You are given the following two IS curves that show how real GDP (Yt) in the current time period t depends on the current interest rate and interest rates in previous periods, where rt is the interest rate in time period t. Furthermore each time period corresponds to a quarter or three months.
I. Yt = 8,800 - 25rt - 25rt-1
- 25rt-2 - 25rt-3 - 20rt-4 - 20rt-5
- 20rt-6 - 15rt-7 - 15rt-8 - 10rt-9
II. Yt = 8,400 - 5rt - 5rt-1
- 5rt-2 - 5rt-3 - 5rt-4 - 10rt-5
- 15rt-6 - 15rt-7 - 15rt-8 - 20rt-9
Suppose that the Fed can set the interest rate and that for the last 10 quarters, the interest rate has been 4 percent.
(a) Verify that initially real GDP equals 8,000 for both IS curves.
(b) Suppose that the Fed lowers the interest rate to 3 percent and keeps it there for the next 10 quarters. Calculate real GDP for the next 10 quarters for each IS curve.
(c) For each IS curve, what is the total increase in real GDP?
(d) For each IS curve, how many quarters does it take for the increase in real GDP to equal one-half of the total increase?
(e) Using Figure 14-2, explain which one of the IS curves resembles the economy’s response to a change in the interest rate prior to 1991 and which one resembles its response since 1991. Explain how your answer is related to the interest-rate parameters in each IS equation.
(f) Given your answers to parts b–d, explain how the changes in the monetary policy effectiveness lag and the interest-rate multiplier affects how much and how long monetary policymakers must change interest rates in response to any given demand shock.