Economic efficiency when prices are not fixed: disentangling quantity and price efficiency

• Cost efficiency measurement when factor prices are not fixed is addressed.
• A model where factor prices and quantities are optimized simultaneously is proposed.
• Overall cost efficiency is decomposed into quantity and price components.
• When factor prices are decision variablesallocative efficiency is not meaningful.
• The proposed approach is compared with others, and its main advantages are shown.

This paper proposes an approach to compute cost efficiency in contexts where units can adjust input quantities and to some degree prices so that through their joint determination they can minimise the aggregate cost of the outputs they secure. The model developed is based on the data envelopment analysis (DEA) framework and can accommodate situations where the degree of influence over prices ranges from minimal to considerable. When units cannot influence prices at all the model proposed reduces to the standard cost efficiency DEA model for the case where prices are taken as exogenous. In addition to the cost efficiency model, we introduce an additive decomposition of potential cost savings into a quantity and a price component, based on Bennet indicators.