Covariances and relationships between price indices: Notes on a theorem of Ladislaus von Bortkiewicz on linear index functions

The note examines a generalization of a theorem of Bortkiewicz which relates the difference between a Paasche and a Laspeyres price index to a covariance between price and quantity relatives. The generalized theorem is used to demonstrate a number of interesting special applications. It turns out that some known relationships between two index functions can be expressed more elegantly. In other cases where not much is known yet about how the two functions are related to one another, we could establish an interesting equation on the basis of this theorem. This demonstrates the remarkable flexibility and usefulness of the generalized Bortkiewicz - theorem.