Non-parametric measurement of economies of scale and scope in non-competitive environment with price uncertainty

In non-competitive market characterized by heterogeneous firms and price uncertainty, we discuss the measurement of economies of scale and scope due to process indivisibilities arising from the task-specific production processes of multiproduct firm. Two competing DEA cost models—one based on the factor-based technology set and the other based on cost-based technology set, are examined in terms of their relative strengths and weakness to reveal scale and scope economies. Given the assumptions underlying both cost models, it is argued that the latter model may be relatively flexible and empirically demanding over the former one. The flexibilities are described in terms of price uncertainty; firms' heterogeneity; and the control over on the mix and quantities of inputs and their prices. And, as regards the underlying linkage of scale with scope properties with respect to diversified vis-à-vis additive firm, we find that the former model not only fails to exhibit one important property, i.e., the independence between scope properties of diversified firm and scale properties of additive firm, but also reveals one strange property, i.e., falling of scale elasticity of an additive firm irrespective of its no economies or diseconomies of scale possibility.