Computation of scale elasticity in presence of exogenously fixed inputs

•Developing computation of scale elasticity in presence of exogenously fixed inputs.•Invoking indirect approach as well as providing the geometry for direct SE computation.•Comparing and contrasting values for scale elasticity with ND inputs with ordinary case using numerical data.•Illustrating the environmental influence on computation of scale elasticity using numerical data.•Comparing and contrasting the proposed approach with selective method in computing scale elasticity.

In this paper, the notion of scale elasticity is initially developed for models with non-discretionary inputs. A new unified formulation, resembling those for classic developments is proposed for computation of scale elasticity in presence of exogenously fixed inputs in the framework of date envelopment analysis.In order to remove the harshness of fixed inputs, we invoke regression of fixed inputs over efficiency measures and therefore units with more favorable environment indices are discounted for pioneers set. This naturally implies that different production possibility sets are induced according to environmental affect. Scale elasticity is then computed using indirect approach for both differentiable and non-differentiable cases.Also, the approach is illustrated with numerical examples and proved its benefit over selective approach, proposed by Podinovski and Førsund, by comparing and contrasting with numerical data. Moreover, the geometry and rationale behind the notion are described.