Profit efficiency in non-competitive markets

This paper develops a non-radial linear programming model based on the concept of directional distance function to examine the profit efficiency (inefficiency) of decision making units (DMUs) in the case where the market prices are available but can be controlled by units, and DMUs can influence simultaneously the prices and quantities of inputs and outputs to maximize the total profit. The optimal solution of the proposed model can help decision makers to evaluate and improve the profit efficiency of DMUs by changing the prices and quantities of inputs and outputs. The proposed model satisfies the important properties, units invariance and translation invariance. We present a decomposition of the profit inefficiency obtained by the optimal solution of the proposed model which can individualize quantity and price contributions to the profit inefficiency of under evaluation DMU. Finally, an empirical application to a set of 50 bank branches will be presented to illustrate the proposed approach.