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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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

Comparative advantage is the basis for trade, is fundamental to economic analysis, and is a topic covered by all principles textbooks. This subsection includes two methods that have been used with some success. There is nothing really new in this section, but I find the methods satisfying. My mantra is (with apology to Shakespeare): “Opportunity cost, opportunity cost, all is opportunity cost.”

Evidently, David Ricardo’s demonstration of comparative advantage as the basis for trade is a stroke of genius. The first seven chapters of his famous book (1821, p. 82) present his model of an economy in which agricultural land is supplied in discrete amounts – a given amount of the best land, a given amount of next-best land, and so on. As the population grows, land of lower quality must be used, which generates land rent for the land of higher quality. The economy is hampered by the nature of land supply and by the tendency for land rent to increase as the population grows. What to do? Ricardo hit upon the idea that England could specialize in the production of cloth, export cloth, and import agricultural products – instead of imposing tariffs (Corn Laws) on the importation of agricultural products. As a Member of Parliament and public intellectual, he argued his case, and the Corn Laws eventually were eliminated after his death in 1823 .

Here is Ricardo’s example, slightly modified. England and Portugal produce wine and cloth. The number of workers needed to produce a “shipload” of wine and cloth in the two countries are as follows:

Note that Ricardo built in the assumption that Portugal has the absolute advantage in both products because fewer workers are needed in Portugal than in England to produce either product (even though by 1819 , England was the world’s premier manufacturer of cloth). Because the opportunity cost of wine for cloth (and cloth for wine) is different in the two countries, there is “room for a deal.” Here’s the deal.
Suppose Portugal shifts 80 workers from cloth production to wine production, thus gaining one shipload of wine at the opportunity cost of $8 / 9$ shipload of cloth. The opportunity cost of cloth is $9 / 8$ shiploads of wine.

At the same time, suppose that England shifts 100 workers from wine production to cloth production, thus gaining one shipload of cloth at the opportunity cost of $5 / 6$ shipload of wine. The opportunity cost of cloth is $6 / 5$ shiploads of cloth.

Assume that the (barter) exchange rate is one shipload of wine for one shipload of cloth. Portugal ships the shipload of wine and England ships the shipload of cloth. I imagine one ship going back and forth. Portugal now has the original amounts of cloth and wine, and England now has the original amounts of cloth and wine as well. But look again. Portugal has gained the output of 10 workers. And England has gained the output of 20 workers. Both countries have gained output with no change in the number of workers because each country has specialized in the product with the lower opportunity cost.

The whole business relies on finding an exchange rate at which both countries gain. An exchange rate of one shipload of wine for one shipload of cloth was assumed. But given that the opportunity costs differ in the two countries, such an exchange rate (really a range of exchange rates) exists and there is a strong incentive for the two countries to find an exchange rate at which to strike a deal.

Ricardo’s example is convincing, but another method makes explicit use of production possibility frontiers. Refer to Figure 1.5. England’s production possibility frontier is labeled E, and Portugal’s is $\mathrm{P}$. The outer line is their combined production possibility curve. The diagram is drawn so that neither country has an absolute advantage, but the opportunity costs in the two countries are different. England has the comparative advantage in cloth, while Portugal has the comparative advantage in wine.

## 经济代写|宏观经济学代写Macroeconomics代考|International trade policy

There are two basic parts to international trade policy – exchange rate policy, and policies that directly impact exports and imports. Consider these in turn.

Exchange rate policy has three basic types. The first one is a floating exchange rate in which the rate is determined by demand and supply in the market for a currency, as shown in Figure 1.4. However, the central bank of the nation can change interest rates and thereby influence the exchange rate by altering the demand and supply of interest-earning assets. The third policy is to maintain a fixed exchange rate with the rest of the world. In this case, the central bank must buy or sell currency to maintain the same exchange rate. In other words, the central bank steps into the market and shifts the supply or demand for its own currency. If the central bank wishes to lower the exchange rate (the price of its own currency in terms of other currencies), it sells its own currency on the international market. To raise the exchange rate, the central bank buys its own currency.

What objective might be pursued using exchange rate policy? If the nation wishes to expand its exports, the central bank can keep the exchange rate lower than it otherwise would be. For example, China did in fact pursue such a policy from about 1997 to 2006 . However, as export industries expand, prices of output may eventually go up. Since 2006 , the price of the yuan has gone from about 8 yuan per dollar to 6 yuan per dollar, pushing up the price of Chinese goods.

What about trade policy that involves direct intervention into export and import markets? Intervention into import markets usually comes in the form of tariffs, which are taxes on the imported goods. The prices of the goods increase to those who purchase them, and the government collects tax revenue from the firms that sell these goods. In effect, the taxes are paid by the consumers. The firms in the exporting nation see a reduction in the quantity of exports and likely no change in the price at which they sell the product. If the tariff is targeted at the exports of one particular exporting nation, purchasers of those products can switch to imports from other nations. Domestic firms that produce the same product in the nation imposing the tariff may see their outputs rise as well.

Other trade policies pertaining to imports include import quotas and health and safety regulations. These policies also reduce imports, but the government receives no tax revenue. Domestic firms will see outputs rise.

Trade policies can also target exports. Export subsidies are used to promote exports. Such subsidies may permit the exporting firms to sell in export markets at below the actual cost of production. International organizations, such as the World Trade Organization (WTO), attempt to limit selling below cost, but proving “dumping” often is difficult.

## 经济代写|宏观经济学代写Macroeconomics代考|how monetary policy works

You need to know how the supply of money is created. The United States has had a central bank, the Federal Reserve System (the Fed), since 1913. And the United Kingdom has had the Bank of England since the 17th century. Countries with advanced economies have central banks. A central bank is not a regular bank but a government agency charged with two missions – to prevent financial panics and to stabilize the economy. A central bank prevents (or at least lessens) a financial panic by being the “lender of last resort” for financial institutions that are running short of cash because creditors are demanding their money. As former Fed chairman Ben Bernanke (2013, 2015) explained, the Federal Reserve undertook a great deal of this sort of effort during the financial crisis that began in 2008 , and these actions will be discussed in Chapter $14 .$
Central banks attempt to stabilize the economy through the use of monetary policy. Here is a simplified balance sheet of a typical bank – call it Bank A.

The basic balance sheet equation is assets equal liabilities plus net worth $(\mathrm{A}=\mathrm{L}+$ NW). Banks take in deposits, both checking accounts and time deposits (certificates of deposit), and make loans to customers, such as home mortgages and loans to businesses. Banks also invest in government bonds and hold reserves. Consider how it works in the United States. Banks are required to hold a certain amount of reserves, and the Fed is responsible for seeing that this requirement is met. Reserves consist of cash on hand (called vault cash) and the bank’s reserve account at the Fed. Assets minus liabilities equal net worth, the value of the bank. As a simple example, suppose that the bank is required to hold reserves in the amount of 10 percent of its deposits. Remember that the supply of money (M1) is the total of the public’s bank accounts and currency in circulation, where bank accounts are the greater part of the money supply. Currency in circulation includes only currency held by the public.

Here is how the Fed exercises control over the money supply. The Fed (through its government bond desk in New York) purchases a $\$ 10,000$government bond from a bond dealer using a check written on itself, and the dealer deposits the check in his/her bank. The bank presents the check to the Fed and the Fed adds that amount to the bank’s reserve account at the Fed. This transaction has increased the bank’s deposits (liabilities) and reserves (assets) by$\$10,000$. The bank now has the ability to make more loans to customers. In fact, the bank can make a loan of $\$ 9,000$to a customer, leaving$\$1,000$ (10 percent) in its reserve account. The bank places the $\$ 9,000$into the customer’s checking account, and the customer spends the money by writing a check. All of the bank’s accounts are in balance. Loans are up by$\$9,000$, deposits are up by the original $\$ 10,000$, and reserves are up by$\$1,000$ ( 10 percent of the increase in deposits). The money supply has increased by $\$ 9,000$because the check for$\$9,000$ is deposited in another bank. Here are the changes in the balance sheet for Bank A.

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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。