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

2023年3月24日

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## 经济代写|微观经济学代写Microeconomics代考|Equilibrium Price and Quantity

An important question is whether a perfectly competitive market can reach an equilibrium. The idea of an equilibrium is well known to civil engineers as they have to find equilibrium conditions in structural analysis to guarantee stability. A typical way of conveying the idea can be found in Figure 5.2. The ball on the left side will come to rest in its initial position after an interference by a force; this is an equilibrium position. The ball to the right will never regain its initial position once disturbed; this is an instable position.

To find out how perfectly competitive markets react, a thought experiment is helpful: Let all producers raise the price from $p^$ to $p^{+}$(Figure 5.3). The producers can sell the quantity demanded $q^$ at price $p^$ but they are unable to sell the quantity supplied at $p^{+}$, there is a surplus. Nobody in the market is willing to by the surplus and storage costs pile up every day. Sooner than later the first producer will lower the price and the others must follow in order to empty the stores. In the end, the market will return to the equilibrium position with price $p^$ and quantity $q^*$.

Something similar happens when the price $p^{-}$is below the equilibrium price $p^*$ (Figure 5.4). Producers are only willing to supply the quantity $q^{-}$at price $p^{-}$while the consumers want the larger quantity demanded at $p^{-}$. This causes a shortage in the market. Either some consumers raise their offer or the producers understand the situation and raise the price by themselves. In both cases the market will end up at the initial equilibrium with $p^$ and $q^$

Thus, the market tends to return to an equilibrium after being disturbed. In the case of a surplus the cause are frustrated producers and in the case of a shortage frustrated consumers. Only at $p^, q^$ the wishes of consumers and producers find a balance. Changes in price always call for changes in quantities and vice versa. Price and quantity are endogenous variables. These are part of the model and a result of the interaction.

## 经济代写|微观经济学代写Microeconomics代考|Elasticities of Demand and Supply

We can describe the shape of the demand curve by using the concept of price elasticity. A demand (supply) is elastic when a small change in price leads to large changes in quantity. It is inelastic when a large change in price leads to small changes in quantity (Figure 5.7). There are two extremes: perfectly elastic demand (supply) and perfectly inelastic demand (supply). It might seem that, for example, a perfectly inelastic supply is a nonexistent extreme. This is not true, if you think of the short-term additional supply in housing. It takes time to develop property, acquire permits, design the housing, procure contractors, and erect the buildings. In the short run (maybe two years), there might be no additional supply on the local market.

There are two very interesting elasticities: price and income elasticity. The definition of price elasticity is the change in quantity $\Delta Q / Q[\%]$ divided by the change in price $\Delta P / P[\%]$. We measure prices in currency (e.g. USD), thus by dividing two prices, we get as dimension percent (\%); the same result applies to dividing quantities. Thus, price elasticity $e_{P, D}$ of demand is defined as:
$$e_{\mathrm{P}, \mathrm{D}}=\Delta Q_{\mathrm{D}} / Q_{\mathrm{D}}[\%] / \Delta P / P[\%]$$
As the demand curve slopes downwards, price elasticity of demand is always negative. If the change in quantity for a unit change in price is large, we call the corresponding price elasticity of demand elastic $\left(e_{\mathrm{P}}<-1\right)$; such a curve is trending toward a horizontal line (Figure 5.7). If the changes in quantity and price are the same, we call the elasticity to be unit elastic $\left(e_{\mathrm{P}}=-1\right)$. Finally, price elasticity is inelastic when quantity changes are small for a unit change in price; such a curve is trending toward a vertical line. A horizontal line represents a perfectly elastic demand $\left(e_{\mathrm{P}}=\infty\right)$ and a vertical line a perfectly inelastic demand $\left(e_{\mathrm{P}}=0\right)$.

Price elasticity of demand is not constant. Figure 5.8 shows a straight-line demand curve. The calculation for point A provides an elastic demand $\left(e_{\mathrm{P}}=-4<-1\right)$, for point $\mathrm{B}$ a unit-elastic demand $\left(e_{\mathrm{P}}=-1\right)$ and for point $\mathrm{C}$, an inelastic demand $\left(e_{\mathrm{P}}=-0.25>-1\right)$ (Table 5.1).
Elasticity is also connected total revenue (P.Q) (Table 5.2).
We can check these conclusions by calculating the total revenue with the data from Figure 5.8 (Table 5.3).

Total revenue changes when the price rises or falls. This is demonstrated in Table 5.3. A specific point on the demand curve allows to calculate total revenue $(P \cdot Q)$ because price $P$ and quantity $Q$ are given for this point. Figure 5.9 shows an example where a fall in prices from 40 (A) to 25 (B) increases total revenue. As point A lies in the elastic part of the demand curve, this comes as no surprise.

# 微观经济学代考

## 经济代写|微观经济学代写Microeconomics代考|Elasticities of Demand and Supply

$\Delta P / P[\%]$. 我们以货币 (例如美元) 衡量价格，因此通 过将两个价格相除，我们得到维度百分比 (1\%); 相同的 结果适用于除以数量。因此，价格弹性 $e_{P, D}$ 需求定义 为:
$$e_{\mathrm{P}, \mathrm{D}}=\Delta Q_{\mathrm{D}} / Q_{\mathrm{D}}[\%] / \Delta P / P[\%]$$

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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。