Page:Stabilizing the dollar, Fisher, 1920.djvu/243

. 9, B] {|
 * | Influence
 * | Tendency
 * | Beginning of 1st interval
 * | 100
 * | During 1st interval
 * | 0
 * | +1
 * | Beginning of 2d interval
 * | 101
 * | During 2d interval
 * | 0
 * | +1
 * | Beginning of 3d interval
 * | 102
 * | During 3d interval
 * | -1
 * | +1
 * | Beginning of 4th interval
 * | 102
 * | During 4th interval
 * | -1
 * | +1
 * | Etc., repeating.
 * }
 * | +1
 * | Beginning of 3d interval
 * | 102
 * | During 3d interval
 * | -1
 * | +1
 * | Beginning of 4th interval
 * | 102
 * | During 4th interval
 * | -1
 * | +1
 * | Etc., repeating.
 * }
 * | 102
 * | During 4th interval
 * | -1
 * | +1
 * | Etc., repeating.
 * }
 * | -1
 * | +1
 * | Etc., repeating.
 * }
 * }
 * }
 * }
 * }

Upon reversal of the assumed price tendency the stabilized index number falls to, and remains slightly below, par. (b) Assumptions same as in standard case except: lag changed to 3 adjustment intervals.

Following the same reasoning as under "a," we find the index number rising to 103, and then remaining at 103, the influence, thereafter, of the 1% adjustment being exactly neutralized so long as the 1% tendency to rise continues.

(c) Conclusion as to lag.

In the preceding examples the stabilization process is very simply and effectively applied, the restraining influence sooner or later (depending on the ratio between the lag and the adjustment interval) taking effect and thereafter, while unable to restore the index number to par on account of the steady upward (or downward) tendency, keeping the index number constant at a point slightly above (or below) par.

We see that the greater the lag in proportion to the adjustment interval, the greater is the range of the index number from par. Yet, even if the lag is many times the adjustment interval, the index number keeps near par.