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经济代写|宏观经济学代写Macroeconomics代考|Hansen, Samuelson and Pigou on the Classical

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)

The idea that the classical stationary state was not necessarily accompanied by full employment was an essential point because it offered the most compelling argument in favor of government expenditure to achieve full employment by supplementing the gap with private autonomous investment. The idea of stagnation at a level of income short of full employment was the focus of his opponents’ attacks in the 1940s. The notion of stagnation raised particular concerns among economists because it questioned the self-adjusting properties of the economic system. Pigou saw Hansen as a major proponent of Keynesian ideas, and attacked him in Pigou (1943) by suggesting that the price system, through its effect on consumption, could help to show that there exists a position of full employment equilibrium for any level of price.

经济代写|宏观经济学代写Macroeconomics代考|Disequilibrium and Instability

Lange managed to build in just three years, at the beginning of the 1940s, 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. ${ }^9$

A second milestone was reached with a 1942 paper where instability issues were connected to problems arising when agents decide “to increase cash balances (relative to the quantity of money available) by more than the excess supply of products, and also by more than the excess supply of factors and direct services” (Lange, 1942: 5859). It is in that context that Lange related the stability properties of the equilibrium to the real balance effect and Say’s law, arguing that “[e]quilibrium can be restored only through abatement of the desire to increase cash balance relative to the quantity of money” (Lange, 1942: 59). When the fall in prices resulting from the excess supply of goods tends to make excess demand of money equal to zero, “we may say that in such cases the conditions for a stable monetary equilibrium are satisfied. Otherwise there is no tendency to reach an equilibrium, and the general stability conditions … are not satisfied” (Lange, 1942: 59). According to him, Malthus was the first one to have realized, unlike Ricardo and Say, that the main cause of unemployment was due to this kind of instability.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Hansen, Samuelson and Pigou on the Classical

在第 7 章中,我们看到 Hansen 为加速器和乘法器之间的相互作用模型奠定了基础,Samuelson 随后设法用数学表达了这一模型。在他的模型的基础上,后者清楚地表明,加速度系数仅影响系统的轨迹,因为它不会完全破坏系统的稳定性,一般来说,随着该系数的增加,系统变得不稳定,但在某种程度上对静止状态没有影响。汉森在其 1941 年的书中明确指出了这一点,他在书中整合了萨缪尔森的分析并强调:“在这种情况下,将加速原则添加到乘数原则不会影响国民收入的最终水平,而只会影响干预措施收入流动的路径”(Hansen,1941:278)。由此可以得出,经济的静止状态仅取决于自主总需求量,这就是他的长期停滞思想发挥作用的地方。汉森认为有几个因素会保持低水平的自主投资和收入的减少:他称之为“长期停滞”,收入停滞在低于充分就业的水平(汉森,1938 年,1939 年)。

在这一点上,汉森没有将固定收入的价值与他在分析中认为固定的工资或价格联系起来。这是因为在他看来,价格灵活性无法确保消费倾向与投资机会相容。最后,这意味着在长期停滞的背景下,通过市场进行协调无法引发充分就业的局面:“古典主义者认为,如果没有技术进步,包括利率在内的价格体系,将逐步推动经济发展到没有净投资的地步。他们错误地认为价格体系也可以确保与这种投资情况相适应的消费倾向,从而提供充分就业”(Hansen,1941:288)

经典静止状态不一定伴随充分就业的观点是一个重要观点,因为它提供了最有说服力的论据,支持政府支出通过私人自主投资补充缺口来实现充分就业。1940 年代他的反对者攻击的焦点是收入水平低于充分就业水平的停滞。停滞的概念引起了经济学家的特别关注,因为它质疑经济体系的自我调节特性。Pigou 将 Hansen 视为凯恩斯主义思想的主要支持者,并在 Pigou (1943) 中攻击他,认为价格体系通过其对消费的影响可以帮助证明在任何价格水平下都存在充分就业均衡的位置.

经济代写|宏观经济学代写Macroeconomics代考|Disequilibrium and Instability

朗格在 1940 年代初仅用了三年时间就成功建立了一种对考尔斯委员会产生重要影响的方法。他于 1937 年离开欧洲,并于 1937-1938 年在加利福尼亚大学担任讲师,之后于 1938 年移居芝加哥,在那里他成为一名助理教授,并于 1939 年被任命为副教授 (Cowles Commission, 1940a: 4)并加入了来自科罗拉多斯普林斯的考尔斯委员会。参战人员动员,以及随后与欧洲部分地区失去联系,使他负责编辑《计量经济学》,并成为委员会最重要的研究人员之一。7在委员会,他的研究首先集中在货币政策和技术性失业之间的联系上,他从理论上和统计学上解决了这个问题。他在助手(梅尔文·雷德,1941-1942 年是列昂尼德·赫维茨)的帮助下,特别是对商业周期进行统计检验,最重要的是研究价格灵活性、就业和经济稳定性之间的关系问题。8

第一个里程碑是在 1941 年的计量经济学会纽约会议上达成的,兰格在会上首次求助于萨缪尔森的稳定性分析。Lange 的目标,正如他论文的标题“经济均衡的稳定性”所证明的那样,是重申“JR Hicks 和……Samuelson 的动态稳定性理论所阐述的一般均衡稳定性理论”(Leavens,1942:176 ). 在很短的时间内,他根据不同的动力系统提出了一个新的“稳定性等级”定理,表明需要多少价格是刚性的才能保证平衡的稳定性,这个定理后来被纳入他 1944 年专着的附录(Lange, 1944),并在他 1945 年在芝加哥大学开设的数理经济学课程中着手。9

1942 年的一篇论文达到了第二个里程碑,其中不稳定问题与代理人决定“增加现金余额(相对于可用货币数量)超过产品供应过剩,也超过产品供应过剩时出现的问题有关要素供应和直接服务”(Lange,1942:5859)。正是在这种情况下,兰格将均衡的稳定性属性与实际余额效应和萨伊定律联系起来,认为“[e]均衡只能通过减少相对于货币数量增加现金余额的愿望来恢复” (兰格,1942:59)。当商品供给过剩导致的价格下跌趋向于使货币的超额需求为零时,“我们可以说,在这种情况下,货币稳定均衡的条件已经满足。否则就没有达到平衡的趋势,一般的稳定条件……不满足”(Lange,1942:59)。据他说,与李嘉图和萨伊不同,马尔萨斯是第一个意识到失业的主要原因是这种不稳定的人。

经济代写|宏观经济学代写Macroeconomics代考

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