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• 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|微观经济学代写Microeconomics代考|Aggregate or Market Demand and the Weak Axiom

If the market demand vector function is as if coming from a representative consumer, then it satisfies the SARP and then also the WARP; this, as we will see in – Chap. 6, makes for some nice results on uniqueness and stability of (acapitalistic) general equilibrium. But the conditions for the existence of a representative consumer appear to be not even vaguely approximated by real economies. What about being content with market demand satisfying only the WARP? Meaning, not that each consumer’s demand function satisfies the WARP, this is implied by the assumption that consumers have standard utility functions; but that the market demand function does. It would mean the following: if at prices $\mathbf{p}$-that determine a market demand vector $\mathbf{x}(\mathbf{p})$ – the total value of market demand $\mathbf{p x}(\mathbf{p})$ would allow the purchase of the different vector $\mathbf{x}(\mathbf{q})$ which is the market demand vector at prices $\mathbf{q}$, then at the latter prices the total value of market demand $\mathbf{q x}(\mathbf{q})$ must be insufficient to demand $\mathbf{x}(\mathbf{p})$. This assumption will be indicated as $\boldsymbol{W A M}$ (Weak Axiom of revealed preference holding for Market demands). Let us state it formally:

Definition of WAM axiom: $\mathbf{p x}(\mathbf{p}) \geq \mathbf{p x}(\mathbf{q})$ and $\mathbf{x}(\mathbf{q}) \neq \mathbf{x}(\mathbf{p})$ imply $\mathbf{q x}(\mathbf{p})>\mathbf{q x}(\mathbf{q})$, where $\mathbf{x}(\mathbf{p}), \mathbf{x}(\mathbf{q})$ are the market vectorial demands, respectively, at prices $\mathbf{p}$ and $\mathbf{q}$.
Now we show with an example that the fact that individual consumers satisfy the SARP does not imply WAM. Assume two consumers, A and B, and 2 goods. The consumers derive their income from given endowments and have the same endowment $\omega$ but different non-homothetic preferences. Consider two different price vectors $\mathbf{p}$ and $\mathbf{q}$ implying different relative prices, and suppose the consumers’ choices are $\mathbf{x}^{\mathrm{A}}(\mathbf{p}), \mathbf{x}^{\mathrm{A}}(\mathbf{q}), \mathbf{x}^{\mathrm{B}}(\mathbf{p}), \mathbf{x}^{\mathrm{B}}(\mathbf{q})$ which correspond to the points so labelled in $\boldsymbol{-}$ Fig. 4.31. Point $\boldsymbol{\omega}$ where the two budget lines cross represents the endowment of each consumer. At prices $\mathbf{p}$, the value of aggregate demand is $2 \mathrm{p} \omega$, at prices $\mathrm{q}$ it is $2 \mathrm{q} \omega$. Instead of representing aggregate demand, $\boldsymbol{-}$ Fig. $4.31$ represents half aggregate demand at $\mathbf{p}$, respectively, at $\mathbf{q}$, as the mid-point between the points indicating the demands of the two consumers at $\mathbf{p}$, respectively, at $\mathbf{q}$. Thus $1 / 2 \mathbf{x}(\mathbf{p})=\left(\mathbf{x}^A(\mathbf{p})+\mathbf{x}^B(\mathbf{p})\right) / 2,1 / 2 \mathbf{x}(\mathbf{q})=\left(\mathbf{x}^A(\mathbf{q})+\mathbf{x}^B(\mathbf{q})\right) / 2$. The fig- ure shows that point $1 / 2 \mathbf{x}(\mathbf{q})$ is below the budget line through $\omega$ at prices $\mathbf{p}$, hence $1 / 2 \mathbf{p x}(\mathbf{q})<\mathbf{p} \omega=1 / 2 \mathbf{p x}(\mathbf{p})$, and analogously $1 / 2 \mathbf{q x}(\mathbf{p})<\mathbf{q} \omega=1 / 2 \mathbf{q x}(\mathbf{q})$. Multiplying by 2 one obtains a violation of WAM: $\mathbf{p x}(\mathbf{p})>\mathbf{p x}(\mathbf{q})$ but also $\mathbf{q x}(\mathbf{q})>\mathbf{q x}(\mathbf{p})$.

## 经济代写|微观经济学代写Microeconomics代考|Production Possibility Sets, Netputs, Production Functions

The purpose of this chapter is to make more precise the study of Chap. 3 of how the marginal approach determines the competitive general equilibrium of an economy where a variety of consumption goods is produced through the use of unproduced (‘original’ or ‘primary’) factors: lands and labour (possibly, different types of labour, treated as distinct factors). But in discussing, as a premise, the marginalist/neoclassical theory of the competitive firm, the presence of produced inputs will be admitted in order to obtain a more general theory.

Some aspects of the economy to be considered are as follows. A production process generally produces first some intermediate stage good (e.g. corn plants, in the production of corn; shaped pieces of wood, in the production of furniture) but the production function does not describe this fact, it only describes the quantity of final product as a function of the quantities of inputs the firm starts with, because the intermediate product is entirely consumed inside the firm in order to produce the final consumption good. ${ }^1$ All production processes last one period (often assumed to be one year); production is in separate cycles, labour and land are hired at the beginning of the period, and consumption goods come out at the end of the period. ${ }^2$ The interest rate is zero, so production costs are the same as if all labour and land services were paid at the same moment when output comes out and is sold. The absence of capital goods means there is no production process where a good appears both among the inputs and the outputs (e.g. corn production, that uses seed-corn as one of its inputs: then it is neces(e.g. corn production, that uses seed-corn as one of its inputs: then it is neces- sary to specify that the corn used as input cannot be the corn output of that process, which appears later in time). Realistic disequilibrium adjustments take time, sometimes several periods are required for the quantities produced to adjust to demand at cost-covering prices. These adjustments can never be perfectly completed because there are always accidental or temporary disturbances and novelties. Therefore the general equilibrium has the role of central position towards which market prices and quantities gravitate, indicative of their averages over a sufficient number of periods, over which the irregularities largely cancel out or compensate one another. ${ }^3$ This role of general equilibrium presumes of course that the data of equilibrium (factor endowments, tastes and technical knowledge) either remain constant for a sufficient time, or change sufficiently slowly (relative to the presumable speed of gravitation towards the equilibrium) for their change to be negligible. The effect of significant changes in the data, e.g. technical progress, or changes in labour supply due to migrations, must be studied via comparative statics.

# 微观经济学代考

## 经济代写|微观经济学代写Microeconomics代考|Aggregate or Market Demand and the Weak Axiom

WAM公理的定义： $\mathbf{p x}(\mathbf{p}) \geq \mathbf{p x}(\mathbf{q})$ 和 $\mathbf{x}(\mathbf{q}) \neq \mathbf{x}(\mathbf{p})$ 意味着 $\mathbf{q x}(\mathbf{p})>\mathbf{q x}(\mathbf{q})$ ，在哪里 $\mathbf{x}(\mathbf{p}), \mathbf{x}(\mathbf{q})$ 是市场矢量需求，分别在价格 $\mathbf{p}$ 和 $\mathbf{q}$. 现在我们用一个例子表明，个人消费者满足 SARP 的事实并不意味着 WAM。假设有两个消费者， $A$ 和 $B$ ，以及 2 件商品。消费者从给定的禀赋中获 得收入并且拥有相同的禀赋 $\omega$ 但不同的非同类偏好。考虑两个不同的价格向量 $\mathbf{p}$ 和 $\mathbf{q}$ 暗示不同的相对价格，并假设消费者的选择是 $\mathbf{x}^{\mathrm{A}}(\mathbf{p}), \mathbf{x}^{\mathrm{A}}(\mathbf{q}), \mathbf{x}^{\mathrm{B}}(\mathbf{p}), \mathbf{x}^{\mathrm{B}}(\mathbf{q})$ 对应于标记的点一图 4.31。观点 $\boldsymbol{\omega}$ 其中两条预算线交叉代表每个消费者的禀赋。按价格 $\mathbf{p}$ ，总需求值为 $2 \mathrm{p} \omega$ ，按价格 $q$ 这是 $2 q \omega$. 而不是代表总需求，一如图。4.31代表总需求的一半 $\mathbf{p}$ ，分别在 $\mathbf{q}$ ，作为表示两个消费者需求的点之间的中点 $\mathbf{p}$ ，分别在 $\mathbf{q}$. 因此 $1 / 2 \mathbf{x}(\mathbf{p})=\left(\mathbf{x}^A(\mathbf{p})+\mathbf{x}^B(\mathbf{p})\right) / 2,1 / 2 \mathbf{x}(\mathbf{q})=\left(\mathbf{x}^A(\mathbf{q})+\mathbf{x}^B(\mathbf{q})\right) / 2$. 该图显示了这一点 $1 / 2 \mathbf{x}(\mathbf{q})$ 低于预算线通过 $\omega$ 价格 $\mathbf{p}$ ，因此 $1 / 2 \mathbf{p x}(\mathbf{q})<\mathbf{p} \omega=1 / 2 \mathbf{p x}(\mathbf{p})$, 和类似地 $1 / 2 \mathbf{q x}(\mathbf{p})<\mathbf{q} \omega=1 / 2 \mathbf{q x}(\mathbf{q})$. 乘以 2 得到违反 WAM： $\mathbf{p x}(\mathbf{p})>\mathbf{p x}(\mathbf{q})$ 但是也 $\mathbf{q x}(\mathbf{q})>\mathbf{q x}(\mathbf{p})$.

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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。

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