Geodesic
On the Monopolist Problem and Its Dual
Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 181-194.

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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.
Keywords: monopolist problem, Dirichlet functional, minimax principle. 
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T. V. Bogachev; A. V. Kolesnikov. On the Monopolist Problem and Its Dual. Matematičeskie zametki, Tome 114 (2023) no. 2, pp. 181-194. http://geodesic.mathdoc.fr/item/MZM_2023_114_2_a1/

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