A derivative-based measure of economies of scope is obtained by exploiting the duality between the shadow cost function and the input distance function. This is a useful measure when the econometric estimation of a cost function is not viable.

Information on the economies of scope (or cost complementarities) between two or more output variables is traditionally obtained from the second derivative properties of an econometrically estimated multi-output cost function. However, in some instances the econometric estimation of a cost...