# 经济代写|国际经济学代写International Economics代考|BEA105

#### Doug I. Jones

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• 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

## 经济代写|国际经济学代写International Economics代考|Endowment Shock and Output Changes

As mentioned earlier, factor endowments of countries are exogenously given in the HOS model. Rybczynski (1955) studied how exogenous changes in the factor endowment of a country, ceteris paribus, change the full-employment output composition of the country at constant commodity prices. He established the result, which is known as the Rybczynski theorem (and more generally as the output magnification effect), that if there is a more than proportionate exogenous growth in capital compared to the growth in labour force, then the production of the capital-intensive good will increase more than the growth in capital, whereas increase in the production of the labour-intensive good, if at all, will be less than proportionate to the growth in labour force. Algebraically stated, given our assumption that computers are relatively capital-intensive, if $\hat{K}>\hat{L}>0$ then output changes will be such as:
$$\hat{X}_c>\hat{K}>\hat{L}>\hat{X}_T$$
But if the labour force grows faster than capital accumulation, both caused by exogenous factors, then production of textiles expands fastest and that of computers expands, if at all, the least:
$$\hat{X}_T>\hat{L}>\hat{K}>\hat{X}_c$$
Essentially, the Rybczynski theorem provides us the direction in which the relative supply curve of a country shifts. Since the above effects on output levels are derived at any set of constant commodity prices, so it means that the relative supply curve $s$ for computers in the home country in Figure $6.3$ shifts to the right if $\hat{K}>\hat{L}>0$, and to the left otherwise. Of course, the relative price will change as a consequence, but the direction of the price change will be governed by the nature of the supply shift.

The above result, however, tells us more than just this compositional effect (an increase or decrease in $\frac{X_C}{X_T}$ ) or the nature of the supply shift. It tells us that output changes will be a magnified proportion of factor endowment changes. Hence, the results stated in equations (6.13) and (6.14) are also known as output magnification effects (see Jones 1965). Put simply, if capital grows by 20 per cent and the labour force by 15 per cent, the difference in growth rates being 5 per cent, then production of computers will grow at more than 20 per cent and that of textiles (if at all) by less than 15 per cent so that the difference in output growths will be larger than 5 per cent.

## 经济代写|国际经济学代写International Economics代考|Price Magnification Effect

Consider an exogenous shock that causes the relative price of computers to rise. How do the factor prices change as a consequence? As established in Jones (1965), if the price of computers rises more than proportionate to the price of textiles in the home country, the real return to capital will unambiguously rise whereas the real wage will unambiguously fall given that computers are relatively more capital-intensive than textiles. That is, if $\hat{P}_C>\hat{P}_T>0$ then:
$$\hat{r}>\hat{P}_C>\hat{P}_T>\hat{W}$$
This strong statement regarding how the changes in commodity prices affect real wages of the two factors of production follows from the excluded-middle phenomenon displayed by (6.15). Due to this property, in (6.15) capital owners’ real incomes rise whereas workers’ real incomes fall regardless of how we measure their real incomes. Since, for economic agents who are free of money illusion, real income is the indicator of their well-being, so in situations like the one stated in (6.15) we can say that an increase in the relative price of computers makes the capital owners unambiguously better off and the workers worse off. Such a strong statement could not be made if the excluded-middle phenomenon did not hold. For example, if the rate of return to capital had been trapped between the two price changes, then the change in real income and welfare of the capital owners would depend on the shares of their incomes spent on computers and textiles. If they spend a larger proportion of their incomes on computers then they would have been worse off by the increase in the relative price of computers. Otherwise, they would have been better off. In the next chapter, we will see when situations like this can arise where the excluded-middle phenomenon is lost and real income changes are ambiguous.
In general, the real return to capital unambiguously rises and the real wage unambiguously declines when the relative price of the good that uses capital intensively rises. Otherwise, the real wage unambiguously rises. Note that a decline in the real wage as in (6.15) does not mean that money wage falls too. What equation (6.15) indicates is that even when the money wage rises it cannot be more than proportionate to the least rising commodity price (in this case, price of textiles). Once again, we have a magnification effect: the rate of increase in the return to capital relative to the wage rate, $\hat{r}-\hat{W}$, is a magnification of the rate of increase in the relative price of computers, $\hat{P}_C-\hat{P}_T$. Stolper and Samuelson (1941) derived this result in the context of a small open economy imposing a tariff. They argued that the real wage of the abundant factor will fall and the real wage of the scarce factor will rise as a consequence of imposition of an import tariff. By the HO theorem, a country exports the good which is intensive in its abundant factor and imports the good which is intensive in its scarce factor. An import tariff raises the domestic relative price of the import-competing good and, therefore, the real wage of the scarce factor that is intensively used in that good. The price magnification effect, however, is a generalized statement in the sense that it does not relate factor price changes to the scarcity or abundance of factors in a country.

# 国际经济学代考

## 经济代写|国际经济学代写国际经济学代考|禀赋冲击与产出变化

$$\hat{X}_c>\hat{K}>\hat{L}>\hat{X}_T$$但是，如果劳动力增长快于资本积累，而且都是由外生因素造成的，那么纺织品生产增长最快，计算机生产增长最少，如果有的话$$\hat{X}_T>\hat{L}>\hat{K}>\hat{X}_c$$从本质上讲，Rybczynski定理为我们提供了一个国家的相对供给曲线移动的方向。由于上述对产出水平的影响是在任意一组不变的商品价格下推导出来的，因此它意味着相对供给曲线 $s$ 图中为母国的计算机 $6.3$ 向右平移，如果 $\hat{K}>\hat{L}>0$否则向左走。当然，相对价格会因此发生变化，但价格变化的方向将由供给转移的性质决定

## 经济代写|国际经济学代写国际经济学代考|价格放大效应

$$\hat{r}>\hat{P}_C>\hat{P}_T>\hat{W}$$关于商品价格的变化如何影响两种生产要素的实际工资的这一强有力的陈述遵循(6.15)所显示的排除中间现象。由于这一性质，在(6.15)中，资本所有者的实际收入上升，而工人的实际收入下降，无论我们如何衡量他们的实际收入。因为，对于没有金钱幻想的经济主体来说，实际收入是他们幸福的指标，所以在(6.15)所述的情况下，我们可以说，计算机相对价格的提高无疑会使资本所有者的境况更好，而工人的境况更糟。如果排除中间现象不成立，就不能作出如此有力的声明。例如，如果资本回报率被困在两种价格变化之间，那么资本所有者的实际收入和福利的变化将取决于他们花在电脑和纺织品上的收入份额。如果他们把收入的更大一部分花在电脑上，那么他们的情况就会因为电脑相对价格的上涨而变得更糟。否则，他们会过得更好。在下一章中，我们将看到当排除中间现象消失和实际收入变化不明确时，这种情况何时会出现。一般来说，当集中使用资本的商品的相对价格上升时，资本的实际回报明显上升，而实际工资明显下降。否则，实际工资无疑会上涨。请注意(6.15)中实际工资的下降并不意味着货币工资也会下降。公式(6.15)表明，即使货币工资上涨，它也不可能超过上涨幅度最小的商品价格(在本例中为纺织品价格)的比例。再一次，我们有了放大效应:资本回报率相对于工资率的增长率， $\hat{r}-\hat{W}$，是计算机相对价格增长率的放大， $\hat{P}_C-\hat{P}_T$。Stolper和Samuelson(1941)在一个征收关税的小型开放经济体的背景下得出了这一结果。他们认为，由于征收进口关税，丰富要素的实际工资将下降，而稀缺要素的实际工资将上升。根据HO定理，一个国家出口其丰富要素的集约化商品，进口其稀缺要素的集约化商品。进口关税提高了与进口竞争的商品的国内相对价格，因此也提高了这种商品中密集使用的稀缺要素的实际工资。然而，价格放大效应是一种广义的说法，因为它没有把一个国家的要素价格变化与要素的稀缺或丰富联系起来

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## 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。

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