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# 经济代写|宏观经济学代考Macroeconomics代写|ECON311 Household Behavio

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## 经济代写|宏观经济学代考Macroeconomics代写|Household Behavio

Let us now turn our attention to the household. The household has some technology for producing income $\mathcal{Y}^1$ that may be a function of the action $a$, so $\mathcal{Y}(a)$. If $a$ is hours worked, then $\mathcal{Y}$ is increasing in $a$, if $a$ is hours of leisure, then $\mathcal{Y}$ is decreasing in $a$ and if $a$ is housewindows then $\mathcal{Y}$ is not affected by $a$. The household will have preferences directly over action $a$ and income net of taxation $\mathcal{Y}(a)-\mathcal{H}(a ; \psi)$. Thus preferences are:
$$U[a, \mathcal{Y}(a)-\mathcal{H}(a ; \psi)] .$$
There is an obvious maximization problem here, and one that will drive all of the analysis in this chapter. As the household considers various choices of $a$ (windows, hours, yachts), it takes into consideration both the direct effect of $a$ on utility and the indirect effect of $a$, through the tax bill term $\mathcal{Y}(a)-\mathcal{H}(a ; \psi)$. Define:
$$V(\psi) \equiv \max {a \in A} U[a, \mathcal{Y}(a)-\mathcal{H}(a ; \psi)] .$$ For each value of $\psi$, let $a{\max }(\psi)$ be the choice of $a$ which solves this maximization problem. That is:
$$V(\psi)=U\left[a_{\max }(\psi), \mathcal{Y}\left(a_{\max }(\psi)\right]-\mathcal{H}\left[a_{\max }(\psi) ; \psi\right)\right] .$$

## 经济代写|宏观经济学代考Macroeconomics代写|The Laffer Curve

How does the function $\mathcal{T}(\psi)$ behave? We shall spend quite a bit of time this chapter considering various possible forms for $\mathcal{T}(\psi)$. One concept to which we shall return several times is the Laffer curve. Assume that, if $a$ is fixed, that $\mathcal{H}(a ; \psi)$ is increasing in $\psi$ (for example, $\psi$ could be the tax rate on house windows). Further, assume that if $\psi$ is fixed, that $\mathcal{H}(a ; \psi)$ is increasing in $a$. Our analysis would go through unchanged if we assumed just the opposite, since these assumptions are simply naming conventions.

Given these assumptions, is $\mathcal{T}$ necessarily increasing in $\psi$ ? Consider the total derivative of $\mathcal{T}$ with respect to $\psi$. That is, compute the change in revenue of an increase in $\psi$, taking in to account the change in the household’s optimal behavior:
$$\frac{d \mathcal{T}(\psi)}{d \psi}=\frac{\partial \mathcal{H}\left[a_{\max }(\psi) ; \psi\right]}{\partial a} \frac{\partial a_{\max }(\psi)}{\partial \psi}+\frac{\partial \mathcal{H}\left[a_{\max }(\psi) ; \psi\right]}{\partial \psi}$$

# 宏观经济学代写

## 经济代写|宏观经济学代考Macroeconomics代写|Household Behavio

$$U[a, \mathcal{Y}(a)-\mathcal{H}(a ; \psi)]$$

$$V(\psi) \equiv \max a \in A U[a, \mathcal{Y}(a)-\mathcal{H}(a ; \psi)] .$$

$$V(\psi)=U\left[a_{\max }(\psi), \mathcal{Y}\left(a_{\max }(\psi)\right]-\mathcal{H}\left[a_{\max }(\psi) ; \psi\right)\right]$$

## 经济代写|宏观经济学代考Macroeconomics代写|The Laffer Curve

$$\frac{d \mathcal{T}(\psi)}{d \psi}=\frac{\partial \mathcal{H}\left[a_{\max }(\psi) ; \psi\right]}{\partial a} \frac{\partial a_{\max }(\psi)}{\partial \psi}+\frac{\partial \mathcal{H}\left[a_{\max }(\psi) ; \psi\right]}{\partial \psi}$$

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## 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。