Page:Stabilizing the dollar, Fisher, 1920.djvu/248

194 the deviation the better stabilization will work—always assuming, of course, that the influence of the adjustment is as in the standard case.

F. Changing the Assumption as to "Influence."

(a) Assumptions same as in standard case except: influence decreased from 1% to ½% (per 1% of adjustment).

We have hitherto assumed that an adjustment of 1% in the dollar's weight would influence its purchasing power 1%. But this need not be assumed and would not be strictly true in practice, especially if the number of dollars, both of money in circulation and of deposits subject to check, were not kept strictly proportioned to the number of gold dollars in the reserve (as by the method described in Appendix I, § 1 and § 7).

The calculations, in the present case, are very similar to those of "E (b)" above.

Calling the original price level 100%, the index number at the end of the first adjustment period will be 101%. The dollar will now be increased by 1% which, according to our present supposition, would tend to lower the price level only half as much, i.e. ½%. As, during the second interval, the price level tends to go up 1% the new index number will be 101-½ +1 or 101½. The excess of 1½% above par will now call for a corresponding increase in the dollar's weight; but the brassage limitation holds it to 1%.

Accordingly, the next adjustment date will see an increase in the dollar's weight of 1% and the price level will be l01½-½+1 or 102. The next increase in the dollar's weight will be again limited to 1% and the index number will be 102-½+1 or 102½, and so on.

Evidently, as the brassage is 1% the power of the system to stabilize will be limited to ½% per adjustment interval.

(b) Assumptions same as in standard case except: influence changed from 1% to ½% and also : brassage changed from 1% to 2% or more.