in the theory ofDcdue and i^r ices. 47 



More generally in a redistribution of incomes without altering 

 their aggregate, in order that no prices may change (1) no condition 

 is necessary for those whose incomes have not changed; (2) for 

 those whose incomes have changed the geometrical character of the 

 cisterns must be such that a proportional shortening of the ordinates 

 for each and every richer man will absorb in the aggregate, the 

 same additional commodity of each sort as is lost in the aggregate 

 by the poorer through a proportional lengthening in the ordinates 

 of each of them. 



If the enriched man or men absorb more of a given commodity 

 than this requirement its price will rise, if less it will fall. 



If the increase of income of I equals the decrease of III effects on 

 prices must be compensatory. If one rises some other or others 

 must fall. If lA is much broader than IIIA but IB is much nar- 

 rower than IIIB, the price of A may rise and of B fall unless 

 counteractions come from other commodities. For if we were to 

 suppose prices unaltered, the cistern lA would absorb from IIIA 

 so much and IB from IIIB so little that the ordinate of IIIA 

 would be too long and of IIIB too short for equilibrium. In order 

 to partially permit this lengthening and shortening there must be a 

 corresponding lengthening and shortening in the whole A and B 

 rows respectively and prices must be proportioned to these ordinates. 

 In this case it is to be noted furthermore that a change in prices 

 causes a change in the distribution of the income of II and all other 

 individuals. 



The marginal utility of money for I decreases, for III increases, 

 and for II may slightly rise or fall, owing to the change of prices. 

 With the breadths of the cisterns properly adapted to the changes 

 in prices there liiay be no change* in the valuation of money for II. 



* If the prices of only two commodities A and B claange and All and BII are 

 straight walled, and if their breadths are inversely proportional to the difference 

 of the squares of the old and the new prices, there will be no change in the valu- 

 ation of money. For, let p and -p' be the old and new prices, let x and a?^ be 

 the breadths (for II) of the A and B cisterns and let y^^ y^ and y^', y^' be their 

 old and new ordinates. Since the marginal utility of money is not to change 

 nor the prices of C, D, etc., their ordinates cannot and therefore their quanti- 

 ties (for II) cannot change. Hence the added expenditure (by II) on A must 

 equal that taken from B, i. e. : 



But since the valuation of money is to be kept constant, 



V _ .^« ^ ^ ^ y'' ^ j^ 



Pa Pa ~ Ph " Pb ~ 



