# 经济代写|宏观经济学代写Macroeconomics代考|Connecting Comparative Statics to Stability Analysis

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes-lab™ 为您的留学生涯保驾护航 在代写宏观经济学Macroeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宏观经济学Macroeconomics代写方面经验极为丰富，各种代写宏观经济学Macroeconomics相关的作业也就用不着说。

• 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
couryes™为您提供可以保分的包课服务

## 经济代写|宏观经济学代写Macroeconomics代考|Connecting Comparative Statics to Stability Analysis

Samuelson’s (1941) Econometrica article had a profound impact on the development of dynamics and stability analysis. ${ }^{16}$ On the one hand, the article clarified the Oxford discussion by providing the first stability analysis of a Keynesian system, which was called for by Frisch and Tinbergen. On the other hand, in connecting comparative statics to stability analysis through his “correspondence principle” (Samuelson, 1947: 5), ${ }^{17}$ Samuelson redirected the debate toward the problem of the stability of full employment equilibrium, pointing to a direction soon followed by Lange (see Chap.9).

Before we see, through the example of the “Keynesian system” presented by Samuelson, how the correspondence principle linked together comparative statics and stability analysis, we present his approach to stability, which is very similar to the econometricians’ and in contrast with Meade’s approach. Samuelson argued that the solution to the problem of stability, “presupposes a theory of dynamics,” namely a theory which determines the adjustment behavior of all variables outside of the equilibrium. He began with a very general approach to show what dynamic analysis could bring to comparative statics. The first sections were thus devoted to the examination of different adjustment mechanisms between supply and demand, from which Samuelson could derive different stability conditions which yielded “meaningful theorems” about the slope of the demand and supply curves. In doing so, he extended the arguments raised by Tinbergen and Frisch against Meade, who had argued that changing the dynamic hypotheses implicit behind his stability analysis could change the theorems obtained. Thus Samuelson underlined, like Tinbergen had done privately with Meade, that “[i]f alternative dynamic models are postulated, completely different conditions are deduced, which in turn lead to alternative theorems in comparative statics” (Samuelson, 1941: 103).

Samuelson argued that with $n$ time-dependent variables to explain $x_1(t), \ldots, x_n(t)$ and $n$ functional equations of the general form $f^i\left(x_1(t), \ldots, x_n(t)\right)$, then their behavior was determined once certain initial conditions are specified. This was made with explicit reference to Frisch’s methodology exposed in Frisch (1936), for instance when he argued that a set of equilibrium values $x_1^0, \ldots, x_n^0$ will satisfy the equations $f^i\left(x_1^0, \ldots, x_n^0\right)=0$ for all times $t$ (Samuelson, 1941: 100) .

For such equilibrium states, the system may be displaced, a displacement being equivalent to an arbitrary change in the initial conditions. Samuelson introduced four different types of stability, two “kinds” which could themselves hold “perfectly” or only “in the small.” Perfect stability of the first kind meant that once displaced, all the variables would approach their equilibrium values in the limit as time became infinite. When the system was only stable of the first kind in the small, equilibrium would be restored only for small displacements away from the equilibrium, highlighting the possibility that in the presence of multiple equilibria, large displacements may definitely destabilize the economy, an idea that Tinbergen had explored in several models (as it has been shown in Chap. 6). Stability in the second kind was related to the behavior of conservative systems showing undamped fluctuations, and was again divided into perfect stability of the second kind and stability of the second kind in the small. In the first case, the limit cycle (to use the modern term for those undamped cycles) was obtained from any initial conditions, while in the second case, the limit cycle was again enclosed in a stability “corridor,” outside of which it could not be attained.

## 经济代写|宏观经济学代写Macroeconomics代考|Meade’s Conditions Compared to Samuelson’s

Differentiating conditions (8.1) to (8.7), Meade found that his system was stable when the expectation elasticity $\pi$ was lower than the proportion of income going to profits $1-\lambda, \lambda$ being the profit share going to wages. In a second case, when the rate of interest is assumed to vary, the stability condition is less severe. This is because the rise in the interest rate resulting from the rise in production limits the rise in investment and the magnitude of the disequilibrium between the interest rate and the marginal efficiency of capital.

Our strategy for deriving a geometrical representation of the “core” of the model is to construct two schedules in the $\left(p_i, y_i\right)$ space, with $p_i$ the supply ( $\left.p_i^s\right)$ or demand $\left(p_i^d\right)$ price of investment goods and $y_i$ the output of investment goods. The first of these schedules is given by equations (8.1) and (8.2) and a production function that we can write as $y_i=A n_i^\lambda$ :
$$p_i^s=\frac{1}{\lambda} A^{\frac{-1}{\lambda}} W y_i^{\frac{1-\lambda}{\lambda}}$$
Equation 8.23 represents the short-run aggregate supply curve of investment goods, with parametric wages, or what Keynes called the investment supply price, that is, the price for which producers of investment goods are ready to start to produce.

The $p_i^d$ line results from the expression of profits in terms of the output of investment goods. If we assume that $P=(1-\lambda) Y$, in line with Meade’s hypotheses, we have $P=(1-\lambda) \frac{p_i{ }^d y_i}{s}$. By inserting it in the condition of equilibrium between the marginal efficiency of capital and the interest rate $r=\frac{E(P)}{p_i{ }^4}$ we obtain:
$$p_i^d=\frac{1}{r}\left[(1-\lambda) \frac{p_i{ }^d y_i}{s}\right]^\pi=r^{\frac{-1}{1-\pi}}\left(\frac{(1-\lambda)}{s}\right)^{\frac{\pi}{1-\pi}} y_i^{\frac{\pi}{1-\pi}},$$
where we have assumed $E(P)=P^\pi$, with $\pi$ is the elasticity of expectations, that is, the expectation of future profits depends on current profits. This schedule can be interpreted as follows: given this price and the level of output $y_i$, the ordinate of the $p_i^d$ curve shows the “investment demand price,” that is the price that investors are ready to pay to purchase capital equipment. Equilibrium is determined at the intersection of both curves. ${ }^{30}$

# 宏观经济学代考

## 经济代写|宏观经济学代写Macroeconomics代考|Meade’s Conditions Compared to Samuelson’s

$$p_i^s=\frac{1}{\lambda} A^{\frac{-1}{\lambda}} W y_i^{\frac{1-\lambda}{\lambda}}$$

p_i线是根据投资货物的产出来表示利润的结果。如果我 们假设与米德的假设一致，我们有。将其代入资本边际 效率与利率均衡的条件下，我们得到: 假设，其中 $p_i^d$
\begin{aligned} & P=(1-\lambda) Y P=(1-\lambda) \frac{p_p{ }^d y_i}{s} r=\frac{E(P)}{p_i{ }^4} \ & p_i^d=\frac{1}{r}\left[(1-\lambda) \frac{p_i{ }^d y_i}{s}\right]^\pi=r^{\frac{-1}{1-\pi}}\left(\frac{(1-\lambda)}{s}\right)^{\frac{\pi}{1-\pi}} y_i^{\frac{\pi}{1-\pi}}, \end{aligned}p_i线是根据投资货物的产出来表示利润的结果。如果我 们假设与米德的假设一致，我们有。将其代入资本边际 效率与利率均衡的条件下，我们得到: 假设，其中 $p_i^d$
\begin{aligned} & P=(1-\lambda) Y P=(1-\lambda) \frac{p_i{ }^d y_i}{s} r=\frac{E(P)}{p_i{ }^4} \ & p_i^d=\frac{1}{r}\left[(1-\lambda) \frac{p_i{ }^d y_i}{s}\right]^\pi=r^{\frac{-1}{1-\pi}}\left(\frac{(1-\lambda)}{s}\right)^{\frac{\pi}{1-\pi}} y_i^{\frac{\pi}{1-\pi}}, \end{aligned}
$E(P)=P^\pi \pi$ 是期望的弹性，即对末来利润的期望取

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)