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经济代写|宏观经济学代写Macroeconomics代考|Supply Lags and Market Movements

Tinbergen proposed a supply lag scheme as early as 1928 , in a paper published in $D e$ Socialistische Gids. The paper was rather long considering that the journal usually published articles of only a dozen pages, and most of it was concerned with problems of exchange related to Cournot’s theories of competition. Incidentally, Tinbergen deplored the fact that Cournot’s work had remained mostly ignored, adding that the mathematical form in which it was published (in 1838) was probably to blame for this (Tinbergen, 1928: 543). ${ }^{14}$

The last part of this paper was concerned with the problem of the temporal element in his analysis, recognizing that this influence was mostly ignored in the previous sections. Tinbergen studied a problem of fluctuations around an equilibrium and based his discussion on a mechanical analogy: solving the “dynamic problem” meant that “as in mechanical dynamics, further data is needed, data which we can denote by inertia and delay, the inertia being related to the effort, the delay to the time of displacement” (Tinbergen, 1928: 544). Tinbergen then proposed to observe the behavior of one market where supply would adjust with a lag, while “demand adapts to supply without delay” (Tinbergen, 1928: 544). Although he did not explicitly present the equations behind his scheme, he did propose a numerical example with a figure of the temporal evolution of the quantities exchanged of a good, which took the form of damped oscillations that were in fact the result of a cobweb mechanism (reproduced in Fig. 2.2).

Obviously this example showed somewhat trivial oscillations from a high point to a low point each period, the only kind allowed by a first-order difference equation. ${ }^{15}$ This did not prevent him from discussing the conclusions one could draw from such a model for the economy as a whole and the observed cycles of three to four years or the longer cycles of seven to ten years, and the problems they posed for the social welfare of workers. Tinbergen also touched upon the problem of the damping of those oscillations, in connection with similar problems in physical system, and briefly considered the case where “the deviations are getting bigger (as in cases of unstable equilibrium),” but he added that these fluctuations could occur “only occasionally” (Tinbergen, 1928: 547).

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and Mixed Equations

In the introduction of his 1931 paper “Ein Problem der Dynamik,” when Tinbergen distinguished several lines of research that expanded “the static theory of social economy,” he finished his review by remarking that no one had yet tried to combine time derivatives and lags into a “systematic design of the dynamic theory” (Tinbergen, 1931a: 169). A scheme was proposed in the paper but it was still floundering; nevertheless, that same year, Tinbergen proposed a straightforward combination of time derivatives and lags, through his model of the shipbuilding cycle.

The choice of shipbuilding was not anecdotal; in a paper published in De Nederlandsche Conjunctuur, the journal of the Centraal Bureau voor de Statistiek (CBS) where he was working at the time, Tinbergen explained that “[t]he branch of industry concerned with shipbuilding has a number of peculiarities which make a study of the relationship between the business cycle and this branch of industry of great importance, especially for shipbuilding itself and for shipping companies” (Tinbergen, 1931c: 14). Shipbuilding was one of the biggest branches of activity in the Netherlands, and Tinbergen saw at least three characteristics that made its study worthwhile: the long production process of building ships, the strong fluctuations in its activity, and the long life of its means of production. This meant that the shipbuilding industry was quite different from the agricultural markets that had spurred the cobweb models of Moore, Schultz, Ricci and Tinbergen. Clearly, trying to explain the fluctuations of a market of durable instead of perishable goods led Tinbergen to important new ideas.

The first study that he published on the question (Tinbergen, 1931c) was very empirical as he tried to determine the lifespan of ships and other characteristics of the cycle. Nevertheless, he was also clearly searching for an explanation of the cycle, for a mechanism that would explain the fluctuations he had found empirically. He argued that a causal mechanism existed in particular between tonnage and its own increase: “[t]here is indeed a clear interaction between tonnage and increase in tonnage, an interaction which will be referred to in the remainder of this article as the ‘own mechanism’ of the development of tonnage” (Tinbergen, 1931c: 17). But he did not try in this paper to give a more mathematical form to this finding, which he reserved for a paper written in German for the Weltwirtschaftliches Archiv, the journal of the Kiel group of economists (Tinbergen 1931b, which was translated in Tinbergen 1959 from which we quote hereafter). ${ }^{24}$

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|Supply Lags and Market Movements

Tinbergen 早在 1928 年就在一篇发表于丁这是Socialistische Gids。考虑到该杂志通常发表的文章通常只有十几页,而且大部分都是与古诺竞争理论相关的交流问题,所以这篇论文相当长。顺便说一句,Tinbergen 对古诺的工作几乎一直被忽视这一事实感到遗憾,并补充说它出版时所用的数学形式(1838 年)可能是造成这种情况的原因(Tinbergen,1928:543)。14

本文的最后一部分在他的分析中关注时间因素的问题,认识到这种影响在前几节中大多被忽略了。丁伯根研究了围绕平衡的波动问题,并将他的讨论基于机械类比:解决“动态问题”意味着“在机械动力学中,需要更多数据,我们可以用惯性和延迟表示的数据,惯性是与努力有关,延迟与流离失所的时间有关”(Tinbergen,1928:544)。Tinbergen 随后提议观察一个市场的行为,在该市场中,供应会滞后调整,而“需求会立即适应供应”(Tinbergen,1928:544)。尽管他没有明确提出他的方案背后的方程式,

显然,这个例子显示了每个周期从高点到低点的轻微振荡,这是一阶差分方程唯一允许的振荡。15这并没有阻止他讨论人们可以从这样一个模型中得出的结论,该模型适用于整个经济和观察到的三到四年或七到十年的更长周期,以及它们对社会福利提出的问题工人。丁伯根还谈到了与物理系统中类似问题相关的这些振荡的阻尼问题,并简要考虑了“偏差越来越大(如不稳定平衡的情况)”的情况,但他补充说,这些波动可能“只是偶尔”发生(Tinbergen,1928:547)。

经济代写|宏观经济学代写Macroeconomics代考|The Shipbuilding Model and Mixed Equations

在他 1931 年的论文“Ein Problem der Dynamik”的引言中,当 Tinbergen 区分了扩展“社会经济的静态理论”的几条研究路线时,他在结束评论时说,还没有人试图将时间导数和滞后结合起来进入“动态理论的系统设计”(Tinbergen,1931a:169)。论文中提出了一个方案,但仍在挣扎;尽管如此,同年,丁伯根通过他的造船周期模型提出了时间导数和滞后的直接组合。

造船的选择不是轶事。在他当时工作的中央统计局 (CBS) 期刊 De Nederlandsche Conjunctuur 上发表的一篇论文中,Tinbergen 解释说,“与造船业有关的行业有许多特点,这使得研究商业周期与这个非常重要的行业分支之间的关系,特别是对于造船业本身和航运公司”(Tinbergen,1931c:14)。造船业是荷兰最大的活动分支之一,丁伯根至少看到了三个值得研究的特点:造船的生产过程漫长、活动波动剧烈,以及生产资料的使用寿命长. 这意味着造船业与刺激了摩尔、舒尔茨、里奇和丁伯根蜘蛛网模型的农业市场截然不同。显然,试图解释耐用品而非易腐烂商品市场的波动使丁伯根产生了重要的新想法。

他发表的关于这个问题的第一项研究(Tinbergen,1931c)非常注重经验,因为他试图确定船舶的寿命和周期的其他特征。尽管如此,他显然也在寻找周期的解释,寻找一种机制来解释他凭经验发现的波动。他认为,特别是在吨位与其自身增长之间存在因果机制:“[t]吨位与吨位增长之间确实存在明显的相互作用,这种相互作用将在本文的其余部分称为“自身”吨位发展的机制”(Tinbergen,1931c:17)。但他并没有在这篇论文中尝试为这一发现提供更多的数学形式,他将其保留在用德语为 Weltwirtschaftliches Archiv 撰写的论文中.

经济代写|宏观经济学代写Macroeconomics代考

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