## 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
• (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。

## 经济代写|宏观经济学代写Macroeconomics代考|ECON6002

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
• (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|Institutions

Last but not least, there is the view that institutions are a fundamental source of economic growth. This idea also has an old pedigree in economics, but in modern times it has been mostly associated, in its beginnings, with the work of Douglass North (who won the Nobel Prize for his work), and more recently with scholars such as Daron Acemoglu and James Robinson. From the very beginning, here is the million-dollar question: what do we mean by institutions?

North’s famous characterisation is that institutions are “the rules of the game” in a society, “the humanly devised constraints that shape human interaction” (North (1990), p. 3). Here are the key elements of his argument:

• Humanly devised: Unlike geography, institutions are chosen by groups of human beings.
• Constraints: Institutions are about placing constraints on human behaviour. Once a rule is imposed, there is a cost to breaking it.
• Shape interactions: Institutions affect incentives.
OK, fair enough. But here is the real question: What exactly do we mean by institutions? A first stab at this question is to follow the Acemoglu et al. (2005) distinctions between economic and political institutions, and between de facto and de jure institutions.

The first distinction is as follows. Economic institutions are those that directly affect the economic incentives: property rights, the presence and shape of market interactions, and regulations. They are obviously important for economic growth, as they constitute the set of incentives for accumulation and technological progress. Political institutions are those that configure the process by which society makes choices: electoral systems, constitutions, the nature of political regimes, the allocation of political power etc. There is clearly an intimate connection between those two types, as political power affects the economic rules that will prevail.

The second distinction is just as important, having to do with formal vs informal rules. For instance, the law may state that all citizens have the right to vote, but in practice it might be that certain groups can have enough resources (military or otherwise) to intimidate or influence others, thereby constraining their right in practice. Formal rules, the de jure institutions, are never enough to fully characterise the rules of the game; the informal, de facto rules must be taken into consideration.

These distinctions help us structure the concepts, but we also hit the same issue that plagues the cultural explanations: since institutions are made by people, we need to understand where they come from, and how they come about. Acemoglu et al. (2005) is a great starting point to survey this literature, and (Acemoglu and Robinson 2012) provides an extremely readable overview of the ideas.

## 经济代写|宏观经济学代写Macroeconomics代考|What have we learned

When it comes to the proximate causes of growth, in spite of the limitations of each specific empirical approach – growth accounting, regression methods, and calibration – the message from the data is reasonably clear, yet nuanced: factor accumulation can arguably explain a substantial amount of income differences, and specific growth episodes, but ultimately differences in productivity are very important. This is a bit daunting, since the fact is that we don’t really understand what productivity is, in a deeper sense. Still, it underscores the importance of the process of technological progress – and the policy issues raised in Chapter 6 – as a primary locus for growth policies.

How about the fundamental causes? There is certainly a role for geography and luck (multiple equilibria), but our reading of the literature is that culture and institutions play a key part. There remains a lot to be learned about how these things evolve, and how they affect outcomes, and these are bound to be active areas of research for the foreseeable future.

Once again, the growth textbook by Acemoglu (2009) is a superb resource, and it contains a more in-depth discussion of the empirical literature on the proximate causes of growth. It also has a very interesting discussion on the fundamental causes, but it’s useful to keep in mind that, its author being one of the leading proponents of the view that institutions matter most, it certainly comes at that debate from that specific point of view.

Specifically on culture, the best places to go next are the survey articles we mentioned in our discussion. The survey by Guiso et al. (2006) is a bit outdated, of course, but still a great starting point. The more recent surveys by Alesina and Giuliano (2015), focusing particularly on the links between culture and institutions, and by Nunn (2020), focusing on the work using historical data, are very good guides to where the literature is and is going.

On institutions, there is no better place to go next than the books by Acemoglu and Robinson (2012) and Acemoglu and Robinson (2019). They are very ambitious intellectual exercises, encompassing theory, history, and empirical evidence, and meant for a broad audience – which makes them a fun and engaging read.

These being very active research fields, there are a lot of questions that remain open. Anyone interested in the social sciences, as the readers of this book most likely are, will find a lot of food for thought in these sources.

## 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|ECOS3007

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
• (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|Geography

This is somewhat related to the luck hypothesis, but certainly distinctive: perhaps the deepest source of heterogeneity between countries is the natural environment they happened to be endowed with. From a very big picture perspective, geographical happenstance of this sort is a very plausible candidate for a determinant of broad development paths, as argued for instance by Jarred Diamond in his 1999 Pulitzer-Prize-winning book Guns, Germs and Steel ${ }^8$. As an example, Diamond suggests that one key reason Europe conquered America, and not the other way around, was that Europe had an endowment of big animal species that were relatively easy to domesticate, which in turn led to improved immunisation by humans exposed to animal-borne diseases, and more technological advances. But can geography also explain differences in economic performance at the scale on which we usually think about them, say between different countries over decades or even a couple of centuries?

On some level, it is hard to think that the natural environment would not affect economic performance, on any time frame. Whether a country is in the middle of the Sahara desert, the Amazon rain forest, or some temperate climate zone must make some difference for the set of economic opportunities that it faces. This idea becomes more compelling when we look at the correlation between certain geographical variables and economic performance, as illustrated by the Figure (7.2), again taken from Acemoglu (2009). It is clear from that picture that countries that are closer to the equator are poorer on average. At the very least, any explanation for economic performance would have to be consistent with this stylised fact. The question, once again, is to assess to what extent these geographical differences underlie the ultimate performance, and this is not an easy empirical question.

Let us start by considering the possible conceptual arguments. The earliest version of the geography hypothesis has to do with the effect of the climate on the effort – the old idea that hot climates are not conducive to hard work. While this seems very naive (and not too politically correct) to our 21 st century ears, the idea that climate (and geography more broadly) affects technological productivity, especially in agriculture, still sounds very plausible. If these initial differences in turn condition subsequent technological progress (as argued by Jared Diamond, as we have seen, and as we will see, in different forms, by Jeffrey Sachs), it just might be that geography is the ultimate determinant of the divergence between societies over the very long run.

A big issue with this modern version of the geography hypothesis is that it is much more appealing to think of geography affecting agricultural productivity, but modern growth seems to have a lot more to do with industrialisation. While productivity in agriculture might have conditioned the development of industry to begin with, once industrial technologies are developed we would have to explain why they are not adopted by some countries. Geography is probably not enough to account for that, at least in this version of the story.

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

What do we mean by culture? The standard definition used by economists, as spelled out by Guiso et al. (2006), refers to “those customary beliefs and values that ethnic, religious, and social groups transmit fairly unchanged from generation to generation” (p. 23). In other words, culture is something that lives inside people’s heads – as opposed to being external to them – but it is not something idiosyncratic to individuals; it is built and, importantly, transmitted at the level of groups.

It is hard to argue against the assertion that people’s beliefs, values, and attitudes affect their economic decisions. It is just as clear that those beliefs, values and attitudes vary across countries (and over time). From this it is easy to conclude that culture matters for economic performance, an argument that goes back at least to Max Weber’s thesis that Protestant beliefs and values, emphasising hard work and thrift, and with a positive view of wealth accumulation as a signal of God’s grace, were an important factor behind the development of capitalism and the modern industrial development. In his words, the “Protestant ethic” lies behind the “spirit of capitalism”.

Other arguments in the same vein have suggested that certain cultural traits are more conducive to economic growth than others (David Landes is a particularly prominent proponent of this view, as in Landes (1998)), and the distribution of those traits across countries is the key variable to ultimately understand growth. “Anglo-Saxon” values are growth-promoting, compared to “Latin” or “Asian” values, and so on. More recently, Joel Mokyr (2018) has argued that Enlightenment culture was the key driving force behind the emergence of the Industrial Revolution in Europe, and hence of the so-called “Great Divergence” between that continent and the rest of the world.

A number of issues arise with such explanations. First, culture is hard to measure, and as such may lead us into the realm of tautology. A country is rich because of its favourable culture, and a favourable culture is defined as that which is held by rich countries. This doesn’t get us very far in understanding the causes of good economic performance. This circularity is particularly disturbing when the same set of values (say, Confucianism) is considered inimical to growth when Asian countries perform poorly, and suddenly becomes growth-enhancing when the same countries perform well. Second, even if culture is indeed an important causal determinant of growth, we still need to figure out where it comes from if we are to consider implications for policy and predictions for future outcomes.

These empirical and conceptual challenges have now been addressed more systematically, as better data on cultural attitudes have emerged. With such data, a vibrant literature has emerged, with economists developing theories and testing their predictions on the role that specific types of values (as opposed to a generic “culture” umbrella) play in determining economic performance. Many different types of cultural attitudes have been investigated: trust, collectivism, gender roles, beliefs about fairness, etc. This literature has often exploited historical episodes – the slave trade, the formation of medieval self-governing cities, colonisation, immigration, recessions – and specific cultural practices – religious rites, civic festivities, family arrangements – to shed light on the evolution of cultural attitudes and their impact on economic outcomes. Our assessment is that this avenue of research has already borne a lot of fruit, and remains very promising for the future. (For an overview of this literature, see the surveys by Guiso et al. (2006), Alesina and Giuliano (2015), and Nunn (2020).

## 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|ECON1120

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
• (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|Balanced growth path

You will recall that a BGP is a situation where all variables grow at a constant rate. From (5.12) and (5.13) (and in the absence of technological progress), we see that constant $\gamma_k$ and $\gamma_h$ require, respectively ${ }^2$,
$$\begin{gathered} (\alpha-1) \gamma_k+\beta \gamma_h=0 \ \alpha \gamma_k+(\beta-1) \gamma_h=0 . \end{gathered}$$
Substituting the second equation into the first equation yields
$$\frac{1-\alpha-\beta}{1-\beta} \gamma_k=0 .$$
But given CRS, we have assumed that $\alpha+\beta<1$, so we must have $\gamma_k=\gamma_h=0$. In other words, just as before, without technical progress ( $A$ constant), this model features constant per-capita capital $k$ and constant per-capita human capital $h$. No growth again! Of course, we can obtain long-run growth again by assuming exogenous (labour-augmenting) technological progress, $\frac{A}{A}=g$. Consider a BGP in which $\frac{k}{k}$ and $\frac{h}{h}$ are constant over time. From (5.12) and (5.13), this requires that $\frac{k}{y}$ and $\frac{h}{y}$ be constant over time. Consequently, if a BGP exists, $y, k$, and $h$, must all be increasing at the same rate. When the production function exhibits CRS, this BGP can be achieved by setting $\frac{\dot{y}}{y}=\frac{k}{k}=\frac{h}{h}=g^3$ The longrun growth rate is thus independent of $s_k, s_h, n$ or anything that policy affects, unless $g$ is endogenised somehow. (But again, long-run levels of income do depend on these behavioural parameters.)

## 经济代写|宏观经济学代写Macroeconomics代考|Still looking for endogenous growth

Why is the long-run growth rate still pinned down by the exogenous rate of technological growth as in the Solow Model? CRS implies that the marginal products of $K$ and $H$ decline as these factors accumulate, tending to hring growth rates down. Morenver, Cohh-Douglas production functions satisfy the Inada conditions so that, in the limit, these marginal products asymptotically go to 0 . In other words, CRS still keeps us in the domain of diminishing returns to capital accumulation, regardless of the fact that we have introduced human capital!

How can we change the model to make long-run growth rates endogenous (i.e., potentially responsive to policy)? You should see immediately from (5.16) that there is a possibility for a BGP, with $\gamma_k$ and $\gamma_h$ different from zero: if $\alpha+\beta=1$. That is to say, if we have constant returns to capital and human capital, the reproducible factors, taken together.
It is easy to see, from (5.12) and (5.13), that in a BGP we must have
$$\frac{\dot{k}}{k}=\frac{\dot{h}}{h} \longrightarrow \frac{k^}{h^}=\frac{s_k}{s_h} .$$

In other words, in a BGP $k$ and $h$ must grow at the same rate. This is possible since diminishing returns does not set in to either factor $(\alpha+\beta=1)$. What rate of growth is this? Using (5.17) in (5.12) and (5.13) we obtain (normalizing $A=1$ for simplicity)
$$\frac{\dot{k}}{k}=\frac{\dot{h}}{h}=s_h\left(\frac{s_k}{s_h}\right)^a-(\delta+n)=s_k^a s_h^{1-\alpha}-(\delta+n) .$$
The long-run (BGP) growth rate of output is
$$\frac{\dot{y}}{y}=\alpha \frac{\dot{k}}{k}+(1-\alpha) \frac{\dot{h}}{h}=s_k^a s_h^{1-\alpha}-(\delta+n) .$$
Now $s_k, s_h$ do affect long-run growth. If policy affects these, then policy affects growth. For instance, increasing the savings rates leads to higher growth in the long run. In other words, when we have human capital and constant returns to reproducible factors of production, it is possible to explain longrun growth (see Figure 5.1).

## 经济代写|宏观经济学代写Macroeconomics代考|Balanced growth path

$$(\alpha-1) \gamma_k+\beta \gamma_h=0 \alpha \gamma_k+(\beta-1) \gamma_h=0 .$$

$$\frac{1-\alpha-\beta}{1-\beta} \gamma_k=0$$

## 经济代写|宏观经济学代写Macroeconomics代考|Still looking for endogenous growth

$$\frac{\dot{k}}{k}=\frac{\dot{h}}{h}=s_h\left(\frac{s_k}{s_h}\right)^a-(\delta+n)=s_k^a s_h^{1-\alpha}-(\delta+n) .$$

$$\frac{\dot{y}}{y}=\alpha \frac{\dot{k}}{k}+(1-\alpha) \frac{\dot{h}}{h}=s_k^a s_h^{1-\alpha}-(\delta+n) .$$

## 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|ECON6002

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
• (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|Productivity shocks and the current account

Suppose the economy initially has total factor productivity $A^H$, with corresponding optimal stock of capital $\left(k^\right)^H$ and consumption level $\left(c^\right)^H$. At time 0 there is an unanticipated and permanent fall in productivity from $A^H$ to $A^L$, where $A^L<A^H$ (maybe because this economy produced oil, guano, or diamonds and its price has come down). This means, from (4.28), that $z(A)$ falls from $z\left(A^H\right)$ to $z\left(A^L\right)$. Capital holdings are reduced: residents sell capital in exchange for bonds, so after the shock they have $\left(k^\right)^L<\left(k^\right)^H$, where $\left(k^\right)^H$ was the optimal stock of capital before the shock. Assets $a_0$ are unchanged on impact. From (4.29) it follows that consumption adjusts instantaneously to its new (and lower) value: $$\left(c^\right)^L=r a_0-(1-\alpha) z\left(A^L\right)<r a_0-(1-\alpha) z\left(A^H\right)=\left(c^*\right)^H \text {, for all } t \geq 0 .$$
What happens to the current account? After the instantaneous shock, assets remain unchanged, and $\dot{b}_t$ is zero. The economy immediately converges to the new BGP, where the current account is in balance.

At this point, you must be really disappointed: don’t we ever get any interesting current account dynamics from this model? Actually, we do! Consider a transitory fall in productivity at time 0 , from $A^H$ to $A^L$, with productivity eventually returning to $A^H$ after some time $T$. Well, it should be clear that consumption will fall, but not as much as in the permanent case. You want to smooth consumption, and you understand that things will get back to normal in the future, so you don’t have to bring it down so much now. At the same time, the capital stock does adjust down fully, otherwise its return would be below what the domestic household could get from bonds. If current output falls just as in the permanent case, but consumption falls by less, where is the difference? A simple inspection of (4.9) reveals that $\dot{b}$ has to fall below zero: it’s a current-account deficit! Quite simply, residents can smooth consumption, in spite of the negative shock, by borrowing resources from abroad. Once the shock reverts, the current account returns to zero, while consumption remains unchanged. In the new BGP, consumption will remain lower relative to its initial level, and the difference will pay for the interest incurred on the debt accumulated over the duration of the shock – or more generally, the reduction in net foreign asset income.
‘This example underscores the role of the current account as a mechanism through which an economy can adjust to shocks. It also highlights one feature that we will see over and over again: the optimal response and resulting dynamics can be very different depending on whether a shock is permanent or transitory.

## 经济代写|宏观经济学代写Macroeconomics代考|Sovereign wealth funds

This stylised model actually allows us to think of other simple policy responses. Imagine a country that has a finite stock of resources, like copper. ${ }^4$ Furthermore let’s imagine that this stock of copper is being extracted in a way that it will disappear in a finite amount of time. The optimal program is to consume the net present value of the copper over the infinite future. So, as the stock of copper declines the economy should use those resources to accumulate other assets. This is the fiscal surplus rule implemented by Chile to compensate for the depletion of their resources. In fact, Chile also has a rule to identify transitory from permanent shocks, with the implication that all transitory increases (decreases) in the price level have to be saved (spent).

Does this provide a rationale for some other sovereign wealth funds? The discussion above suggests that a country should consume:
$$r \int_{-\infty}^{\infty} R_t e^{-r t} d t,$$
where $R$ is the value of the resources extracted in period $t$. This equation says that a country should value its intertemporal resources (which are the equivalent of the $a_0$ above, an initial stock of assets), and consume the real return on it.

Is that how actual sovereign funds work? Well, the Norwegian sovereign fund rule, for instance, does not do this. Their rule is to spend at time $t$ the real return of the assets accumulated until then:
$$r \int_{-\infty}^t R_t e^{-r(s-t)} d s$$
This rule san only be rationalised if you expest no further dissoveries and reat sach uew dissovery as a surprise. Alternatively, one could assume that the future is very uncertain, so one does not want to commit debt ahead of time. (We will come back to this precautionary savings idea in our study of consumption in Chapter 11.) In any event, the key lesson is that studying our stylised models can help clarify the logic of existing policies, and where and why they depart from our basic assumptions.

## 经济代写|宏观经济学代写Macroeconomics代考|Productivity shocks and the current account

‘这个例子强调了经常账户作为经济体可以调整中击的机制的作用。它还强调了我们将一遍又一遍地看到的一个特 征：最佳响应和产生的动态可能会因冲击是永久性的还是暂时的而有很大不同。

## 经济代写|宏观经济学代写Macroeconomics代考|Sovereign wealth funds

$$r \int_{-\infty}^{\infty} R_t e^{-r t} d t$$

$$r \int_{-\infty}^t R_t e^{-r(s-t)} d s$$

## 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|ECOS3007

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
• (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 steady state consumption and current account

Now that you have the level of income you should be able to compute the level of consumption. How do we do that? By solving the differential equation that is the budget constraint (4.9), which we can rewrite as
$$\dot{a}_t-r a_t=f\left(k^\right)-r k^-c^,$$ using the solutions for optimal consumption and capital stock. Using our strategy of integrating factors, we can multiply both sides by $e^{-r t}$, and integrate the resulting equation between 0 and $t$ : $$a_t e^{-r t}-a_0=\frac{c^+r k^-f\left(k^\right)}{r}\left(e^{-r t}-1\right) .$$
Now evaluate this equation as $t \rightarrow \infty$. Considering the NPC and the TVC, it follows that:
$$c^=r a_0+f\left(k^\right)-r k^* .$$
We can also find the optimal level of debt at each time period. It is easy to see that $a_t$ is kept constant at $a_0$, from which it follows that $b_t=b_0+k_0-k^*$. The current account is zero. In other words, the NGM delivers a growth model with no growth, as we saw in the last chapter, and a model of the current account dynamics without current account surpluses or deficits.

Not so fast, though! We saw that the NGM did have predictions for growth outside of the BGP. Let’s look at the transitional dynamics here as well, and see what we can learn.

## 经济代写|宏观经济学代写Macroeconomics代考|The inexistence of transitional dynamics

There are no transitional dynamics in this model: output per capita converges instantaneously to that of the rest of the world!

Suppose that initial conditions are $k_0<k^$ and $b_0>0$. But, condition (4.19) says that capital must always be equal to $k^$. Hence, in the first instant, capital must jump up from $k_0$ to $k^*$. How is this accomplished? Domestic residents purchase the necessary quantity of capital (the single good) abroad and instantaneously install it. Put differently, the speed of adjustment is infinite.

How do the domestic residents pay for this new capital? By drawing down their holdings of the bond. If $\Delta k_0=k^-k_0$, then $\Delta b_0=-\Delta k_0=-\left(k^-k_0\right)$. Note that this transaction does not affect initial net national assets, since
$$\Delta a_0=\Delta k_0+\Delta b_0=\Delta k_0-\Delta k_0=0 .$$

Suppose now that the production function is given by
$$f\left(k_t\right)=A k_t^a, A>0,0 \leq \alpha \leq 1 .$$
This means that condition (4.19) is
$$\alpha A\left(k^\right)^{\alpha-1}=r$$ so that the level of capital on the BGP is $$k^=\left(\frac{\alpha A}{r}\right)^{\frac{1}{1-\alpha}},$$
which is increasing in $A$ and decreasing in $r$.
Using this solution for the capital stock we can write $y^$ as $$y^=A k^{* \alpha}=A\left(\frac{\alpha A}{r}\right)^{\frac{\alpha}{1-\alpha}}=A^{\frac{1}{1-\alpha}}\left(\frac{\alpha}{r}\right)^{\frac{a}{1-\alpha}} \equiv z(A),$$
with $z(A)$ increasing in $A$.
It follows that consumption can be written as
$$c^=r u_0-r k^+z(A)=r u_0+(1-\alpha) z(A),$$
with $z^{\prime}(A)>0$.

## 经济代写|宏观经济学代写Macroeconomics代考|The steady state consumption and current account

$c^{\wedge}=r^{\prime} a_{-} 0+f$ lleft(k^\ight) $-\mathrm{k}^{\wedge} \mathrm{k}^{\star}$

## 经济代写|宏观经济学代写Macroeconomics代考|The inexistence of transitional dynamics

$$c^{=} r u_0-r k^{+} z(A)=r u_0+(1-\alpha) z(A)$$

## 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|ECON305

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
• (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|Dynamic inefficiency

For a given production function and given values of $n$ and $\delta$, there is a unique BGP value $k^{}>0$ for each value of the saving rate, s. Denote this relation by $k^{}(s)$, with $d k^{}(s) / d s>0$. The level of per capita consumption on the BGP is $c^{}=(1-s) \cdot f\left[k^{}(s)\right]$. We know from $(2.12)$ that $s \cdot f\left(k^{}\right)=(n+\delta) \cdot k^{}$; hence we can write an expression for $c^{}$ as
$$c^{}(s)=f\left[k^{}(s)\right]-(n+\delta) \cdot k^{} .$$ Figure $2.7$ shows the relation between $c^{}$ and $s$ that is implied by $(2.20)$. The quantity $c^{}$ is increasing in $s$ for low levels of $s$ and decreasing in $s$ for high values of $s$. The quantity $c^{+}$attains its maximum when the derivative vanishes, that is, when $\left[f^{\prime}\left(k^{}\right)-(n+\delta)\right] \cdot d k^{} / d s=0$. Since $d k^{} / d s>0$, the term in brackets must equal 0 . If we denote the value of $k^{}$ by $k_{g}$ that corresponds to the maximum of $c^{}$, then the condition that determines $k_{g}$ is
$$f^{\prime}\left(k_{g}\right)=(n+\delta) .$$
The corresponding savings rate can be denoted as $s_{g}$, and the associated level of per capita consumption on the BGP is given by $c_{g}=f\left(k_{g}\right)-(n+\delta) \cdot k_{g}$ and is is called the “golden rule” consumption rate.
If the savings rate is greater than that, then it is possible to increase consumption on the BGP, and also over the transition path. We refer to such a situation, where everyone could be made better off by an alternative allocation, as one of dynamic inefficiency. In this case, this dynamic inefficiency is brought about by oversaving: everyone could be made better off by choosing to save less and consume more. But this naturally begs the question: why would anyone pass up this opportunity? Shouldn’t we think of a better model of how people make their savings decisions? We will see about that in the next chapter.

## 经济代写|宏观经济学代写Macroeconomics代考|Absolute and conditional convergence

Equation (2.15) implies that the derivative of $\gamma_{k}$ with respect to $k$ is negative:
$$\partial \gamma_{k} / \partial k=\frac{s}{k}\left[f^{\prime}(k)-\frac{f(k)}{k}\right]<0$$
Other things equal, smaller values of $k$ are associated with larger values of $\gamma_{k}$. Does this result mean that economies with lower capital per person tend to grow faster in per capita terms? Is there convergence across economies?

We have seen above that economies that are structurally similar in the sense that they have the same values of the parameters $s, n$, and $\delta$ and also have the same production function, $F(\cdot)$, have the same BGP values $k^{}$ and $y^{}$. Imagine that the only difference among the economies is the initial quantity of capital per person, $k(0)$. The model then implies that the less-advanced economies – with lower values of $k(0)$ and $y(0)$ – have higher growth rates of $k$. This hypothesis is known as conditional convergence: within a group of structurally similar economies (i.e. with similar values for $s, n$, and $\delta$ and production function, $F(\cdot)$ ), poorer economies will grow faster and catch up with the richer one. This hypothesis does seem to match the data – think about how poorer European countries have grown faster, or how the U.S. South has caught up with the North, over the second half of the 20 th century.

An alternative, stronger hypothesis would posit simply that poorer countries would grow faster without conditioning on any other characteristics of the economies. This is referred to as absolute convergence, and does not seem to fit the data well. ${ }^{8}$ Then again, the Solow model does not predict absolute convergence!

## 经济代写|宏观经济学代写Macroeconomics代考|Dynamic inefficiency

$$f^{\prime}\left(k_{g}\right)=(n+\delta) .$$

## 经济代写|宏观经济学代写Macroeconomics代考|Absolute and conditional convergence

$$\partial \gamma_{k} / \partial k=\frac{s}{k}\left[f^{\prime}(k)-\frac{f(k)}{k}\right]<0$$

\gamma_{k} \equiv \frac{\dot{k}}{k}=\frac{s \cdot f(k)}{k}-(n+\delta) .
$$Equation (2.15) says that \gamma_{k} equals the difference between two terms, s \cdot f(k) / k and (n+\delta) which we plot against k in Figure 2.5. The first term is a downward-sloping curve, which asymptotes to infinity at k=0 and approaches 0 as k tends to infinity. The second term is a horizontal line crossing the vertical axis at n+\delta. The vertical distance between the curve and the line equals the growth rate of capital per person, and the crossing point corresponds to the BGP. Since n+\delta>0 and s \cdot f(k) / k falls monotonically from infinity to 0 , the curve and the line intersect once and only once. Hence (except for the trivial solution k^{}=0, where capital stays at zero forever), the BGP capital-labour ratio k^{}>0 exists and is unique. Note also that output moves according to$$
\frac{\dot{y}}{y}=\alpha \frac{\dot{k}}{k}=\alpha \gamma_{k} .
$$A formal treatment of dynamics follows. From (2.11) one can calculate$$
\frac{d \dot{k}}{d k}=s \cdot f^{\prime}(k)-(n+\delta) .
$$We want to study dynamics in the neighbourhood of the BGP, so we evaluate this at k^{} :$$ \left.\frac{d \dot{k}}{d k}\right|_{k=k^{}}=s \cdot f^{\prime}\left(k^{*}\right)-(n+\delta) .
$$## 经济代写|宏观经济学代写Macroeconomics代考|Policy experiments Suppose that the economy is initially on a BGP with capital per person k_{1}^{}. Imagine that the government then introduces some policy that raises the saving rate permanently from s_{1} to a higher value s_{2}. Figure 2.6 shows that the s \cdot f(k) / k schedule shifts to the right. Hence, the intersection with the n+\delta line also shifts to the right, and the new BGP capital stock, k_{2}^{}, exceeds k_{1}^{*}. An increase in the saving rate generates temporarily positive per capita growth rates. In the long run, the levels of k and y are permanently higher, but the per capita growth rates return to 0 . A permanent improvement in the level of the technology has similar, temporary effects on the per capita growth rates. If the production function, f(k), shifts upward in a proportional manner, then the s \cdot f(k) / k curve shifts upward, just as in Figure 2.6. Hence, \gamma_{k} again becomes positive temporarily. In the long run, the permanent improvement in technology generates higher levels of k and y, but no changes in the per capita growth rates. ## 宏观经济学代考 ## 经济代写|宏观经济学代写Macroeconomics代考|Transitional dynamics 此外，Solow 模型确实会在向 BGP 的过渡中产生增长。要了解这方面的含义，请注意将（2.11) 的两边除以 k 意味 蔶增长率 k 是 (谁) 给的$$
\gamma_{k} \equiv \frac{\dot{k}}{k}=\frac{s \cdot f(k)}{k}-(n+\delta)
$$方程 (2.15) 说 \gamma_{k} 等于两项之差， s \cdot f(k) / k 和 (n+\delta) 我们密谋反对 k 在图 2.5 中。第一项是向下倾斜的曲线，在 k=0 并接近 0 作为 k 趋于无穷大。第二项是与垂直轴相交的水平线 n+\delta. 曲线与直线的垂直距离等于人均资本增 长率，交叉点对应BGP。自从 n+\delta>0 和 s \cdot f(k) / k 从无穷大单调下降到 0 ，曲线和直线相交一次且仅一次。因 此 (除了平凡的解决方案 \ \mathrm{k} \wedge{}=0, wherecapitalstaysatzeroforever), the BGPcapital-labourratio k^{\wedge}{}>0 existsandisunique. Notealsothatoutputmovesaccordingto \frac{\dot{y}}{y}=\alpha \frac{\dot{k}}{k}=\alpha \gamma_{k}. Aformaltreatmentofdynamics follows. From \left(2.11\right. ) onecancalculate \frac{d k}{d k}=s \cdot f^{\prime}(k)-(n+\delta). Wewanttostudydynamicsintheneighbourhoodofthe B G P, soweevaluatethisat \mathrm{k} \wedge{}: \|l e f t .| f r a c{d \ \$$

## 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|ECOS3007

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
• (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 Kaldor facts

The modern study of economic growth starts in the post-war period and was mostly motivated by the experience of the developed world. In his classical article (Kaldor 1957), Nicolas Kaldor stated some basic facts that he observed economic growth seemed to satisfy, at least in those countries. These came to be known as the Kaldor facts, and the main challenge of growth theory as initially constituted was to account simultaneously for all these facts. But, what were these Kaldor facts? Here they are: ${ }^{2}$

1. Output per worker shows continuous growth, with no tendency to fall.
2. The capital/output ratio is nearly constant. (But what is capital?)
3. Capital per worker shows continuous growth (… follows from the other two).
4. The rate of return on capital is nearly constant (real interest rates are flat).
5. Labour and capital receive constant shares of total income.
6. The growth rate of output per worker differs substantially across countries (and over time, we can add, miracles and disasters).

Most of these facts have aged well. But not all of them. For example, we now know the constancy of the interest rate is not so when seen from a big historical sweep. In fact, interest rates have been on a secular downward trend that can be dated back to the 1300’s (Schmelzing 2019). (Of course rates are way down now, so the question is how much lower can they go?) We will show you the data in a few pages.

In addition, in recent years, particularly since the early 1980s, the labour share has fallen significantly in most countries and industries. There is much argument in the literature as to the reasons why (see Karabarbounis and Neiman (2014) for a discussion on this) and the whole debate about income distribution trends recently spearheaded by Piketty (2014) has to do with this issue. We will come back to it shortly.

As it turns out Robert Solow established a simple model (Solow 1956) that became the first working model of economic growth. ${ }^{3}$ Solow’s contribution became the foundation of the NGM, and the backbone of modern growth theory, as it seemed to fit the Kaldor facts. Any study of growth must start with this model, reviewing what it explains – and, just as crucially, what it fails to explain. ${ }^{4}$

## 经济代写|宏观经济学代写Macroeconomics代考|The law of motion of capital

The change in the capital stock over time is given by (2.2). If we divide both sides of this equation by $L$, then we get
$$\dot{K} / L=s \cdot f(k)-\delta k .$$
The right-hand side contains per capita variables only, but the left-hand side does not. We can write $K / L$ as a function of $k$ by using the fact that
$$\dot{k} \equiv \frac{d(K / L)}{d t}=\dot{K} / L-n k,$$
where $n=\dot{L} / L$. If we substitute (2.10) into the expression for $\dot{K} / L$ then we can rearrange terms to get
$$\dot{k}=s \cdot f(k)-(n+\delta) \cdot k .$$
The term $n+\delta$ on the right-hand side of (2.11) can be thought of as the effective depreciation rate for the capital/labour ratio, $k \equiv K / L$. If the saving rate, $s$, were 0 , then $k$ would decline partly due to depreciation of $K$ at the rate $\delta$ and partly due to the growth of $L$ at the rate $n$.

Figure $2.4$ shows the workings of (2.11). The upper curve is the production function, $f(k)$. The term $s \cdot f(k)$ looks like the production function except for the multiplication by the positive fraction $s$. The $s \cdot f(k)$ curve starts from the origin (because $f(0)=0$ ), has a positive slope (because $f^{\prime}(k)>0$ ), and gets flatter as $k$ rises (because $f^{\prime \prime}(k)<0$ ). The Inada conditions imply that the $s \cdot f(k)$ curve is vertical at $k=0$ and becomes perfectly flat as $k$ approaches infinity. The other term in $(2.11),(n+\delta) \cdot k$, appears in Figure $2.1$ as a straight line from the origin with the positive slope $n+\delta$.

## 经济代写|宏观经济学代写Macroeconomics代考|The Kaldor facts

1. 人均产出呈持续增长趋势，没有下降的趋势。
2. 资本/产出比几乎是恒定的。（但什么是资本？）
3. 每个工人的资本显示出持续增长（……紧随其他两个）。
4. 资本回报率几乎不变（实际利率持平）。
5. 劳动力和资本在总收入中所占份额不变。
6. 每个工人的产出增长率在各国之间存在很大差异（随着时间的推移，我们可以添加奇迹和灾难）。

## 经济代写|宏观经济学代写Macroeconomics代考|The law of motion of capital

$$\dot{K} / L=s \cdot f(k)-\delta k .$$

$$\dot{k} \equiv \frac{d(K / L)}{d t}=\dot{K} / L-n k,$$

$$\dot{k}=s \cdot f(k)-(n+\delta) \cdot k .$$

## 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|Fall 2022

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
• (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|Macroeconomics and Globalization

Macroeconomic analysis has changed over time. After profound changes in the world with the fall of the Soviet Union in 1989 and the gradual integration of countries into the world economy, especially China and India, the economy has become truly globalized for the first time in history. Since many goods are produced using inputs from different countries, this process has led to a sharp increase in international trade, higher capital flows financing foreign investments, and the internationalization of production. What is certain is that the events of the international economy are increasingly affecting national economies, as evidenced by the international financial crisis that started in 2008-2009. This process has gained momentum, so economic analysis must consider interactions with the rest of the world. Even the US economy, the largest and most important in the world, is affected by what happens in other countries, and, of course, the rest of the world is affected by US economic trends.

Several countries in the world are experiencing sustained growth processes, which has reduced the global preeminence of the industrialized economies of North America and Europe. This situation has forced economists to pay more attention to what happens in other economies and has highlighted the need for deeper and more careful analysis. Ultimately, macroeconomic developments in different parts of the globe will increasingly affect people’s lives in other parts, which translates into a greater need for understanding the forces of macroeconomics in a globalized context.

## 经济代写|宏观经济学代写Macroeconomics代考|PRODUCTION AND EMPLOYMENT

In this chapter, we first analyze the main aspects that link economic activity with employment, then present the most important characteristics of employment and the unemployment rate.

There is a close relationship between GDP growth and employment: job creation falls in recessions-sometimes even below zero, meaning more jobs disappear than are created-while employment grows in times of economic expansion. This is not the case with respect to the relationship between GDP growth and the unemployment rate, which measures the proportion of people who are unemployed relative to the total labor force (i.e., those who are willing to work and able to do so).

Recessions generate a rapid and significant increase in unemployment, whereas expansions tend to decrease the unemployment rate gradually. It is instructive to look at the latest financial crisis in the United States: the unemployment rate increased drastically together with a contraction of GDP in 2008, and, despite the strong measures taken by the Fed (Federal Reserve, the central bank of the United States, created to provide a stable banking system for the United States) to stimulate the economy, it took around five years to return to its initial level. A similar case was observed in Chile after the 1999 recession: unemployment began to fall only after 2005 . It is partly because of these persistent effects on unemployment that economists are often so emphatic about the social costs of recessions. These facts seem to reveal the wisdom in the popular saying “It is easier to destroy than to build”-applied, in this case, to the creation and destruction of employment.

## 经济代写|宏观经济学代写Macroeconomics代考|PRODUCTION AND EMPLOYMENT

GDP 增长与就业之间有着密切的关系：在经济衰退时期创造的就业机会下降——有时甚至低于零，这意味着消失的就业机会多于创造的就业机会——而就业机会在经济扩张时期增长。就 GDP 增长与失业率之间的关系而言，情况并非如此，失业率衡量的是失业人口相对于总劳动力的比例（即愿意工作并能够这样做的人）。

## 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。