Efficiency

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 38 in Conjugate Duality in Economic Analysis, 2026, pp 277-283 from Springer

Abstract: Abstract Paralleling the chapter “Weak Efficiency,” an efficiency primal and an efficiency dual obtain a necessary and sufficient condition for efficiency: a vector is efficient if and only if the optimum value is zero. The efficiency primal chooses a vector to maximize the efficiency function on the feasible set. The efficiency dual looks for a positive price to minimize the support to the feasible set. Alternatively, the efficiency dual is equivalent to a Karush-Kuhn-Tucker efficiency dual. The exceptional case applies: a vector is efficient if and only if the Lagrange multiplier is zero. The primal/dual pair leads to a direct proof of the fundamental characterization of vector efficiency, by invoking the Ekeland variational principle.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_38

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