Interconvertible rules between an aggregative index and a log-change index

This paper describes interconvertible rules between an aggregative index like the Laspeyres index and a log-change index like the Tӧrnqvist index. Thus we can compare an aggregative index with a log-change index in the same form. Using these rules, we formulate the logarithmic difference between the Laspeyres price index and the Tӧrnqvist price index. One of the rules may be combined with another. By using these combined rules, we can change from given weights to other weights in an aggregative index (or a log-change index) of which the value is invariable.