Tutorial 1 for 5QQMN937 - Macroeconomics
Questions
Michele Pi↵er⇤
1
Question 1
Consider the following specification of the IS-LM model
Yd =C +I +G
C = C̄ + c · (Y T )
I = I¯ d · (i + f¯)
G = Ḡ, T = T̄
(1)
(2)
(3)
(4)
C̄ = 5, c = 0.5, T̄ = 3, I¯ = 3,
d = 0.4, f¯ = 1, Ḡ = 3
(5)
(6)
with parameter values
Use an excel file/calculator and a graph to answer the following questions:
a) compute the value of the intercepts and the slope of the IS curve in the space
(i, Y );
b) suppose the central bank wants the economy to reach an equilibrium level of
output equal to Y ⇤ = 15.80. What is the level of the nominal interest rate ī
consistent with this target? Show it on a graph. Then, compute the value of
each component of aggregate demand in equilibrium;
⇤
King’s Business School, King’s College London, UK. Email: michele.pi↵er@kcl.ac.uk, personal
web page: https://sites.google.com/site/michelepi↵ereconomics/.
1
c) suppose the government is concerned with the level of public debt and decides
to lower Ḡ by 1, while leaving T̄ unchanged in order to generate a government
budget surplus of 1. Study how the IS curve moves in response to the new
fiscal policy. Compute the new level of equilibrium output and discuss how
each component of aggregate demand changes;
d) suppose the central bank decides to use monetary policy to avoid the decrease
in output triggered by the fiscal contraction. Find the new level of interest
rate that ensures that output remains unchanged. Show the new equilibrium
graphically and discuss how each component of aggregate demand changes;
e) comment the following interpretation of the dynamics associated with point d):
“In response to an expected decrease in inflation triggered by the fiscal policy
contraction, the central bank lowers the interest rate”.
2
Question 2
Consider the IS-LM model in closed economy studied during the lectures. Abandon
the assumption of lump-sum taxes T = T̄ and assume T = T̄ + tY : taxes now
increase in the level of output, a feature consistent with taxation in the real world.
The full model is given by
Yd =C +I +G
C = C̄ + c · (Y T )
I = I¯ d · (i + f¯)
G = Ḡ, T = T̄ + tY
(7)
(8)
(9)
(10)
with 0 < c < 1, 0 < t < 1.
a) Derive the IS curve and compare it to the case of lump-sum taxes T = T̄ ;
b) derive the equilibrium of the model, given the interest rate ī set by the central
bank;
c) suppose the government increases public spending by Ḡ units and leaves
(T̄ , t) unchanged. By how much does the equilibrium level of output change?
Compute the fiscal multiplier. Compute by how much total taxes and government budget surplus change. Compare your results to the case of lump-sum
taxes T = T̄ .
2
3
Question 3
Consider the IS-LM model from the lecture notes:
a) study what happens if the cost of borrowing increases for exogenous reasons
due to, say, a financial crisis, as modelled by an increase in f¯;
b) can the central bank do anything in response to the increase in f¯?
3
Key Terms
monetary expansion, 118
monetary contraction, 118
monetary tightening, 118
monetary-fiscal policy mix, 119
confidence band, 125
IS curve, 113
LM curve, 115
fiscal contraction, 116
fiscal consolidation, 116
fiscal expansion, 116
Questions and Problems
Copyright © 2013. Pearson Education, Limited. All rights reserved.
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1. Using the information in this chapter, label each of the following
statements true, false, or uncertain. Explain briefly.
a. The main determinants of investment are the level of sales
and the interest rate.
b. If all the exogenous variables in the IS relation are constant, then a higher level of output can be achieved only
by lowering the interest rate.
c. The IS curve is downward sloping because goods market
equilibrium implies that an increase in taxes leads to a
lower level of output.
d. If government spending and taxes increase by the same
amount, the IS curve does not shift.
e. The LM curve is horizontal at the central bank’s policy
choice of the interest rate.
f. The real money supply is constant along the LM curve.
g. If the nominal money supply is $400 billion and the price
level rises from an index value of 100 to an index value of
103; the real money supply rises.
h. If the nominal money supply rises from $400 billion to
$420 billion and the price level rises from an index value
of 100 to 102, the real money supply rises.
i. An increase in government spending leads to a decrease in
investment in the IS-LM model.
2. Consider first the goods market model with constant investment
that we saw in Chapter 3. Consumption is given by
C = c0 + c11Y - T2
and I, G, and T are given.
a. Solve for equilibrium output. What is the value of the multiplier for a change in autonomous spending?
Now let investment depend on both sales and the interest rate:
I = b0 + b1Y - b2i
b. Solve for equilibrium output using the methods learned
in Chapter 3. At a given interest rate, why is the effect of a
change in autonomous spending bigger than what it was
in part (a)? Why? (Assume c1 + b1 6 1.)
c. Suppose the central bank chooses an interest rate of iQ.
Solve for equilibrium output at that interest rate.
d. Draw the equilibrium of this economy using an IS-LM
diagram.
Chapter 5
3. The response of the economy to fiscal policy
a. Use an IS-LM diagram, show the effects on output of a decrease in government spending. Can you tell what happens
to investment? Why?
Now consider the following IS-LM model:
C
I
Z
i
=
=
=
=
c0 + c11Y - T2
b0 + b1Y - b2i
C + I + G
Qi
b. Solve for equilibrium output when the interest rate is Qi .
Assume c1 + b1 6 1. (Hint: You may want to rework
through Problem 2 if you are having trouble with this step.)
c. Solve for equilibrium level of investment.
d. Let’s go behind the scene in the money market. Use the
equilibrium in the money market M/P = d1Y - d2i to
solve for the equilibrium level of the real money supply
when i = Qi . How does the real money supply vary with
government spending?
4. Consider the money market to better understand the horizontal
LM curve in this chapter.
M
The money market relation (equation 5.3) is
= Y L1i2
P
a. What is on the left-hand side of equation (5.3)?
b. What is on the right-hand side of equation (5.3)?
c. Go back to Figure 4-3 in the previous chapter. How is the
function L(i) represented in that figure?
d. You need to modify Figure 4-3 to represent equation (5.3)
in two ways. How does the horizontal axis have to be relabeled? What is the variable that now shifts the money
demand function? Draw a modified Figure 4-3 with the
appropriate labels.
e. Use your modified Figure 4-3 to show that (1) as output
rises, to keep the interest rate constant, the central bank
must increase the real money supply; (2) as output falls,
to keep the interest rate constant, the central bank must
decrease the real money supply.
5. Consider the following numerical example of the IS-LM model:
C = 100 + 0.3YD
I = 150 + 0.2Y - 1000i
T = 100
G = 200
i = .01
Goods and Financial Markets; The IS-LM Model
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:07:43.
127
(M/P)s = 1200
(M/P)d = 2Y - 4000i
a. Find the equation for aggregate demand (Y).
b. Derive the IS relation.
c. Derive the LM relation if the central bank sets an interest
rate of 1%.
d. Solve for the equilibrium values of output, interest rate, C
and I.
e. Expansionary monetary policy. Suppose that the central
bank increases money supply to 1500. What is the impact of
this expansionary monetary policy on the IS and LM curves?
Find the new equilibrium values of output, interest rate, C
and I.
f. Expansionary fiscal policy. Suppose that the government
increases its spending G to 300. What is the impact of
this expansionary fiscal policy on the IS and LM curves?
Find the new equilibrium values of output, interest rate, C
and I.
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6. Investment and the interest rate
The chapter argues that investment depends negatively on the
interest rate because an increase in the cost of borrowing discourages investment. However, firms often finance their investment
projects using their own funds.
If a firm is considering using its own funds (rather than
borrowing) to finance investment projects, will higher interest
rates discourage the firm from undertaking these projects?
Explain. (Hint: Think of yourself as the owner of a firm that
has earned profits and imagine that you are going to use the
profits either to finance new investment projects or to buy
bonds. Will your decision to invest in new projects in your
firm be affected by the interest rate?)
7. The Fiscal-Monetary policy mix in the aftermath of the global
financial crisis
The global financial crisis of 2008 left many nations with slow
GDP growth rates and high levels of public debt. While most nations
followed a unanimous monetary policy, some nations simply lowered income taxes while others massively expanded fiscal spending.
a. Compare and contrast the expected impact of each of these
two policy mixes on output.
b. Why do you think nations followed different policy mixes
in 2008?
c. Were these policy mixes successful in combatting the global
meltdown?
8. What policy mix of monetary and fiscal policy is needed to meet
the objectives given here?
a. Increase Y while keeping Qi constant. Would investment (I)
change?
b. Decrease a fiscal deficit while keeping Y constant. Why
must Qi also change?
128
The Short Run
9. The (less paradoxical) paradox of saving
A chapter problem at the end of Chapter 3 considered the effect
of a drop in consumer confidence on private saving and investment,
when investment depended on output but not on the interest rate.
Here, we consider the same experiment in the context of the IS-LM
framework, in which investment depends on the interest rate and output but the central bank moves interest rates to keep output constant.
a. Suppose households attempt to save more, so that consumer confidence falls. In an IS-LM diagram where the central
bank moves interest rates to keep output constant, show the
effect of the fall in consumer confidence on the equilibrium
in the economy.
b. How will the fall in consumer confidence affect consumption, investment, and private saving? Will the attempt to
save more necessarily lead to more saving? Will this attempt
necessarily lead to less saving?
EXPLORE FURTHER
10. The Clinton-Greenspan policy mix
As described in this chapter, during the Clinton administration
the policy mix changed toward more contractionary fiscal policy
and more expansionary monetary policy. This question explores the
implications of this change in the policy mix, both in theory and fact.
a. What must the Federal Reserve do to ensure that if G falls and
T rises so that combination of policies has no effect on output.
Show the effects of these policies in an IS-LM diagram. What
happens to the interest rate? What happens to investment?
b. Go to the Web site of the Economic Report of the President
(www.whitehouse.gov/administration/eop/cea/economicreport-of-the-President) Look at Table B-79 in the statistical appendix. What happened to federal receipts (tax
revenues), federal outlays, and the budget deficit as a percentage of GDP over the period 1992 to 2000? (Note that
federal outlays include transfer payments, which would be
excluded from the variable G, as we define it in our IS-LM
model. Ignore the difference.)
c. The Federal Reserve Board of Governors posts the recent history of the federal funds rate at http://www.
federalreserve.gov/releases/h15/data.htm. You will have
to choose to look at the rate on a daily, weekly, monthly, or
annual interval. Look at the years between 1992 and 2000.
When did monetary policy become more expansionary?
d. Go to Table B-2 of the Economic Report of the President and
collect data on real GDP and real gross domestic investment for the period 1992 to 2000. Calculate investment
as a percentage of GDP for each year. What happened to
investment over the period?
e. Finally, go to Table B-31 and retrieve data on real GDP per
capita (in chained 2005 dollars) for the period. Calculate
the growth rate for each year. What was the average annual growth rate over the period 1992 to 2000? In Chapter
10 you will learn that the average annual growth rate
of U.S. real GDP per capita was 2.6% between 1950 and
2004. How did growth between 1992 and 2000 compare
to the Post World War II average?
The Core
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:07:43.
11. Consumption, investment, and GDP in China
Along with other emerging market economies, China has been
considered as the main driver of global growth especially during the
global financial crisis. Since 1990, the Chinese economy has been
able to sustain the highest levels of GDP growth, rendering it one
of the largest economies in the world, second to USA. But why has
the Chinese economy started to show slower GDP growth after the
global financial crisis? To answer this question, you need to examine
(1) the changes in the components of GDP over this period and (2)
the movements of investment and consumption in China during
the last two or three decades and its relative slowdown since the
global financial crisis. Go to the Web site of the Bureau of Economic
Analysis (www.stats.gov.cn). Find the annual National Accounts
Tables and examine the Composition of Gross Domestic Product,
which shows the percentage contribution of the components of GDP
to the overall growth.
a. Track the change in GDP components since 1990. Which
component changed most? How can these changes
explain the pattern of changes in the Chinese economy?
How has this pattern led to higher GDP growth from 1990
till 2010?
b. Why has this trend been reversed since the global financial
crisis? To answer this question, you need to examine the
levels of Chinese exports. Also, examine the exchange rate
of the Yuan in order to study the policies adopted by the
Chinese government to boost its exports. Explain whether
these policies have been successful or unsuccessful.
c. Plot the changes in investment (gross capital formation)
and final consumption expenditure since 1990. Which
variable had the bigger percentage change since 1990?
d. Which region in China contributes most to investment
expenditure, final consumption expenditure, and GDP
growth? How can you explain these changes? Research the
factors that have enabled each of these regions to achieve
these levels of consumption and investment.
Further Reading
■ A description of the U.S. economy, from the period of
in The Great Unraveling, W.W. Norton, 2003. New York.
(Warning: Krugman did not like the Bush administration
or its policies!)
Copyright © 2013. Pearson Education, Limited. All rights reserved.
“irrational exuberance” to the 2001 recession and the role
of fiscal and monetary policy, is given by Paul Krugman,
Chapter 5
Goods and Financial Markets; The IS-LM Model
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:07:43.
129
Tutorial 2 for 5QQMN937 - Macroeconomics
Questions
Michele Pi↵er⇤
Question 1
Take China as the domestic economy and the USA as the foreign economy. China
uses the RMB (renminbi), the US uses the $ (US dollar). Suppose the forex market
trades 6 RMB against 1 $. Compute the nominal exchange rate using both the
indirect and the direct definitions. Suppose the market moves to trade at 8 RMB
against 1 $. What happens to the nominal exchange rate? Interpret.
Question 2
Consider China as the domestic economy and the USA as the foreign economy.
Suppose that the RBM appreciates nominally by 5%, that Chinese prices increase
by 2% and that US prices increase by 10%. What happens to the RMB and the $
in real terms, i.e. to the competitiveness of Chinese goods compared to US goods?
What is the rate of nominal appreciation that would make the real exchange rate
constant despite the movement in prices? Answer the question using both the indirect
and the direct definition of the nominal exchange rate.
Question 3
Select the correct words in italics:
⇤
King’s Business School, King’s College London, UK. Email: michele.pi↵er@kcl.ac.uk, personal
web page: https://sites.google.com/site/michelepi↵ereconomics/.
1
Under flexible exchange rates, an economy that registers a positive capital account is increasing/decreasing its net foreign assets. This is the counterpart of
a positive/negative current account, due to exports of goods and services being
higher/lower than imports of goods and services.
Question 4
Select the correct words in italics:
Consider a country that follows a fixed exchange rate regime. Suppose the current
and capital accounts initially balance, i.e. CA = KA. Suddenly, there is an
increase in capital inflows, for example because international investors become very
positive about the growth potential of the country and want to invest in it. This
means that the demand of domestic currency suddenly exceeds/falls short of the
supply of domestic currency. As a consequence, the domestic currency tends to
appreciate/depreciate. Since we are in a fixed exchange rate regime, the central bank
intervenes by buying/selling foreign currency and ultimately preventing the foreign
currency from appreciating/depreciating. The indirect e↵ect of such an operation is
that the domestic money supply increases/decreases.
Question 5
Consider the uncovered interest parity equation,
(1 + i) = (1 + iw )
E
E+e
(1)
Show that it implies the following approximation:
E+e E
E
E E+e
i ⇡ iw +
E+e
i ⇡ iw
(2)
(3)
Interpret. Then use an excel file or a calculator to compute the approximation error
when iw = 0.02, E = 3 an E+e = 2.9. Hint: take logs and apply a first order Taylor
expansion.
2
Questions and Problems
Copyright © 2013. Pearson Education, Limited. All rights reserved.
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1. Using the information in this chapter, label each of the following
statements true, false, or uncertain. Explain briefly.
a. If there are no statistical discrepancies, countries with
current account deficits must receive net capital inflows.
b. Although the export ratio can be larger than one—as it
is in Singapore—the same cannot be true of the ratio of
imports to GDP.
c. The fact that a rich country like Japan has such a small
ratio of imports to GDP is clear evidence of an unfair playing field for U.S. exporters to Japan.
d. Uncovered interest parity implies that interest rates must be
the same across countries.
e. The nominal exchange rate in this chapter is defined as the
domestic currency price of a unit of foreign currency.
f. The nominal exchange rate and the real exchange rate always move in the same direction.
g. The nominal exchange rate and the real exchange rate
usually move in the same direction.
h. If the dollar is expected to appreciate against the yen, uncovered interest parity implies that the U.S. nominal interest rate must be greater than the Japanese nominal interest
rate.
i. Given the definition of the exchange rate adopted in this
chapter, if the dollar is the domestic currency and the euro
the foreign currency, a nominal exchange rate of 0.75
means that 0.75 dollars is worth 0.75 euros.
j. A real appreciation means that domestic goods become less
expensive relative to foreign goods.
2. Consider two fictional economies, one called the domestic country
and the other the foreign country. Given the transactions listed in
(a) through (g), construct the balance of payments for each country. If necessary, include a statistical discrepancy.
a. The domestic country purchased $100 in oil from the
foreign country.
b. Foreign tourists spent $25 on domestic ski slopes.
c. Foreign investors were paid $15 in dividends from their
holdings of domestic equities.
d. Domestic residents gave $25 to foreign charities.
e. Domestic businesses borrowed $65 from foreign banks.
f. Foreign investors purchased $15 of domestic government
bonds.
g. Domestic investors sold $50 of their holdings of foreign
government bonds.
3. Each of the governments of Brazil and Turkey has issued bonds in
Brazilian real (BRL) and Turkish liras (TRY), respectively. Assume
that both are one-year bonds, i.e. paying the face value of the bonds
in one year.
Suppose that the exchange rate (E) is 1 Brazilian Real = 0.79
Turkish Lira.
Chapter 17
The following table shows the face value and price for both bonds:
Face Value
Price
Brazil
BRL 10,000
BRL 9,630
Turkey
TRY 10,000
TRY 9,450
a. Calculate the nominal interest rate for each of the bonds.
b. Given that the condition of interest rate parity persists, calculate the exchange rate one year from now.
c. If you expect the real to depreciate in comparison to the
lira, which bond should you buy?
d. Assume that you are a Brazilian investor. You exchange the
reals for liras and buy the Turkish bond. One year from now
it turns out that the exchange rate (E) is 0.75, i.e. 0.75 liras
buy one real. What is your realized rate of return in reals
compared to the realized rate of return you would have
made had you held the Brazilian bond?
e. Explain whether the differences in the rates of return in the
previous question are or are not consistent with the uncovered interest rate parity condition.
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4. Consider a world with three equal-sized economies (A, B, and C)
and three goods (food, clothes, and cars). Assume that consumers in
all three economies want to spend an equal amount on all three goods.
The following table shows the value of production of each good
in the three economies.
A
Food
B
C
5
10
0
Clothes
5
10
0
Cars
0
5
10
a. What is the GDP in each economy? Assume that the total
value of GDP is consumed and no country borrows from
abroad. How much will consumers in all of the three economies spend on each of the goods?
b. What is the trade balance in each country if none of the 3
countries borrows from abroad? What goods will be traded
in the world? What will be the pattern of trade between the
3 nations?
c. Will there be a zero trade balance between any of the
three countries? Explain your answer.
d. Due to their large intra-trade volume, the EU-28 (the 28
nations of the EU, which may change following the Brexit
results) has a small trade balance deficit. The EU-28 has a
trade deficit with some of its trading partners and a trade
surplus with others, but the trade deficit is much larger specifically with China. Suppose the EU-28 eliminates its overall trade deficit with the world as a whole. Do you expect
the EU-28 to have a zero trade balance with every one of its
Openness in Goods and Financial Markets
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:15:00.
387
partners? Does the especially large trade deficit with China
indicate that China does not allow EU-28 goods to compete
on an equal basis with Chinese goods?
5. 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.”
Copyright © 2013. Pearson Education, Limited. All rights reserved.
EXPLORE FURTHER
6. Retrieve the nominal exchange rates between the euro (EUR) and
the South African rand (ZAR) from the European Central Bank statistics section: “Euro foreign exchange reference rates.” It is quoted
as ZAR per 1 EUR.
a. According to the terminology of the chapter when the exchange rate is quoted as ZAR per EUR which of the two currencies is treated as the domestic currency?
b. Plot the ZAR per EUR curve since 1995. During which
times did the rand appreciate? During which periods did the
rand depreciate?
c. One way of boosting its economy is for the South African
government to make its commodities more attractive. Does
this require an appreciation or depreciation of the rand?
d. What has happened to the rand since the global financial
crisis of 2008? Has it appreciated or depreciated and is this
good or bad for South Africa?
7. The International Monetary Fund provides a number of publications on its Web site (www.imf.org). Extract from the Statistical
Appendix of the World Economic Outlook (WEO) the table titled
“Balances on Current Account,” which lists current account balances around the world. Use the data for the most recent year to
answer parts (a) through (c).
a. What is the sum of the world current account balances?
Does the sum of the current account balances round the
world equal zero as noted in the chapter? What are the
sources of this discrepancy and what would it imply?
b. Compare the regions of the world in terms of borrowing
and lending.
c. Egypt and Tunisia are two nations that have emerged
from popular revolutions in 2010–2011. How do their
current account balances reflect the economic impact of
these uprisings?
d. The WEO usually provides projections for the following two
years. What is the projected outlook in terms of regional
borrowing/lending? How do you explain the projected
changes for fuel and non-fuel export earnings?
8. Saving and Investment throughout the world
Refer once more to the publications of the International
Monetary Fund on its Web site (www.imf.org). Extract from the
Statistical Appendix of the World Economic Outlook (WEO) the
table titled “Summary of Net Lending and Borrowing” which lists
savings and investment (as a percentage of GDP) around the world.
Use the data for the most recent year to answer parts (a) and (b).
a. Does world saving equal investment?
b. How does the UK saving compare to its investment? How
is the UK able to finance its investment? (We explain this
in the next chapter, but you might be able to figure it out
by now.)
c. From the World Bank Database compare GDP and GNP
(also known as GNI or Gross National Income) for China
and Germany for the periods 2006–2010 and 2011–2015.
For each of these countries is GDP higher or lower than
GNP? What is the reason for the differences?
Further Readings
■ If you want to learn more about international trade and
■ If you want to know current exchange rates between nearly
international economics, a very good textbook is by Paul
Krugman, Marc Melitz, and Maurice Obstfeld. Prentice Hall,
International Economics, Theory and Policy, 10th ed. (2014).
388
The Open Economy
any pair of currencies in the world, look at the “currency
converter” on http://www.oanda.com/currency/converter/.
Extensions
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:15:00.
Tutorial 3 for 5QQMN937 - Macroeconomics
Questions and Solutions
Michele Pi↵er⇤
Question 1
The uncovered interest parity states that the equality
(1 + it ) = (1 + iw
t )
Et
e
Et+1
(1)
must hold, with it the domestic nominal interest rate, iw
t the foreign nominal interest
rate, Et the nominal exchange rate (defined as the ratio of units of foreign currency
e
per one unit of domestic currency), and Et+1
the nominal exchange expected at time
t for period t + 1.
a) Suppose iw = 0.02 and Et = 3. Suppose the domestic currency is expected to
(nominally) depreciate by 5%. Compute the e↵ective nominal return that a
domestic resident expects to earn if he invests abroad;
b) suppose instead that the domestic currency does not depreciate by 5% as expected, but it appreciates by 2%. Compute the e↵ective nominal return that
a domestic resident earns if he invests abroad.
⇤
King’s Business School, King’s College London, UK. Email: michele.pi↵er@kcl.ac.uk, personal
web page: https://sites.google.com/site/michelepi↵ereconomics/.
1
Question 2
Select the correct words in italics:
A domestic monetary policy expansion takes the form of an increase/a decrease
in the domestic interest rate. This can lead to an increase/a decrease in the capital account, which is defined as the di↵erence between capital inflows and capital
outflows/capital outflows and capital inflows. In a flexible exchange rate regime,
the change in the capital account can lead to an appreciation/a depreciation of the
domestic currency, which in turn increases/decreases exports, lowering/stimulating
domestic aggregate demand.
Question 3
Select the correct words in italics:
A sudden improvement in the economic prospects of the domestic country can
lead to a capital inflow/capital outflow, which increases/decreases the capital account. The flow of capital puts pressure on the exchange rate, generating a tendency
for the domestic currency to appreciate/depreciate. In a fixed exchange rate regime,
the domestic central bank must buy/sell foreign assets and increase/decrease the
domestic money supply. This leads to an increase/a decrease in the domestic interest rate, which reduces/increases the capital account by increasing/lowering the
incentives to invest in the domestic economy.
Question 4
Use the IS-LM model in closed and open economy to compare how the e↵ects of
a monetary policy contraction di↵er depending on whether the economy is closed,
open with a flexible exchange rate, or open with a fixed exchange rate. For each case
considered, give your answer mathematically, graphically, and with the underlying
economic intuition.
2
fixed exchange rates (or pegs), to the adoption of a common
currency. Under fixed exchange rates, a country maintains
a fixed exchange rate in terms of a foreign currency or a
basket of currencies.
■ Under fixed exchange rates and the interest parity condi-
tion, a country must maintain an interest rate equal to the
foreign interest rate. The central bank loses the use of monetary policy as a policy instrument. Fiscal policy becomes
more powerful than under flexible exchange rates, however,
because fiscal policy triggers monetary accommodation,
and so does not lead to offsetting changes in the domestic
interest rate and exchange rate.
Key Terms
bands, 424
central parity, 424
euro, 424
Mundell-Fleming model, 411
peg, 423
crawling peg, 423
European Monetary System (EMS), 424
Copyright © 2013. Pearson Education, Limited. All rights reserved.
Questions and Problems
QUICK CHECK
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similar Quick Check problems and get instant feedback.
1. Using the information in this chapter, label each of the following
statements true, false, or uncertain. Explain briefly.
a. The interest rate parity condition means that interest rates
are equal across countries.
b. Other things being equal, the interest parity condition implies that the domestic currency will appreciate in response
to an increase in the expected exchange rate.
c. If financial investors expect the dollar to depreciate against
the yen over the coming year, one-year interest rates will be
higher in the United States than in Japan.
d. If the expected exchange rate appreciates, the current
exchange rate immediately appreciates.
e. The central bank influences the value of the exchange rate
by changing the domestic interest rate relative to the foreign interest rate.
f. An increase in domestic interest rates, all other factors
equal, increases exports.
g. A fiscal expansion, all other factors equal, tends to increase
net exports.
h. Fiscal policy has a greater effect on output in an economy
with fixed exchange rates than in an economy with flexible
exchange rates.
i. Under a fixed exchange rate, the central bank must keep the
domestic interest rate equal to the foreign interest rates.
2. 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?
3. In this chapter, we showed 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.
Chapter 19
a. How does the reduction in interest rates in an economy with
flexible exchange rates affect consumption and investment?
b. How does the reduction in interest rates in an economy
with flexible exchange rates affect net exports?
4. 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 1Y2 and the
exchange rate 1E2, 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 1Y2 and the
exchange rate 1E2, when the domestic central bank leaves
the policy interest rate unchanged. Explain in words.
5. 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 1Y 2 and the exchange rate 1E2,
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 1Y 2 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 1Y 2 unchanged. Explain in words. When might such
a policy be necessary?
Output, the Interest Rate, and the Exchange Rate
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:29:06.
427
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6. Fixed exchange rates and foreign macroeconomic policy
Consider a fixed exchange rate system, in which a group of
countries (called follower countries) peg their currencies to the
currency of one country (called the leader country). Because the
currency of the leader country is not fixed against the currencies of
countries outside the fixed exchange rate system, the leader country
can conduct monetary policy as it wishes. For this problem, consider
the domestic country to be a follower country and the foreign
country to be the leader country.
a. How does an increase in interest rates in the leader country
affect the interest rate and output in the follower country?
b. How does the increase in leader country interest rates
change the composition of output in the follower country?
Assume the follower country does not change fiscal policy.
c. Can the follower country use fiscal policy to offset the effects of the leader country’s reduction in interest rates and
leave domestic output unchanged? When might such a fiscal policy be desirable?
d. Fiscal policy involves changing government spending or
changing taxes. Design a fiscal policy mix that leaves consumption and domestic output unchanged when the leader
country increases interest rates. What component of output is changed?
7. The exchange rate as a policy tool
The effectiveness of monetary policy in an open economy is
enhanced when the central bank has the flexibility to change the
exchange rate and the willingness to change interest rates. Suppose
that there is a decrease in consumer confidence in Tunisia given the
lengthy political turmoil after the 2010 uprising. This leads households to increase their savings, for a given level of disposable income.
Assume that UIP stands for the uncovered interest rate parity condition and its associated curve.
a. Using the AS-AD and IS-LM-UIP diagram, show the short
run effects of the decline in consumer confidence on output
and the exchange rate if the Central Bank of Tunisia does
not change interest rates. Explain what happens to output,
the interest rate, and the price level in the short run.
b. Now that foreign investors become scared about this country, they require a premium to invest in Tunisia. What happens if the Central Bank of Tunisia is willing to raise interest rates to restore foreign investors’ confidence?
c. Compare the response of an economy to a temporary fall
in foreign demand for its exports under fixed and flexible
exchange rates.
d. What are the advantages and disadvantages of central
banks adopting a flexible exchange rate?
EXPLORE FURTHER
This question explores how an increase in global demand for
U.K. assets is likely to slow down the depreciation of the British
pound. Here we modify the IS-LM-UIP framework (where UIP
stands for uncovered interest rate parity) to analyze the effects of an
increase in the demand for U.K. assets. Write the uncovered interest
rate parity condition as:
11 + it2 = 11 + it21Et >Ete + 12 - x
Where x represents factors affecting the relative demand for domestic assets. An increase in x means that investors are willing to hold
domestic assets at a lower interest rate (given the foreign interest
rate and the current and expected exchange rates).
a. Solve the UIP condition for the current exchange rate, Et .
b. Substitute the result from part a in the IS curve and construct the UIP diagram. As in the text you may assume that
P and P* are constant and equal to one.
c. The British pound has a higher interest rate in comparison to the euro. According to the UIP condition, explain
whether the expected rate of the pound (Ete + 1) is supposed
to appreciate or depreciate in the future. What are the effects on output and net exports? How is this reflected in the
IS-LM-UIP diagram?
d. Suppose that there are expectations that the expansionary
monetary policy by the Bank of England will result in a permanent future increase in the money supply. If the prices of
goods and services are fully flexible, do you expect the spot
exchange rate to respond immediately?
e. What is the effect of an increase in the demand for domestic assets x? Do you expect that this increase will prevent
the depreciation of the pound?
9. Bond yields and long run currency movements
a. Go the Web site of The Economist (www.economist.com)
and find data on 10-year interest rates. Look in the section
“Markets & Data” and then the subsection “Economic and
Financial Indicators.” Look at the 10-year interest rates for
the United States, Japan, China, Britain, Canada, Mexico,
and the Euro area. For each country (treating the Euro area
as a country), calculate the spreads as that country’s interest rate minus the U.S. interest rate.
b. From the uncovered interest parity condition, the spreads
from part (a) are the annualized expected appreciation
rates of the dollar against other currencies. To calculate
the 10-year expected appreciation, you must compound.
(So, if x is the spread, the 10-year expected appreciation is
[11 + x210 - 1]. Be careful about decimal points.) Is the
dollar expected to depreciate or appreciate by much against
the currency of any of its six major trading partners?
c. Given your answer to part (b), for which country(ies) is
a significant appreciation or depreciation of the dollar
expected over the next decade? Does your answer seem
plausible?
8. Demand for U.K. assets, the pound, and the trade deficit
428
The Open Economy
Extensions
Blanchard, O 2013, Macroeconomics, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central. [5 April 2023].
Created from kcl on 2023-04-05 10:29:06.
Tutorial 4 for 5QQMN937 - Macroeconomics
Questions
Michele Pi↵er⇤
Question 1
Consider the utility function
u(c, l) = log(c) + ✓log(l)
(1)
where the base of the logarithm is e.
a) Use a first order Taylor expansion to approximate by how much utility increases when consumption increases from c = 5 to c = 5.1. Compare the exact
percentage increase in utility with the percentage increase obtained using the
approximation;
b) repeat the analysis when consumption increases from c = 5 to c = 6;
c) show the approximation errors from points a) and b) on a graph.
⇤
King’s Business School, King’s College London, UK. Email: michele.pi↵er@kcl.ac.uk, personal
web page: https://sites.google.com/site/michelepi↵ereconomics/. These notes can be reproduced
freely for educational and research purposes as long as they contain this notice and are retained for
personal use or distributed for free. All errors are mine. Please get in touch if you find typos or
mistakes.
1
Question 2
Consider the utility function
u(c, l) = log(c) + ✓log(l)
(2)
We showed in the lectures that this utility function implies the following marginal
rate of substitution between consumption and leisure:
✓c
l
(3)
Check that this computation is correct by computing the derivative
the utility function using the Implicit Function Theorem:
dc
=
dl
du(c, l)/dl
du(c, l)/dc
dc
dl
implied by
(4)
Question 3
Consider the maximization problem
c1
1
c,l
1
subject to c = wn
n1+
1+
max
1
,
>0
(5)
(6)
with c as consumption and n as hours worked, and c, n
0.
a) Derive the first order condition of the maximization problem and interpret it;
b) solve for the equilibrium level of consumption and labour supply. Can you
derive the solution in closed form?
c) study if labour supply is an increasing or a decreasing function of the real wage.
Answer the question both mathematically and graphically;
d) compute the utility function in the special case of
2
= 1.
Question 4
Consider the following modification of Question 2:
c1
1 n1+
c,l
1
1+
subject to c = wn + ⇡
max
1
with c as consumption and n as hours worked, and c, n
,
>0
(7)
(8)
0.
a) Derive the first order condition of the maximization problem and interpret it;
b) is it possible derive the closed form solution of the maximization problem?
c) asses if labour supply is an increasing or a decreasing function of the real wage.
HINT: use a graph;
3
Tutorial 5 for 5QQMN937 - Macroeconomics
Questions
Margaret Davenport∗
Question 1
Empirical evidence shows that after a 1% drop in interest rates consumer
spending in the UK rises by more than consumer spending in Japan. Use
the 2 period consumption diagram used in lecture to analyse the substitution
and income effects. Show how the difference may be explained if the typical
UK household is a net borrower while the typical Japanese household is a
net saver.
Question 2
Consider the standard consumption-saving model, but with an infinite horizon and uncertainty. Households have rational expectations and there are
perfect capital markets. Consumption in period t is ct , the real interest rate
is r and households save st in each period. They enter the first period with
initial assets s0 . Assume that (1 + r) = 1.
∗
King’s Business School, King’s College London, UK. Email: margaret.davenport@kcl.ac.uk, . Thank you to Alistair Macaulay for allowing the use of these questions
for the course.
1
The utility functional form is given by:
b
(ct c̄)2 ,
2
where b and c̄ are positive and given constants.
u(ct ) =
(a) Derive the consumption Euler equation. Does this household engage
in precautionary saving?
(b) Assume that the distribution of income in any period follows,
(
ylow
with probability 0.5
yt =
yhigh
with probability 0.5
ylow < yhigh and expected income is given y ⇤ = low 2 high .
why can we write the intertemporal budget constraint (IBC) as:
"1
#
X
ct
1+r ⇤
E
= (1 + r)s0 +
y .
t
(1 + r)
r
t=0
P
a
t
hint: recall that 1
t=0 ak = 1 k
y
+y
(c) Consider the initial period. If households choose c0 after learning their
income is equal to either ylow or yhigh , but not thereafter. How much
does the household consume if they received y0 = ylow ? What if y0 =
yhigh ?
Question 3
Now assume a log utility function u(ct ) = ln(ct ).
(a) Use the consumption Euler equation to explain why Hall’s random walk
result for consumption fails.
(b) Can properties of logarithmic utility account for the excess smoothness
of consumption?
(c) Briefly describe what other factors may be able to account for evidence
of excess smoothness in consumption.
2
Question 4
(a) How is it possible that consumption displays both excess smoothness
and excess sensitivity simultaneously?
(b) How could you test if a household’s consumption displays excess sensitivity? How might you explain your finding in the case of a positive
result?
3
Tutorial 6 for 5QQMN937 - Macroeconomics
Questions
Margaret Davenport∗
Question 1
Suppose that governments plan fiscal expenditures through the end of the
current parliamentary term.
(a) Would this invalidate Ricardian Equivalence? Why, or why not?
Now, assume that Ricardian Equivalence holds. In period t, there is an
announcement of fiscal contraction financed by a reduction in government
purchases in period t+1.
(b) How would the announcement of this policy affect aggregate real expenditure in period t, t + 1 and beyond?
(c) How would your responses to sub-question (b) change if the fiscal policy
was to be financed with increase in taxes instead of a reduction in
government purchases?
∗
King’s Business School, King’s College London, UK. Email: margaret.davenport@kcl.ac.uk, . Thank you to Alistair Macaulay for allowing the use of these questions
for the course.
1
Question 2
Consider an economy where households take decisions to maximise:
U =E
"
1
X
t=0
t
✓
act
b 2
c
2 t
◆#
,
subject to the period budget constraint,
ct + st = (1 + r)st
1
+ yt
Tt .
(1)
where initial assets s0 are given and (1 + r) = 1. Assume constant income
over time, yt = y 8t. Taxes are non-distortionary, lump-sum taxes.
The government budget constraint is given:
Bt+1 = (1 + rb )Bt + Gt
Tt
B0 is the initial level of government debt and government spending is assumed
to stay constant Gt = G 8t. The interest rate at which the government can
borrow is rb . Note: The interest rate for the government rb need not be equal
to that for households r.
(a) Assume that Tt = T 8t. Show mathematically how consumption
changes with G and B0 . What is the intuition behind this?
(b) Now assume that rb < r. The government plans a stream of taxation,
such that T0 = 0 and Tt = T ⇤ . T ⇤ is the level of taxation for which the
intertemporal budget constraint is satisfied. Show mathematically how
aggregate demand changes compared with sub-question (a). What is
the intuition?
Question 3
Assume the government can only raise revenue through distortionary taxation ⌧t . The expected welfare losses from taxation are given:
"1
#
X 1 ⌧2
E
.
2 (1 + r)t
t=0
2
The government budget constraint is given:
Bt+1 = (1 + r)Bt + Gt
⌧t .
Gt is government expenditure, r is the interest rate, and Bt is government
debt.
(a) Show that optimal taxes follow a random walk. Explain the intuition.
(b) Consider an increase in Gt during Covid to stimulate the economy.
How should taxes have responded at the beginning of the pandemic?
How does your answer depend on expectations about how long the
pandemic would last.
3
Tutorial 7 for 5QQMN937 - Macroeconomics
Questions
Margaret Davenport∗
Question 1
Tobin’s Q is defined as:
Q=
Market value of firm capital
Replacement cost of capital
(a) How can a firm use this ratio to inform their investment decisions?
Answer intuitively (i.e., you do not need to show any mathematical
result).
A logistics firm owns 20 lorries, which each cost $50,000 each. The public
firm has 7500 outstanding shares, which are valued at $150 each.
(b) What is the value of Tobin’s Q?
(c) Should the firm increase its fleet and purchase more lorries?
∗
King’s Business School, King’s College London, UK. Email: margaret.davenport@kcl.ac.uk, . Thank you to Alistair Macaulay for allowing the use of these questions
for the course.
1
Question 2
Consider a secular, persistent decline in interest rates over recent decades.
(a) If there are no capital installation costs, how would such a decline in r
impact investment? Assume output prices remain constant, the price
of new capital is fixed at 1, there are no credit constraints for firms
in the economy. Derive your answer mathematically, and provide the
economic intuition.
(b) How would your response change if there were capital installation costs:
C(It , Kt ) =
2
✓
It
Kt
◆2
Kt
(c) A sustained period of lower interest rates increased the likelihood of
the economy hitting the zero lower bound, in which case the central
bank would be constrained in stabilising the economy during future
recessions. This would increase uncertainty over the price that firms
would be able to charge in the the future. How would the elevated
uncertainty impact investment?
Question 3
How might macroeconomic policy be used to raise the level of investment?
What determines the effectiveness of the policy option(s) you describe?
2
Tutorial 8 for 5QQMN937 - Macroeconomics
Questions
Margaret Davenport∗
Question 1
Consider the bathtub model of unemployment. The unemployed in period t
is ut . The model consists of the following equation (assume a constant labour
force equal to 1):
ut+1
ut =
f ut + s(1
ut ).
where f is the job finding rate and s is the job separation rate.
(a) Solve for the steady unemployment rate as a function of f and s.
(b) Suppose now that 5% of employed workers lose their jobs each period,
and 20% of unemployed workers find jobs. In period 0, the unemployment rate is 10%. What is the unemployment rate in period 1,
assuming no changes in s or f ? What happens to the unemployment
rate as more time passes?
Now assume that s and f are determined in the following way. The
job finding rate is given by f (e) = e where e takes values in [0,1],
∗
King’s Business School, King’s College London, UK. Email: margaret.davenport@kcl.ac.uk, . Thank you to Alistair Macaulay for allowing the use of the first question
for the course.
1
and e denotes the worker’s effort. This effort is, in turn, given by
e(b) = 0.5 0.05b, where b denotes the level of unemployment benefits.
Assume that b takes values in [0,10]. The job separation rate is given
by s(c) = 0.1 0.02c, where c is the fee that a firm has to pay in order
to terminate a work relationship (also known as a firing cost). Assume
that c takes values in [0,5].
(c) What is the economic intuition behind the determination of the job
finding rate and the job separation rate above?
(d) Write the steady-state unemployment rate as a function of b and c.
Does steady-state unemployment depend positively or negatively on b
and c? Discuss.
Question 2
Consider a two period version of the consumption saving model. Households
maximize lifetime utility
U = u(c0 ) + E [u(c1 )] ,
subject to the period budget constraints,
c 0 + s0 = y 0
c1 = y1 + (1 + r)s0 .
As evident in the above period budget constraints, households are born in
period 0 with no financial assets and can save at a constant rate of return, r.
Households earn an exogenously given income y0 in period 0 and y1 in
period 1. This income is uncertain and characterized by the following process
y0 = ȳ + ✏0 ,
y1 = ⇢y0 + ✏1 ,
where ✏t ⇠ N (0,
2
✏)
for t = 0, 1.
2
(a) First assume a period utility function u(ct ) = ct 2✓ c2t , with ✓ > 0.
Derive the Euler equation and solve for the consumption function c0 .
(b) Solve for the consumption function in terms of period 0 shock y0 and
show mathematically how it depends on ⇢. Provide the intuition for
this result.
c1
(c) Now assume a period utility function that is isoelastic u(ct ) = t1
,
2
with > 0. Explain what effect an increase in ✏ will have on consumption in this case. You need to show the precautionary saving condition
is satisfied and explain the intuition.
1
Question 3
Consider a two period version of the consumption saving model. with a role
for government. There is no uncertainty.
Households maximize lifetime utility
U = u(c0 ) + u(c1 ),
subject to the period budget constraints,
c 0 + s0 = y 0 T 0
c1 = y1 T1 + (1 + r)s0 .
Households have no initial assets, and can borrow and save freely at
interest rate r. Assume that income is constant over the two periods y0 =
y1 = ȳ. In addition, there is a constant level of government expenditure in
each period G.
The government budget constraints are given
B0 = (G0 T0 )
B1 = (1 + rb )B0 + (G1
T1 )
Assume (1 + r) = 1 so that the standard Euler equation that comes out
of this model is
c0 = c1 .
3
(a) If there are large tax cuts in period 0, such that T0 = 0, what level of
taxation in period 1 must households expect if Ricardian equivalence
holds?
You are given the following parameterisation of the model:
ȳ
1
G
1
T0
0
T1
?
(b) Use the above parameters in the model and assume that r = rb . Are
the government expenditures sustainable? In other words, can any
debt generated by tax cuts in this example be repaid?
4