On the Monopolist Problem and Its Dual

In this paper, we study the functional that arises in numerous economic applications, in particular, in the monopolist problem. A special feature of these problems is that the domains of such functionals are nonclassical (in our case, increasing convex functions). We use an appropriate minimax theor...

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Veröffentlicht in:	Mathematical Notes 2023-08, Vol.114 (1-2), p.147-158
Hauptverfasser:	Bogachev, T. V., Kolesnikov, A. V.
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Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Functionals Mathematics Mathematics and Statistics Minimax technique
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description	In this paper, we study the functional that arises in numerous economic applications, in particular, in the monopolist problem. A special feature of these problems is that the domains of such functionals are nonclassical (in our case, increasing convex functions). We use an appropriate minimax theorem to prove the duality relation for . In particular, an important corollary is obtained stating that the dual functional (defined on a space of measures and known as the “Beckmann functional) attains its minimum. The present approach also provides simpler proofs of some previously known results.
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title	On the Monopolist Problem and Its Dual
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