartments in this row fuller than the front. The back levelwill be temporarily above the water level of the tank and (as thecisterns will sink) the front level will be temporarily below. Theeffect of the former is to bulge out the movable rear wall in the Irow, to extend the rods and to cause the same expansion in the backcompartments of the II, III, etc. rows. This makes the back liquidsin these rows lower and the front liquids higher than the tank level.Hence the front cisterns of the II, III, etc. rows pour part of theircontents into the I row whose level as we have seen is below that ofthe tank.

In economic language to give a greater money value to one indi-vidual causes for him smaller marginal utilities (cisterns sink), alower marginal utility of money, and increased consumption of com-modities. For other individuals it increases marginal utilities (cis-terns rise), decreases consumption, increases prices (back cisternsexpand), and may increase or decrease their marginal utility ofmoney-income according as marginal utilities (ordinates) increasefaster than prices (back thicknesses) or the reverse.

So much for the effect on different individuals. Now as to theeffect on the various commodities. Prices in general have risen butnot necessarily of all articles. Suppose article C is consumed littleor not at all (cistern narrow) by the enriched individual I but is ex-tensively used by those whose valuation of money has increased.Then since the valuation of money to II is equal to the quotient ofthe ordinate of IIC divided by the thickness of the back cistern ofIIC, and since this ordinate has not lengthened by any appreciableloss of commodity C from II to I, the thickness must have lessened,that is, the price has been reduced.

Not only may there be such exceptional commodities but theremay be exceptional individuals. Thus a man may be the principalconsumer of just those commodities and those only whose price hasfallen. His consumption will increase, his marginal utility of money