CH14, Problem 1 – 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

(a) Verify that initially real GDP equals 8,000 for both IS curves

(b) Suppose that the Fed lowers the interest rate to 3% 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 incease in real GDP to equal one-half of the total increase?

(e) Using Figure 14-2 above, 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.

 

CH17, Problem 3 – Suppose that instead of persisting as is assumed in problem 2, the decline in the real exchange rate is only temporary in that the real exchange rate is only temporary in that after the initial change in the price level that you found in part c of problem 2, aggregate demand returns to its original level.

(a) Given that monetary policymakers, firms, and workers all recognize that the decline in the real exchange rate is only temporary and given the three policy responses described in part d of problem 2, again calculate what the long-run equilibrium price level is and what the expected price level is under response by monetary policymakers. Again calculate by how much monetary policymakers must change the nominal money supply for the expectations of firms and workers to be realized.

(b) Compare your answers to part d of problem 2 with those of part a of this problem and explain why they are different.

(c) Explain what data or other factors that monetary policymakers, firms, workers might analyze in attempting to determine if the decline in the real exchange rate is temporary or will persist. Finally, suppose that monetary policymakers are better able than firms and workers to determine if a change in the real exchange rate is temporary or will persist and that firms and workers know this. Given your answer to part d of problem 2 and part a of this problem, explain how once monetary policymakers have determined whether the change in the real exchange rate is only temporary or will persist, they could signal their findings to firms and workers

 

 

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