非线性I-O或动态CGE模型解的存在性和惟一性

Existence and uniqueness of solutions using nonlinear input-output models or the dynamic CGE model

在Leontief投入产出(I-O)模型中生产要素不可替代。该文推广了Leontief投入产出(I-O)模型。对应于一般规模报酬不变生产函数,推导出一种非线性动态I-O模型及相应按成本定价方程,再讨论解的存在性与惟一性。依利润最大法则求单位产出要素需求函数,将这种情况下的CGE(可计算一般均衡)模型表成I-O形式;所得到的模型又可看作动态CGE模型。利用非负参数非线性系统的Peron-Frobenius定理,讨论按成本定价方程的解。得到按成本定价方程解的存在性与惟一性定理,并指出Peron-Frobenius根的实际意义,给出计算产品价格的简便迭代算法。

The Leontief input-output （I-O） model with production factors was extended to a nonlinear dynamic I-O model with cost-based-pricing equation deduced from the universal constant-return-to-scale production function, The existence and uniqueness of solutions of the cost-based-pricing equation were verified. The factor-demand function per unit output was developed by maximizing the profit in a dynamic CGE （computable general equilibrium） model with inputs and outputs way. The Peron-Frobenius theory of nonlinear systems with non-negative parameters was used to analyze the solutions of the cost-based-prlcing equation. And a exist and unique theorem was given. The results illustrate the practical significance of the Peron-Frobenius root. A simple iterative algorithm was given to calculate the production price.