| Title: |
A mean field model for the interactions between firms on the markets of their inputs |
| Authors: |
Achdou, Yves, Carlier, Guillaume, Petit, Quentin, Tonon, Daniela |
| Publication Year: |
2022 |
| Subject Terms: |
Mathematics - Analysis of PDEs |
| More Details: |
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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2207.05411 |
| Accession Number: |
edsarx.2207.05411 |
| Database: |
arXiv |
