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.
1. Yt= 8800-25Rt-25Rt-t
- 25Rt-2 - 25Rt-3 - 20Rt-4 - 20Rt-5
- 20Rt-6 - 15Rt-7 - 15Rt-8 - 10Rt-9
2. Yt= 8400 - 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 interest rate and that for the last 10 quarters, the interest rate has been 4 percent. (a) verify that initially real GDP equals 8000 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. (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 figure? (e) given your answers in 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.
To find the value of GDP, insert the interest rate for Rt in each equation:
1. Yt= 8800-25*4-25*4
- 25*4 - 25*4 - 20*4 - 20*4
- 20*4- 15*4 - 15*4 - 10*4 = 8000
2. Yt= 8400 -5*4 - 5*4
- 5*4- 5*4 - 5*4 - 10*4
- 15*4- 15*4- 15*4 - 20*4= 8000
For a ...
Effects of interest rate adjustments over time due to monetary policy effectiveness lag and the interest-rate multiplier