### 经济代写|微观经济学代写Microeconomics代考|ECON2516

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• 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

## 经济代写|微观经济学代写Microeconomics代考|Robinson Crusoe and Market Valuation

The marginal approach views the efficiency it attributes to the working of markets as satisfying universal, a-historical efficiency requirements. This is highlighted by how the approach compares the working of markets with the decisions of a single consumer-producer, Robinson Crusoe, who, alone on a desert island, must decide how much of his time he should dedicate to producing consumption goods rather than to leisure.

Let us assume that Robinson produces a single consumption good via a differentiable production function $q=f(L, T)$ where $L$ is labour hours per month, $T$ land and $q$ consumption per month. The amount of land available to Robinson is given; Robinson must only decide how many hours to work per month on average, the remaining hours being leisure time. Robinson’s utility depends on the amount of consumption good, and on the amount of labour: more consumption means more utility; more labour contributes to utility indirectly by increasing consumption, but the direct effect of more labour is to decrease utility because it reduces leisure time and possibly because labour is intrinsically unpleasant. So we can write $u=u(q, L)$ and since $q$ depends only on $L$ because $T$ is given, utility ultimately depends only on $L: u=u(q(L), L)$. Let $M P_{L}$ be the marginal product of labour in the production of the consumption good, and let $M U_{L}:=\partial u / \partial L$ be the direct marginal effect of an increase of $L$ on $u$, which is negative. The total mar= ginal effect of an increase of $L$ on $u$ is $d u / d L=M P_{L} \cdot \partial \mathrm{u} / \partial \mathrm{q}-\left|M U_{L}\right|$. Note the difference between $\partial u / \partial L$ and $d u l d L$.

It is reasonable to assume that the marginal utility of consumption is initially very high and decreases as $q$ increases, that the marginal product of labour at least after a point decreases as $L$ increases, and that the marginal disutility of labour-the absolute value of $M U_{L}$-increases as $L$ increases; therefore $d u / d L$ initially is positive, decreases as $L$ increases, becomes zero at a certain point, and then negative. The optimal amount of labour is where $d u / d L=0$, that is
$$M U_{L} / M U_{q}=-M P_{L}$$

## 经济代写|微观经济学代写Microeconomics代考|The Rate of Interest in the Exchange Economy

So far the rate of interest has not appeared. In order to determine it, the marginal approach once again refers to an equilibrium between supply and demand, this time supply and demand for savings, that is, for income not spent on consumption goods. Let us examine the logic of this explanation at first in the exchange economy where corn and meat are exchanged. Consider time as divided into ‘periods’, with only one market day in each period, for example (if the period is a month) only on the first day of each month. In this economy, let us now assume there is the possibility to transfer purchasing power from one period to another through loans and debts (but not through storage of goods). In a period a consumer can consume more than the income obtained from her endowments in that period by borrowing purchasing power from other consumers, i.e. by selling a (real) bond – a promise of repayment of a certain amount of some good in some future period – to some other consumer. Both corn and meat are perishable, and they cannot be stored from one period to the next.

Suppose corn, good 1, is the numéraire and only one type of bond can be emitted, a promise to give one unit of corn to the bond holder one period later. Purchasing such a bond in period t means to lend an amount of good 1 to the issuer of the bond, against a promise of repayment of 1 unit of good 1 in period $\mathrm{t}+1$. If the price of the bond is $0.909$, lending $0.909$ units of good 1 yields 1 unit of the same good after one period, with a rate of interest $\mathrm{r}=10 \%$. The price $0.909$ of the bond is the price to be paid now for a unit of the good one period later, so it can be seen as the relative price of good 1 of period $t+1$ in terms of good 1 of period later. Because corn at $t+1$ will have price 1 , this price $0.909$ is also called period later. Because corn at $t+1$ will have price 1 , this price $0.909$ is also called the discounted value at $t$ of a unit of good 1 at date $t+1$. The discount factor (the discounted value at $t)$ is $1 /(1+r)$ with the rate of interest $r=10 \%$. The price of a bond in our economy coincides with the discount factor.

## 经济代写|微观经济学代写Microeconomics代考|Robinson Crusoe and Market Valuation

$$M U_{L} / M U_{q}=-M P_{L}$$

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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。