Macroeconomics I (22104-22105)
2023-2024
Problem Set #3: Deadline Tuesday Nov 7th, midnight
-------------------------------------------------------------------------------------------------------------------------
Instructions: Work with your seminar group. Submit ONE answer in PDF in Aula Global (Turnitin) by
the deadline. For math questions, clearly indicate the main steps needed to get your answer. In your
graphs, clearly label the axis, variables, and equilibriums.
-------------------------------------------------------------------------------------------------------------------------------
Exercise #1: Monetary Policy Responses Across the Atlantic
For many years after the Great Recession, the nominal interest rate in the US was close to zero (at the zero
lower bound or ZLB). After a period of increasing rates, it went back down to zero during the Covid-19
pandemic. Since March 2022, however, due to the elevated inflation rate, the Federal Reserve (also known
as the FED, the Central Bank of the US) has increased the interest rate eleven times. In their July 2023
meeting, the policy rate was increased by 25 basis points (0.025 percentage points), bringing the interest
rate to around 5.4% (midpoint of the target range of 5.25% to 5.5%). In their September 2023 meeting
they kept rates unchanged while also indicating that rates could stay higher for longer. See Figure 1.
Figure 1. Federal Reserve Policy Rate (July 2006 – Oct 2023)
The policy rate of the European Central Bank has a similar pattern, with several years at the ZLB followed
by sharp increases over the last year and a half, reaching a level of 4.5% in September 2023. See Figure 2.
Figure 2. ECB Policy Rate (July 2006 – Oct 2023)
Source: European Central Bank. Main refinancing rate.
MACROECONOMICS I – 2023/24
page 1 of 3
As an economic advisor, you are asked to analyze the short-run effects of the latest FED policy on both
sides of the Atlantic. The US variables will be denoted with stars (i.e., 𝑌𝑌∗), as they represent a foreign
economy from the point of view of the Eurozone. Through the question, assume 𝑃𝑃∗ = 𝑃𝑃 = 1.
1) Short-run effects of the FED policy in the U.S. economy.
Consider the U.S. as a closed economy with the following 𝐼𝐼𝐼𝐼 relationship:
𝑌𝑌∗ = 800 − 2500𝑖𝑖∗
where 𝑌𝑌∗ denotes U.S. output in billions of dollars and 𝑖𝑖∗ U.S. nominal interest rate (in decimal points).
Money demand 𝑀𝑀𝐷𝐷∗ in the U.S. is given by:
𝑀𝑀
where 𝑃𝑃∗ denotes US price level.
a) Solve for the equilibrium output and money supply during the zero lower bound period.
b) Consider now an increase in the interest rate to 𝑖𝑖∗ = 0.054. What are the new equilibrium output
and money supply?
c) The Federal Reserve had to sell billions of government bonds to contract the monetary base, and
US government bond prices have decreased.
2) Short-run effects of the FED policy in the Eurozone economy.
Consider the Eurozone as a small open economy with a flexible exchange rate that can be described with
the following 𝐼𝐼𝐼𝐼 relationship:
𝑌𝑌∗ 120
𝑌𝑌 = 100 − 4000𝑖𝑖 + + 4
𝜀𝜀
where 𝑌𝑌 and 𝑖𝑖 denote Eurozone output and ECB nominal interest rate, 𝑌𝑌∗ denotes U.S. output and 𝜀𝜀
the real exchange rate.
Money demand 𝑀𝑀𝐷𝐷 is given by:
𝑀𝑀𝐷𝐷 = 𝑃𝑃(𝑌𝑌 − 50𝑖𝑖)
where 𝑃𝑃 denotes the price level.
During the years of the ZLB on both sides of the Atlantic, the nominal exchange rate was equal to 𝐸𝐸 =
1.2 dollars/euro.
MACROECONOMICS I – 2023/24
page 2 of 3
Please answer the following questions:
a) Solve for the equilibrium output and money supply in the Eurozone during the ZLB period,
considering your answers for the US in the previous exercise. Assume the UIP holds.
b) According to the UIP, what were the exchange rate expectations 𝐸𝐸𝑒𝑒 during the ZLB period?
c) Now compute the new equilibrium (output and real exchange rate) after the interest rate increases
to 𝑖𝑖∗ = 0.054 and 𝑖𝑖 = 0.045. For your answer, assume that the UIP holds and that 𝐸𝐸𝑒𝑒=1.
d) Given the exchange rate expectations and the interest rate differentials, the euro has suffered
a___________ (depreciation/appreciation) of ________ % with respect to the dollar.
e) Show graphically in an IS-LM-UIP diagram the equilibrium of the Eurozone economy at the ZLB
and in recent years. Make sure to label clearly curves, axis, and equilibrium points.
f) Describe in words the developments in the Euro/U.S. dollar exchange rate, output levels, and
nominal interest rates in the Eurozone before and after the increases in the domestic and foreign
interest rates.
g) Suppose the ECB decided to fix the exchange rate euro/dollar at 𝐸𝐸 = 𝐸𝐸𝑒𝑒=1. Also, suppose that
in its December 2023 meeting, the FED raises interest rates an additional 100 basis points to reach
𝑖𝑖∗ = 0.064. According to the UIP, what interest rate should the ECB set? What would the new
equilibrium look like in the eurozone? Draw a diagram to illustrate your answer under this
scenario.
h) What policy would you recommend to the ECB (flexible or fixed exchange rate) and why?
Exercise #2: Quizzes on Expectations
This is an individual activity!
In Aula Global, you will find two multiple-choice quizzes on Expectations.
a. Each quiz contains 10 questions that should be answered in a limited time (10 minutes).
b. You have unlimited trials, and every time you enter a quiz, new random questions will appear.
c. Only the highest score will count, so try it as many times as possible until you get it all perfect.
d. You must complete them by the deadline!
Deadlines:
• Expectations #1: November 12th, midnight
• Expectations #2: November 19th, midnight
MACROECONOMICS I – 2023/24
page 3 of 3
