Problem set 6

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Problem set 6
Macroeconomı́a II
2017
Open economy
Exercise 1. (adpated from Blanchard). a. Using the definition of the real exchange rate and some approxi-
mations show that (the notation is standard)
εt − εt−1
εt−1
= Et − Et−1
Et−1
+ πt − π∗t
In words, the percentage real appreciation equals the percentage nominal appreciation plus the difference between
domestic and foreign inflation.
b. If domestic inflation is higher than foreign inflation, and the domestic country has a fixed exchange rate, what
happens to the real exchange rate over time? Assume that the Marshall-Lerner condition holds. What happens to
the trade balance over time? Explain in words.
c. Suppose the real exchange rate is currently at the level required for net exports (or the current account)
to equal zero. In this case, if domestic inflation is higher than foreign inflation, what must happen over time to
maintain a trade balance of zero?
Exercise 2. (Blanchard). [Multipliers, openness, and fiscal policy.] Consider an open economy characterized by
the following equations:
C = c0 + c1 (Y − T )
I = d0 + d1Y
IM = m1Y
X = x1Y ∗
The parameters m1 and x1 are the propensities to import and export. Assume that the real exchange rate is
fixed at a value of 1 and treat foreign income, Y ∗, as fixed. Also assume that taxes are fixed and that government
purchases are exogenous (i.e., decided by the government). We explore the effectiveness of changes in G under
alternative assumptions about the propensity to import.
a. Write the equilibrium condition in the market for domestic goods and solve for Y .
b. Suppose government purchases increase by one unit. What is the effect on output? (Assume that 0 < m1 <
c1 + d1 < 1. Explain why.)
c. How do net exports change when government purchases increase by one unit?
Now consider two economies, one with m1 = 0.5 and the other with m1 = 0.1. Each economy is characterized by
(c1 + d1) = 0.6.
d. Suppose one of the economies is much larger than the other. Which economy do you expect to have the larger
value of m1? Explain.
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e. Calculate your answers to parts (b) and (c) for each economy by substituting the appropriate parameter
values.
f. In which economy will fiscal policy have a larger effect on output? In which economy will fiscal policy have a
larger effect on net exports?
Exercise 3. (Blanchard). [Policy coordination and the world economy.] Consider an open economy in which the
real exchange rate is fixed and equal to one. Consumption, investment, government spending, and taxes are given by
C = 10 + 0.8(Y − T ), I = 10, G = 10, and T = 10. Imports and exports are given by IM = 0.3Y and X = 0.3Y ∗
where Y ∗ denotes foreign output.
a. Solve for equilibrium output in the domestic economy, given Y ∗. What is the multiplier in this economy? If
we were to close the economy—so exports and imports were identically equal to zero—what would the multiplier be?
Why would the multiplier be different in a closed economy?
b. Assume that the foreign economy is characterized by the same equations as the domestic economy (with
asterisks reversed). Use the two sets of equations to solve for the equilibrium output of each country. [Hint: Use the
equations for the foreign economy to solve for Y ∗ as a function of Y and substitute this solution for Y ∗ in part (a).]
What is the multiplier for each country now? Why is it different from the open economy multiplier in part (a)?
c. Assume that the domestic government, G, has a target level of output of 125. Assuming that the foreign
government does not change G∗, what is the increase in G necessary to achieve the target output in the domestic
economy? Solve for net exports and the budget deficit in each country.
d. Suppose each government has a target level of output of 125 and that each government increases government
spending by the same amount. What is the common increase in G and G∗ necessary to achieve the target output in
both countries? Solve for net exports and the budget deficit in each country. e. Why is fiscal coordination, such as
the common increase in G and G∗ in part (d), difficult to achieve in practice?
Exercise 4. (Blanchard). [The exchange rate and the labor market.] Suppose the domestic currency depreciates
(i.e., E falls). Assume that P and P* remain constant.
a. How does the nominal depreciation affect the relative price of domestic goods (i.e., the real exchange rate)?
Given your answer, what effect would a nominal depreciation likely have on (world) demand for domestic goods? on
the domestic unemployment rate?
b. Given the foreign price level, P*, what is the price of foreign goods in terms of domestic currency? How
does a nominal depreciation affect the price of foreign goods in terms of domestic currency? How does a nominal
depreciation affect the domestic consumer price index? (Hint: Remember that domestic consumers buy foreign
goods (imports) as well as domestic goods.)
c. If the nominal wage remains constant, how does a nominal depreciation affect the real wage?
d. Comment on the following statement. “A depreciating currency puts domestic labor on sale.”
Exercise 5. (Blanchard). Consider an open economy with flexible exchange rates. Suppose output is at the
natural level, but there is a trade deficit. The goal of policy is to reduce the trade deficit and leave the level of
output at its natural level. What is the appropriate fiscal and monetary policy mix?
Exercise 6. (Blanchard). In chapter 19 it was shown that a reduction in the interest rate in an economy
operating under flexible exchange rates leads to an increase in output and a depreciation of the domestic currency.
a. How does the reduction in interest rates in an economy with flexible exchange rates affect consumption and
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investment? b. How does the reduction in interest rates in an economy with flexible exchange rates affect net
exports?
Exercise 7. (Blanchard). [Flexible exchange rates and foreign macroeconomic events.] Consider an open
economy with flexible exchange rates. Let UIP stand for the uncovered interest parity condition.
a. In an IS-LM–UIP diagram, show the effect of an increase in foreign output, Y ∗, on domestic output (Y ) and
the exchange rate (E), when the domestic central bank leaves the policy interest rate unchanged. Explain in words.
b. In an IS-LM–UIP diagram, show the effect of an increase in the foreign interest rate, i∗, on domestic output
(Y ) and the exchange rate (E), when the domestic central bank leaves the policy interest rate unchanged. Explain
in words.
Exercise 8. (Blanchard). [Flexible exchange rates and the responses to changes in foreign macroeconomic policy.]
Suppose there is an expansionary fiscal policy in the foreign country that increases Y ∗ and i∗ at the same time.
a. In an IS-LM–UIP diagram, show the effect of the increase in foreign output, Y ∗, and the increase in the
foreign interest rate, i∗, on domestic output (Y ) and the exchange rate (E), when the domestic central bank leaves
the policy interest rate unchanged. Explain in words.
b. In an IS-LM–UIP diagram, show the effect of the increase in foreign output, Y ∗, and the increase in the
foreign interest rate, i∗, on domestic output (Y ) and the exchange rate (E), when the domestic central bank matches
the increase in the foreign interest rate with an equal increase in the domestic interest rate. Explain in words.
c. In an IS-LM–UIP diagram, show the required domestic monetary policy following the increase in foreign
output, Y ∗, and the increase in the foreign interest rate, i∗, if the goal of domestic monetary policy is to leave
domestic output (Y ) unchanged. Explain in words. When might such a policy be necessary?
Exercise 9. (Blanchard). [Policy choices when the real exchange rate is “too high” and the nominal exchange
rate is fixed.] An overvalued real exchange rate is a rate such that domestic goods are too expensive relative to
foreign goods, net exports are too small, and by implication the demand for domestic goods is too low.This leads to
difficult policy choices for the goversnment and central bank. The equations that describe the economy are:
The IS curve:
Y =
(
EP
P ∗
, G, T, i∗ − πe, Y ∗
)
(−,+,−,−,+)
The Phillips curves for the domestic and the foreign economy:
Domestic Phillips curve: π − π = (α/L) (Y − Yn)
Foreign Phillips curve:π∗ − π∗ = (α∗/L∗)(Y ∗ − Y ∗n )
In the text and in this question, we are going to make two critical assumptions. These are explored in parts (a) and
(b). Then we move to the analysis of the policy options when a country is experiencing an overvalued exchange rate.
a. We are going to assume that the foreign economy is always in medium-run equilibrium. What are the
implications of that assumption for foreign output and foreign inflation?
b. We are going to assume that the domestic and foreign economies share the same anchored value for the level
of expected inflation denoted π and π∗. What is the implication of that assumption once both the domestic and
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foreign economies are both in medium-run equilibrium?
c. Draw the IS-LM-UIP diagram for the case where the domestic country has an overvalued nominal exchange
rate. What is the key feature of that diagram? Under fixed exchange rates without a devaluation, how does the
economy return to its medium-run equilibrium?
d. Draw the IS-LM-UIP diagram for the case where the do- mestic country has an overvalued nominal exchange
rate. Show how the economy can return to its to medium-run equilibrium when a devaluation is a policy choice.
e. Recall that the assumption has been made that interest rate parity holds so i = i∗ at all times. Compare
the returns on the domestic bond and the returns on the foreign bond in the period of the devaluation. Will bond
holders continue to believe there is a completely fixed nominal exchange rate? If bond holders believe another
devaluation is possible, what are the consequences for domestic interest rates?
Monetary policy
Exercise 10. (Blanchard). [Implementing a political business cycle.] You are the economic adviser to a newly
elected president. In four years he or she will face another election. Voters want a low unemployment rate and a low
inflation rate. However, you believe that voting decisions are influenced heavily by the values of unemployment
and inflation in the last year before the election, and that the economy’s performance in the first three years of a
president’s administration has little effect on voting behavior.
Assume that inflation last year was 10%, and that the unemployment rate was equal to the natural rate. The
Phillips curve is given by
πt = πt−1 − α(ut − un)
Assume that you can use fiscal and monetary policy to achieve any unemployment rate you want for each of the
next four years. Your task is to help the president achieve low unemployment and low inflation in the last year of
his or her administration.
a. Suppose you want to achieve a low unemployment rate (i.e., an unemployment rate below the natural rate) in
the year before the next election (four years from today). What will happen to inflation in the fourth year?
b. Given the effect on inflation you identified in part (a), what would you advise the president to do in the early
years of the administration to achieve low inflation in the fourth year?
c. Now suppose the Phillips curve is given by
πt = πet − α(ut − un)
In addition, assume that people form inflation expecta-tions, πet , based on consideration of the future (as opposed to
looking only at inflation last year) and are aware that the president has an incentive to carry out the policies you
identified in parts (a) and (b). Are the policies you described in those parts likely to be successful? Why or why not?
Exercise 11. (Blanchard.) New Zealand rewrote the charter of its central bank in the early 1990s to make low
inflation its only goal. Why would New Zealand want to do this?
Exercise 12. (adapted from Blanchard.) [Political expectations, inflation, and unemployment.] Consider a
country with two political parties, Democrats and Republicans. Democrats care more about unemployment than
Republicans, and Republicans care more about inflation than Democrats. When Democrats are in power, they
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choose an inflation rate of πD , and when Republicans are in power, they choose an inflation rate of πR. We assume
that
πD > πR
The Phillips curve is given by
πt = πet − α(ut − un)
An election is about to be held. Assume that expectations about inflation for the coming year (represented by πet )
are formed before the election. (Essentially, this assumption means that wages for the coming year are set before the
election.) Moreover, Democrats and Republicans have an equal chance of winning the election.
a. Solve for expected inflation, in terms of πD and πR.
b. Suppose the Democrats win the election and implement their target inflation rate, πD. Given your solution
for expected inflation in part (a), how will the unemployment rate compare to the natural rate of unemployment?
c. Suppose the Republicans win the election and implement their target inflation rate, πR . Given your solution
for expected inflation in part (a), how will the unemployment rate compare to the natural rate of unemployment?
e. Now suppose that everyone expects the Democrats to win the election, and the Democrats indeed win. If the
Democrats implement their target inflation rate, how will the unemployment rate compare to the natural rate?
Exercise 13. (adapted from Blanchard.) [Unwinding unconventional monetary policy.] It was noted in the
text that the Federal Reserve purchased, in addition to Treasury bills, large amounts of mortgage-backed securities
and long-term government bonds as part of quantitative easing. Figure 23-2 in the book shows that as of the end of
2015, there were about 4.5 trillion dollars of assets in the monetary base. These assets were roughly distributed as
0.2 trillion in Treasury securities with less than one year to maturity; 2.2 trillion in Treasury securities of more than
one year to maturity; and 1.7 trillion in mortgage-backed securities.
a. Why did the Federal Reserve Board buy the mortgage-backed securities?
b. Why did the Federal Reserve Board buy the long-term Treasury bonds?
c. What would you predict as the consequences of the fol- lowing operation by the Federal Reserve Board: selling
0.5 trillion in mortgage-backed securities and buying 0.5 trillion in Treasury securities with less than one year to
maturity?
d. What would you predict as the consequences of the fol- lowing operation by the Federal Reserve Board: selling
0.5 trillion in Treasury securities with maturity longer than one-year and buying 0.5 trillion in Treasury securi- ties
with less than one year to maturity?
Exercise 14. (Mankiw.) A central bank has decided to adopt inflation targeting and is now debating whether
to target 5 percent inflation or zero inflation. The econo- my is described by the following Phillips curve:
u = 5 − 0.5 (π − πe)
where u and π are the unemployment rate and inflation rate measured in percentage points. The social cost of
unemployment and inflation is described by the following loss function:
L = u+ 0.05π2
The central bank would like this loss to be as small as possible.
a. If the central bank commits to targeting 5 percent inflation, what is expected inflation?
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If the central bank follows through, what is the unemployment rate? What is the loss from inflation and
unemployment?
b. If the central bank commits to targeting zero inflation, what is expected inflation? If the central bank follows
through, what is the unemployment rate? What is the loss from inflation and unemployment?
c. Based on your answers to parts (a) and (b), which inflation target would you recommend? Why?
d. Suppose the central bank chooses to target zero inflation, and expected inflation is zero. Suddenly, however,
the central bank surprises people with 5 percent inflation. What is unemployment in this period of unexpected
inflation? What is the loss from inflationand unemployment?
e. What problem does your answer to part (d) illustrate?
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