Marginal rates and elasticities of substitution with additive models in DEA

Marginal rates and elasticities of substitution are derived from the optima l slack values obtained from modified versions of additive DEA models. Proj ection formulas are used to ensure that all points are on the efficient fro ntier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes mov ement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is th erefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includ es, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency-as in standard versions of additive models.