- I Question 4 On Page 275 Of The Textbook Treasury Bills Have A Fixed Face Value Say 1000 And Pay Interest By Sell 1 (144.16 KiB) Viewed 34 times
- I Question 4 On Page 275 Of The Textbook Treasury Bills Have A Fixed Face Value Say 1000 And Pay Interest By Sell 2 (104.86 KiB) Viewed 34 times
I.- Question 4 on page 275 of the Textbook. Treasury bills have a fixed face value (say, $1000) and pay interest by selling at a discount. For example, if a one-year bill with a $1000 face value sells today for $950, it will pay $1000-$950-$50 in interest over its life. The interest rate on the bill is, therefore, 50/950 0.0526 or 5.26 percent. a. Suppose the price of the Treasury bill falls to $925. What happens to the interest rate? b. Suppose, instead, that the price rises to $975. What is the interest rate now? c. Now generalize this example. Let P be the price of the bill and r be the interest rate. Develop a formula expressing r in terms of P. (Hint: The interest earned is $1000-P. What is the percentage interest rate? Show that this formula illustrates the point made in the text: Higher bond prices mean lower interest rates. II.- Question 8 on page 276 of the Textbook. Consider an economy in which government purchases, taxes, and net exports are all zero. The consumption function is: C=300+0.75Y And investment spending (I) depends on the rate of interest (r) in the following way: I= 1000-100r Find the equilibrium GDP (or Y) if the Fed sets the rate of interest at (a) 2 percent (r= 0.02), (b) 5 percent and (c) 10 percent. Hint: In this and following problems, first substitute, say, 0.02 for r in the investment function to find amount of I at that level of interest rate. Then the problem is reduced to one of those you had in the second take home problem set.
III.- Now consider the following model and answer related questions. Y=C+I+G+ X - IM C=49+0.9DI I=300-2000r G=800 T = 10 + 1/3(Y) X-IM 60 a. If fed decides to set the interest rate at r = 0.05, how much will be the equilibrium GDP? b. At that rate how much is budget deficit or surplus? c. By how much GDP will change if government cuts tax rate from 1/3 to 0.20 and at the same time the Fed raises the interest rate from 0.05 to 0.06? d. Now suppose net exports drops by 20. In order to offset its contractionary impact on GDP, Fed decides to lower the rate of interest from 0.05 to 0.04. How much is your prediction for a change in GDP? IV. Consider the following model and again answer related questions. Y=C+I+G+X-IM C=300+0.75DI where DIY-T I=600 - 1000r G=300 X-IM = 100 T=0 a. How much is equilibrium level of income or output if Fed decides to set the rate of interest at 10 percent (r=0.10). b. In an effort to cool down the economy, the Fed raises the rate of interest to r = 0.15. By how much will Y change? c. To coordinate the fiscal and monetary policies, assume government decides to balance the budget by raising taxes by 300. At the same time Fed decides to counter the contractionary effect of the tax hike and lowers the rate of interest to r = 0.05. Can you predict the change in Y?