## 经济代写|微观经济学代写Microeconomics代考|BU1003

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|Partial Equilibrium

As a first step towards the study of the competitive general equilibrium of production and exchange, let us discuss in greater detail the Marshallian construction often referred to in this chapter: the determination, via the intersection of a supply curve and a demand curve, of the partial equilibrium (or particular equilibrium, the original and more precise denomination) of a single competitive market studied in isolation. ${ }^{34} \mathrm{~A}$ famous 1926 article describes this approach as follows:
) This point of view assumes that the conditions of production and the demand for a commodity can be considered, in respect to small variations, as being practically independent, both in regard to each other and in relation to the supply and demand of all other commodities. It is well known that such an assumption would not be illegitimate merely because the independence may not be absolutely perfect, as, in fact, it never can be; and a slight degree of interdependence may be overlooked without disadvantage if it applies to quantities of the second order of smalls, as would be the case if the effect (for example, an increase of cost) of a variation in the industry which we propose to isolate were to react partially on the price of the products of other industries, and this latter effect were to influence the demand for the product of the first industry. (Sraffa 1926, p. 538)

The motivation behind the partial equilibrium approach is that it allows the study of comparative statics of a market’s equilibrium (e.g. how price and quantity change if some input cost decreases, or if consumers’ tastes change and the desire for the good increases), and of some welfare aspects, without needing simultaneously to consider what is happening in all other markets. In $>$ Chap. 3 we saw that, rigorously speaking, in the neoclassical approach the simultaneous consideration of all markets cannot be avoided, because any change in some of the data of general equilibrium will have repercussions on all markets; for example, a change in tastes in favour of a good will alter equilibrium income distribution and hence all prices and quantities. However,
)) when the expenditure on the good under study is a small portion of a consumer’s total expenditure, ony a small fraction of any additional dollar of wealth will be spent on this good; consequently, we can expect wealth effects for it to be small. Second. with similarly dispersed substitution effects, the small size of the market under study should lead the prices of other goods to be approximately unaffected by changes in this market. (Mas-Colell et al. 1995, p. 316; “wealth effects” stands for income effects)

## 经济代写|微观经济学代写Microeconomics代考|Stability of Partial Equilibria

We have noted that the markets that can be studied with the partial-equilibrium methodology are consumption goods’ markets. Then the partial-cquilibrium demand curve for a product derives from consumer choices. It is based on given incomes of consumers and given other prices. So the partial-equilibrium approach presupposes a previous determination of income distribution-which determines the normal prices of other goods and the input costs of the industry under study – and of the general level of economic activity, which by determining labour employment determines aggregate consumer incomes. In the marginal approach the implicit assumption is that there is general equilibrium, income distribution is the equilibrium one, and there is full employment of labour and of all resources. Some economists argue that other theories of income distribution and of labour employment too can be the background to the use of Marshallian partial equilibrium for the study of consumer markets. Other economists disagree, but this is not the place to study this debate, we are interested now in understanding the marginal/neoclassical approach.

Given the very low likelihood of Giffen goods, demand curves for produced consumption goods can be assumed decreasing. Short-period supply curves can be assumed upward-sloping, so the short-period equilibrium price is stable. If it is greater than $\operatorname{Min} L A C$, in the long run there will be entry of new firms, or the existing firms will build new plants, and the short-period supply curve will shift to the right, and price will decrease. So the long-period partial equilibrium is stable too. If the good is homogeneous (undifferentiated), then on average all units of the good sell at the same price. Of course this can only be approximately true in actual markets, but, as already pointed out several times, the equilibrium position can only aim at describing the average position resulting over sufficient time from the trial-and-error higgling of the market.

There is a reason for representing price in ordinate and quantity in abscissa; then a supply curve and a demand curve represent supply price and demand price as functions of the quantity of the good – the prices that are necessary in order to obtain, respectively, convenience to supply, or to demand, the given quantity measured in abscissa. In this way a horizontal supply curve, or the saw-like supply curve of $\boldsymbol{\bullet}$ Fig. 5.9, are nonetheless functions.

## 经济代写|微观经济学代写微观经济学代考|部分均衡

)这一观点假设，一种商品的生产条件和需求，就微小的变化而言，可以被认为是实际上独立的，无论是彼此之间的关系，还是与所有其他商品的供求关系。众所周知，这种假设并不仅仅是因为独立可能不是绝对完美的，事实上，它永远不可能是绝对完美的;如果它适用于第二级的小量，那么轻微程度的相互依赖可能会被忽略而没有不利的影响，就像我们建议分离的行业的变化的影响(例如，成本的增加)将部分地对其他行业的产品价格产生反应，而后者的影响将影响对第一行业产品的需求一样。(Sraffa 1926, p. 538)

## 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。

## 经济代写|微观经济学代写Microeconomics代考|ECON106

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|Functional Separability: Leontief Separability

Suppose we can separate the $m+n$ inputs to a production function into two subvectors, $\mathbf{x}=\left(x_1, \ldots, x_m\right)$ and $\mathbf{y}=\left(y_1, \ldots, y_n\right)$, having, respectively, rental vectors $\mathbf{v}$ and $\mathbf{w}$, and that the production function satisfies
$$f(\mathbf{x}, \mathbf{y})=f(z(\mathbf{x}), \mathbf{y}),$$
where the scalar function $z(\cdot)$ has the characteristics of a production function: then it is as if inputs $\mathbf{x}$ produced an intermediate good which then produces the final output in combination with inputs $\mathbf{y}$. This can be simply a mathematical property of the form of the production function, but it can also reflect the fact that the production of the final output requires the production of an intermediate good first, which does not appear in the production function because produced and immediately re-utilized in the process of producing the final output. An example can be bread production that requires first the production of dough, utilizing a different kind of labour from the labour which produces bread from dough.

If $z(\mathbf{x})$ is differentiable and $f(z, \mathbf{y})$ is also differentiable, then $\partial f l \partial x_i=(\partial f / \partial z) \cdot\left(\partial z / \partial x_i\right)$; as a result, the Leontief weak separability condition holds: the marginal rate of substitution between any two $x$-goods is independent of the amounts of $y$-goods:
$$M R S_{x j, x i}=-\left(\partial f / \partial x_i\right) /\left(\partial f / \partial x_j\right)=-\left(\partial z / \partial x_i\right) /\left(\partial z / \partial x_j\right) .$$ Vice versa if the Leontief weak separability condition holds for the subgroup $\mathbf{x}$ of inputs, then a differentiable $f(\mathbf{x}, \mathbf{y})$ can be written as $f(z(\mathbf{x}), \mathbf{y})$ where $z(\mathbf{x})$ is a scalar function (I omit the somewhat complex proof; see Kreps 2013 pp. 39-42).
The term ‘weakly separable’ is used to distinguish the notion from that of strongly separable production functions, which means additively separable, i.e. represented by an additive production function: $f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2, \ldots, x_n\right)$. The term ‘strong separability’ is sometimes restricted to completely additively separable production functions $f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2\right)+\ldots+v_n\left(x_n\right)$.

Under weak separability, the firm can adopt a two-stage cost-minimization procedure: it can first determine the cost-minimizing input combination of the $x$-inputs for each level of $z$, and the resulting cost of $z$; and then it can determine the cost-minimizing input combination of $(z, \mathbf{y})$ for each level of output. This is what a firm would do that produces itself some of its inputs in a separate plant. If $f(\cdot)$ has constant returns to scale, so does $z(\cdot)$; then the cost function for the ‘good’ $z$ can be written as $\varepsilon(\mathbf{v}) \cdot z$, with $\varepsilon(\mathbf{v})$ representing the unit price of $z$.

## 经济代写|微观经济学代写Microeconomics代考|Elasticity of Substitution

Cost minimization requires that firms intending to produce a given output locate themselves on the point of the corresponding (convex) isoquant touching the isocost closest to the origin-a point of tangency if the isoquant is smoothly convex. A change in the relative rental of two factors can induce no substitution, little substitution and extensive substitution. For example, if factors are perfect complements, then isoquants (with two factors) are L-shaped and cost-minimizing firms will locate themselves at the kink: changes in relative factor ‘prices’ induce no substitution. In order to measure the effect of changes in relative factor rentals on the proportions in which firms find it optimal to combine two factors, economists use the elasticity of substitution, already met in Sect. 4.11.3. The analysis here will be restricted to only two factors. When applied to production functions, this elasticity – to be indicated now with the symbol $\sigma$ – is the ratio between the percentage change in $\mathrm{x}2 / \mathrm{x}_1$ along a given isoquant, and the percentage change (pay attention to the different order of the indices!) of $\mathrm{MP}_1 / \mathrm{MP}_2$ or $v_1 / v_2$ : $$\sigma{21}=\frac{\frac{d\left(x_2 / x_1\right)}{x_2 / x_1}}{\frac{d\left(\mathrm{MP}1 / \mathrm{MP}_2\right)}{\mathrm{MP}_1 / \mathrm{MP}_2}}-\frac{\partial\left(x_2 / x_1\right)}{\partial\left(v_1 / v_2\right)} \cdot \frac{v_1 / v_2}{x_2 / x_1} .$$ The second of the above two expressions for the elasticity of substitution is based on the assumption that the firm chooses the factor proportion that satisfies $-\mathrm{TRS}{2,1}=v_1 / v_2$; therefore the elasticity of substitution measures the sensitivity, of the proportion in which factors are demanded, to relative factor rentals; it gives an indication of what happens to the relative shares of factors in total cost as relative factor rentals vary. The relative share of factor 2 in total cost is given by $\left(v_2 x_2 /\left(v_1 x_1\right)\right.$, which can be rewritten as $\left(x_2 / x_1\right) \cdot\left(v_1 / v_2\right)$ or $\left(x_2 / x_1\right) \cdot\left|\mathrm{TRS}_{2,1}\right|$. When $v_1 / v_2$ increases by $1 \%, x_2 / x_1$ increases by $\sigma \%$; an elasticity of substitution equal to 1 means that relative factor shares in total cost do not change. An elasticity of substitution less than 1 means that when factor 1 becomes relatively more expensive, $x_2 / x_1$ increases less than in proportion, so $v_2 x_2 /\left(v_1 x_1\right)$ decreases: the relative share of factor 2 in national income decreases, and that of factor 1 increases. Note that a given percentage change in $x_2 / x_1$ is the same (with the opposite sign of course) as the corresponding percentage change in $x_1 / x_2$.

## 经济代写|微观经济学代写微观经济学代考|功能可分性:Leontief可分性

$$f(\mathbf{x}, \mathbf{y})=f(z(\mathbf{x}), \mathbf{y}),$$
，其中标量函数$z(\cdot)$具有生产函数的特征:然后，就好像输入$\mathbf{x}$产生了一个中间商品，然后该中间商品与输入$\mathbf{y}$结合产生最终的输出。这可能只是生产函数形式的一个数学性质，但它也可以反映这样一个事实，即最终产出的生产首先需要生产中间产品，而中间产品并不出现在生产函数中，因为在生产最终产出的过程中，中间产品被生产出来并立即被重新利用。例如，面包生产首先需要生产面团，使用的劳动与用面团生产面包的劳动不同

$$M R S_{x j, x i}=-\left(\partial f / \partial x_i\right) /\left(\partial f / \partial x_j\right)=-\left(\partial z / \partial x_i\right) /\left(\partial z / \partial x_j\right) .$$反之亦然如果Leontief弱可分条件成立于输入的子群$\mathbf{x}$，那么一个可微的$f(\mathbf{x}, \mathbf{y})$可以写成$f(z(\mathbf{x}), \mathbf{y})$，其中$z(\mathbf{x})$是一个标量函数(我省略了有些复杂的证明;见Kreps 2013第39-42页)。“弱可分”一词用来区分强可分生产函数与弱可分生产函数的概念，强可分生产函数是指可加可分的，即由可加生产函数$f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2, \ldots, x_n\right)$表示。术语“强可分性”有时被限制为完全可加可分的生产函数$f\left(x_1, \ldots, x_n\right)=v_1\left(x_1\right)+v_2\left(x_2\right)+\ldots+v_n\left(x_n\right)$ .

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|The Proft Function and Hotelling’s Lemma

Let us now define a new notion, the price-taking firm’s profit function $\pi(p, \mathbf{v})$ defined as the value function of the (unconstrained) maximization problem with $p$ and $\mathbf{v}$ as parameters
$$\max _x p f(\mathbf{x})-\mathbf{v x} .$$
The profit function must not be confused with the function $\pi(q)=p q-C(q)$, which is not called ‘profit function’, where profit is a function of output at given output price and factor rentals. The profit function describes how maximum profit changes with changes in output price or factor rentals.

The profit function is not always defined nor continuous. Suppose the firm has CRS and all factors are variable: for each given vector $\mathbf{v}$, marginal cost is constant and equal to minimum average cost; if $p>M C$ there is no maximum profit (the profit function is not defined), if $p=M C$ maximum profit is zero and output is indeterminate, if $p<M C$ maximum profit is zero and optimal output is zero; such a profit function is of very little use! The profit function has useful properties when, at least in an interval of output and input prices, profit-maximizing output and inputs are well defined and change continuously with $(p, \mathbf{v})$; then the profit function allows useful conclusions on how output and inputs change with changes in $p$ or in input rentals. This obtains if the analysis is a short-period one, output is positive, the factors considered are only the variable factors, and profit is defined as revenue minus variable cost, that is, without including quasi-rents into cost (otherwise profit would be zero always, as argued).

## 经济代写|微观经济学代写Microeconomics代考|Conditional and Unconditional Factor Demands

When the profit function is well defined, for each output price $p$ and vector of factor rentals $\mathbf{v}$ there is an optimal output and an associated vector of optimal factor utilizations: the latter vector need not be unique if isoquants are not strictly convex, but I will assume it is. In this case we can define the supply function (of the individual firm) $S(p, v)$ that indicates the optimal output as a function of factor rentals $\mathbf{v}$ and of the output price $p$; we also define the (vectorial) unconditional factor demand function $\mathbf{x}(p$, $v)$ that indicates the associated optimal factor employment vector. The connection between unconditional and conditional factor demand is
$$\mathbf{x}(p, \mathbf{y})=h(\mathbf{y}, S(p, \mathbf{y})) .$$
When the supply function and the unconditional factor demand function exist, what about the sign of their partial derivatives?

If profit is considered a function of $q$, we know that its maximization requires solving $\max _q p q-c(\mathbf{v}, q)$, whose first-order necessary condition is $p=M C(\mathbf{v}, q)$; the second-order sufficient condition is that $M C$ must be rising at the optimal $q$. If both conditions are satisfied it is:
$$\partial S(p, \mathbf{y}) / \partial p>0,$$
the supply function (graphically, the supply curve, usually drawn as an inverse supply curve, with $p$ in ordinate and $q$ in abscissa) is increasing. (Hotelling’s Lemma proved it was non-decreasing, here we are proving it is increasing: why this difference? Here we are assuming an upward-sloping MC curve at the optimal $q$, i.e. we are excluding a vertical MC curve which would indicate that it is impossible further to increase output.)

On the sign of $\partial x_{(}(p, \mathbf{v}) / \partial v_i$, Hotelling’s Lemma plus the convexity of the profit function imply $\partial \mathrm{x}{\mathrm{i}}(\mathrm{p}, \mathbf{v}) / \partial \mathrm{v}{\mathrm{i}} \leq 0$ : the own-rental effect is non-positive (and generally negative).

Does this result on input use imply $\partial S(p, \mathbf{v}) / \partial v_i \leq 0$ ? that is, is it always the case that the optimal output, when it exists, does not increase and generally decreases if the rental of a factor in positive use rises? Surprisingly, not always. When the rental of a factor rises, supply rises if the factor is an inferior input. An input is (locally) inferior when its conditional demand falls as output increases, that is, when $\partial h_i(\mathbf{v}, q) / \partial q<0$ (in a neighbourhood of the initial $q$ ), meaning that at the given input rentals the cost-minimizing way to increase $q$ is by increasing some input other than $i$ and decreasing input $i$.

## 经济代写|微观经济学代写微观经济学代考|利润函数和霍特林引理

$$\max _x p f(\mathbf{x})-\mathbf{v x} .$$

## 经济代写|微观经济学代写微观经济学代考|条件和无条件的要素需求

$$\mathbf{x}(p, \mathbf{y})=h(\mathbf{y}, S(p, \mathbf{y})) .$$

$$\partial S(p, \mathbf{y}) / \partial p>0,$$

## 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。

## 经济代写|微观经济学代写Microeconomics代考|ECON1001

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|Money Metric Utility Function

Public policy decisions often require comparing their disadvantages with their advantages. To assess whether a public intervention should be approved, economists advocate the use of cost-benefit analysis, which tries to reach a one-dimensional quantitative measure (usually a monetary valuation) of the costs and of the benefits of a policy in terms of utility variations, so as to see whether the balance is positive or negative. Here I present one way to reach a monetary valuation of the effects upon consumers’ utility of the change in a good’s price; it may allow deciding whether the intervention that causes that price to change is good or bad. To such an end economists propose to use the consumers’ own monetary valuation of the effect of the price change.

Imagine a price reduction will affect 1000 consumers, some of whom would be ready to pay up to 10 dollars a year in order to obtain the expected price reduction, some 20 dollars and some would on the contrary suffer a damage and would want a compensation of 5 dollars a year ${ }^{46}$; suppose the sum of these positive and negative amounts yields a net total of 10,000 dollars, then one possible valuation of the aggregate utility increase caused by the price reduction is 10,000 dollars. The monetary valuation of the utility gains of the several consumers makes them commensurable, so one can add them and compare the result with the cost of the intervention (e.g. a public investment) that would cause the price reduction. Of course the use of this sum for policy evaluation implies a far from uncontroversial value judgement that an extra 1 dollar of benefit has the same social relevance independently of who gets it, with the implication that a 1 dollar benefit of one individual compensates a 1 dollar loss of another individual independently of who and of how wealthy they are. We do not discuss now this criterion and its proposed justifications (see $>$ Chap. 14); we only discuss how to determine a consumer’s monetary valuation of a price change.

## 经济代写|微观经济学代写Microeconomics代考|Price Indices and Infation

That the expenditure function is concave has an interesting implication for the appraisal of the effects of inflation on the welfare of consumers. The usual consumer price index, CPI, is determined as follows: a vector of goods $\mathbf{x}^0$ is chosen to represent the consumptions of an ‘average’ household in the base year, year 0 ; the value of this basket at year 0 is determined on the basis of that year’s money prices as $\mathbf{p}^0 \mathbf{x}^0$; the CPI for year $t$ is determined as $\mathbf{p}^{\mathbf{t}} \mathbf{x}^0 / \mathbf{p}^0 \mathbf{x}^0$, so it is 1 for year 0 and greater than 1 for subsequent years if money prices have risen, the excess over 1 yielding the percentage variation relative to the base year. This percentage variation measures the percentage by which the income of the average household should increase so as to allow purchasing the same consumption basket $\mathbf{x}^0$, and it is usually argued that if the income increases by that percentage, the household is as well of as before.

The interesting observation is that, if relative prices change too, the household whose income increases sufficiently to buy $\mathbf{x}^{\circ}$ at the new prices will in fact be better off than before, because the money income sufficient to buy $\mathbf{x}^0$ will be used to buy a different basket allowing a higher utility level ( $\mathbf{x}^*$ in $\mathbf{-}$ Fig. 4.29: in this Figure, the reader is asked to draw the budget line that at the new prices allows no change in utility). So if inflation is accompanied by changes in relative prices, in order for the utility of a household not to decrease its $m$ needs to increase by a lesser percentage than CPI.

The CPI is an instance of a Laspeyres price index that measures the ratio of the new to the initial value of the initial basket:
$$\operatorname{LPI}(t)=\frac{p^t \cdot x^0}{p^0 \cdot x^0}, \quad t>0 .$$

## 经济代写|微观经济学代写Microeconomics代考|Price Indices and Infation

CPI 是 Laspeyres 价格指数的一个实例，用于衡量初始篮子的新值与初始值的比率:
$$\operatorname{LPI}(t)=\frac{p^t \cdot x^0}{p^0 \cdot x^0}, \quad t>0$$

## 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。

## 经济代写|微观经济学代写Microeconomics代考|BEA470

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|Labour Supply. Saving Decision

The Walrasian UMP permits the study of factor supply decisions. For many consumers, the income to buy consumption goods comes from supplying labour services. An important issue is how consumers decide labour supply. In real economies, of ten one must accept either a full-time job or nothing; but even then the average labour supply of an entire household can be varied by varying how many in the household work and how much during the period (part-time, overtime, vacation periods, etc.). So by interpreting the consumer as a household including several members, and referring to labour supply over not too short a period (say, a year), it is not too absurd to assume that labour supply can be varied more or less continuously.

Suppose that the consumer’s endowment consists only of potential labour hours, i.e. of leisure hours usable to work; measure the supply of labour $L$ per period (e.g. per week) as the difference between the endowment of leisure hours $M$ per period ( $168 \mathrm{~h}$ per week) and the demand $x$ for leisure hours per period. ${ }^{.2}$ (The supply of labour, $L=M-x$, is then identical with the net supply of leisure, and I am implicitly assuming that the consumer is indifferent between different types of labour.) Assume only two consumption goods, leisure $x$ and consumption $c,{ }^{43}$ the price of consumption is 1 . The price of leisure is the real hourly wage $w$, because one less hour of leisure is one more hour of work, which yields the consumer $w$ more units of income to spend on consumption. The budget constraint is $c=w L=w(M-x)$; if we assume that the consumer has in addition an initial endowment of non-labour income that permits the purchase of $\mathrm{c}^{\circ}$ units of consumption, then the budget constraint is $c=w(M-x)+c^{\circ}$ : in either case, with leisure measured in abscissa and consumption in ordinate, the slope of the budget constraint is $-w$. As long as labour supply is positive, $M>x$, for leisure the total income effect is positive if leisure is a normal good; thus as the real wage increases from an initial level where labour supply is positive, the demand for leisure may well increase, entailing a decrease in the supply of labour (cf. $\mathbf{-}$ Figs. $4.19$ and $4.20$ ).

## 经济代写|微观经济学代写Microeconomics代考|Some Notes on the Usefulness

The results of consumer theory on the plausible sign of the influence of price changes on demands and on supplies are clearly important, for example the distinction between substitution effect, ordinary income effect and endowment income effect is very important. Less clear is the relevance of the results reached by consumer theory for applied research. What are the suggestions from consumer theory, important for the applied economist interested in estimating the effect of a tax on a good on the quantity demanded of the good? Mainly, it would seem that the attempts to estimate demand functions, supply functions, the effect of a tax should use assumptions, mathematical functions, systems of functions that do not contradict consumer theory. But it is not easy to make this general idea more concrete.

Consumer theory is rich of results about the demand functions of a single consumer. We have seen in Sect. $4.12$ that the Slutsky matrix derivable from these demand functions should be negative semidefinite and symmetric. The other restrictions that consumer theory imposes on the (Marshallian) system of demand functions of an individual consumer are that its demand functions must be homogeneous of degree zero in (p, m) and must satisfy the balanced budget restriction (expenditures on the several goods must add up to total income). It can be proved (I omit the proof) that homogeneity of degree zero, balanced budget and a negative semidefinite and symmetric Slutsky matrix are all the restrictions that standard consumer theory imposes on the system of differentiable demand functions coming from the choices of a consumer. (Actually it can be proved that homogeneity of degree zero is implied by budget balancedness plus symmetry of the Slutsky matrix, hence is not an additional restriction, cf. Jehle and Reny 2011, p. 85.)

## 经济代写|微观经济学代写Microeconomics代考|Labour Supply. Saving Decision

Walrasian UMP 允许研究要素供应决策。对于很多消费者来说，购买消费品的收入来自于提供劳务。一个重要的问题是消费者如何决定劳动力供给。在实体经济中，十个人必须接受全职工作或不接受任何工作；但即便如此，整个家庭的平均劳动力供应也可以通过改变家庭工作的数量和期间（兼职、加班、假期等）的数量来改变。因此，通过将消费者解释为一个包括几个成员的家庭，并指代在不太短的时期（例如一年）内的劳动力供应，假设劳动力供应可以或多或少地连续变化并不太荒谬。

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|The CES Utility Function

It follows that $\varrho=(\xi-1) / \xi$ and therefore another way to write a CES function that makes its elasticity of substitution explicit is
$$\left(a_1 x_1^{(\xi-1) / \xi}+a_2 x_2^{(\xi-1) / \xi}\right)^{\xi /(\xi-1)} .$$
The CES function, invented to be used as a production function, is homogeneous of degree 1: the easy proof is left to the reader. When $a_1=a_2=1$, a monotonic transformation sometimes used which is not homogeneous of degree 1 but is very simple to use is
$$x_1^\delta / \delta+x_2^\delta / \delta .$$
Its elasticity of substitution is, again, constant and given by $\xi=1 /(1-\delta)$.
As one lets $Q$ vary, the CES approaches other well-known types of utility functions. For $\varrho$ tending to 1 from below, the elasticity of substitution tends to $+\infty$, that is, to the case of perfect substitutes. Indeed if one sets $Q=1$, one obtains the separable additive utility function of perfect substitutes, $u=a_1 x_1+a_2 x_2$. As $\varrho$ decreases, the elasticity of substitution decreases too, tending to 1 as $\varrho$ tends towards zero.

For $\varrho=0$ the CES function is not defined owing to division by zero, but if one lets $\varrho$ tend to 0 , the CES tends in the limit to have indifference curves identical to those of a Cobb-Douglas. Indeed, if $\varrho$ tends to zero the MRS tends to $-a_1 x_2 /\left(a_2 x_1\right)$ which is the same as for the generalized Cobb-Douglas $x_1{ }^\alpha x_2{ }^\beta$.

For $\varrho$ tending to $-\infty$ the indifference curves approach the L-shaped indifference curves of the case of perfect complementarity. ${ }^{35}$ The MRS, $-\left(a_1 / a_2\right) \cdot\left(x_2 /\right.$ $\left.x_1\right)^{1-e}$, tends to $-\left(a_1 / a_2\right) \cdot\left(x_2 / x_1\right)^{\infty}$ which has value $-\infty$ if $x_2>x_1$, zero if $x_2<x_1$; thus, indifference curves tend to become L-shaped with the corners on the $45^{\circ}$ straight line through the origin (which can always be obtained with an opportune choice of units for the goods).

## 经济代写|微观经济学代写Microeconomics代考|The Slutsky Equation

We finally tackle the issue of how the (Marshallian) demand for a good reacts to changes in prices. All the functions to appear below are assumed continuously differentiable, indifference curves are strictly convex, and the initial consumer choice is an interior basket, $x \gg 0$.

Let $\mathbf{p}^, m^$ be prices and income in the initial situation, and let $u^=v\left(\mathbf{p}^\right.$, $\left.m^\right)=u\left(\mathbf{x}\left(\mathbf{p}^, m^\right)\right), x_j^=x_j\left(\mathbf{p}^, m^\right)$. Differentiate both sides of $h_f(\mathbf{p}, u)=x_i(\mathbf{p}$, $e(\mathbf{p}, u))=x_i(\mathbf{p}, m)$ with respect to $p_j$
$$\frac{\partial h_i\left(\mathbf{p}^, u^\right)}{\partial p_j}=\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial p_j}+\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial e\left(\mathbf{p}^, u^\right)} \cdot \frac{\partial e\left(\mathbf{p}^, u^\right)}{\partial p_j},$$
where $\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial e\left(p^, u^\right)}$ can also be written $\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial m^}$, because initially $m=m^=e\left(\mathbf{p}^, u^\right)$ and under a balanced budget a variation in expenditure is the same thing as a variation in income. Furthermore, by Shephard’s Lemma $\partial e\left(\mathbf{p}^, u^\right) / \partial p_j=h_j\left(\mathbf{p}^, u^\right)$ $=x_j\left(\mathbf{p}^, e\left(\mathbf{p}^, u^\right)\right)=x_j^$. Hence
$$\frac{\partial h_i\left(\mathbf{p}^, u^\right)}{\partial p_j}=\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial p_j}+\frac{\partial x_i\left(\mathbf{p}^, m^\right)}{\partial m} \cdot x_j^* .$$
Let us indicate as $S(\mathbf{p}, m) \equiv\left[s_{i j}\right]$ the $n \times n$ Jacobian matrix of the vector of Hicksian demand functions for individual goods which form $\mathbf{h}(\mathbf{p}, u)$. Element $(i, j)$ of this matrix is
$$s_{i j}=\frac{\partial h_i\left(\mathbf{p}^, u^\right)}{\partial p_j},$$
for which equality (4.6) holds. Matrix $S(\mathbf{p}, m) \equiv\left[s_{i j}\right]$ is called Slutsky matrix or also matrix of Hicksian substitution effects. It yields
$$\mathrm{dh}=S \mathbf{d p}^T$$
as the variation of compensated demands for infinitesimal variations $\mathrm{d} p$ of the price vector (the superscript $T$ indicates transposition because we treat $\mathbf{p}$ as a row vector).

The usefulness of (4.6) is that, rearranging so as to isolate on one side of the equality sign the price effect on Marshallian demand, we obtain the Slutsky equation for Marshallian demand.

## 经济代写|微观经济学代写Microeconomics代考|The CES Utility Function

$$\left(a_1 x_1^{(\xi-1) / \xi}+a_2 x_2^{(\xi-1) / \xi}\right)^{\xi /(\xi-1)} .$$

$$x_1^\delta / \delta+x_2^\delta / \delta .$$

## 经济代写|微观经济学代写Microeconomics代考|The Slutsky Equation

$$\mathrm{dh}=S \mathbf{d} \mathbf{p}^T$$

(4.6) 的用处在于，重新排列以便在等号的一侧隔离价格对马歇尔需求的影响，我们得到马歇尔需求的斯卢茨基方 程。

## 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。

## 经济代写|微观经济学代写Microeconomics代考|BU1003

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

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

The analytical differences just illustrated entail radically different answers to the question of the nature of income from the property of capital.

In the classical approach the answer that implicitly emerges to the question ‘what is the origin of profits?’ is: profits originate in the fact that, because of the capitalists’ collective monopoly of means of production, workers can only work if capitalists give them permission by hiring them, and the permission will only be given if the workers’ wages leave a surplus for the capitalists. Marx-re-expressing in more precise terms what had been already argued by other critics of capitalism, for example the so-called Ricardian Socialists Gray, Bray, Hodgskin-concludes that, behind the veil of the apparent freedom and formal (i.e. juridical) equality of the two parties to the wage contract, there is a substantial inequality of bargaining position that determines an exploitation of wage labour analogous to the exploitation of feudal serfs through corvées: only part of the labour time contributed by workers goes to produce what they get, the further labour time produces the profits of capitalists. In feudal society, however, the thing is more evident than under capitalism, where the apparent equality and freedom of the parties to the wage contract, plus the fact that the means of production are owned by the capitalist, makes it more difficult to perceive the reality of the situation; it may seem that the capitalist, because he contributes the capital goods to the productive process, does have a right to a share of output. In fact the capitalist class owns the capital goods only because it was able to appropriate the surplus in previous periods.

A marginalist author would reply that such a characterization of the origin of profits or interest derives from an imperfect comprehension of the forces that determine income distribution. Each unit of each factor receives a reward equal to the value of its marginal product, i.e. equal to its contribution to social production and to the utility of consumers, where this contribution is measured as what society would lose if that unit of factor were withdrawn from production. Indeed, if a worker stopped working, society would lose an output equal to the wage the worker earns, so the wage equals the worker’s contribution. ${ }^{19}$ Analo= gously, the owner of a unit of capital receives as interest the (net) marginal product of her capital, i.e.

## 经济代写|微观经济学代写Microeconomics代考|Technical Progress, Relative Wages, Unequal Exchange

According to the marginal approach, technical progress has no persistent negative effect on employment. Innovations can cause the bankruptcy of some firms and hence an increase in frictional unemployment, but only temporarily. As to the effect of an innovation on wages, this will generally be positive, owing to a generally positive effect of technical progress on the full-employment marginal product of labour. It is not inconceivable that technical progress may raise the product per person while at the same time reducing the full-employment marginal product of labour; this possibility is shown in $\boldsymbol{-}$ Fig. 3.24, which illustrates two total labour productivity curves.

• Figure $3.24$ shows a case in which technical progress alters the total productivity curve of labour such that the total product of the full-employment amount of labour $L^{*}$ rises, but its marginal product (the slope of the total productivity curve) decreases. This is not impossible, but (it is argued) highly unlikely, and anyway soon to be reversed by the general tendency – shown, it is argued, by historical experience – toward a rise in the marginal product of labour. Thus technical progress is viewed as generally beneficial to workers.

In the classical approach, on the contrary, technical progress makes a rise in real wages without a decrease of the rate of profits possible, but its immediate effect is generally to cause firings because it allows the production of the same quantities with less labour, and the increase in unemployment will probably tend to decrease wages. This effect can be countered by increases in the quantities produced, but these increases need not happen, and especially so when technical progress takes the form of process innovation, i.e. of ways of producing the same final products in a cheaper way and therefore, most of the time, with less labour. The overall effect of technical progress on employment and wages can therefore be negative even for very long periods, and particularly so in periods of slow growth of aggregate production.

## 经济代写|微观经济学代写Microeconomics代考|Technical Progress, Relative Wages, Unequal Exchange

• 数字3.24显示了一个案例，其中技术进步改变了劳动的总生产率曲线，使得充分就业劳动量的总产品大号∗上升，但其边际产量（总生产率曲线的斜率）下降。这并非不可能，但（有人认为）极不可能，而且无论如何很快就会被总趋势所逆转——据认为，历史经验表明——劳动边际产品的上升。因此，技术进步被视为对工人普遍有利。

## 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。

## 经济代写|微观经济学代写Microeconomics代考|ECON106

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|The Diferent Data When Determining

We now have the elements to grasp the radical difference between the classical or surplus approach, and the marginal or neoclassical approach.

The central difference is in the explanation of how the net product, net also of land rent, gets divided between wages on the one side, and on the other side income from the property of capital (profits in classical terminology, interest in marginalist terminology). The rent of land is explained on the basis of similar principles in the two approaches, ${ }^{46}$ so we can concentrate on the differences in the explanation of wages and profits (interest), by assuming land is free. In the classical approach capitalists are able to appropriate part of the product owing to their bargaining strength that derives from their control of the means of production and their capacity to resist more in case of conflict; the sociopolitical elements that determine the relative bargaining strength of labour and capital fix the real wage, and profits are determined as the residue. In the marginal approach the real wage rate and the rate of interest are determined by a symmetrical mechanism, that determines both simultaneously, through the tendency toward an equilibrium between supply and demand.

The root of the difference does not lie simply in whether the labour market is seen as competitive (with each individual acting separately from the others) or not competitive (with labourers and capitalists acting as two coalitions). It lies in the presence in the marginalist authors, and absence in the classical authors, of the conception of production as a cooperation of factors of production which are substitutable one for the other, so that technical choices and consumer choices activate factor substitution mechanisms which engender a decreasing demand curve for each factor.

## 经济代写|微观经济学代写Microeconomics代考|The Role of Social and Political Elements

The presence in the marginalist authors, and absence in the classical authors, of the notion of a negative elasticity of labour employment with respect to real wages entails a different role of social and political elements in the two approaches, and a different conception of how competition in the labour market operates.

In the marginal approach a wage fixed by sociopolitical elements is an impediment to the free working of competition, which if left free to operate would produce a fully determinate level of the real wages. The marginalist conception itself of the ‘free working of competition’ in labour markets relies on this: without a significant positive effect of decreases of real wages upon employment, the marginalist conception of competition in the labour market, entailing an indefinite downward flexibility of wages as long as there is unemployment, would clearly be unacceptable: its operation would bring wages to zero (or anyway to implausibly low levels) whenever unemployment persisted, with a clear contradiction with observation.

In the classical approach the absence of the notion of a decreasing demand curve for labour would have entailed precisely such implausible results, if competition had been thought to operate as the marginalists conceive it: the little response of labour employment to changes in wages and the nearly universal presence of unemployment in capitalist economies would have entailed a prediction of a tendency of wages to zero, clearly incompatible with observation. It is understandable then that in the classical approach one does not find the view that wages will decrease as long as the demand for labour is less than its supply, and one finds instead a stress on custom, on the need to defend social status, on relative bargaining power, on collective behaviours, on fear of popular revolts, and the like, as the elements capable of determining real wages and their variations. The social customs and political elements that in the marginal approach are, if at all, superposed upon a self-sufficient mechanism and impede its autonomous working are, to the contrary, indispensable in a classical approach and are accordingly viewed as an obvious component of an economy based on wage labour. Hence for a classical economist social, political, institutional and historical considerations are an integral part of economic analysis. ${ }^{47}$

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 经济代写|微观经济学代写Microeconomics代考|Money and the Rate of Interest

The rate of interest has been determined so far by the equilibrium between supply and demand for corn-capital. In real economies, it might be objected, the rate of interest is the ‘price’ of credit, and loans are normally in money terms. Can the above theory apply to an economy where goods are exchanged against money and the rate of interest is the ‘price’ of monetary loans?

The basic idea of the marginal approach on this issue is that (if financial intermediaries do not disturb the process and if, for simplicity, we assume no inflation) the equilibrium rate of interest brings at the same time into equality the supply and demand for capital (stocks), and the supply and demand for monetary gross savings or ‘loanable funds’ (flows). ${ }^{45}$ Gross savings are the sum of funds set aside to replace the used-up capital goods and net savings. Let us leave aside consumer credit which is a complication whose consideration adds little to the basic insight. If the supply of gross savings is greater than the demand for them coming from firms, the rate of interest decreases, and according to the marginal approach firms become ready to employ more capital per unit of labour than before, up to the point where the net marginal product of capital becomes equal (neglecting risk) to the rate of interest. There will be an increase of investment that will gradually increase the stock of capital until the stock of capital becomes such that its marginal product equals the rate of interest. Now, the greater the stock of capital,capital goods. For example, if each period the capital goods to be replaced are worth $1 / 10$ of the value of the capital stock, then each period firms need to borrow loanable funds of a value equal to $1 / 10$ of the value of the capital stock if they intend to keep it unchanged. This flow of borrowing increases if the capital stock increases. If the net savings are positive and gradually increase the stock of capital, then the flow demand for loanable funds by firms to replace used-up capital goods increases and finally swallows up the entire flow supply of gross savings, bringing net savings to zero. At that point the rate of interest that makes firms satisfied with the existing stock of capital – hence, the rate of interest equal to the marginal product of the existing stock of capital – also produces equilibrium between supply and demand for the flow of gross savings. The rate of interest will never go far above that level because firms will not be ready to borrow at a rate above the rate of return they can hope to earn on the capital bought with the loans, rate of return equal to the marginal product of capital. In other words, the demand for loans drops rapidly if the rate of interest goes above the marginal product of the existing stock of capital. As to decreases of the rate of interest below the current marginal product of capital, they too can be expected to be quite limited, as increases in the absorption of a flow of net savings will only very slowly reduce the marginal product of capital. The considerable elasticity of the flow demand for loanable funds implies that the equilibrium rate of interest, although directly determined by the equilibrium between supply and demand for loanable funds, is in fact determined by the full-employment marginal product of capital, in the sense that it will always be very close to the latter.

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

At this point we can ask: why does the quantity of capital tend to grow as time passes? In the marginal approach, the answer is: Because consumers decide not to spend on consumption goods their entire net income and lend the remainder to firms at a rate of interest that induces the firms to borrow those net savings and to use them to raise the capital/labour ratio in production by purchasing more new capital goods than required to replace the used-up capital goods. So the stock of capital grows. The increased demand for newly produced capital goods is satisfied by using the productive factors left free by the reduced demand for consumption goods.

For example, in the economy producing corn with corn-capital and labour, with wages paid at the end of the year, if 1100 units of corn are produced in a certain year with the employment of 400 units of corn-capital (hence the net product is 700 ), and if consumers decide to consume only 600 units of corn, they are left with 500 units of unspent income; they will offer it as loans to firms, and if the rate of interest becomes low enough firms will decide they want to borrow that income and use it to buy corn-capital raising the capital-labour ratio in production, employing 500 units of corn-capital instead of the old 400 ; so the net savings of consumers equal in value to 100 units of corn become net investment, and the stock of corn-capital grows from 400 to 500 .

In such a perspective, the capital stock of an economy is the result of the sum of past decisions by consumers to perform net savings out of full-employment production.

Evidently – marginalist economists conclude – since there has been and there continues to be capital accumulation, consumers have been having such preferences that, at the rate of interest corresponding to the full-employment marginal product of capital, in the aggregate they prefer to consume in each period less than the net product of that period, in order to consume more in the future. Nothing in the theory prevents consumers from preferring to consume more than the net product, in which case there would be decumulation of capital; but this has not happened. Evidently the rate of interest is such and preferences are such as to induce consumers to perform net savings, preferring to trade off some present consumption for more consumption in the future.

The marginalist view is that, were it not for the continuous growth of labour supply, and for technical progress that raises the marginal product of capital and contrasts the scarcity of land, this continuous capital accumulation would have caused a continuous decrease of the rate of interest, down probably to zero.

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写微观经济学Microeconomics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。我们的专家在代写微观经济学Microeconomics代写方面经验极为丰富，各种代写微观经济学Microeconomics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

## 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

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

## 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。