This article surveys duality in producer theory, consumer theory and welfare economics. As opposed to the usual analysis through first-order conditions for optimization, the various dualities are derived here from convex duality theory, using Fenchel transforms and subdifferentials.
KeywordsAntonelli, G.B. Bergson–Samuelson social welfare function Convex programming Convexity Cost functions Cyclic monotonicity Duality Envelope th Fenchel transform Firm, theory of the Hicksian-compensated demand Hotelling, H. Hotelling’s lemma Hyperplanes Indirect utility function Lagrange multipliers Marginal revolution Monotonicity Profit functions Quasi-equilibrium Saddlepoints Separation th Shephard, R.W. Shephard’s lemma
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