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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.

61

changes in the valuation of money are of course subject to the con-dition that each income measured in money remains the same.

7. Depress all income stoppers proportionally, i. e. increase allincomes in the same ratio. Then will all prices increase and thevaluation of money decrease exactly in this ratio. There will beno change in the distribution of commodities. There is merely adepreciated standard of money. Formerly the whole marketedcommodity was valued at a given number of dollars, now thisnumber is increased.

We have seen under number 1, that an increase in the moneyincome of a single individual without an increase in commoditiesis a benefit to him, but such an increase when universal is bene-ficial to no one.

8. Remove cistern IA and replace it with a shallower one, i. e.suppose a change in the taste of I for A, making the article lessattractive.

It is as if we raise .the bottom of the original cistern IA. Moreof A will flow to other consumers and more of Is money will flowto the purchase of other commodities. A will fall in price, mostother articles will rise. Is valuation of money will fall. For thosewho consume A extensively the valuation of money will fall. Forothers it may rise.

If all of the I cisterns grow shallower there will be a fall in thevaluation of money for I, but either prices will not change or theirchanges must be compensatory, for the quantities of commoditieshave not been altered nor their aggregate value. If all of the I rowcisterns change so as to admit of a uniform percentage shorteningof ordinates without any commodity flowing out of any cistern, nocommodity will flow out, no prices will change and there will beno change whatsoever in the distribution of commodities nor in thevaluation of money to other people. If one cistern shortens morethan this requirement, the effects will be analogous to those justdescribed for a single cistern.

If all the cisterns of the A row are made shallower the price ofA will decrease.* That of other articles will in general increase.In order that the distribution of commodities may not change, theA cisterns must be so changed as to admit of a shortening of ordin-

* Otherwise while the A ordinates shorten and their ratio to other ordinateslessens, the back cisterns would have a relatively too great thickness comparedwith the other thicknesses.