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

#### Doug I. Jones

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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
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## 经济代写|微观经济学代写Microeconomics代考|MARKET EQUILIBRIUM

The concept of equilibrium is employed in both the physical and social sciences, and it is of central importance in economic analysis. In general, a system is in equilibrium when all forces at work within the system are canceled by others, resulting in a balanced or unchanging situation. In physics, for example, a ball hanging from a spring is said to be in equilibrium when the spring has stretched sufficiently that the upward force it exerts on the ball is exactly counterbalanced by the downward force of gravity. In economics, a market is said to be in equilibrium when no participant in the market has any reason to alter his or her behavior, so that there is no tendency for production or prices in that market to change.

If we want to determine the final position of a ball hanging from a spring, we need to find the point at which the forces of gravity and spring tension are balanced and the system is in equilibrium. Similarly, if we want to find the price at which a good will sell (which we will call the equilibrium price) and the quantity of it that will be sold (the equilibrium quantity), we need to find the equilibrium in the market for that good. The basic tools for finding the equilibrium in a market for a good are the supply and demand curves for that good. For reasons we will explain, the equilibrium price and equilibrium quantity of a good are the price and quantity at which the supply and demand curves for the good intersect. For the hypothetical supply and demand curves shown earlier for the pizza market in Chicago, the equilibrium price will therefore be $\$ 3$per slice, and the equilibrium quantity of pizza sold will be 12,000 slices per day, as shown in Figure 2.3. Note that at the equilibrium price of$\$3$ per slice, both sellers and buyers are “satisfied” in the following sense: buyers are buying exactly the quantity of pizza they wish to buy at that price (12,000 slices per day) and sellers are selling exactly the quantity of pizza they wish to sell (also 12,000 slices per day). And since they are satisfied in this sense, neither buyers nor sellers face any incentives to change their behavior.

Note the limited sense of the term satisfied in the definition of market equilibrium. It doesn’t mean that sellers would be displeased to receive a price higher than the equilibrium price. Rather, it means only that they’re able to sell all they wish to sell at that price. Similarly, to say that buyers are satisfied at the equilibrium price doesn’t mean that they wouldn’t be happy to pay less than that price. Rather, it means only that they’re able to buy exactly as many units of the good as they wish to at the equilibrium price.

Note also that if the price of pizza in our Chicago market were anything other than $\$ 3$per slice, either buyers or sellers would be frustrated. Suppose, for example, that the price of pizza were$\$4$ per slice, as shown in Figure 2.4. At that price, buyers wish to buy only 8,000 slices per day, but sellers wish to sell 16,000 . And since no one can force someone to buy a slice of pizza against her wishes, this means that buyers will buy only the 8,000 slices they wish to buy. So when price exceeds the equilibrium price, it is sellers who end up being frustrated. At a price of $\$ 4$in this example, they are left with an excess supply, or surplus, of 8,000 slices per day. ## 经济代写|微观经济学代写Microeconomics代考|Rent Controls Reconsidered Consider again the market for rental housing units in New York City and suppose ure 2.7. This market, left alone, would reach an equilibrium monthly rent of$\$1,600$, at which 2 million one-bedroom apartments would be rented. Both landlords and tenants would be satisfied, in the sense that they would not wish to rent either more or fewer units at that price.

This wouldn’t necessarily mean, of course, that all is well and good. Many potential tenants, for example, might simply be unable to afford a rent of $\$ 1,600$per month and thus be forced to remain homeless (or to move out of the city to a cheaper location). Suppose that, acting purely out of benign motives, legislators made it unlawful for landlords to charge more than$\$800$ per month for one-bedroom apartments. Their stated aim in enacting this law was that no person should have to remain homeless because decent housing was unaffordable.

But note in Figure $2.8$ that when rents for one-bedroom apartments are prevented from rising above $\$ 800$per month, landlords are willing to supply only$1 \mathrm{mil-}$lion apartments per month, 1 million fewer than at the equilibrium monthly rent of$\$1,600$. Note also that at the controlled rent of $\$ 800$per month, tenants want to rent 3 million one-bedroom apartments per month. (For example, many people who would have decided to live in New Jersey rather than pay$\$1,600$ a month in New York will now choose to live in the city.) So when rents are prevented from rising above $\$ 800$per month, we see an excess demand for one-bedroom apartments of 2 million units each month. Put another way, the rent controls result in a housing shortage of 2 million units each month. What is more, the number of apartments actually available declines by 1 million units per month. If the housing market were completely unregulated, the immediate response to such a high level of excess demand would be for rents to rise sharply. But here the law prevents them from rising above$\$800$. Many other ways exist, however, in which market participants can respond to the pressures of excess demand. For instance, owners will quickly learn that they are free to spend less on maintaining their rental units. After all, if there are scores of renters knocking at the door of each vacant apartment, a landlord has considerable room to maneuver. Leaking pipes, peeling paint, broken furnaces, and other problems are less likely to receive prompt attention-or, indeed, any attention at all-when rents are set well below market-clearing levels.

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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。

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