Mat 16, 1913] 



SCIENCE 



761 



more readily will we exchange it for other 

 goods; hence prices of other goods, as meas- 

 ured in gold, must rise. Such an argument 

 does not introduce the equation of exchange; 

 it is based on a sort of value theory of gold, 

 partly quantitative, but largely psychological. 

 We must not forget that according to theoret- 

 ical economics the equilibrium of exchanges 

 and the relative prices of goods do depend on 

 the marginal utilities of the goods, that is, 

 upon the relative values of the final infinitesi- 

 mal quantities of goods entering into the ex- 

 change as these values are estimated by the 

 individual traders. The value theory or, bet- 

 ter, the marginal utility theory is therefore 

 fundamental and the above mentioned facile 

 argument is qualitatively correct. 



When, however, we desire to take the equa- 

 tion of exchange as fundamental and for a 

 quantitative discussion this seems the readiest 

 if not the only thing to do, we have to examine 

 merely the effects of a flood of gold upon the 

 various elements of that equation. Suppose 

 that 258 grains of standard gold are mined 

 and turned over to the government for coin- 

 age into $10 or for exchange for a gold certifi- 

 cate of like amount. Then M is thereby in- 

 creased to the extent of $10. As V is about 

 20, there is a contribution of some $200 to the 

 product PT. If a half billion of gold were 

 thus injected into the circulation in the 

 United States each year, it would cause an 

 increase of ten billion in PT. Now in recent 

 years trade has been increasing here in the 

 United States at the rate of some fifteen bil- 

 lions per year. The half billion of gold, prac- 

 tically the total world output per year, would 

 therefore not suiEce to maintain prices, to say 

 nothing of advancing them, here in our own 

 country if we added all of it to the circulation, 

 and provided, of course, that we did not 

 otherwise inflate the circulation. 



Suppose, however, that the 258 grains of 

 gold went into the reserves of a bank operating 

 under a rule of 25 per cent, reserve against 

 deposits. The quantity M' would then be 

 swelled not merely by $10, but by $40, and as 

 V is in the neighborhood of 50, the term 



M'V would be increased by something like 

 $2,000, ten times as much as the term MV was 

 increased on the previous hypothesis. Hence 

 an addition of 75 millions in gold to the re- 

 serve stocks of banks operating under a 25 

 per cent, ratio would swell the term M'V by 

 the fifteen billion requisite to keep pace with 

 trade, and a greater increase of gold would 

 more than keep the pace, it would force 

 prices to rise. These figures are very rough 

 and are cited merely to enforce the idea that it 

 is the expansion of credit by the influx of gold 

 into bank reserves, and not the increase of 

 gold in circulation, which must be the chief 

 cause in the rise of prices as determined by 

 the equation of exchange. We make no at- 

 tempt to take secondary effects into considera- 

 tion. 



In the last chapter of the work the author 

 discusses the possibility of stabilizing the 

 purchasing power of the dollar, that is, of 

 maintaining an approximately constant price 

 level. The scheme he there suggests for ac- 

 complishing this purpose has undergone suc- 

 cessive modifications in a considerable series 

 of printed papers or privately circulated mono- 

 graphs until its present form appears in an 

 article only two months old.° Unfortunately 

 he abandons his equation of exchange and 

 proceeds with general arguments or special 

 hypotheses which seem far from substantial 

 foundation. Such a change in style may be 

 necessary to make an impression on a general 

 public, and it is only by making such a gen- 

 eral impression that any actual change of 

 standard of value could be made into law; 

 but for a mathematician the way would have 

 been better lighted had the equation of ex- 

 change been constantly in evidence. 



Briefly, the plan is to have the various gold- 

 standard governments of the world pay less 

 for gold as the general level of prices rises. 

 Thus instead of giving a dollar for 25.8 

 grains of coin-gold, the United States would 

 require 27 or 30 grains in exchange for a dol- 

 lar. The author has an elaborately worked 



'"A Compensated Dollar, ' ' Quarterly Journal 

 of Economics, Vol. 27, February, 1913. 



