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# 数学代写|数值方法作业代写numerical methods代考|Numerical Solution Methods

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## 数学代写|数值方法作业代写numerical methods代考|Why Do We Need to Compute Numerical Solutions to Growth Models?

We have described above how the desire to incorporate microeconomic foundations into models for the aggregate economy leads to growth models that are made of the interaction of economic agents of different types, each solving a particular dynamic, stochastic optimization problem. We have also seen how the endogeneity of prices leads to nonlinear decision rules that involve expectations of functions of future variables and cannot possibly be reduced to the type of aggregate linear functions usually considered in structural macroeconomic models like those in previous sections. Except by very few exceptions, the nonlinear stochastic systems summarizing the properties of growth models lack an analytical solution, and the model’s implications regarding the behavior of the main variables, their comovements, or their responses to exogenous shocks or to policy interventions can only be characterized through numerical solutions. Hence, we face the need to obtain numerical solutions, a process that goes significantly beyond the procedures to simulate the linear dynamic macroeconomic models above because of stability and indeterminacy issues that we address below.

## 数学代写|数值方法作业代写numerical methods代考|Stability

To obtain a numerical solution to a nonlinear, stochastic dynamic system, we need it to be complete, i.e., to have as many equations as decision variables at each point in time. However, the three aspects of the model: (a) nonlinear, (b) stochastic, and (c) dynamic, lead to nontrivial issues regarding such computation. First, a complete nonlinear system is not guaranteed to have a solution, or if it does, there is no guarantee that the solution will be unique. Second, a stochastic system will include expectations of future variables that should be solved consistently with the structure of the model, at least under rational expectations, a maintained assumption throughout this book. Expectations are additional endogenous variables that break down the completeness of the model, and appropriate methods need to be used to obtain a solution. ${ }^{40}$ Lastly, an additional issue when solving a dynamic system is the stability of the solution, which is never guaranteed.

## 数学代写|数值方法作业代写NUMERICAL METHODS代考|Indeterminacy

The solution to a growth model can display two types of indeterminacy. Global indeterminacy refers to the fact that a dynamic general equilibrium model may present multiple steady-states, as in the well known monetary model of Cagan. Since the steady-state is usually the solution to a nonlinear system of equations, multiple solutions might well arise. More generally, in models implying steady-state growth, global indeterminacy refers to the possible existence of multiple balanced growth paths, steady-states in which per-capita variables grow at a constant rate. In contrast, local indeterminacy arises when given a steady-state or a balanced growth path, there might exist a continuum of trajectories converging to it. We focus here on explaining how local indeterminacy may arise.

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。