This paper shows how scale efficiency can be measured from an arbitrary parametric hyperbolic distance function with multiple outputs and multiple inputs. It extends the methods introduced by Ray (J Product Anal 11:183–194, <CitationRef CitationID="CR8">1998</CitationRef>), and Balk (J Product Anal 15:159–183, <CitationRef CitationID="CR1">2001</CitationRef>) and Ray (<CitationRef CitationID="CR9">2003</CitationRef>)...</citationref></citationref></citationref>

Introduction of new products into the market place poses a difficult problem for the calculation of a cost-of-living (COL) index. The problem is that the reservation prices of new products in the periods before their introduction are unobservable. This paper introduces a new index number formula...