Average-cost efficiency and optimal scale sizes in non-parametric analysis

• We propose a new cost-efficiency measure based on the notions of ray average cost and optimal scale size.
• The new efficiency measure (ACE) extends Banker and Thrall's (1992) TSRE measure to cost analysis.
• We establish a monotone inequality relationship between production-based and cost-based scale efficiency measures.
• We prove that optimal scale size is a more restrictive notion than most productive scale size.
• Our approach allows for a simultaneous determination of the regime and degree of scale economies.

Under fairly general assumptions requiring neither a differentiable frontier nor a constant-returns-to-scale technology, this paper introduces a new definition of an optimal scale size based on the minimization of unit costs. The corresponding measure, average-cost efficiency, combines scale and allocative efficiency, and generalizes the measurement of scale economies in efficiency analysis while providing a performance criterion which is stricter than both cost efficiency and scale efficiency measurement. The average-cost efficiency is not reliant upon the uniformity of the firms’ input-price vector, and we supply procedures to compute it in both convex and non-convex production technologies. Empirical illustration of the theoretical results is given with reference to large sets of production units.