The foreign inflation rate

a. The foreign inflation rate is 7% (per year) and the home inflation rate is 4%.
According to relative PPP, what is the approximate expected rate of depreciation
(per year) of the home currency?
________________________ %
b. Bulgaria pegs its currency, the lev, to the euro and has capital mobility. They
would like to depreciate the lev. Briefly explain why this is impossible (the
trilemma).

c. Suppose C=72, I=21, G=18, TB=–10, NFIA=+7, and NUT=–4. What is GDP?
d. After a (temporary) fiscal expansion, will a floating exchange appreciate or
depreciate?
e. As of now (2020) how many countries are in the Eurozone? ________
And which country is currently in the ERM (Exchange Rate Mechanism)?

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2. PPP and an Exchange Rate Forecast [10 points]
   Assume: The current dollar-euro exchange rate E is $1.32 per euro. A U.S. basket
   that costs $120 would cost €100 in the Eurozone. For the next year, U.S. inflation is
   expected to be 6% and Eurozone inflation is expected to be 1%.
   a. What is expected U.S. minus Eurozone inflation (pUS – pEUR) in the next year? [1]
   b. What is the current U.S. real exchange rate (q) with the Eurozone? (price of
   Eurozone basket relative to U.S. basket) [1]
   c. Based on PPP, by how much (in % terms) is the dollar undervalued versus the
   euro (i.e., by what percentage is q bigger than 1)? [2]
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   d. Assume that 20% (or 1/5) of the deviation from PPP (i.e., 20% of the difference
   between q and 1) is eliminated each year through gradual adjustment (arbitrage). If
   so, what would be the expected level of q one year from now? [2]
   e. Based on the last answer, how much (in %) will the dollar be undervalued versus
   the euro next year, assuming nothing else happens? And what is the expected rate of
   change in q (i.e., what is Dq/q) from this year to next year? [2]
   f. Given the expected rate of change in q (in part e), and the expected inflation
   differential (in part a), what is the expected rate of nominal depreciation DE/E for
   the dollar (versus the euro) for the coming year? [2]
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3. Consumption Smoothing [10 points]
   Consider the case of a home country where under normal conditions the level of
   GDP is Q=1000 and consumption C=1000 and I=G=0. Initially, these conditions are
   expected to last forever.
   The world interest rate is r*=0.05=5%. Assume it is now time 0, and that external
   wealth at the end of all previous period was zero.
   a. At time 0, under this scenario [1]:
   What is the present value of output? PV(Q) = _
   What is the present value of consumption? PV(C) = _
   b. Now suppose conditions have changed, and the country has learned of a negative
   output shock at time t=0.
   This shock is expected to last one year, and will lead to an output drop of 210
   units. That is, GDP at time 0 falls to Q0 = 790, then returns to 1000.
   At time 0, under this scenario [1]:
   What is the present value of output? PV(Q) = _
   What is the present value of consumption? PV(C) = _
   Assume forward-looking agents desire smooth consumption over time.
   Compute the new planned levels of consumption at t = 0 and 1 under this
   scenario. [1]
   C0 = _
   C1 = _
   Compute the trade balance, NFIA, current account, and wealth at t = 0 and 1
   under this scenario. [1]
   TB0 = NFIA0 = _ CA0 = __ W0 = __
   TB1 = NFIA1 = _ CA1 = __ W1 = __
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   c. Suppose period 0 ends as above. Now it is time 1, and suppose conditions have
   changed again, and the country learns of an identical negative output shock at
   time t=1. This shock is expected to last one year, and will lead to another output
   drop of 210 units. That is, GDP at time 1 falls to Q1 = 790, instead of 1000.
   Compute the new planned levels of consumption at t = 0, 1, 2 under this scenario
   building on what has already happened in t=0. [1]
   C0 = _
   C1 = _
   C2 = _
   Compute the trade balance, NFIA, current account, and wealth at t = 0, 1, 2 under
   this scenario building on what has already happened in t=0. [1]
   TB0 = NFIA0 = _ CA0 = __ W0 = __
   TB1 = NFIA1 = _ CA1 = __ W1 = __
   TB2 = NFIA2 = _ CA2 = __ W2 = __
   d. Now return to that initial situation at t=0. Now suppose agents had learned at
   time t=0 that output was going to be at the level of 790 in both years 1 and 2,
   instead of 1000.
   At time 0, under this scenario:
   What is the present value of output? [1] PV(Q) = _
   What is the present value of consumption? [1] PV(C) = _
   How would planned levels of consumption differ here from the previous case
   where agents only learned in each year about the output drop in that year? [2]
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4. Imperian Wealth Effects [10 points]
   Assume that the country of Imperia (whose currency is the Imperian dollar
   or I-dollar) has external assets of $20,000 billion, 50% of which are
   denominated in euros (€), the rest in I-dollars(I$). It also has external
   liabilities of $30,000 billion, 20% of which are denominated in euros (€), and
   the rest in I-dollars (I$).
   Assume the exchange rate of Imperia is currently 1 Imperian dollar = 1 euro.
   a. What is Imperia’s external wealth in Imperian dollars? Is Imperia a net
   creditor or debtor? [2]
   b. What is Imperia’s net position in euro-denominated assets in Imperian
   dollars? [2]
   c. Suppose the Imperian dollar depreciates to 1.2 Imperian dollars per euro.
   What is the change in Imperian external wealth (in Imperian dollars)? [2]
   d. Compared to a scenario with no net FX exposure, is this Imperian
   depreciation likely to be more or less expansionary? Briefly explain. [4]
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5. Perfidious Albion Speculators [10 points]
   The home country of Albion is pegging its pound to the euro. Interest rates in Albion
   (i) and euro (i) are currently both at i=i=4%, the peg is credible, and output is 100
   in each country. But speculators may decide to attack the Albion pound.
   The ECB, which controls the euro, now decides to change its interest rate i* for some
   reason. It will pick a rate of 4, 5, 6, 7, 8, 9, or 10%. The change is unanticipated.
   If the Albion home interest rate i rises, all else equal, the effect is to lower
   employment and output in the short run. Suppose Albion output falls respectively
   with each 1% point increase in the home interest rate to 99, 98, 97, 96, 95, and so
   on. (I.e., 1 unit of output is lost for every 1% point increase above 4%.)
   Assume that politically, as everyone knows, the Albion government won’t sacrifice
   its economy to the peg once output falls to a level of 96 (or lower): at that point
   everyone believes the Albion government will allow the exchange rate to follow a
   2% depreciation for one year, and then remain fixed forever at the new rate.
   a. If speculators think the peg is credible, there is no currency premium and
   i=i*. But if they think the peg is going to break as above, and is not credible, what
   size of currency premium (in % per year) will they impose on the pound? [2]
   %
   b. Fill in this table, one row at a time; hint: some entries are provided: [5]
   ECB interest rate
   choice
   4% 5% 6% 7% 8% 9% 10%
   In the case where
   speculators think the
   peg is credible
   Albion
   interest rate 4% 5% 6% 7%
   Albion output 100 99
   In the case where
   speculators think the
   peg is not credible
   and the currency
   premium is present
   Albion
   interest rate 6% 7%
   Albion output
   In the last 3 parts of the question refer to the columns in the table in your answers
   c. At what ECB rates are speculators certain not to attack? [1] ____________
   d. At what ECB rates are they certain to attack? [1] ______________________
   e. At what ECB rates are there two equilibria? [1] _____________________
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6. Ins and Outs of the Eurozone [10 points]
   Use the FIX/OCA diagram to discuss the following.
   a. Suppose Denmark and Sweden have similar levels of symmetry and
   integration with the Eurozone. Draw their positions on two separate
   FIX/OCA diagrams below. In this setup, how could we explain why
   Denmark has a peg to the euro but Sweden has decided to float? [5]
   Answer part a using the chart below. Label axes and points carefully.
   Include OCA and FIX lines. In your explanation refer to other relevant
   economic and political considerations.
   Denmark Sweden
   Explanation:
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   b. Suppose Greece has less symmetry and integration with the Eurozone
   than UK. Draw their positions on two separate FIX/OCA diagrams
   below. In this setup, how could we explain why Greece joined the euro
   and yet the UK preferred floating (before Brexit)? [5]
   Answer part b using the chart below. Label axes and points carefully.
   Include OCA and FIX lines. In your explanation refer to other relevant
   economic and political considerations.
   Greece UK
   Explanation:

Sample Solution

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