Decompositions of Profitability Change Using Cost Functions: A Comment

Recently Diewert (2014) decomposed cost change into the product of four drivers. He then combined three of these drivers with a novel measure of returns to scale to decompose profitability change. We use an implicit Konus input quantity index to show that his expression for profitability change is the product of a price recovery index and an implicit productivity index, and we extend his analysis by exploiting new relationships between theoretical Konus and empirical Fisher price indexes to obtain two new decompositions of profitability change. One pairs a Konus price recovery index with a Fisher implicit productivity index, the other has pure Fisher structure, and we note the advantages of each.