A mean field model for the interactions between firms on the markets of their inputs

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 cannot fall below given threshold (state constraint). aim at modeling the interactions between on markets different long term. The stationary equlibria described system coupled non-linear differential equations: Hamilton–Jacobi equation describing optimal control problem single atomistic firm; continuity distribution individual state variable (the capital) population firms; equilibria production factors. prove existence under suitable assumptions.