## 经济代写|国际经济学代写International Economics代考|EC340

statistics-lab™ 为您的留学生涯保驾护航 在代写国际经济学International Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写国际经济学International Economics代写方面经验极为丰富，各种代写国际经济学International Economics相关的作业也就用不着说。

• 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|Trade Indifference Curves and Alternative Derivation of Offer Curves

Trade indifference curves (TICs) are a useful tool in discussing the welfare properties of free or restricted trade equilibrium. James Meade used TICs to propose an alternative way of deriving offer curves. A TIC for a country is the locus of different combinations of its export supply and import demand that yield the same national welfare for the country. Accordingly, the country is indifferent among all such combinations. In the export-import space, each TIC is positively sloped. The reason is as follows. An increase in export supply by the country means lesser units of the export good are now available for domestic consumption. This lowers the welfare of the country. Thus, to compensate and keep the national welfare at the same level, the other good (which is imported by the country) must be available for domestic consumption in greater quantity. Hence, along a TIC, an increase in export supply must be accompanied by an increase in import demand.

The other properties of TICs are similar to that of CICs, since TICs by definition replicate CICs in the excess-demand (or offer) space. That is, each TIC is convex to the export-axis and a higher TIC, which is further away from the country’s export-axis, represents a higher national welfare. That a higher (non-intersecting) TIC represents a higher national welfare is easily comprehensible, and is left as an exercise. It is also assumed that taste patterns are such that TICs do not intersect each other so that, like the CICs, we can attach a unique utility or welfare index to each TIC and the export-import combinations on different TICs can be Pareto ranked in the sense discussed earlier. The TIC map for the home country is illustrated in Figure A4.3.
Actual offer of exports in exchange for import demand by the home country, however, should be consistent with its budget constraints at the post-trade prices. The budget constraints for different TOT are shown by TOT lines through the origin. Thus facing the TOT indicated by the ray $O a_1$, the home country makes an offer of the combination $b_1$ that maximizes its welfare. An improved TOT enables the country to improve its welfare by offering $b_2$, and so on. Note that each of these offers is consistent with balanced trade. The locus connecting this welfare-maximizing and balanced trade offers traces out the offer curve for the home country. From this alternative derivation of a country’s offer curve emerges the welfare property of offers made by it for different TOT. Any point on the offer curve represents an offer of export supply and import demand for which trade is balanced and welfare is maximized for the corresponding TOT.

Note that by construction, at the free trade international equilibrium point $E$ in Figure $4.5$, the trade indifference curves of the two countries are tangent to the TOT line $O E$ and hence are mutually tangent to each other.

## 经济代写|国际经济学代写International Economics代考|Measurement and Trends in Barter TOT

A country may export and import thousands of commodities, and thus it only makes sense to measure a country’s TOT by the export price index relative to the import price index. Often these price indices are measured by the unit value indices for exports and imports. These unit value indices are constructed from data on exports and imports-both value and volumereported by countries. The unit value of exports, as a proxy for the export price index, is simply the index of value of exports divided by the index of volume of exports. The unit value of imports is similarly calculated. Finally, the ratio of the unit value index of exports to the unit value index of imports gives us the net barter terms of trade of a country.

Figure A4.4 illustrates movements in net barter TOT for four developed countries – Canada, Japan, UK, and USA-during 2000-19 with 2000 as the base year, as reported in UNCTAD Trade Statistics 2020. Both UK and the United States have stable and almost unchanged net barter TOT during this period. Canada experienced steady improvement in its net barter TOT till 2008 before it worsened. But, the net barter TOT for Japan deteriorated sharply before improving marginally after 2016. Figure A4.5, on the other hand, illustrates movements in net barter TOT for the developing countries like Brazil, China, India, Korea, and Mexico during the same period. Similar to Japan, Korea experienced continuous worsening of its net barter TOT till it stabilized to some extent after 2015 . The most interesting observation that can be made is movements in TOT of the other four countries. TOT of China and India, on the one hand, and of Brazil and Mexico, on the other hand, moved in tandem though almost exactly in the opposite directions. That is, while China and India experienced worsening of their respective TOTs during 2000-12, Brazil and Mexico enjoyed improving TOT. Subsequently, after 2015 in particular, the trends reversed for these countries.

There are many plausible explanations for such wide variations in TOT movement both across time and across countries as we will learn in later chapters.

## 经济代写|国际经济学代写国际经济学代考|贸易无差异曲线和报价曲线的可选推导

.

tic的其他属性与CICs相似，因为tic从定义上复制了过剩需求(或提供)空间中的CICs。也就是说，每个TIC都是出口轴的凸点，越高的TIC，越远离国家的出口轴，代表越高的国家福利。较高的(不交叉的)TIC代表较高的国家福利，这一点很容易理解，因此就留作练习。我们还假设，味觉模式是这样的，TIC之间不会交叉，因此，像CICs一样，我们可以给每个TIC附加一个独特的效用或福利指数，不同TIC上的进出口组合可以按照前面讨论的意义进行帕累托排序。母国的议会地图见图A4.3。但是，本国以出口换取进口需求的实际提议应符合其在贸易后价格下的预算限制。不同TOT的预算约束由通过原点的TOT线表示。因此，面对射线$O a_1$所表示的TOT，母国提出了使其福利最大化的组合$b_1$。一个改进的TOT使国家能够通过提供$b_2$来改善其福利，等等。请注意，这些提议都符合平衡贸易。连接福利最大化和平衡贸易提供的轨迹是母国提供曲线的轨迹。从这个对一国提供曲线的替代推导中，可以得出该国为不同TOT所提供的服务的福利性质。报价曲线上的任何一点都代表出口供给和进口需求的报价，对于相应的TOT，贸易是平衡的，福利是最大化的。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|国际经济学代写International Economics代考|ECN422

statistics-lab™ 为您的留学生涯保驾护航 在代写国际经济学International Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写国际经济学International Economics代写方面经验极为丰富，各种代写国际经济学International Economics相关的作业也就用不着说。

• 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|Global Pareto optimality of free trade bundle

Free trade bundle, despite being sub-optimal for each large country in the case specified and illustrated above, is globally Pareto optimal. A Pareto optimal bundle is the one such that if we deviate from this bundle then at least one of the countries will be worse off. This can be verified from Figure 4.7. All the bundles along the aE segment of the foreign offer curve lie in the better set to the free trade bundle for the home country, but in the worse set to the free trade bundle for the foreign country. Thus, for all such trade bundles, achieved by the home country through a trade restriction policy, the home country will be better off but the foreign country will be worse off. Similarly, for all trade bundles along aE segment of the home offer curve, achieved by the foreign country through a trade restriction policy, the foreign country will be better off but the home country will be worse off. On the other hand, for any trade bundle that lie below $T I C_f$ below $T I C_f^$ and-such as bundles along the Oa segment of the home offer curve and along the $\mathrm{Oa}^*$ segment of the foreign offer curve-both countries are worse off relative to free trade.
Note that, free trade bundle emerges as the globally Pareto optimal bundle because of the fact that a pair of TICs of both the countries are tangent to each other for this bundle. If the TICs would have crossed each other at the free trade bundle, then some other trade bundles would have existed for which either both countries would have been better off; or one of them would have been better off with the other country being indifferent, that is, having the same welfare as for the free trade bundle.

This global Pareto optimality property of the free trade bundle has some far-reaching implications for trade wars, and for formation of regional trading blocs, as we will learn later.

## 经济代写|国际经济学代写International Economics代考|Existence, Uniqueness, and Stability of International Equilibrium

Existence of international equilibrium depicted in Figure $4.5$ requires that the two offer curves must cross each for a trade bundle containing strictly positive volumes of export offer and import demand. The assumption of non-decreasing opportunity costs and corresponding convexity of offer curves though help in this regard, but they may not be sufficient. Assuming that the offer curves are continuous, a sufficient condition for existence of international equilibrium is that at least one offer curve must be backward bending. However, though this might ensure existence, it may lead to multiple equilibria. This is evident from Figure 4.6.

Algebraically, the conditions of existence, uniqueness, and stability can be derived using the excess demand function approach. Consider the world market for the good imported by the home country and exported by the foreign country (that is, the world market for computers). Referring back to equation (4.2), define excess demand function $E\left(p^n\right)$ as:
$$E\left(p^n\right)=M\left(p^\right)-X^\left(p^w\right)$$
By the world-clearing condition (4.1) in the text, the (world) equilibrium price $p_c^{\text {” }}$ is such that, $E\left(p_c^w\right)=0$. Then, if this excess demand function is continuous in $p^w$, the following conditions ensure that $p_e^w>0$ (that is, an equilibrium price exists):
(a) There exists a price $p_0^w>0$ such that $E\left(p_0^w\right)>0$
(b) There exists a price $p_1^w>0$ such that $E\left(p_1^w\right)<0$ Figure A4.2 under the assumption that $p_0^w0$ will be unique. This is illustrated in Figure A4.2b. As it appears, the uniqueness is ensured by a monotonic excess demand function.

## 经济代写|国际经济学代写国际经济学代考|国际均衡的存在性、唯一性和稳定性

$$E\left(p^n\right)=M\left(p^\right)-X^\left(p^w\right)$$

(a)存在一个价格$p_0^w>0$使得$E\left(p_0^w\right)>0$
(b)存在一个价格$p_1^w>0$使得$E\left(p_1^w\right)<0$图A4.2在假设$p_0^w0$是唯一的情况下。图A4.2b说明了这一点。正如它所显示的那样，唯一性是由一个单调的超额需求函数保证的

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|国际经济学代写International Economics代考|ECON440

statistics-lab™ 为您的留学生涯保驾护航 在代写国际经济学International Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写国际经济学International Economics代写方面经验极为丰富，各种代写国际经济学International Economics相关的作业也就用不着说。

• 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|WELFARE PROPERTIES OF THE INTERNATIONAL EQUILIBRIUM

Welfare property of the international equilibrium can be discussed in terms of a set of trade indifference curves (TICs). A TIC for a country is the locus of different combinations of her export supply and import demand that yield the same level of her national welfare. As explained in the appendix, a TIC is positively sloped in the offer space. It has similar properties as the CIC. The most relevant in the present context is that a higher TIC (that is a TIC away from the country’s export axis) represents higher national welfare. That is, while national welfare realized from a trade bundle is indicated by the TIC on which that trade bundle lie, a higher welfare is realized from a trade bundle on a higher TIC than from a trade bundle on a lower TIC. Thus, at free-trade equilibrium $\mathrm{E}$ in Figure 4.7, the home country attains the welfare level as indicated by $T I C_f$ and the foreign country attains the welfare level as indicated by $\mathrm{TIC}_f^*$ Moreover, from the alternative derivation of offer curves as suggested by James Meade, and discussed in the appendix to this chapter, it follows that the pair of TICs of the home and foreign country passing through free trade bundle E will be tangent to the terms of trade line $\mathrm{OE}$, and consequently will be tangent to each other. This tangency property of the free trade bundle makes it a globally Pareto optimal bundle. We will return to this dimension of the free trade bundle after revisiting the gains from trade.

## 经济代写|国际经济学代写International Economics代考|Gains from trade revisited

Figure $4.7$ provides an alternative illustration of the gains from trade (GFT). Since a higher TIC represents higher welfare so the better set to the free trade bundle for the home country is the region above $T I C_f$ and the worse set is the region below it. Similarly, for the foreign country, the region above (or to the right of) represents the better set to the free trade bundle and the region below it (or to the left of it) $T I C_f^*$ represents the worse set. The autarkic bundle $(0,0)$ lies in the worse set to the equilibrium trade bundle E for both the countries. Hence, both countries gain as they open up trade between them.

However, though free trade raises welfare for both the countries, it does not maximize their welfare levels. The home country can gain further by offering any trade bundle along the segment aE of the foreign curve since all such trade bundles lie in the better set to the free trade bundle. By similar reasoning, the foreign country can gain further by offering any trade bundle along the segment $a^* E$ of the home offer curve. Therefore, the gains from trade do not mean that welfares of the trading nations are maximized under free trade. It simply states that free trade will make trading nations better off relative to no-trade or autarchy. What follows from this is that each country will have unilateral incentive to deviate from the offer of the free trade bundle E. As we will see in Chapter 9, each country can achieve these preferred bundles by trade restrictive policies like tariff (or import tax) and import quota. Of course, the size of the countries, or their importance in world trade, will matter as we will learn later. For countries that are large enough in world trade to influence the terms of trade by altering their export offers (or import demand), free trade does not maximize their respective national welfare levels, even though it raises welfare above the autarchic level. This forms the basis for welfare motive for restricting trade, rather than pursuing free trade, for such countries.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|劳动经济学代写Labor Economics代考|ECON045

statistics-lab™ 为您的留学生涯保驾护航 在代写劳动经济学Labor Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写劳动经济学Labor Economics代写方面经验极为丰富，各种代写劳动经济学Labor Economics相关的作业也就用不着说。

• 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|劳动经济学代写Labor Economics代考|Can the Laws of Derived Demand Be Applied to Cross-Elasticities?

The Hicks-Marshall laws of derived demand are based on four technological or market conditions that determine the size of own-wage elasticities. Each of the four conditions influences the substitution or the scale effect, and as noted above, the relative strengths of these two effects are also what determine the sign of cross-elasticities. The laws that apply to own-wage elasticities cannot be applied directly to cross-elasticities because with cross-elasticities, the substitution effect (if there is one) and the scale effect work in opposite directions. The same underlying considerations, however, are basic to an analysis of cross-elasticities.

As we discuss these four considerations in the context of cross-elasticities, it will be helpful to have an example in mind. Let us return, then, to the question of what might happen to the demand for adult workers if the wages of teenage workers were to fall. As noted above, the answer depends on the relative strengths of the scale and substitution effects. What determines the strength of each?

The Scale Effect The most immediate effect of a fall in the wages of teenagers would be reduced production costs for those firms that employ them. Competition in the product market would ensure that lower costs are followed by price reductions, which should stimulate increases in both product demand and the level of output. Increased levels of output will tend to cause increases in employment of all kinds of workers, including adults. This chain of events obviously describes behavior underlying the scale effect, and we now investigate what conditions are likely to make for a strong (or weak) scale effect.
The initial cost (and price) reductions would be greater among those employers for whom teenage wages constituted a higher proportion of total costs. Other things equal, greater price reductions would result in greater increases in both product demand and overall employment. Thus, the share of total costs devoted to the productive factor whose price is changing will influence the size of the scale effect. The larger this share, other things equal, the greater the scale effect (and the more likely it is that gross complementarity will exist). This tendency is analogous to the fourth Hicks-Marshall law discussed earlier; the difference is that with cross-elasticities, the factor whose price is changing is not the same as the one for which employment changes are being analyzed.
The other condition that greatly influences the size of the scale effect is product demand elasticity. In the earlier case of teenage wage reductions, the greater the increase in product demand when firms reduce their prices, the greater the tendency for employment of all workers, including adults, to increase. More generally, the greater the price elasticity of product demand, other things equal, the greater the scale effect (and thus the greater the likelihood of gross complementarity). The effects of product demand elasticity are thus similar for both own-wage and cross-wage elasticities.

## 经济代写|劳动经济学代写Labor Economics代考|Estimates Relating to Cross-Elasticities

Estimating at least the sign of cross-wage labor demand elasticities is useful for answering many public-policy questions. For example, if we were to reduce the teenage minimum wage, how would this affect the demand for adult labor? If capital were to be subsidized, how would this affect the demand for labor? Or, to take a hotly debated issue in recent years (and one we will return to in chapter 10), when immigrant labor becomes cheaper and more available, what are the likely effects on the demand for various grades of native labor? These questions, of course, are really asking whether the pairs of inputs italicized in each sentence are gross complements or gross substitutes.

While the major policy interest is whether two inputs are gross complements or gross substitutes, obtaining credible estimates is challenging (because it is difficult to estimate scale effects). Therefore, most of the cross-wage empirical studies to date focus on whether two factors are substitutes or complements in production. These studies estimate the employment response for one category of labor to a wage or price change elsewhere, holding output constant (which in effect allows us to focus just on changes in the mix of factors used in production). The factors of production paired together for analysis in these studies are numerous, and the results are not always clear-cut; nevertheless, the findings taken as a whole offer at least a few generalizations: $\frac{10}{}$

1. Labor and energy are clearly substitutes in production, although their degree of substitutability is small. Labor and materials are probably substitutes in production, with the degree of substitutability again being small.
2. Skilled labor and unskilled labor are substitutes in production. 11
3. We are not certain whether either skilled or unskilled labor is a substitute for or a complement with capital in the production process. What does appear to be true is that skilled (or well-educated) labor is more likely to be complementary with capital than is unskilled labor-and that if they are both substitutes for capital, the degree of substitutability is smaller for skilled labor: $12$
4. The finding summarized in 3 above suggests that skilled labor is more likely than unskilled labor to be a gross complement with capital. This finding is important to our understanding of recent trends in the earnings of skilled and unskilled workers (see chapter 15 ), because the prices of computers and other high-tech capital goods have fallen dramatically in the past decade or so.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|劳动经济学代写Labor Economics代考|ECON308

statistics-lab™ 为您的留学生涯保驾护航 在代写劳动经济学Labor Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写劳动经济学Labor Economics代写方面经验极为丰富，各种代写劳动经济学Labor Economics相关的作业也就用不着说。

• 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|劳动经济学代写Labor Economics代考|Applying the Laws of Derived Demand: Inferential Analysis

Because empirical estimates of demand elasticities that may be required for making particular decisions are often lacking, it is frequently necessary to guess what these elasticities are likely to be. In making these guesses, we can apply the laws of derived demand to predict at least relative magnitudes for various types of labor. Consider first the demand for unionized New York City garment workers. As we shall discuss in chapter 13 , because unions are complex organizations, it is not always possible to specify what their goals are. Nevertheless, it is clear that most unions value both wage and employment opportunities for their members. This observation leads to the simple prediction that, other things equal, the more elastic the demand for labor, the smaller the wage gain that a union will succeed in winning for its members. The reason for this prediction is that the more elastic the demand curve, the greater the percentage employment decline associated with any given percentage increase in wages. As a result, we can expect the following:

1. Unions would win larger wage gains for their members in markets with inelastic labor demand curves.
2. Unions would strive to take actions that reduce the wage elasticity of demand for their members’ services.
3. Unions might first seek to organize workers in markets in which labor demand curves are inelastic (because the potential gains to unionization are higher in these markets).

Because of foreign competition, the price elasticity of demand for the clothing produced by New York City garment workers is extremely high. Furthermore, employcrs can easily find other inputs to substitute for these workers-namely, lower-paid nonunion garment workers in the South or in other countries. These facts lead one to predict that the wage elasticity of demand for New York City unionized garment workers is very high. Consequently, union wage demands have historically been moderate. The union has also sought to reduce the elasticity of product demand by supporting policies that reduce foreign competition, and it has pushed for higher federal minimum wages to reduce employers’ incentives to move their plants to the South.

## 经济代写|劳动经济学代写Labor Economics代考|The Cross-Wage Elasticity of Demand

Because firms may employ several categories of labor and capital, the demand for any one category can be affected by price changes in the others. For example, if the wages of carpenters rose, more people might build brick homes and the demand for masons might increase. An increase in carpenters’ wages might decrease the overall level of home building in the economy, however, which would decrease the demand for plumbers. Finally, changes in the price of capital could increase or decrease the demand for workers in all three trades.

The direction and magnitude of the above effects can be summarized by examining the elasticities of demand for inputs with respect to the prices of other inputs. The elasticity of demand for input $j$ with respect to the price of input $k$ is the percentage change in the demand for input $j$ induced by a 1 percent change in the price of input $k$. If the two inputs are both categories of labor, these cross-wage elasticities of demand are given by
$$\eta \mathrm{jk}=\% \Delta \mathrm{Ej} \% \Delta \mathrm{Wk} x \quad \text { (4.2) }$$
and
$$\eta \mathrm{kj}=\% \Delta \mathrm{Ek} \% \Delta \mathrm{Wj}$$
where, again, the Greek letter $\eta$ is used to represent the elasticity. If the cross-elasticities are positive (with an increase in the price of one “category” increasing the demand for the other), the two are said to be gross substitutes. If these cross-elasticities are negative (and an increase in the price of one “category” reduces the demand for the other), the two are said to be gross complements (refer back to Figure 3.3).

It is worth reiterating that whether two inputs are gross substitutes or gross complements depends on the relative sizes of the scale and substitution effects. To see this, suppose we assume that adults and teenagers are substitutes in production. A decrease in the teenage wage will thus have opposing effects on adult employment. On the one hand, there is a substitution effect: for a given level of output, employers will now have an incentive to substitute teens for adults in the production process and reduce adult employment. On the other hand, there is a scale effect: a lower teenage wage reduces costs and provides employers with an incentive to increase employment of all inputs, including adults.

.

## 经济代写|劳动经济学代写劳动经济学代考|需求的跨工资弹性

$$\eta \mathrm{jk}=\% \Delta \mathrm{Ej} \% \Delta \mathrm{Wk} x \quad \text { (4.2) }$$

$$\eta \mathrm{kj}=\% \Delta \mathrm{Ek} \% \Delta \mathrm{Wj}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|劳动经济学代写Labor Economics代考|ECO433

statistics-lab™ 为您的留学生涯保驾护航 在代写劳动经济学Labor Economics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写劳动经济学Labor Economics代写方面经验极为丰富，各种代写劳动经济学Labor Economics相关的作业也就用不着说。

• 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|劳动经济学代写Labor Economics代考|The Hicks-Marshall Laws of Derived Demand

The factors that influence own-wage elasticity can be summarized by the HicksMarshall laws of derived demand-four laws named after two distinguished British economists, John Hicks and Alfred Marshall, who are closely associated with their development. ${ }^3$ These laws assert that, other things equal, the own-wage elasticity of demand for a category of labor is generally higher under the following conditions:

1. When the price elasticity of demand for the product being produced is higher.
2. When other factors of production can be more easily substituted for the category of labor.
3. When the supply of other factors of production is more highly elastic (that is, usage of other factors of production can be increased without substantially increasing their prices).
4. When the cost of employing the category of labor is a larger share of the total costs of production.

In seeking to explain why these laws generally hold, it is useful to act as if we could divide the process by which an increase in the wage rate affects the demand for labor into two steps. First, an increase in the wage rate increases the relative cost of the category of labor in question and induces employers to use less of it and more of other inputs (the substitution effect). Second, when the wage increase causes the marginal costs of production to rise, there are pressures to increase product prices and reduce output, causing a fall in employment (the scale effect). The four laws of derived demand each deal with substitution or scale effects.

Demand for the Final Product We noted above that wage increases cause production costs to rise and tend to result in product price increases. The greater the price elasticity of demand for the final product, the larger the percentage decline in output associated with a given percentage increase in price-and the greater the percentage decrease in output, the greater the percentage loss in employment (other things equal). Thus, the greater the elasticity of demand for the product, the greater the elasticity of demand for labor.

## 经济代写|劳动经济学代写Labor Economics代考|Estimates of Own-Wage Labor Demand Elasticities

We now turn to the results of studies that estimate own-wage demand elasticities for labor as a generic input (that is, labor undifferentiated by skill level). The estimates we discuss are based on studies that utilize wage, output, and employment data from firms or narrowly defined industries. Thus, the employment responses being estimated approximale those that would be expected to vecur in a firm that had to raise wages to remain competitive in the labor market. These estimates are suggestive of what might be a “typical” response but, of course, are not indicative of what would happen with any particular firm.

As our analysis has indicated, employers’ labor demand responses to a wage change can be broken down into two components: a scale effect and a substitution effect. These two effects can themselves be expressed as elasticities, and their sum is the own-wage labor demand elasticity. In Table 4.1, we display the results of estimates of (a) the shortrun scale effect, (b) the substitution effect, and (c) the overall elasticity of demand for

labor in the long run.
The scale effect (expressed as an elasticity) is defined as the percentage change in employment associated with a given percentage change in the wage, holding production technology constant; that is, it is the employment response that occurs without a substitution effect. By definition, the short-run labor demand elasticity includes only the scale effect, although we noted earlier that the scale effect is likely to be greater in the long run than it is in the short run (owing to greater possibilities for product market substitutions in the long run). Therefore, estimates of short-run labor demand elasticities will be synonymous with the short-run scale effect, which may approximate the long-run scale effect if product market substitutions are relatively swift. A study using data from British manufacturing plants estimated the short-run, own-wage labor demand elasticity to be $-0.53$ (see Table 4.1). The short-run labor demand curve for a typical firm or narrowly defined sector, therefore, would appear to be inelastic.

## 经济代写|劳动经济学代写劳动经济学代考|派生需求的希克斯-马歇尔定律

1. 当对所生产产品的需求的价格弹性较高时。当其他生产要素可以更容易地替代劳动范畴时。
2. 当其他生产要素的供给具有较强的弹性时(也就是说，其他生产要素的使用可以在不大幅度提高其价格的情况下增加)。
3. 当雇用这一类劳动力的成本占生产总成本的比例较大时。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|微观经济学代写Microeconomics代考|BU1003

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics相关的作业也就用不着说。

• 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|微观经济学代写Microeconomics代考|Partial Equilibrium

As a first step towards the study of the competitive general equilibrium of production and exchange, let us discuss in greater detail the Marshallian construction often referred to in this chapter: the determination, via the intersection of a supply curve and a demand curve, of the partial equilibrium (or particular equilibrium, the original and more precise denomination) of a single competitive market studied in isolation. ${ }^{34} \mathrm{~A}$ famous 1926 article describes this approach as follows:
) This point of view assumes that the conditions of production and the demand for a commodity can be considered, in respect to small variations, as being practically independent, both in regard to each other and in relation to the supply and demand of all other commodities. It is well known that such an assumption would not be illegitimate merely because the independence may not be absolutely perfect, as, in fact, it never can be; and a slight degree of interdependence may be overlooked without disadvantage if it applies to quantities of the second order of smalls, as would be the case if the effect (for example, an increase of cost) of a variation in the industry which we propose to isolate were to react partially on the price of the products of other industries, and this latter effect were to influence the demand for the product of the first industry. (Sraffa 1926, p. 538)

The motivation behind the partial equilibrium approach is that it allows the study of comparative statics of a market’s equilibrium (e.g. how price and quantity change if some input cost decreases, or if consumers’ tastes change and the desire for the good increases), and of some welfare aspects, without needing simultaneously to consider what is happening in all other markets. In $>$ Chap. 3 we saw that, rigorously speaking, in the neoclassical approach the simultaneous consideration of all markets cannot be avoided, because any change in some of the data of general equilibrium will have repercussions on all markets; for example, a change in tastes in favour of a good will alter equilibrium income distribution and hence all prices and quantities. However,
)) when the expenditure on the good under study is a small portion of a consumer’s total expenditure, ony a small fraction of any additional dollar of wealth will be spent on this good; consequently, we can expect wealth effects for it to be small. Second. with similarly dispersed substitution effects, the small size of the market under study should lead the prices of other goods to be approximately unaffected by changes in this market. (Mas-Colell et al. 1995, p. 316; “wealth effects” stands for income effects)

## 经济代写|微观经济学代写Microeconomics代考|Stability of Partial Equilibria

We have noted that the markets that can be studied with the partial-equilibrium methodology are consumption goods’ markets. Then the partial-cquilibrium demand curve for a product derives from consumer choices. It is based on given incomes of consumers and given other prices. So the partial-equilibrium approach presupposes a previous determination of income distribution-which determines the normal prices of other goods and the input costs of the industry under study – and of the general level of economic activity, which by determining labour employment determines aggregate consumer incomes. In the marginal approach the implicit assumption is that there is general equilibrium, income distribution is the equilibrium one, and there is full employment of labour and of all resources. Some economists argue that other theories of income distribution and of labour employment too can be the background to the use of Marshallian partial equilibrium for the study of consumer markets. Other economists disagree, but this is not the place to study this debate, we are interested now in understanding the marginal/neoclassical approach.

Given the very low likelihood of Giffen goods, demand curves for produced consumption goods can be assumed decreasing. Short-period supply curves can be assumed upward-sloping, so the short-period equilibrium price is stable. If it is greater than $\operatorname{Min} L A C$, in the long run there will be entry of new firms, or the existing firms will build new plants, and the short-period supply curve will shift to the right, and price will decrease. So the long-period partial equilibrium is stable too. If the good is homogeneous (undifferentiated), then on average all units of the good sell at the same price. Of course this can only be approximately true in actual markets, but, as already pointed out several times, the equilibrium position can only aim at describing the average position resulting over sufficient time from the trial-and-error higgling of the market.

There is a reason for representing price in ordinate and quantity in abscissa; then a supply curve and a demand curve represent supply price and demand price as functions of the quantity of the good – the prices that are necessary in order to obtain, respectively, convenience to supply, or to demand, the given quantity measured in abscissa. In this way a horizontal supply curve, or the saw-like supply curve of $\boldsymbol{\bullet}$ Fig. 5.9, are nonetheless functions.

## 经济代写|微观经济学代写微观经济学代考|部分均衡

)这一观点假设，一种商品的生产条件和需求，就微小的变化而言，可以被认为是实际上独立的，无论是彼此之间的关系，还是与所有其他商品的供求关系。众所周知，这种假设并不仅仅是因为独立可能不是绝对完美的，事实上，它永远不可能是绝对完美的;如果它适用于第二级的小量，那么轻微程度的相互依赖可能会被忽略而没有不利的影响，就像我们建议分离的行业的变化的影响(例如，成本的增加)将部分地对其他行业的产品价格产生反应，而后者的影响将影响对第一行业产品的需求一样。(Sraffa 1926, p. 538)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|微观经济学代写Microeconomics代考|ECON106

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics相关的作业也就用不着说。

• 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|微观经济学代写Microeconomics代考|Functional Separability: Leontief Separability

Suppose we can separate the $m+n$ inputs to a production function into two subvectors, $\mathbf{x}=\left(x_1, \ldots, x_m\right)$ and $\mathbf{y}=\left(y_1, \ldots, y_n\right)$, having, respectively, rental vectors $\mathbf{v}$ and $\mathbf{w}$, and that the production function satisfies
$$f(\mathbf{x}, \mathbf{y})=f(z(\mathbf{x}), \mathbf{y}),$$
where the scalar function $z(\cdot)$ has the characteristics of a production function: then it is as if inputs $\mathbf{x}$ produced an intermediate good which then produces the final output in combination with inputs $\mathbf{y}$. This can be simply a mathematical property of the form of the production function, but it can also reflect the fact that the production of the final output requires the production of an intermediate good first, which does not appear in the production function because produced and immediately re-utilized in the process of producing the final output. An example can be bread production that requires first the production of dough, utilizing a different kind of labour from the labour which produces bread from dough.

If $z(\mathbf{x})$ is differentiable and $f(z, \mathbf{y})$ is also differentiable, then $\partial f l \partial x_i=(\partial f / \partial z) \cdot\left(\partial z / \partial x_i\right)$; as a result, the Leontief weak separability condition holds: the marginal rate of substitution between any two $x$-goods is independent of the amounts of $y$-goods:
$$M R S_{x j, x i}=-\left(\partial f / \partial x_i\right) /\left(\partial f / \partial x_j\right)=-\left(\partial z / \partial x_i\right) /\left(\partial z / \partial x_j\right) .$$ Vice versa if the Leontief weak separability condition holds for the subgroup $\mathbf{x}$ of inputs, then a differentiable $f(\mathbf{x}, \mathbf{y})$ can be written as $f(z(\mathbf{x}), \mathbf{y})$ where $z(\mathbf{x})$ is a scalar function (I omit the somewhat complex proof; see Kreps 2013 pp. 39-42).
The term ‘weakly separable’ is used to distinguish the notion from that of strongly separable production functions, which means additively separable, i.e. represented by an additive production function: $f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2, \ldots, x_n\right)$. The term ‘strong separability’ is sometimes restricted to completely additively separable production functions $f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2\right)+\ldots+v_n\left(x_n\right)$.

Under weak separability, the firm can adopt a two-stage cost-minimization procedure: it can first determine the cost-minimizing input combination of the $x$-inputs for each level of $z$, and the resulting cost of $z$; and then it can determine the cost-minimizing input combination of $(z, \mathbf{y})$ for each level of output. This is what a firm would do that produces itself some of its inputs in a separate plant. If $f(\cdot)$ has constant returns to scale, so does $z(\cdot)$; then the cost function for the ‘good’ $z$ can be written as $\varepsilon(\mathbf{v}) \cdot z$, with $\varepsilon(\mathbf{v})$ representing the unit price of $z$.

## 经济代写|微观经济学代写Microeconomics代考|Elasticity of Substitution

Cost minimization requires that firms intending to produce a given output locate themselves on the point of the corresponding (convex) isoquant touching the isocost closest to the origin-a point of tangency if the isoquant is smoothly convex. A change in the relative rental of two factors can induce no substitution, little substitution and extensive substitution. For example, if factors are perfect complements, then isoquants (with two factors) are L-shaped and cost-minimizing firms will locate themselves at the kink: changes in relative factor ‘prices’ induce no substitution. In order to measure the effect of changes in relative factor rentals on the proportions in which firms find it optimal to combine two factors, economists use the elasticity of substitution, already met in Sect. 4.11.3. The analysis here will be restricted to only two factors. When applied to production functions, this elasticity – to be indicated now with the symbol $\sigma$ – is the ratio between the percentage change in $\mathrm{x}2 / \mathrm{x}_1$ along a given isoquant, and the percentage change (pay attention to the different order of the indices!) of $\mathrm{MP}_1 / \mathrm{MP}_2$ or $v_1 / v_2$ : $$\sigma{21}=\frac{\frac{d\left(x_2 / x_1\right)}{x_2 / x_1}}{\frac{d\left(\mathrm{MP}1 / \mathrm{MP}_2\right)}{\mathrm{MP}_1 / \mathrm{MP}_2}}-\frac{\partial\left(x_2 / x_1\right)}{\partial\left(v_1 / v_2\right)} \cdot \frac{v_1 / v_2}{x_2 / x_1} .$$ The second of the above two expressions for the elasticity of substitution is based on the assumption that the firm chooses the factor proportion that satisfies $-\mathrm{TRS}{2,1}=v_1 / v_2$; therefore the elasticity of substitution measures the sensitivity, of the proportion in which factors are demanded, to relative factor rentals; it gives an indication of what happens to the relative shares of factors in total cost as relative factor rentals vary. The relative share of factor 2 in total cost is given by $\left(v_2 x_2 /\left(v_1 x_1\right)\right.$, which can be rewritten as $\left(x_2 / x_1\right) \cdot\left(v_1 / v_2\right)$ or $\left(x_2 / x_1\right) \cdot\left|\mathrm{TRS}_{2,1}\right|$. When $v_1 / v_2$ increases by $1 \%, x_2 / x_1$ increases by $\sigma \%$; an elasticity of substitution equal to 1 means that relative factor shares in total cost do not change. An elasticity of substitution less than 1 means that when factor 1 becomes relatively more expensive, $x_2 / x_1$ increases less than in proportion, so $v_2 x_2 /\left(v_1 x_1\right)$ decreases: the relative share of factor 2 in national income decreases, and that of factor 1 increases. Note that a given percentage change in $x_2 / x_1$ is the same (with the opposite sign of course) as the corresponding percentage change in $x_1 / x_2$.

## 经济代写|微观经济学代写微观经济学代考|功能可分性:Leontief可分性

$$f(\mathbf{x}, \mathbf{y})=f(z(\mathbf{x}), \mathbf{y}),$$
，其中标量函数$z(\cdot)$具有生产函数的特征:然后，就好像输入$\mathbf{x}$产生了一个中间商品，然后该中间商品与输入$\mathbf{y}$结合产生最终的输出。这可能只是生产函数形式的一个数学性质，但它也可以反映这样一个事实，即最终产出的生产首先需要生产中间产品，而中间产品并不出现在生产函数中，因为在生产最终产出的过程中，中间产品被生产出来并立即被重新利用。例如，面包生产首先需要生产面团，使用的劳动与用面团生产面包的劳动不同

$$M R S_{x j, x i}=-\left(\partial f / \partial x_i\right) /\left(\partial f / \partial x_j\right)=-\left(\partial z / \partial x_i\right) /\left(\partial z / \partial x_j\right) .$$反之亦然如果Leontief弱可分条件成立于输入的子群$\mathbf{x}$，那么一个可微的$f(\mathbf{x}, \mathbf{y})$可以写成$f(z(\mathbf{x}), \mathbf{y})$，其中$z(\mathbf{x})$是一个标量函数(我省略了有些复杂的证明;见Kreps 2013第39-42页)。“弱可分”一词用来区分强可分生产函数与弱可分生产函数的概念，强可分生产函数是指可加可分的，即由可加生产函数$f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2, \ldots, x_n\right)$表示。术语“强可分性”有时被限制为完全可加可分的生产函数$f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2\right)+\ldots+v_n\left(x_n\right)$ .

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|微观经济学代写Microeconomics代考|ECON2516

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics相关的作业也就用不着说。

• 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|微观经济学代写Microeconomics代考|The Proft Function and Hotelling’s Lemma

Let us now define a new notion, the price-taking firm’s profit function $\pi(p, \mathbf{v})$ defined as the value function of the (unconstrained) maximization problem with $p$ and $\mathbf{v}$ as parameters
$$\max _x p f(\mathbf{x})-\mathbf{v x} .$$
The profit function must not be confused with the function $\pi(q)=p q-C(q)$, which is not called ‘profit function’, where profit is a function of output at given output price and factor rentals. The profit function describes how maximum profit changes with changes in output price or factor rentals.

The profit function is not always defined nor continuous. Suppose the firm has CRS and all factors are variable: for each given vector $\mathbf{v}$, marginal cost is constant and equal to minimum average cost; if $p>M C$ there is no maximum profit (the profit function is not defined), if $p=M C$ maximum profit is zero and output is indeterminate, if $p<M C$ maximum profit is zero and optimal output is zero; such a profit function is of very little use! The profit function has useful properties when, at least in an interval of output and input prices, profit-maximizing output and inputs are well defined and change continuously with $(p, \mathbf{v})$; then the profit function allows useful conclusions on how output and inputs change with changes in $p$ or in input rentals. This obtains if the analysis is a short-period one, output is positive, the factors considered are only the variable factors, and profit is defined as revenue minus variable cost, that is, without including quasi-rents into cost (otherwise profit would be zero always, as argued).

## 经济代写|微观经济学代写Microeconomics代考|Conditional and Unconditional Factor Demands

When the profit function is well defined, for each output price $p$ and vector of factor rentals $\mathbf{v}$ there is an optimal output and an associated vector of optimal factor utilizations: the latter vector need not be unique if isoquants are not strictly convex, but I will assume it is. In this case we can define the supply function (of the individual firm) $S(p, v)$ that indicates the optimal output as a function of factor rentals $\mathbf{v}$ and of the output price $p$; we also define the (vectorial) unconditional factor demand function $\mathbf{x}(p$, $v)$ that indicates the associated optimal factor employment vector. The connection between unconditional and conditional factor demand is
$$\mathbf{x}(p, \mathbf{y})=h(\mathbf{y}, S(p, \mathbf{y})) .$$
When the supply function and the unconditional factor demand function exist, what about the sign of their partial derivatives?

If profit is considered a function of $q$, we know that its maximization requires solving $\max _q p q-c(\mathbf{v}, q)$, whose first-order necessary condition is $p=M C(\mathbf{v}, q)$; the second-order sufficient condition is that $M C$ must be rising at the optimal $q$. If both conditions are satisfied it is:
$$\partial S(p, \mathbf{y}) / \partial p>0,$$
the supply function (graphically, the supply curve, usually drawn as an inverse supply curve, with $p$ in ordinate and $q$ in abscissa) is increasing. (Hotelling’s Lemma proved it was non-decreasing, here we are proving it is increasing: why this difference? Here we are assuming an upward-sloping MC curve at the optimal $q$, i.e. we are excluding a vertical MC curve which would indicate that it is impossible further to increase output.)

On the sign of $\partial x_{(}(p, \mathbf{v}) / \partial v_i$, Hotelling’s Lemma plus the convexity of the profit function imply $\partial \mathrm{x}{\mathrm{i}}(\mathrm{p}, \mathbf{v}) / \partial \mathrm{v}{\mathrm{i}} \leq 0$ : the own-rental effect is non-positive (and generally negative).

Does this result on input use imply $\partial S(p, \mathbf{v}) / \partial v_i \leq 0$ ? that is, is it always the case that the optimal output, when it exists, does not increase and generally decreases if the rental of a factor in positive use rises? Surprisingly, not always. When the rental of a factor rises, supply rises if the factor is an inferior input. An input is (locally) inferior when its conditional demand falls as output increases, that is, when $\partial h_i(\mathbf{v}, q) / \partial q<0$ (in a neighbourhood of the initial $q$ ), meaning that at the given input rentals the cost-minimizing way to increase $q$ is by increasing some input other than $i$ and decreasing input $i$.

## 经济代写|微观经济学代写微观经济学代考|利润函数和霍特林引理

$$\max _x p f(\mathbf{x})-\mathbf{v x} .$$

## 经济代写|微观经济学代写微观经济学代考|条件和无条件的要素需求

$$\mathbf{x}(p, \mathbf{y})=h(\mathbf{y}, S(p, \mathbf{y})) .$$

$$\partial S(p, \mathbf{y}) / \partial p>0,$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 经济代写|宏观经济学代写Macroeconomics代考|EC4505

statistics-lab™ 为您的留学生涯保驾护航 在代写宏观经济学Macroeconomics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写宏观经济学Macroeconomics代写方面经验极为丰富，各种代写宏观经济学Macroeconomics相关的作业也就用不着说。

• 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|宏观经济学代写Macroeconomics代考|The decentralized equilibrium

Here we present a discrete time model initially developed by Diamond (1965), building on earlier work by Samuelson (1958), in which individuals live for two periods (young and old). The economy lasts forever as new young people enter in every period. We first characterise the decentralised competitive equilibrium of the model. We then ask whether the market solution is the same as the allocation that would be chosen by a central planner, focusing on the significance of the golden rule, which will allow us to discuss the possibility of dynamic inefficiency (i.e. excessive capital accumulation).

The market economy is composed of individuals and firms. Individuals live for two periods. They work for firms, receiving a wage. They also lend their savings to firms, receiving a rental rate.
An individual born at time $t$ consumes $c_{1 t}$ in period $t$ and $c_{2 t+1}$ in period $t+1$, and derives utility
$$\left(\frac{\sigma}{\sigma-1}\right) c_{1 \mathrm{t}}^{\frac{\sigma-1}{\sigma}}+(1+\rho)^{-1}\left(\frac{\sigma}{\sigma-1}\right) c_{2 f+1}^{\frac{\sigma-1}{\sigma}}, \rho \geq 0, \sigma \geq 0 .$$
Note that the subscript ” 1 ” refers to consumption when young, and ” 2 ” labels consumption when old. Individuals work only in the first period of life, inelastically supplying one unit of labour and earning a real wage of $w_t$. They consume part of their first-period income and save the rest to finance their second-period retirement consumption. The saving of the young in period $t$ generates the capital stock that is used to produce output in period $t+1$ in combination with the labour supplied by the young generation of period $t+1$.
The time structure of the model appears in Figure 8.1.
The number of individuals born at time $t$ and working in period $t$ is $L_t$. Population grows at rate $n$ so that $L_t=L_0(1+n)^t$.

## 经济代写|宏观经济学代写Macroeconomics代考|Individuals

Consider an individual born at time $t$. His maximisation problem is
$$\max \left{\left(\frac{\sigma}{\sigma-1}\right) c_{1 t}^{\frac{\sigma-1}{\sigma}}+(1+\rho)^{-1}\left(\frac{\sigma}{\sigma-1}\right) c_{2 t+1}^{\frac{\sigma-1}{\sigma}}\right}$$
subject to
$$c_{1 t}+s_t=w_t,$$
$$c_{2 t+1}=\left(1+r_{t+1}\right) s_t,$$
where $w_t$ is the wage received in period $t$ and $r_{t+1}$ is the interest rate paid on savings held from period $t$ to period $t+1$. In the second period the individual consumes all his wealth, both interest and principal. (Note that this assumes that there is no altruism across generations, in that people do not care about leaving bequests to the coming generations. This is crucial.)
The first-order condition for a maximum is
$$c_{1 t}^{-\frac{1}{\sigma}}-\left(\frac{1+r_{t+1}}{1+\rho}\right) c_{2 t+1}^{-\frac{1}{\sigma}}=0,$$
which can be rewritten as
$$\frac{c_{2 t+1}}{c_{1 t}}=\left(\frac{1+r_{t+1}}{1+\rho}\right)^\sigma \text {. }$$
This is the Euler equation for the generation born at time $t$. Note that this has the very same intuition, in discrete time, as the Euler equation (Ramsey rule) we derived in the context of the NGM.
Next, using (8.3) and (8.4) to substitute out for $c_{1 t}$ and $c_{2 t+1}$ and rearranging we get
$$s_t=\left(\frac{1}{\left(1+r_{t+1}\right)^{1-\sigma}(1+\rho)^\sigma+1}\right) w_t .$$
We can think of this as a saving function:
$$s_t=s\left(w_t, r_{t+1}\right), \quad 0<s_w \equiv \frac{\partial s_t}{\partial w_t}<1, s_r \equiv \frac{\partial s_t}{\partial r_{t+1}} \geq 0 \text { or } \leq 0 .$$
Saving is an increasing function of wage income since the assumption of separability and concavity of the utility function ensures that both goods (i.e. consumption in both periods) are normal. The effect of an increase in the interest rate is ambiguous, however, because of the standard income and substitution effects with which you are familiar from micro theory. An increase in the interest rate decreases the relative price of second-period consumption, leading individuals to shift consumption from the first to the second period, that is, to substitute second- for first-period consumption. But it also increases the feasible consumption set, making it possible to increase consumption in both periods; this is the income effect. The net effect of these substitution and income effects is ambiguous. If the elasticity of substitution between consumption in both periods is greater than one, then in this two-period model the substitution effect dominates and an increase in interest rates leads to an increase in saving.

## 经济代写|宏观经济学代写宏观经济学代考|分散均衡

$$\left(\frac{\sigma}{\sigma-1}\right) c_{1 \mathrm{t}}^{\frac{\sigma-1}{\sigma}}+(1+\rho)^{-1}\left(\frac{\sigma}{\sigma-1}\right) c_{2 f+1}^{\frac{\sigma-1}{\sigma}}, \rho \geq 0, \sigma \geq 0 .$$

## 经济代写|宏观经济学代写宏观经济学代考|个人

$$\max \left{\left(\frac{\sigma}{\sigma-1}\right) c_{1 t}^{\frac{\sigma-1}{\sigma}}+(1+\rho)^{-1}\left(\frac{\sigma}{\sigma-1}\right) c_{2 t+1}^{\frac{\sigma-1}{\sigma}}\right}$$

$$c_{1 t}+s_t=w_t,$$
$$c_{2 t+1}=\left(1+r_{t+1}\right) s_t,$$
，其中$w_t$是在$t$期间收到的工资，$r_{t+1}$是在$t$至$t+1$期间持有的储蓄支付的利率。在第二阶段，个人消费他所有的财富，包括利息和本金。(请注意，这是假设没有跨代的利他主义，即人们不关心给下一代留下遗产。

$$c_{1 t}^{-\frac{1}{\sigma}}-\left(\frac{1+r_{t+1}}{1+\rho}\right) c_{2 t+1}^{-\frac{1}{\sigma}}=0,$$
，可以改写为
$$\frac{c_{2 t+1}}{c_{1 t}}=\left(\frac{1+r_{t+1}}{1+\rho}\right)^\sigma \text {. }$$

$$s_t=\left(\frac{1}{\left(1+r_{t+1}\right)^{1-\sigma}(1+\rho)^\sigma+1}\right) w_t .$$

$$s_t=s\left(w_t, r_{t+1}\right), \quad 0<s_w \equiv \frac{\partial s_t}{\partial w_t}<1, s_r \equiv \frac{\partial s_t}{\partial r_{t+1}} \geq 0 \text { or } \leq 0 .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。