## 经济代写|宏观经济学代写Macroeconomics代考|Unpleasant monetary arithmetic

2023年4月13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
• (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|Unpleasant monetary arithmetic

In this section we will review one of the most celebrated results in monetary theory, the unpleasant monetarist arithmetic presented initially by Sargent and Wallace (1981). The result states that a monetary contraction may lead to higher inflation in the future. Why? Because, if the amount of government spending is exogenous and is not financed with seigniorage, it has to be financed with bonds. If eventually seigniorage is the only source of revenue, the higher amount of bonds will require more seigniorage and, therefore, more inflation. Of course, seigniorage is not the only financing mechanism, so you may interpret the result as applying to situations when, eventually, the increased cost of debt is not financed, at least entirely, by other revenue sources. Can it be the case that the expected future inflation leads to higher inflation now? If that were the case, the contractionary monetary policy would be ineffective even in the short run! This section discusses if that can be the case.

The tools to discuss this issue are all laid out in the Sidrauski model discussed in section 19.2, even though the presentation here follows Drazen (1985).
Consider the evolution of assets being explicit about the components of $a$,
$$\dot{b}_t+\dot{m}_t=-\pi_t m_t+y+\rho b_t-c_t$$

Where we assume $r=\rho$ as we ve done before. The evolution of real money follows
$$\dot{m}_t=\left(\sigma-\pi_t\right) m_t$$
Replacing (19.45) into (19.44), we get
$$\dot{b}_t=-\sigma m_t+y-c_t+\rho b_t$$
where the term $y-c$ can be interpreted as the fiscal deficit. ${ }^4$ Call this expression $D$. Replacing $(19.20)$ in (19.45) we get
$$\dot{m}_t=\left(\sigma+\rho-v^{\prime}\left(m_t\right)\right) m_t .$$

## 经济代写|宏观经济学代写Macroeconomics代考|Pleasant monetary arithmetic

Let’s imagine now that the government needs to finance a certain level of government expenditure, but can choose the inflation rates over time. What would be the optimal path for the inflation tax? To find out, we assume a Ramsey planner that maximises consumer utility, internalising the optimal behaviour of the consumer to the inflation tax itself, much in the same way we did in the previous chapter in our discussion of optimal taxation; and, of course, subject to it’s own budget constraint. ${ }^6$ The problem is then to maximise
$$\int_0^{\infty}\left[u(y)+v\left(L\left(i_t, y\right)\right] e^{-\rho t} d t,\right.$$
where we replace $c$ for $y$ and $m_t$ for $L\left(i_t, y\right)$, as per the results of the Sidrausky model. The government’s budget constraint is
$$a_t=\rho a_t-i_{\mathrm{t}} m_t+\tau_t$$
where $a_t=\frac{B_t+M_t}{P_t}$ is the real amount of liabilities of the government, $d_t$ is the government deficit and we’ve replaced $r=\rho$. The Ramsey planner has to find the optimal sequence of interest rates, that is, of the inflation rate. The FOCs are
$$v_m L_i+\lambda_t\left[L\left(i_t, y\right)+i_t L_i\right]=0$$
plus
$$\dot{\lambda}_t=\rho \lambda_t-\rho \lambda_t$$
The second FOC show that $\lambda$ is constant. Given this the first FOC shows the nominal interest is constant as well. Optimal policy smooths the inflation tax across periods, a result akin to our tax smoothing result in the previous chapter (if we include a distortion from taxation, we would get that the marginal cost of inflation should equal the marginal cost of taxation, delivering the result that inflation be countercyclical).

What happens now if the government faces a decreasing path for government expenditures, that is
$$d_t=d_0 e^{-\delta t}$$
The solution still requires a constant inflation rate but now the seigniorage needs to satisfy
$$i^* m^*=\rho a_0+\rho \frac{d_0}{\rho+\delta}$$

# 宏观经济学代考

## 经济代写|宏观经济学代写Macroeconomics代考|Unpleasant monetary arithmetic

$$\dot{b}t+\dot{m}_t=-\pi_t m_t+y+\rho b_t-c_t$$ 我们假设 $r=\rho$ 正如我们之前所做的那样。真实货币的 演变如下 $$\dot{m}_t=\left(\sigma-\pi_t\right) m_t$$ 将 (19.45) 代入 (19.44)，我们得到 Idot{b}_t=-Isigma $m{-} t+y-c _t+\mid r h o b _t$
$$\dot{b}_t=-\sigma m_t+y-c_t+\rho b_t$$

$$\dot{m}_t=\left(\sigma+\rho-v^{\prime}\left(m_t\right)\right) m_t .$$

## 经济代写|宏观经济学代写Macroeconomics代考|Pleasant monetary arithmetic

$$\int_0^{\infty}\left[u(y)+v\left(L\left(i_t, y\right)\right] e^{-\rho t} d t\right.$$

$$a_t=\rho a_t-i_{\mathrm{t}} m_t+\tau_t$$

$$v_m L_i+\lambda_t\left[L\left(i_t, y\right)+i_t L_i\right]=0$$

$$\dot{\lambda}_t=\rho \lambda_t-\rho \lambda_t$$

$$d_t=d_0 e^{-\delta t}$$

$$i^* m^*=\rho a_0+\rho \frac{d_0}{\rho+\delta}$$

## 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。