  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.
