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

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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|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.

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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。