ECN001HW5 Mathematics & Economics Coursework Question-Answer

If the current yield curve is the one represented by Yield Curve 1 (Normal), then we can guess that the bond market participants expect the one-year interest rates one year hence and two years hence to be percent, respectively. On the other hand, if the yield curve was the inverted one, we could conclude that the bond market participants expect the one-year interest rates one year hence and two years hence to bepercent, respectivelyNote:
1. Use the approximate formula.
2. Assume risk neutrality.percent andpercent and

Let's see if we can figure this one out. Actually, it is pretty easy. There are two one-year discount bonds in the market. One of them is a municipal bond issued by a city government to raise money to invest in a desalination plant. This bond is tax-free. The other is a Treasury bond issued by the U.S. Treasury Department to finance the government's spending on various programs. This bond is NOT tax-free. You have to pay a tax on the interest you earn from this bond. So, for example, if you earn $100 from this bond in interest and the tax rate is 20%, then you will have to pay 0.20 x $100 = $20 to the government and will get to pocket only $80. Obviously, you care about the after-tax interest income. Both bonds are risk-free.
Suppose the interest rate on the tax-free municipal bond is 7.5% and the average tax rate is 25%.
Then, arbitrage will ensure that the interest rate on the Treasury bond equals
percent.
Note: In the real world the tax rate will depend on your household income. In the U.S., we have a progressive tax system. This means, the higher your household income, the higher will be your tax rate. So for the sake of this question, we assume that every bond buyer faces a tax rate of 25%.

A one-year U.S. Treasury discount bond has a face value of $52,500.00 and is selling for $50,000.00 today. A corporation bond haa face value of $45,000.00. The corporation bond is quite risky and carries a risk premium of 20% over the Treasury bond. So, the price of the corporation bond in themarket should beî»dollars.1»11On a particular day, a corporation issues a one-year bond, a two-year bond, and a three-year bond. The interest rate on the one-year bond is 2%. Investors in the bond market expect the one year interest rates after one year and after two-years to be 4% and 9% respectively. Because of arbitrage,the interest rate on the two-year bond will equalthree-year bond will beNote:1. Use the approximate formulas.
2. Assume risk neutrality.

Ignore all those nasty things that happened in Question 2 and go back to Question 1.

This time assume that because of some good economic news (a war ends, foreign countries buy more domestic goods, etc.), people become optimistic about the future state of the economy and start spending more. The increase in demand for goods and services causes companies to hire more workers and increase the prices of the goods and services they sell. As a result, the nominal wage increases to W = 800 and the price level goes up to P = 400.Because of these developments, cyclical rate of unemployment now equalsunits. Therefore, the overall rate ofpercent and the real GDP equalspercent and there areunemployment ispersons unemployed(naturally and cyclically).

Suppose that a special bank account is paying an annual interest of R = 10 percent on deposits. You open an account in this bank on January 1,2019 and deposit $10,000 in it. You leave the money in the account for two years until January 1,2021. After one year, on January 1,2020, you deposit another $10,000 in the same account and leave it there for one year until January 1,2021. On January 1,2021 you will have a total of dollars on your account at this bank.

|qjg9 1»Suppose that a one-year Treasury bond has a face value of $110,000.00 and is currently selling in the bond market for $100,000.00. This bond is safe, because the U.S. Treasury never defaults on its promises. For the sake of this question (and to make life easier for all of us), assume that the face value and the price of this bond will remain the same throughout the story.
The Treasury issues another one-year bond with a face value of $174,900.00 and a starting price of $170,000. However, nobody buys this bond. People believe it is too expensive. (Why you think they believe this is expensive?) Consequently, the price of this bond in the bond market drops to
dollars.

A one-year discount bond promises to pay 1,568 dollars next year. Brad requires a 12% rate of return from this bond. In other words, if the rate of return from this bond is less than 12%, he will not buy it. Another way of saying the same thing is that, Brad is not willing to pay a penny more than
dollars for this bond.There is another bond that also promises to pay 1,568 dollars next year. However, this bond has been issued by a corporation that is somewhat in financial trouble. So the bond is riskier than the previous one. So Brad requires an interest rate of 25% from this bond. In other words, he is willing to pay on;y
dollars for this bond.>>A one-year discount bond promises to pay 88,000 dollars next year. Call this Bond A. Brad requires a 10% rate of return from this bond. In other words, if the rate of return from this bond is less than 10%, he will not buy it. Another way of saying the same thing is that, Brad is not willing to pay a penny moredollars for this bond.There is another bond, Bond B that has been issued by a different corporation. However, this bond is riskier than Bond A. So Brad requires an interest rate of 25% from this bond. In other words, for Brad to be willing to pay the same price for Bond Bas he is willing to pay for Bond A, Bond B has to promise
to pay next year.

You may find this question shocking. But it is really easy. If you spell out the ratios, you can find the answer quickly.

Fraction of total population that are able to do civilian work = 90 percent.
Fraction of those who are able to do civilian work that are also willing to do civilian work = 80 percent. Overall unemployment rate = 5 percent.
Average labor productivity = 1,000 unitsSo, GDP per capita =1»A quick and easy bond question to warm up. A one-year discount bond promises to pay $96,750 dollars next year. The price of this bond today in the bond market is $90,000. So, the interest rate onthis bond isThere is another discount bond in the market whose face value is the same as the previous one. This bond is riskier than the previous one and, thus, investors are willing to pay only 80,625 dollars for it.So, the interest rate on this second bond is

We have not covered this particular case in the class, or the text. But I am sure you can do it. Just use the arbitrage argument to solve it. Compare two investment strategies: (1) Should I buy a three-year bond today; or (2) should I buy a one-year bond today and a two-year bond next year?

The interest rate on a one-year bond today is 2% and people expect the interest rate on two-year bonds next year to be 5%. In that case, because of arbitrage, the interest rate on a three-year bondtoday will beNote:
1. Use the approximate formula.
2. Assume risk neutrality.

Question 1 continued.
People become pessimistic about the state of the economy and become cautious about their spending. The reduction in the demand for goods and services causes companies to lay off workers and reduce the prices of the goods and services they sell. As a result, the nominal wage goes down by 20% and the price level goes down by 60%.Because of these developments, cyclical rate of unemployment now equalsunits. Therefore, the overall rate ofpercent and the real GDP equalspercent and there areunemployment ispersons unemployed(naturally and cyclically).

Let's do a little bit of quick and easy review first before moving to better and bigger things. You are going to say, "Oh no, not again! Sick and tired of this graph"! Yes, take a look at the graph named Labor Market Graph. Suppose that nominal wages and prices are rigid in the short run, but flexible in the long run. Also, consistent with the real world observation, we assume that wages are more rigid than prices. Normally, 4% of labor force is naturally unemployed. Currently, the nominal wage is W = 600 and the general price level is P = 200. Economists have estimated the Okun's alpha to be 2.00 and the potential GDP to be Yp = 500,000.Currently, cyclical rate of unemployment equalsunits. Therefore, the overall rate of unemployment ispersons unemployed (naturally and cyclically).