ABSTRACT
For any pair of demands, a necessary and sufficient condition for the existence of a compatible homogeneous utility, and hence of a compatible (or ‘true’) price index, is the PL-inequality, which is that the Paasche index does not exceed that of Laspeyres. This is the condition for the PL-interval, or the set of points bounded above andbelowby theLaspeyres andPaasche indices, to be non-empty.Acompatible price index being one determined in respect to some compatible homogeneous utility, its possible values are identical with the points of the PL-interval. When the interval is non-empty, the Fisher ‘ideal’ index is one of its points and therefore has this property of compatibility like any other. These are results coming directly from Chapter III.
