Duality and continuity

This paper fills the one remaining lacuna in (multiple-output) duality theory by provingjoint continuity (in input and output vectors) of cost, benefit, and (input and output) distance functions. Continuity is an important property where measurement error exists, for it provides assurance that small errors of measurement (of quantities or prices) result only in small errors in concepts like minimal cost. We consider continuity not only in prices and quantities, but also in technologies. Continuity in technologies might be more important than continjity in prices or quantities, because production technologies are almost certainly measured (or estimated) with error.

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