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# 经济代写|宏观经济学代写MACROECONOMICS代写|ECON1120 Lange: Disequilibrium and Instability

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## 经济代写|宏观经济学代写MACROECONOMICS代写|Lange: Disequilibrium and Instability

Lange managed to build in just three years, at the beginning of the 1940 s, an approach which had an important impact on the Cowles Commission. He had left Europe in 1937 and had been a lecturer at the University of California in 1937-1938, before moving to Chicago in 1938 where he became an assistant professor, and in 1939 he was appointed associate professor (Cowles Commission, 1940a: 4) and joined the Cowles Commission who arrived from Colorado Springs. Staff mobilization in the war effort, along with the subsequent loss of communication with parts of Europe, left him in charge of editing Econometrica and one of the most important researchers of the Commission. ${ }^{7}$ At the commission, his research was focused at first on the link between monetary policy and technological unemployment, a problem that he addressed both theoretically and statistically. He was helped by his assistants (Melvin Reder, then Leonid Hurwicz in 1941-1942) in particular to conduct statistical tests of business cycles and most importantly to work on the issue of the relationship between price flexibility, employment and economic stability. ${ }^{8}$

A first milestone was reached at the 1941 New York meeting of the Econometric Society, in which Lange resorted for the first time to Samuelson’s stability analysis. Lange’s goal, as evidenced by the title of his paper, “The stability of economic equilibrium” was to restate “the theory of stability of general equilibrium as formulated by J. R. Hicks and … the dynamic stability theory of Samuelson” (Leavens, 1942 : 176). In a short period of time, he came up with a new theorem on “stability rank” based on different dynamical systems indicating how many prices need to be rigid to guarantee the stability of equilibrium, a theorem later incorporated into the appendix of his 1944 monograph (Lange, 1944) and set out in his course on mathematical economics given in 1945 at the University of Chicago. ${ }^{9}$

## 经济代写|宏观经济学代写MACROECONOMICS代写|Instability and Empirical Research in Klein’s Work

Klein finished his undergraduate studies at Berkeley, where he studied economics, mathematics and statistics at one of the only places where he could follow mathematical economics classes (Klein and Mariano, 1987: 410). He studied in particular mathematics under the students of Griffith Evans, economics with Leo Rogin who introduced him to Keynesian economics and statistics with Jerzy Neyman. ${ }^{27}$ After a summer internship estimating the demand for California lemons with George Kuznets (the brother of the Nobel Prize winner), he transferred to MIT for his graduate studies, where he became Samuelson’s assistant (Klein and Mariano, 1987: 411) and eventually his first PhD student. His background in statistics, but also in economic theory and his knowledge of Keynesian economics led him to connect with the burgeoning group of economists working in New York, Cambridge (Massachusetts) and Chicago on econometric issues and mathematical economics. At MIT, he organized a statistical seminar where he managed to invite, among others, Haavelmo, Wald and Hotelling, in addition to his doctoral advisor Samuelson, and the latter’s former professor at Harvard, E. B. Wilson (Klein, 1991).

Klein was also the heir of Hansen, Pigou and Samuelson on the issue of the existence and stability of full employment, and he went a long way to clarify the different arguments with the help of economic models. ${ }^{28}$ This was the work he began in his $1944 \mathrm{PhD}$ thesis (Klein, 1944), which was published in 1947 as The Keynesian Revolution (1947a), and which helped him get noticed by Marschak, when he presented parts of it at the 1944 Cleveland Meeting of the Econometric Society (Hurwicz et al., 1945: 84-85). That paper favorably impressed Marschak who chaired the session and was looking for a young able economist to develop the modeling program that he was launching at the time. Marschak, Koopmans, Hurwicz and Klein discussed the idea of recruiting Klein at the Cowles Commission at a dinner during the last day of the meeting (Bjerkholt, 2014), and eventually Klein chose to join the Commission where he produced his first macroeconometric work.

## 经济代写|宏观经济学代写 MACROECONOMICS代写|Instability and Empirical Research in Klein’s Work

Marschak 的注意，当时他在 1944 年的克利夫兰计量经济学会会议上展示了其中的一部 分 (Hurwicz 等人，1945：84-85) 。那篇论文给会议主席马沙克留下了深刻的印象， 他正在寻找一位年轻有能力的经济学家来开发他当时正在启动的建模程序。Marschak、
Koopmans、Hurwicz 和 Klein 在会议的最后一天 (Bjerkholt，2014 年) 的一次晩宴上 讨论了在 Cowles 委员会招幕 Klein 的想法，最终 Klein 选择加入该委员会，在那里他完 成了他的第一份宏观计量经济学工作。

## 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。