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# 经济代写|宏观经济学代写MACROECONOMICS代写|ECON202 Disentangling Issues on Existence and Stability

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## 经济代写|宏观经济学代写MACROECONOMICS代写|Introduction

As we saw, a lot happened between the first models of Tinbergen with one market of raw goods and the beginning of the 1940s when economists used the Keynesian framework to model the dynamics of the whole economy. As we saw in Chaps. 2, 4 and 5 , Tinbergen began to analyze the solutions of mixed difference differential equations which were subsequently used by Frisch and Kalecki in the early 1930 s to account for the movements of the whole economy. Tinbergen also developed linear and nonlinear models which included the possibility to account for unstable trajectories and to stabilize the economy (Chap. 6) before designing new economic policies to reach higher levels of employment and production (Chap. 7). Shortly after, Samuelson connected static analysis to stability analysis and provided a new understanding of Keynesian systems (Chap. 8).

In that last chapter, we show that Samuelson’s approach led to two separate but connected enquiries into the stability properties of the economy: in the work of Oskar Lange, ${ }^{1}$ which was carried out at the Cowles Commission in the early 1940 s, and in the work of Lawrence Klein, which was also carried out at the Cowles Commission after he moved there from MIT in the second part of the 1940s. Samuelson’s approach, arising from the econometricians’ critique of Meade’s stability analysis, had a significant impact not only on his approach of the underlying model of the economy, but also on the fact that a dynamic approach was necessary to study stability. Both economists also showed after Samuelson that they were more interested in the stability of an equilibrium position rather than in the fluctuations which were studied by the econometricians. And both also wrote in the framework of a debate on the stability of full employment equilibrium, which was begun in the early $1940 \mathrm{~s}$ between Hansen, Pigou and Samuelson. In the end, when Klein moved to the Cowles Commission, he was able to integrate Lange’s vision of instability and Samuelson’s approach to dynamic processes to his empirical approach.

Alvin Hansen (1941) had claimed that price and wage flexibility did not guarantee that a stationary state would be necessarily accompanied by full employment. His point was that there may be no positive rate of interest-for any positive level of prices and wages – equating savings and investment at full employment level. Pigou (1943) strongly opposed Hansen’s claim. He admitted that investment and savings may be interest-inelastic, but he disagreed that full employment could not be achieved through lower prices and wages, which would eventually increase the real value of the stock of money enough to reduce savings until full employment would be achieved. Samuelson (1941a), accepting that such an equilibrium with full employment may exist, objected that the problem could lie in its stability properties. Full employment equilibrium might be unstable, and if this was the case it could not be reached after price adjustments. Combining Samuelson’s stability analysis with Hicks’s general equilibrium theory, Lange concluded that this was most likely to be the case in market economies.

## 经济代写|宏观经济学代写MACROECONOMICS代写|Hansen, Samuelson and Pigou on the Classical Stationary State

In Chap. 7, we saw that Hansen laid the ground for a model of the interaction between the accelerator and the multiplier, which Samuelson subsequently managed to express mathematically. On the basis of his model, the latter made clear that the acceleration coefficient affected only the trajectory of the system, insofar as it did not completely destabilize the system, and generally speaking as this coefficient increased the system became unstable but in a way that had no effect on the stationary state. This was noted explicitly by Hansen in his 1941 book, where he integrated Samuelson’s analysis and underlined that: “the addition of the Acceleration Principle to the Multiplier Principle does not, in this case, affect the ultimate level of the national income but only the intervening path through which the income moves” (Hansen, 1941: 278). From this it followed that the stationary state of the economy only depended on the amount of autonomous aggregate demand, and this is where his idea of secular stagnation came into play. Hansen thought that several factors would maintain a low level of autonomous investment and a tapering off of income: he called this “secular stagnation,” a stagnation of income at a level below full employment (Hansen, 1938, 1939).

At this point, Hansen did not link the value of stationary income to either wages or prices which he deemed fixed in his analysis. This is because price flexibility, in his opinion, could not ensure a propensity to consume compatible with investment opportunities. In the end, this meant that in the context of secular stagnation, coordination through markets was unable to induce a situation of full employment: “The classicals were quite right when they argued that without technological progress the price system, including the rate of interest, would progressively drive the economy to the point at which there would be no net investment. They were wrong in assuming that the price system could also ensure a propensity to consume compatible with this investment situation so as to provide full employment” (Hansen, 1941: 288)

## 经济代写|宏观经济学代写 MACROECONOMICS代 写|Introduction

Alvin Hansen (1941) 声称价格和工资的灵活性并不能保证静止状态必然伴随着充分就 业。他的观点是，对于任何正的价格和工资水平，可能不存在正利率一一将储蕃和投资等 同于充分就业水平。庇古 $(1943)$ 强烈反对汉森的主张。他承认投资和储萰可能没有利息 弹性，但他不同意通过降低价格和工资来实现充分就业，这最終会增加货雨存量的实际价 值，跃以减少储萰，直到实现充分就业. 萨䌻尔森 (Samuelson，1941a) 承认可能存在 这样的充分就业均衡，并反对问题可能在于其稳定性属性。充分就业均衡可能不稳定，如 果是这样的话，在价格调整后无法达到。将萨缪尔森的稳定性分析与希克斯的一般均衡理 论相结合，兰格得出结论，市场经济中最有可能出现这种情况。

## 经济代写|宏观经济学代写 MACROECONOMICS代写|Hansen, Samuelson and Pigou on the Classical Stationary State

(Hansen，1941: 278)。由此得出，经济的静止状态仅取决于自主总需求的数量，这 就是他的长期停滞思想发挥作用的地方。汉森认为有几个因嫊会维持低水平的自主投资和 收入的逐渐减少：他称之为“长期停滞”，即收入停滞在低于充分就业的水平（汉森， $1938,1939)$ 。

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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。