assignmentutor-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 resource constraint

The resource constraint of the economy is
$$\dot{K}{t}=Y{t}-C_{t}=F\left(K_{t}, L_{t}\right)-C_{t},$$
with all variables as defined in the previous chapter. (Notice that for simplicity we assume there is no depreciation.) In particular, $F\left(K_{t}, L_{t}\right)$ is a neoclassical production function – hence neoclassical growth model. You can think of household production: household members own the capital and they work for themselves in producing output. Each member of the household inelastically supplies one unit of labour per unit of time.

This resource constraint is what makes the problem truly dynamic. The capital stock in the future depends on the choices that are made in the present. As such, the capital stock constitutes what we call the state variable in our problem: it describes the state of our dynamic system at any given point in time. The resource constraint is what we call the equation of motion: it characterises the evolution of the state variable over time. The other key variable, consumption, is what we call the control variable: it is the one variable that we can directly choose. Note that the control variable is jumpy: we can choose whatever (feasible) value for it at any given moment, so it can vary discontinuously. However, the state variable is sticky: we cannot change it discontinuously, but only in ways that are consistent with the equation of motion.

Given the assumption of constant returns to scale, we can express this constraint in per capita terms, which is more convenient. Dividing (3.2) through by $L$ we get
$$\frac{\dot{K}{t}}{L{t}}=F\left(k_{t}, 1\right)-c_{t}=f\left(k_{t}\right)-c_{t},$$
where $f(.)$ has the usual properties. Recall
$$\frac{\dot{K}{t}}{L{t}}=\dot{k}{t}+n k{t} .$$
Combining the last two equations yields
$$\dot{k}{t}=f\left(k{t}\right)-n k_{t}-c_{t},$$
which we can think of as the relevant budget constraint. This is the final shape of the equation of motion of our dynamic problem, describing how the variable responsible for the dynamic nature of the problem – in this case the per capita capital stock $k_{t}$ – evolves over time.

## 经济代写|宏观经济学代写Macroeconomics代考|Solution to consumer’s problem

The household’s problem is to maximise (3.1) subject to (3.5) for given $k_{0}$. If you look at our mathematical appendix, you will learn how to solve this, but it is instructive to walk through the steps here, as they have intuitive interpretations. You will need to set up the (current value) Hamiltonian for the problem, as follows:
$$H=u\left(c_{t}\right) e^{n t}+\lambda_{t}\left[f\left(k_{t}\right)-n k_{t}-c_{t}\right] .$$
Recall that $c$ is the control variable (jumpy), and $k$ is the state variable (sticky), but the Hamiltonian brings to the forefront another variable: $\lambda$, the co-state variable. It is the multiplier associated with the intertemporal budget constraint, analogously to the Lagrange multipliers of static optimisation.

Just like its Lagrange cousin, the co-state variable has an intuitive economic interpretation: it is the marginal value as of time $t$ (i.e. the current value) of an additional unit of the state variable (capital, in this case). It is a (shadow) price, which is also jumpy.
First-order conditions (FOCs) are
$$\begin{gathered} \frac{\partial H}{\partial c_{t}}=0 \Rightarrow u^{\prime}\left(c_{t}\right) e^{n t}-\lambda_{t}=0, \ \dot{\lambda}{t}=-\frac{\partial H}{\partial k{t}}+\rho \lambda_{t} \Rightarrow \dot{\lambda}{t}=-\lambda{t}\left[f^{\prime}\left(k_{t}\right)-n\right]+\rho \lambda_{t}, \ \lim {t \rightarrow \infty}\left(k{t} \lambda_{t} e^{-\rho t}\right)=0 . \end{gathered}$$
What do these optimality conditions mean? First, (3.7) should be familiar from static optimisation: differentiate with respect to the control variable, and set that equal to zero. It makes sure that, at any given point in time, the consumer is making the optimal decision – otherwise, she could obviously do better… The other two are the ones that bring the dynamic aspects of the problem to the forefront. Equation (3.9) is known as the transversality condition (TVC). It means, intuitively, that the consumer wants to set the optimal path for consumption such that, in the “end of times” (at infinity, in this case), they are left with no capital. (As long as capital has a positive value as given by $\lambda$, otherwise they don’t really care…) If that weren’t the case, I would be “dying” with valuable capital, which I could have used to consume a little more over my lifetime.

# 宏观经济学代考

## 经济代写|宏观经济学代写Macroeconomics代考|The resource constraint

$$\ \$$

$$\frac{\dot{K} t}{L t}=F\left(k_{t}, 1\right)-c_{t}=f\left(k_{t}\right)-c_{t},$$

$$\frac{\dot{K} t}{L t}=\dot{k} t+n k t$$

$$\dot{k} t=f(k t)-n k_{t}-c_{t},$$

## 经济代写|宏观经济学代写Macroeconomics代考|Solution to consumer’s problem

$$H=u\left(c_{t}\right) e^{n t}+\lambda_{t}\left[f\left(k_{t}\right)-n k_{t}-c_{t}\right]$$

$$\frac{\partial H}{\partial c_{t}}=0 \Rightarrow u^{\prime}\left(c_{t}\right) e^{n t}-\lambda_{t}=0, \dot{\lambda} t=-\frac{\partial H}{\partial k t}+\rho \lambda_{t} \Rightarrow \dot{\lambda} t=-\lambda t\left[f^{\prime}\left(k_{t}\right)-n\right]+\rho \lambda_{t}, \lim t \rightarrow \infty\left(k t \lambda_{t} e^{-\rho t}\right)=0$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师