%0 Journal Article %T A mean field model for the interactions between firms on the markets of their inputs %+ Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) %+ Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN) %+ CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) %+ EDF R&D (EDF R&D) %+ Università degli Studi di Padova = University of Padua (Unipd) %A Achdou, Yves %A Carlier, Guillaume %A Petit, Quentin %A Tonon, Daniela %Z All the authors were partially supported by the ANR (Agence Nationale de la Recherche) through MFG project ANR-16-CE40-0015-01.Y.A. acknowledges partial support from the Chair Finance and Sustainable Development and the FiME Lab (Institut Europlace de Finance) . G.C. acknowledges the support of the Lagrange Mathematics and Computing Research Center. %< avec comité de lecture %@ 1862-9679 %J Mathematics and Financial Economics %I Springer Verlag %8 2023-03 %D 2023 %Z 2207.05411 %R 10.1007/s11579-023-00333-z %Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles %X We consider an economy made of competing firms which are heterogeneous in their capital and use several inputs for producing goods. Their consumption policy is fixed rationally by maximizing a utility and their capital cannot fall below a given threshold (state constraint). We aim at modeling the interactions between firms on the markets of the different inputs on the long term. The stationary equlibria are described by a system of coupled non-linear differential equations: a Hamilton-Jacobi equation describing the optimal control problem of a single atomistic firm; a continuity equation describing the distribution of the individual state variable (the capital) in the population of firms; the equilibria on the markets of the production factors. We prove the existence of equilibria under suitable assumptions. %G English %2 https://hal.science/hal-03720158/document %2 https://hal.science/hal-03720158/file/draft_2.pdf %L hal-03720158 %U https://hal.science/hal-03720158 %~ CNRS %~ INRIA %~ UNIV-DAUPHINE %~ INRIA-ROCQ %~ INSMI %~ CEREMADE %~ LJLL %~ TESTALAIN1 %~ INRIA2 %~ TDS-MACS %~ PSL %~ EDF %~ INRIA-PSL %~ SORBONNE-UNIVERSITE %~ SORBONNE-UNIV %~ SU-SCIENCES %~ UNIV-PARIS %~ UNIVERSITE-PARIS %~ UP-SCIENCES %~ UNIV-DAUPHINE-PSL %~ SU-TI %~ ANR %~ ALLIANCE-SU