## 经济代写|宏观经济学代写Macroeconomics代考|ECOS3007

2022年9月23日

couryes-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
couryes™为您提供可以保分的包课服务

## 经济代写|宏观经济学代写Macroeconomics代考|Overlapping generations in continuous time

The trick to model the OLG model in a continuous-time framework is to include an age-independent probability of dying $p$. By the law of large numbers this will also be the death rate in the population. Assume a birth rate $n>p$. Together these two assumptions imply that population grows at the rate $n-p .^5$ This assumption is tractable but captures the spirit of the OLG model: not everybody is the same at the same time.

As in Blanchard (1985), we assume there exist companies that allow agents to insure against the risk of death (and, therefore, of leaving behind unwanted bequests). This means that at the time of death all of an individual’s assets are turned over to the insurance company, which in turn pays a return of $p$ on savings to all agents who remain alive. If $r_t$ is the interest rate, then from the point of view of an individual agent, the return on savings is $r_t+p$.

We will also assume logarithmic utility which will make the algebra easier. As of time $t$ the representative agent of the generation born at time $\tau$ maximises
$$\int_t^{\infty} \log c_{s, \tau} e^{-(\rho+p)(s-t)} d s$$
subject to the flow budget constraint
$$\dot{a}{t, \tau}=\left(r_t+p\right) a{t, \tau}+y_{t, \tau}-c_{t, \tau},$$
where $a_{t, \tau}$ is the stock of assets held by the individual and $y_{t, \tau}$ is labour income. The other constraint is the no-Ponzi game condition requiring that if the agent is still alive at time $s$, then
$$\lim {s \rightarrow \infty} a{s, r} e^{-\int_i^2\left(r_v+p\right) d v} \geq 0 .$$
If we integrate the first constraint forward (look at our Mathematical Appedix!) and use the second constraint, we obtain
$$\int_t^{\infty} c_{s, \tau} e^{-\int_t^x\left(r_\tau+p\right) d v} d s \leq a_{t, \tau}+h_{t, \tau}$$
where
$$h_{t, \tau}=\int_t^{\infty} y_{s, \tau} e^{-\int_t^x\left(r_v+p\right) d v} d s,$$
can be thought of as human capital. So the present value of consumption cannot exceed available assets, a constraint that will always hold with equality.
With log utility the individual Euler equation is our familiar
$$\dot{c}{s, \tau}=\left(r_s-\rho\right) c{s, \tau},$$
which can be integrated forward to yield
$$c_{s, \tau}=c_{t, \tau} e^{\int_t^x\left(r_v-\rho\right) d v} .$$

## 经济代写|宏观经济学代写Macroeconomics代考|The closed economy

We have not taken a stance on what kind of asset $a_t$ is. We now do so. In the closed economy we assume that $a_t=k_t$, and $k_t$ is per-capita productive capital that yields output according to the function $y_t=k_t^a$, where $0<\alpha<1$. In this context profit maximisation dictates that $r_t=\alpha k_t^{a-1}$, so that our two differential equations become \begin{aligned} &\dot{c}_t=\left(\alpha k_t^{a-1}-\rho\right) c_t-n(p+\rho) k_t, \ &\dot{k}_t=(1+\alpha) k_t^a-(n-p) k_t-c_t . \end{aligned} In steady state we have $$\begin{gathered} \frac{c}{k^2}=\frac{n(\rho+\rho)}{\alpha k^{-1}-\rho}, \ (1+\alpha) k^{ \alpha-1}-(n-p)=\frac{c^2}{k^v} \end{gathered}$$ Combining the two yields $$(1+\alpha) k^{* \alpha-1}=(n-p)+\frac{n(p+\rho)}{\alpha k^{* a-1-\rho}},$$ which pins down the capital stock. For given $k^$, the first SS equation yields consumption. Rewrite the last equation as $$\alpha k^{ \alpha-1}-\rho=\frac{n(p+\rho)}{(1+\alpha) k^{* \alpha-1}-(n-p)}>0 .$$
So the steady-state level of the (per capita) capital stock is smaller than the modified golden rule level that solves $\alpha k^{a-1}=\rho$, implying under-accumulation of capital. ${ }^7$ This is in contrast to the NGM, in which the modified golden rule applies, and the discrete-time OLG model with two-period lives, in which over-accumulation may occur. Before examining that issue, consider dynamics, described in Figure 8.5.

Along the saddle-path $c_t$ and $k_t$ move together. If the initial condition is at $k>k^$, then consumption will start above its SS level and both $c_t$ and $k_t$ will gradually fall until reaching the steady-state level. If, by contrast, the initial condition is at $k$, then consumption will start below its steadystate level and both $c_t$ and $k_t$ will rise gradually until reaching the steady state.

# 统计推断代考

## 经济代写|宏观经济学代写宏观经济学代考|连续时间的重叠代

$$\int_t^{\infty} \log c_{s, \tau} e^{-(\rho+p)(s-t)} d s$$

$$\dot{a}{t, \tau}=\left(r_t+p\right) a{t, \tau}+y_{t, \tau}-c_{t, \tau},$$
，其中$a_{t, \tau}$是个人持有的资产的股票，$y_{t, \tau}$是劳动收入。另一个约束是无庞氏博弈条件，要求如果代理在$s$时仍然活着，那么
$$\lim {s \rightarrow \infty} a{s, r} e^{-\int_i^2\left(r_v+p\right) d v} \geq 0 .$$

$$\int_t^{\infty} c_{s, \tau} e^{-\int_t^x\left(r_\tau+p\right) d v} d s \leq a_{t, \tau}+h_{t, \tau}$$
，其中
$$h_{t, \tau}=\int_t^{\infty} y_{s, \tau} e^{-\int_t^x\left(r_v+p\right) d v} d s,$$

$$\dot{c}{s, \tau}=\left(r_s-\rho\right) c{s, \tau},$$
，它可以向前积分得到
$$c_{s, \tau}=c_{t, \tau} e^{\int_t^x\left(r_v-\rho\right) d v} .$$

## 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。