Abstract
In this paper, we study the functional \(\Phi\) 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 \(\Phi\). 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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Funding
The work was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics. This work was financially supported by the Russian Science Foundation, project 22-21-00566, https://rscf.ru/en/project/22-21-00566/.
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Translated from Matematicheskie Zametki, 2023, Vol. 114, pp. 181–194 https://doi.org/10.4213/mzm13933.
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Bogachev, T.V., Kolesnikov, A.V. On the Monopolist Problem and Its Dual. Math Notes 114, 147–158 (2023). https://doi.org/10.1134/S0001434623070167
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DOI: https://doi.org/10.1134/S0001434623070167