Page:Stabilizing the dollar, Fisher, 1920.djvu/242

188 B. Changing the Assumption as to the "Lag." (a) Assumptions same as in standard case except: lag changed from 1 to 2 adjustment intervals.

The index number, being uninfluenced by stabilization, will follow the assumed tendency for two adjustment intervals, and run: 100, 101, 102.

That is, at the start, or beginning of the first interval, there is no deviation from par and so no adjustment in weight; at the beginning of the second interval there is an adjustment in weight of +1%; but, as the lag between this adjustment and its influence on the index number is now assumed to be two adjustment periods, the following index number is unaffected and remains 102.

The par-ward influence (assumed as 1%) of the 1% adjustment made at the beginning of the second interval will, under our present assumptions, be felt during the third interval. During that interval this par-ward influence will strive to bring the index number down 1% from 102. But the assumed upward tendency of 1% keeps the index number at 102. At the beginning of the third interval, the 2% deviation would cause a 2% increase in the weight of the dollar, were it not for the brassage charge limiting any one increase in the dollar's weight to 1%, which will therefore be the increase effected. This 1% increase in the dollar's weight, made at the beginning of the third adjustment interval, influences the index number during the fourth interval to pull it downward; but the upward tendency will keep it still at 102, Thus the formula will be: 102 (the index number at any adjustment date) – 1 (the influence of the adjustment at the preceding date) + 1 (the tendency to increase) = 102.

The following table shows the results: