A Note on the Flexibility of the Barnett and Hahm Functional Form

It is very desirable to find flexible functional forms for unit cost (or profit) functions that are globally concave (or convex). It is easy to find flexible functional forms that are locally well behaved but do not satisfy the required regularity conditions globally. This note examines the global flexibility properties of a unit profit function that was originally suggested by Barnett and Hahm (1994). It is found that this functional form is an improvement over other locally flexible functional forms, in that Barnett and Hahm (BH) functional form for a unit profit function can maintain global convexity while at the same time, it can allow for an arbitrary pattern of substitutes and complements for pairs of outputs and inputs. However, an example shows that the BH functional form is not fully flexible.