## 经济代写|国际经济学代写International Economics代考|ECON390

2022年9月23日
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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|ASSUMPTIONS AND THE STRUCTURE OF THE HOS MODEL

The basic HOS model has a $2 \times 2 \times 2$ structure: two countries, the home country and the foreign country, produce two goods, computers and cotton textiles, using two factors of production, labour $(L)$ and physical capital $(K)$. There are certain assumptions of the model that apply equally for both the countries, and there are others that differentiate the two countries. Among the first set comes the assumption that each factor of production is homogeneous everywhere (in all lines of production and in both countries) and can move freely and without any cost from one sector to another within each country. That is, both computers and textiles use the same type of labour and physical capital. The homogeneity and free mobility of labour and capital together imply that each factor earns the same return everywhere within each country. But factors cannot move from one country to the other, and thus labour (and capital) may earn different wages in the two countries. The second assumption is that all markets are perfectly competitive. Perfect competition in commodity markets implies that producers earn no supernormal profit at the long-run equilibrium. On the other hand, competition in factor markets along with fully flexible factor prices ensure that the labour force is fully employed and all physical capital is fully exhausted in production in both the countries. However, maintaining full employment is more of a concern under autarchy because production of commodities (and consequently derived demand for labour and capital) cannot exceed domestic demand. But when trade opens up, if the output produced by fully utilizing all domestic resources exceeds domestic demand, the excess output can be exported and thereby full employment of all domestic resources can be maintained.

Third, the production technology for each good follows constant returns to scale with diminishing returns to the variable factor. Fourth, unlike Ricardo, Heckscher and Ohlin assumed that each good is produced by the same technology in both the countries and thereby ruled out technology asymmetry as an explanation of trade amongst nations. But the production technologies for these goods differ from each other in each country. That is, both labour and capital are needed to produce these two goods, but the combination in which these factors are used differs in the two lines of production. More important, there should not be any factor intensity reversals meaning that for all possible factor price ratios, one good must be relatively capital-intensive and the other good must be relatively labour-intensive. In other words, the two goods must be uniquely ranked in terms of their relative factor intensities. Cases of factor intensity reversals, whereby the same good is relatively capital-intensive for some smaller values of factor price ratios and relatively labour-intensive for some larger values of factor price ratios, are ruled out by assumption because these may invalidate both the $\mathrm{HO}$ and the FPE theorems as we will see later.

## 经济代写|国际经济学代写International Economics代考|AUTARCHIC EQUILIBRIUM AND THE PATTERN OF TRADE

The HO theorem states that if trade opens up between these two countries, the relatively labour-abundant home country will export the relatively labour-intensive cotton textiles and the relatively capital-abundant foreign country will export the relatively capital-intensive computers. As explained earlier in Chapter 1, for this pattern of trade to emerge the pre-trade relative price of computers must be higher in the home country than in the foreign country: $p_c>p_c^*$. Alternatively, textiles must be cheaper at home than abroad. Thus, to explain the $\mathrm{HO}$ theorem and check its validity, we need to determine pre-trade prices in the two countries.
Referring back to the set of conditions specified above, first of all note that for any given set of commodity prices, the factor prices and corresponding input choices are determined by the conditions in equations (6.3)-(6.5). Finally, given these input coefficients, full employment conditions determine output levels. Any change in the relative commodity price affects these outputs through changes in input choices consequent upon induced factor price changes. The emerging supply relationship is the one shown in Figure 6.3. The algebraic derivation of the relative supply curve in the home country is set out in Appendix A6. Note that regardless of the factor intensity ranking of the two goods, the relative supply of computers rises with the increase in its relative price. An alternative derivation of the relative supply curve is as follows.
As explained earlier in Chapter 1, the production possibility frontier (PPF) is the locus of combinations of output levels of computers and textiles that maintain full employment. Given the above mentioned assumption of CRS technology with diminishing returns to the variable factor, PPF will be bowed out (or concave downwards) as illustrated in Figure 6.2. At the competitive equilibrium, the output combinations will be such as to satisfy the condition $M R T$ $=p_T$, for any given relative price of textiles $p_T$. That is, the equilibrium output combination will correspond to the tangency point between the price line and the PPF. For a very low relative price of textiles, as labeled by $p_{\min }$, the home country will produce only computers. That is, the price of textiles relative to that of computers is so low that it makes sense to put all the resource of the economy in the production of computers. A higher relative price of textiles (or a lower relative price of computers) makes the production of textiles profitable. The home country then starts producing textiles along with computers. For successively higher relative price of textiles more and more units of textiles and less and less units of computer are being produced so that the relative supply of textiles, $s=\frac{X_T}{X_C}$ rises. Note that the trade-off in production comes from the full employment of factors. At the other extreme, a very high relative price of textiles $p_{\max }$ chokes off production of computers and all resources are put in the production of textiles. Thus as we approach this $p_{\max }$, the relative supply of textiles becomes asymptotic as shown in Figure 6.3.

# 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|自动均衡和贸易模式

HO定理指出，如果这两个国家之间的贸易开放，劳动力相对充裕的母国将出口劳动力相对密集的棉织品，而资本相对充裕的外国将出口资本相对密集的计算机。正如第一章前面所解释的，要出现这种贸易模式，计算机的贸易前相对价格必须在母国高于在国外:$p_c>p_c^*$。或者，国内的纺织品必须比国外便宜。因此，为了解释$\mathrm{HO}$定理并检验其有效性，我们需要确定这两个国家的贸易前价格。回到上面指定的条件集，首先要注意，对于任何给定的商品价格集，要素价格和相应的投入选择是由式(6.3)-(6.5)中的条件决定的。最后，考虑到这些投入系数，充分就业条件决定了产出水平。相对商品价格的任何变化都是通过因诱发的要素价格变化而导致的投入选择的变化来影响这些产出的。新出现的供应关系如图6.3所示。母国相对供给曲线的代数推导见附录A6。注意，无论两种商品的要素强度排名如何，计算机的相对供应量都随着其相对价格的增加而增加。相对供给曲线的另一种推导如下。正如第一章前面所解释的，生产可能性边界(PPF)是维持充分就业的计算机和纺织品的产出水平组合的轨迹。在上述CRS技术对变量因子收益递减的假设下，PPF将会向下弯曲(或向下凹)，如图6.2所示。在竞争均衡中，对于纺织品的任何给定相对价格$p_T$，输出组合将满足条件$M R T$$=p_T$。也就是说，均衡产出组合将对应于价格线和PPF之间的切点。由于纺织品的相对价格非常低，如$p_{\min }$所标示的那样，母国将只生产计算机。也就是说，纺织品的价格相对于计算机的价格是如此之低，以至于把所有的经济资源都投入到计算机的生产中是有道理的。较高的纺织品相对价格(或较低的计算机相对价格)使纺织品生产有利可图。然后母国开始生产纺织品和计算机。由于纺织品的相对价格不断上升，越来越多的纺织品和越来越少的计算机被生产出来，因此纺织品的相对供给$s=\frac{X_T}{X_C}$上升。请注意，生产中的权衡来自于要素的充分利用。在另一个极端，非常高的相对价格的纺织品$p_{\max }$窒息了计算机的生产和所有的资源被投入到生产纺织品。因此，当我们接近这个$p_{\max }$时，纺织品的相对供应变得渐近，如图6.3所示

## 有限元方法代写

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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。