| Sumario: | Section 1 of the paper defines the distance function and discusses its properties. Particular attention is focused on the duality between the distance and cost functions and on the use of the former in deriving compensated inverse demand functions. These latter seem to have been first systematically treated by Hicks (1956, Chapter XVI) who used them to define "q-complements" and "q-substitutes" in contrast to the now standard "p-complements" and "p-substitutes". The matrix of q-substitution effects is the Antonelli matrix of integrability theory, Samuelson (1950), and we show how this and the Slutsky matrix of p-substitution effects can be regarded as generalized inverses of one another. Section 2 takes up Malmquist's (1953) analysis and discusses the theory of quantity and utility indices based on the distance function and its dual relation to the price and utility indices based on the cost function. Finally, Section 3 gives a brief foretaste of the application of the analysis. The familiar Ramsey rule for optimal taxation in an equity disregarding society is derived in a new and very simple form. Instead of stating the optimal tax rule in terms of its effects upon quantities, the distance function approach allows a direct characterization of the tax rates themselves.
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