## 经济代写|微观经济学代写Microeconomics代考|ECON20002

2022年9月23日

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## 经济代写|微观经济学代写Microeconomics代考|The Exchange Economy

The supply-and-demand (or marginal or neoclassical) approach to value and distribution argues that in a competitive market economy prices and quantities are determined by the competitive interaction of buyers and sellers, which pushes a market economy towards a situation of equality, or equilibrium, between supply and demand simultaneously on all markets. The theory’s credibility requires:

1. that such a notion of general equilibrium is logically consistent: the system of equations or disequations that a general equilibrium must satisfy has a solution; this is the problem of existence of a general equilibrium;
2. that there isn’t a multiplicity of solutions, so that the prices and quantities, that should result from the tendency towards equilibrium, are not left indeterminate (in real economies there does not seem to be any such indeterminateness); this is the problem of uniqueness of equilibrium;
3. that the spontaneous working of competitive markets causes the economy to tend towards the general equilibrium position; this is the problem of stability of equilibrium;
4. that the solutions of the general equilibrium system are not wildly in contrast with observation, for example equilibrium real wages should not be zero; this is the problem of correspondence of the theory’s predictions with observation.
This chapter summarizes the main results reached on the first three issues by the theory of general equilibrium, first for the model of an exchange economy, then for the model of a non-capitalistic production economy, that is with only non-produced productive factors (types of labour, types of land). The latter model, according to modern general equilibrium theory, can be reinterpreted (in a way to be explained in $\$ Chap. 8) so as to accommodate capital goods too,

but this reinterpretation introduces dated goods: bread today is treated as a different good from bread tomorrow; on the contrary the production economy to be analysed in this chapter has no need to date goods because its equilibrium is a long-period equilibrium, a persistent repetitive situation, and its determination determines the average quantities produced and consumed per period (traditionally, per year); this difference is sometimes underlined by qualifying the model as atemporal, not in the sense that there is no time in the model (production, for example, definitely takes time in the model) but in the sense that no time index is attached to goods, see Sect. $5.28$.

I start with the exchange economy. The notion of general equilibrium of an exchange economy was met in $>$ Chap. 3 and again in Chap. 4 . The reader is invited to re-examine in particular Sect. $4.22$ for the definition (which will not be repeated here) of the exchange economy and of its general equilibrium and – Sect. $4.7$ for some first considerations on existence.

## 经济代写|微观经济学代写Microeconomics代考|Properties of the Market Excess Demand

The basic element in the search for equilibrium in the exchange economy is the (vectorial) market excess demand function or correspondence, $\mathbf{z}(\mathbf{p})=\left(z_1(\mathbf{p}), \ldots, z_n(\mathbf{p})\right)$. This is guaranteed to be a function (i.e. uniquely determined for each $\mathbf{p}$ ) only if one assumes that, for each price vector, the choice of each consumer is uniquely determined. As we know from $\$ Chap. 4 (and most readers already knew from elementary microeconomics), this is only guaranteed if the indifference curves of consumers are strictly convex. If not, it is possible that at a price vector $\mathbf{p}$ certain choices of consumers out of their possible choices at that $\mathbf{p}$ guarantee a general equilibrium, but others do not; then the question arises, whether anything guarantees that the choices will be the equilibrium ones. This issue is discussed later. Now I assume $\mathbf{z}(\mathbf{p})$ is a function.

Several properties of $\mathbf{z}(\mathbf{p})$, all except the last one already proved in $\$ Chap. 4 , are listed below.

1. $\mathbf{z}(\mathbf{p})$ is homogeneous of degree zero in $\mathbf{p}$, because for each consumer, since income or wealth is the value of the given endowments, the budget hyperplane passes through the endowment point and therefore the budget constraint does not move if all prices change in the same proportion. This makes it legitimate to restrict attention to relative prices, by choosing a numéraire, nowadays often consisting of a basket containing one unit of each good, i.c. one sets the sum of all prices as equal to 1 and then prices vary in the price simplex $\mathrm{S}^{\mathrm{n}-1}$.
2. $\mathbf{z}(\mathbf{p})$ satisfies Walras’ Law, i.e. $\mathbf{p z}(\mathbf{p})=\mathbf{0}$ because local non-satiation is assumed and then consumers’ budgets are balanced.
3. $\mathbf{z}(\mathbf{p})$ is possibly not defined if some price is zero: if there is even only one consumer who is never satiated of a good, then at a zero price the demand for that good is infinite, i.e. not defined.

# 微观经济学代考

## 经济代写|微观经济学代写Microeconomics代考|The Exchange Economy

1. 这种一般均衡的概念在逻辑上是一致的：一般均衡必须满足的方程或不等式系统有解；这是一般均衡存在的问题；
2. 不存在多重解，因此应该由趋于均衡的趋势导致的价格和数量不是不确定的（在实体经济中似乎没有任何这种不确定性）；这就是均衡唯一性问题；
3. 竞争市场的自发运作导致经济趋向一般均衡状态；这就是平衡稳定性的问题；
4. 一般均衡系统的解与观察结果没有太大的反差，例如均衡实际工资不应该为零；这是理论预测与观察的对应问题。
本章总结了一般均衡理论在前三个问题上取得的主要成果，首先是交换经济模型，然后是非资本主义生产经济模型，即只有非生产性生产要素（劳动种类、土地种类）。后一种模型，根据现代一般均衡理论，可以重新解释（在第 8 章中解释的方式）以适应资本货物，

## 经济代写|微观经济学代写Microeconomics代考|Properties of the Market Excess Demand

1. 和(p)是零次齐次的p，因为对于每个消费者，由于收入或财富是给定禀赋的价值，预算超平面通过禀赋点，因此如果所有价格以相同比例变化，预算约束不会移动。这使得限制对相对价格的关注是合法的，通过选择一个numéraire，现在通常由一个包含每个商品一个单位的篮子组成，ic one 将所有价格的总和设置为等于 1，然后价格在单一价格中变化小号n−1.
2. 和(p)满足瓦尔拉斯定律，即p和(p)=0因为假设当地不满足，然后消费者的预算是平衡的。
3. 和(p)如果某个价格为零，则可能未定义：如果甚至只有一个消费者从未对某种商品感到满意，那么在零价格下，对该商品的需求是无限的，即未定义。

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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。