Divisia price and quantity indices: 80 years after

This paper reviews and extends the theory of price and quantity indices which are defined as line integrals, the two types being those of Divisia and Montgomery. The properties of these indices are systematically explored, whereby in particular attention is paid to the path-(in)dependency issue. Two sections discuss the problem of how to approximate the line integral indices when only data at discrete points of time are available. It appears that every bilateral index can be conceived as the outcome of a line integral index over a particular curve in price-quantity space. The classical position is that chained bilateral indices are rationalized by Divisia indices. This rationalization is only interesting when the Divisia indices themselves possess a proper foundation in economic theory. The final sections are therefore devoted to the role played by the Divisia indices in micro-economic theory.