Q1- Treasury bills have a fixed face calue (say,$ 1,000) and pay interest by selling at discount. For example, if a one-year bill with a $1,000 face value sells today for $950, it will pay $1.000-950=$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 generalized this example. Let P be the price of the bill and r be the interest rate. Develop an algebraic formula expressing r in terms of P. ( Hint: The interest earned is $1,000- 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.
Q2- 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 =1,000 - 100r
Find the equilibrium GDP if the fed makes the rate of interest (a) 2 percent ( r =0.02) , (b) 5 percent, and (c) 10 percent.
Q3 . Answer questions 4 and 8 on page 278. (also practice 5 on the same page and check your answers with those at the end of the book.)
II. 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 (just like during Asian crisis). How much is your prediction for a change in GDP?
Q4 - Consider the following model and again answer related questions.
Y = C + I + G + X - IM
C = 300 + 0.75DI where DI = Y - 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?