Marginal rates and elasticities of substitution with additive models in DEA

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier 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 movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, 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.