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

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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|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

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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。