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

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## 经济代写|微观经济学代考Microeconomics代写|Stackelberg Duopoly

In the Cournot model, both firms made their decisions simultaneously and without knowing the other’s decision. In the Stackelberg model, they decide one after the other. We call the one that chooses first, the Leader and the other one the Follower.

We have two firms.

They set quantities (and the price is set by the market).

Leader first decides on her quantity, and then Follower decides on hers.

We will use the same reaction function as in the Cournot model, but the analysis will now be different since they do not choose simultaneously. Leader, who sets her quantity first, has an advantage. She knows that Follower will later set her quantity according to her reaction function. Therefore, Leader sets her quantity to maximize her own profit, given Follower’s optimal response.

## 经济代写|微观经济学代考Microeconomics代写|Bertrand Duopoly

In the two preceding models, we have assumed that the firms set quantities. What happens if, instead, they set prices? The Bertrand model assumes that

• We have two firms.
• They set prices (and quantities are set by the market).
• They set prices simultaneously, without knowing which price the other one sets.

The previous models produced results that were very favorable for the firms but less so for the consumers. The Bertrand model, however, puts the two firms in a Prisoner’s Dilemma-type of situation (see Section 13.2), and forces them to set $p=M C$, i.e. they set the same price as firms would do in a perfectly competitive market. This is, of course, unfavorable for the firms, but an improvement for consumers and society.

To see that the firms will set $\mathrm{p}=\mathrm{MC}$, suppose that we know that the other firm has set a high price. Which is then the best price we can set? Remember that we have homogenous (meaning identical) goods, so the consumers will not care from whom they buy it. Furthermore, they have perfect information about all prices. If we choose a price that is just below our competitor’s, all customers will buy from us. This is a good situation for us, but far from optimal for the other firm. If they reason in the same way, they will want to set a price just below ours. Then we would lose all customers… and so forth.

# 微观经济学代写

## 经济代写|微观经济学代考Microeconomics代写|Bertrand Duopoly

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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。