Caves et al. in 1982 introduced a productivity measure ''that does not
proceed from a continuous timer presentation''. They named these inde
xes after Sten Malmquist who in 1953 used ratios of distance functions
to formulate quantity indexes in the consumer context. In a later pap
er, Diewert proposed an alternative definition of productivity also ba
sed on distance functions, which he attributed to Hicks and Moorsteen.
In this letter we provide necessary and sufficient conditions for the
Malmquist productivity index to equal the Hicks-Moorsteen index.