Page:Stabilizing the dollar, Fisher, 1920.djvu/246

192 case. The higher brassage makes no difference because it was already high enough not to limit the adjustment, the tendency and lag also being as assumed.

(b) Assumptions same as in standard case except: brassage changed from 1% to 2%, and also: tendency, first upward and later downward, changed from 1% to 2%.

Under these conditions, the restraining influence exactly neutralizes the tendency and the index number is stabilized at 102 (during the upward tendency) and at 98 (during the downward tendency).

(c) Assumptions same as in standard case except: brassage changed from 1% to 2% and also: lag changed from 1 to S adjustment intervals. In this case, the stabilization process results, while the price tendency is upward, in a movement of the index number between 1% below par and 5% above par. At reversal, the index number at first drops as low as 93, but recovers and (during the downward tendency) fluctuates between 1% above par and 5% below par.

(d) Conclusion as to brassage.

We conclude that, in general, the greater the brassage the greater the freedom of the index number to vary. It is freer to approach toward par; but it is also freer to depart from par, if the lag is very great, i.e. if the adjustment interval is made a very small fraction of the lag.

Practically, the brassage should be between, say, 1 % and 3%. Within such limits it makes remarkably little difference to the result whether the exact figure is near one extreme or the other and any figure within these limits is adequate to secure a close approximation of the index number to par except under most extraordinary conditions such as those existing in a World War.

E. Changing the Assumption as to the "Adjustment."

(a) Assumptions same as in standard case except: adjustment changed from 1% to 2% (per 1% deviation).

The results are exactly the same as in the standard