### 经济代写|宏观经济学代写Macroeconomics代考|ECON305

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|宏观经济学代写Macroeconomics代考|Dynamic inefficiency

For a given production function and given values of $n$ and $\delta$, there is a unique BGP value $k^{}>0$ for each value of the saving rate, s. Denote this relation by $k^{}(s)$, with $d k^{}(s) / d s>0$. The level of per capita consumption on the BGP is $c^{}=(1-s) \cdot f\left[k^{}(s)\right]$. We know from $(2.12)$ that $s \cdot f\left(k^{}\right)=(n+\delta) \cdot k^{}$; hence we can write an expression for $c^{}$ as
$$c^{}(s)=f\left[k^{}(s)\right]-(n+\delta) \cdot k^{} .$$ Figure $2.7$ shows the relation between $c^{}$ and $s$ that is implied by $(2.20)$. The quantity $c^{}$ is increasing in $s$ for low levels of $s$ and decreasing in $s$ for high values of $s$. The quantity $c^{+}$attains its maximum when the derivative vanishes, that is, when $\left[f^{\prime}\left(k^{}\right)-(n+\delta)\right] \cdot d k^{} / d s=0$. Since $d k^{} / d s>0$, the term in brackets must equal 0 . If we denote the value of $k^{}$ by $k_{g}$ that corresponds to the maximum of $c^{}$, then the condition that determines $k_{g}$ is
$$f^{\prime}\left(k_{g}\right)=(n+\delta) .$$
The corresponding savings rate can be denoted as $s_{g}$, and the associated level of per capita consumption on the BGP is given by $c_{g}=f\left(k_{g}\right)-(n+\delta) \cdot k_{g}$ and is is called the “golden rule” consumption rate.
If the savings rate is greater than that, then it is possible to increase consumption on the BGP, and also over the transition path. We refer to such a situation, where everyone could be made better off by an alternative allocation, as one of dynamic inefficiency. In this case, this dynamic inefficiency is brought about by oversaving: everyone could be made better off by choosing to save less and consume more. But this naturally begs the question: why would anyone pass up this opportunity? Shouldn’t we think of a better model of how people make their savings decisions? We will see about that in the next chapter.

## 经济代写|宏观经济学代写Macroeconomics代考|Absolute and conditional convergence

Equation (2.15) implies that the derivative of $\gamma_{k}$ with respect to $k$ is negative:
$$\partial \gamma_{k} / \partial k=\frac{s}{k}\left[f^{\prime}(k)-\frac{f(k)}{k}\right]<0$$
Other things equal, smaller values of $k$ are associated with larger values of $\gamma_{k}$. Does this result mean that economies with lower capital per person tend to grow faster in per capita terms? Is there convergence across economies?

We have seen above that economies that are structurally similar in the sense that they have the same values of the parameters $s, n$, and $\delta$ and also have the same production function, $F(\cdot)$, have the same BGP values $k^{}$ and $y^{}$. Imagine that the only difference among the economies is the initial quantity of capital per person, $k(0)$. The model then implies that the less-advanced economies – with lower values of $k(0)$ and $y(0)$ – have higher growth rates of $k$. This hypothesis is known as conditional convergence: within a group of structurally similar economies (i.e. with similar values for $s, n$, and $\delta$ and production function, $F(\cdot)$ ), poorer economies will grow faster and catch up with the richer one. This hypothesis does seem to match the data – think about how poorer European countries have grown faster, or how the U.S. South has caught up with the North, over the second half of the 20 th century.

An alternative, stronger hypothesis would posit simply that poorer countries would grow faster without conditioning on any other characteristics of the economies. This is referred to as absolute convergence, and does not seem to fit the data well. ${ }^{8}$ Then again, the Solow model does not predict absolute convergence!

## 经济代写|宏观经济学代写Macroeconomics代考|Dynamic inefficiency

$$f^{\prime}\left(k_{g}\right)=(n+\delta) .$$

## 经济代写|宏观经济学代写Macroeconomics代考|Absolute and conditional convergence

$$\partial \gamma_{k} / \partial k=\frac{s}{k}\left[f^{\prime}(k)-\frac{f(k)}{k}\right]<0$$

另一种更强有力的假设将简单地假设较炃穷的国家会增长得更快，而不需要以经济体的任何其他特征为条件。这被 称为绝对收敛，似乎不能很好地拟合数据。 ${ }^{8}$ 话又说回来，索洛模型并不能预测绝对收敛!

## 有限元方法代写

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## 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。