论文标题
公司在投入市场上企业之间互动的平均现场模型
A mean field model for the interactions between firms on the markets of their inputs
论文作者
论文摘要
我们考虑了一个由竞争公司创造的经济，其资本是异质的，并使用多个投入来生产商品。他们的消费政策是通过最大化公用事业的理性固定的，其资本不能低于给定阈值（状态约束）。从长远来看，我们旨在建模公司之间在不同投入的市场上的相互作用。固定的equlibria通过耦合的非线性微分方程系统描述：汉密尔顿 - 雅各比方程描述了单个原子型公司的最佳控制问题；一个描述单个状态变量（资本）在公司人口中的分布的连续性方程；生产因素市场上的平衡。我们在适当的假设下证明了平衡的存在。
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.
