### 金融代写|利率理论代写portfolio theory代考|FNCE 463

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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

## 金融代写|利率理论代写portfolio theory代考|Determining Equilibrium Interest Rates

We take another look at the investor’s possible decision to see how it can help in determining equilibrium conditions in the market. The optimum decision could occur in three sections of Figure 1.3: $A$ to $B$, point $B$, or $B$ to $C$. If the optimum occurs in the segment $A B$, then the investor lends money at the $5 \%$ rate. If the optimum occurs at point $B$, then the investor is neither a borrower nor a lender. Finally, if the optimum occurs in segment $B C$, then the investor borrows against future income at the $5 \%$ rate.

In this simple framework, equilibrium in the marketplace is easy to determine. At a $5 \%$ interest rate this investor wishes to lend $\$ 2,000$, the difference between$\$10,000$ in income and $\$ 8,000$in consumption. Summing across all investors who wish to lend when the interest rate is$5 \%$gives one point on the supply curve. Similarly, summing across investors who wish to borrow at a$5 \%$interest rate gives one point on the demand curve. As the interest rate changes, the amount our hypothetical investor wishes to lend also changes. In fact, if the interest rate is low enough, the investor may change from a lender to a borrower. By varying the interest rate, the supply and demand curve can be traced out, and the equilibrium interest rate can be determined. The equilibrium interest rate is that rate at which the amount investors wish to borrow is equal to the amount investors wish to lend. This is often called a market clearing condition. The equilibrium interest rate depends on what each investor’s decision problem looks like, or the characteristics of a figure like Figure$1.3$for each investor. Figure$1.3$depends on the investor’s income in the two periods and the investor’s tastes or preferences. Thus, in this simple world, equilibrium interest rates are also determined by the same influences: investors’ tastes and investors’ income. ## 金融代写|利率理论代写portfolio theory代考|QUESTIONS AND PROBLEMS 1. Walking down an unfamiliar street one day, you come across an old-fashioned candy store. They have red hots five for one penny, and rock candy – one small piece for one penny. You decide to purchase some for yourself and your friends, but you find that you have only$\$1.00$ in your pocket. Construct your opportunity set both geometrically and algebraically. Draw in your indifference map (set of indifference curves). Explain why you have drawn your indifference curves as you have drawn them.
2. Let us solve a two-period consumption investment decision similar to the one presented in the text. Assume that you have income equal to $\$ 20$in each of two periods. Furthermore, you have the ability to both lend and borrow money at a$10 \%$rate. Draw the opportunity set and your indifference map. Show the optimum amount of consumption in each period. 3. Assume you can lend and borrow at$10 \%$and have$\$5,000$ in income in each of two periods. What is your opportunity set?
4. Assume you can lend and borrow at $5 \%$ and have $\$ 20,000$in income in each of two periods. Further assume you have current wealth of$\$50,000$. What is your opportunity set?
5. An individual has two employment opportunities involving the same work conditions but different incomes. Job 1 yields $Y_{1}=50, Y_{2}=30$. Job 2 yields $Y_{1}=40$, $Y_{2}=40$. Given that markets are perfect and bonds yield $5 \%$, which should be selected?
6. Assume you have income of $\$ 5,000$in each of two periods and can lend at$10 \%$but pay$20 \%$on borrowing. What is your opportunity set? 7. Assume your preference function$P$is$P=C_{1}+C_{2}+C_{1} C_{2}$. Plot the location of all points with$P=50, P=100$. 8. In Problem 3, what is the preferred choice if the preference function discussed in Problem 7 holds? 9. Suppose you have$\$10.00$ to spend on dinner. There are two possibilities: pizza at $\$ 2.00$a slice or hamburgers at$\$2.50$ a piece. Construct an opportunity set algebraically and graphically. Add indifference curves according to your own individual taste.

## 金融代写|利率理论代写portfolio theory代考|Determining Equilibrium Interest Rates

2. 让我们解决一个类似于文本中提出的两期消费投资决策。假设你的收入等于$20在两个时期的每一个时期。此外，您有能力借钱和借钱10%速度。画出机会集和你的无差异地图。显示每个时期的最佳消费量。 3. 假设您可以在10%并且有$5,000在两个时期的每个时期的收入。你的机会是什么？
4. 假设您可以在5%并且有$20,000在两个时期的每个时期的收入。进一步假设您目前拥有$50,000. 你的机会是什么？
5. 一个人有两个就业机会，涉及相同的工作条件但收入不同。工作 1 产量是1=50,是2=30. 工作 2 产量是1=40, 是2=40. 鉴于市场是完美的，债券收益率5%，应该选择哪个？
6. 假设您的收入为$5,000在两个时期中的每一个时期，并且可以在10%但付钱20%关于借贷。你的机会是什么？ 7. 假设您的偏好功能磷是磷=C1+C2+C1C2. 绘制所有点的位置磷=50,磷=100. 8. 在问题 3 中，如果问题 7 中讨论的偏好函数成立，那么首选是什么？ 9. 假设你有$10.00吃晚饭。有两种可能：披萨在$2.00一片或汉堡$2.50一块。以代数和图形方式构建机会集。根据自己的个人喜好添加无差异曲线。

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