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. Yt = 8,800 - 25rt - 25rt-1

25rt-2 - 25rt-3 - 20rt-4 - 20rt-5

20rt-6 - 15rt-7 - 15rt-8 - 10rt-9

Yt = 8,400 - 5rt - 5rt-1

5rt-2 - 5rt-2 - 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. Verify that initially real GDP equals 8,000 for both IS curves. Answer: Since the interest rate has been 4 percent for the last ten quarters, then IS curve I equals 8,800 - 25(4) - 25(r) - 25(r) - 25(4) - 20(r) - 20(4) - 20(4) - 15(4) - 15(4) - 10(4) = 8,000. IS curve II equals 8,400 - 5(4) - 5(4) - 5(4) - 5(4) - 5(4) - 10(4) - 15(4) - 15(4) - 15(4) - 20(4) = 8,000. Therefore, initially real GDP equals 8,000 for both IS curves.

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. Answer: Real GDP for IS curve I = 8,025

Yt = 8,800 - 25(3) - 25(4) - 25(4) - 25(4) - 20(4) - 20(4) - 20(4) - 15(4) - 15(4) - 10(4) = 8,025 Real GDP for IS curve II = 8,005

Yt = 8,400 - 5(3) - 5(4) - 5(4) - 5(4) - 5(4) - 10(4) - 15(4) - 15(4) - 15(4) - 20(4) = 8,005 Quarters |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 | |IS Curve I |8,025 |8,050 |8,075 |8,100 |8,120 |8,140 |8,160 |8,175 |8,190 |8,200 | |IS Curve II |8,005 |8,010 |8,015 |8,020 |8,025 |8,035 |8,050 |8,065 |8,080 |8,100 | |

Fore each IS curve, what is the total increase in real GDP?

Answer: Total increase for IS curve I = 200 billion; Total increase for IS curve II = 100 billion

For each IS curve, how many quarters does it take for the increase in real GDP to equal one-half of the total increase. Answer: IS curve I = 4 quarters; IS curve II = 7 quarters

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. Answer: IS curve I resembles the economy’s response prior to 1991. The increase in output in response to a decline in the interest rate is larger than IS curve II and one-half of the total increase in output occurs much sooner with IS curve I as compared to IS curve II. IS curve II resembles the economy’s response to a change in the interest rate since 1991. The reasons why IS curve I resembles the economy’s response prior to 1991 is that its interest rate parameters for the first six quarters are large than those of IS curve II. These parameters reflect the fact that since 1991, the monetary policy effectiveness lag has been longer and the interest rate multiplier has been smaller.

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. Answer: During the recession, if the economy is operating on IS curve II, a monetary policy change will have a longer effectiveness lag and a smaller interest-rate multiplier effect because the interest rate coefficients for the first few quarters are smaller and get bigger progressively. Thus, the Fed will need to change the interest rate by a lot and for a long period of time. In contrast, since IS curve I has larger interest rate coefficients in the first few quarters, a change in the monetary policy will have immediate impact and won’t require too large of a change in interest rate.

Chapter 17

(had to answer this first to answer #3)

Suppose that the equation for the aggregate demand is Y = $9,000 + Mˢ/P, where Mˢ...