Farrell Revisited—Visualizing Properties of DEA Production Frontiers

The contributions of the paper are threefold: (i) compare with mathematical rigour the data envelopment analysis (DEA) model of Charnes, Cooper, and Rhodes and the Farrell model exhibiting constant returns to scale, (ii) reinterpret the contribution of Farrell and Fieldhouse that extended the analysis to variables returns to scale and establish the connection with the approach in Banker, Charnes, and Cooper, and (iii) provide graphical visualization of properties of the frontier function. Both papers by Farrell emphasized the importance of graphical visualization of non-parametric frontier functions, but, to our knowledge, this is seldom followed up in the literature. We use a graphical package (Effi Vision) with a numerical representation of the frontier functions, representing the contemporary development of visualization. By making suitable cuts through the DEA frontier in multidimensional space, various graphical representations of features of economic interest can be done. Development of ray average cost function and scale elasticity plots are novel illustrations.