At beginning of the 1st interval 100.
At the beginning of the 2d interval 1% above 100 or 101.
At the beginning of the 3d interval 1% above 101 or 102.01.
At the beginning of the 4th interval 1% above 102.01 or 103.0301.
At the beginning of the 5th interval 1% above 103.0301 or 104.060401.
Etc., increasing as by compound interest.
Not to put too fine a point on these figures, we may omit decimals and use the figures 100, 101, 102, 103, 104, etc., until the "compounding" produces an appreciable effect. When, for instance, the index number is in the neighborhood of 150 the 1% increase will make the next index number greater by about 1½; and when it is in the neighborhood of 200, the 1% increase will make a difference of about 2. Thus, if we assume that (were it not for stabilization) the course of prices would rise 1% each adjustment interval from 100 to 200 and then fall, the index numbers would run approximately as follows: 100, 101, 102, 103, 104, . . . 150, 151½, 153, . . . 198, 200, 198, 196, . . . 150, 148½, 147, . . . .
Under the fifth assumption, we may distinguish four types of price movements—the four which could take place in actual experience,—a rise, a fall, a reverse after an upward movement, a reverse after a downward movement.
We are now ready to calculate[1] what, under the five assumptions formulated, the stabilized course of the index number will be.
At the start, the index number being 100 or par, no adjustment in the dollar's weight will be made. Con-
- ↑ In all the calculations of this section it is assumed that either the mint price rules the market all the time or the redemption price rules it all the time. If, or when, the market price shifts between the two, in the manner discussed in Appendix I, § 2, the results would be slightly different, as can readily be calculated.
