A Dual Measure of Economies of Scope

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 function may not be viable, because cost or input price data are not readily available or because the assumption of cost minimising behaviour is not appropriate in the industry at hand, perhaps due to government ownership or regulatory controls. In this paper we address this issue by utilising the duality between the cost and input distance functions in deriving an expression for a measure of economies of scope in terms of the derivatives of an input distance function. We derive expressions for the special cases of the CES and translog functional forms, and then provide an empirical illustration using sample data on Australian aged care facilities, an industry which is currently undergoing a major pricing and regulatory review. Our empirical results indicate that there is some evidence for existence of economies of scope between high care and low care patients, a result which is of particular interest to policy makers in this industry.