Examiners’ commentaries 2016
Examiners’ commentaries 2016
EC2065 Macroeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2016).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
General remarks
Learning outcomes
At the end of this course and having completed the Essential reading and activities you should be
able to:
•
define and analyse the determinants of business cycles, long-run economic growth,
unemployment, inflation
•
use and apply a wide range of economic models to analyse contemporary and historical
macroeconomic events, and formulate and propose appropriate macroeconomic policies.
Format of the examination
Section A comprises 8 questions, all of which must be answered (accounting for 40% of the total
marks). Section B comprises 6 questions from which 3 must be answered (accounting for 60% of the
total marks).
Short questions (Section A) have a ‘True/False? Briefly explain your answer’ format. You are
expected not only to provide an answer but also briefly to justify it on the basis of the relevant
theory. Full formal derivation of the relevant model is not expected, and often a graphic or
descriptive (non-analytical) answer is sufficient. On average, only nine minutes should be allocated
to any individual short question.
Long questions (Section B) have an analytical model-based format. These are subdivided into at
least three parts. In this section you are to be as precise as possible in your answers, and often
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EC2065 Macroeconomics
formally to derive the relevant models, possibly in addition to a graphical or descriptive approach.
On average, only 36 minutes should be allocated to any individual long question.
Textbooks
The readings given in the Examiner’s commentaries refer to chapters of the subject guide (2016).
You are encouraged to read the relevant chapters of the following textbooks referred to in the
subject guide:
•
Blanchard, O. and D.R. Johnson, Macroeconomics, Prentice–Hall, (6th edition)
•
Dornbusch, R., S. Fischer and R. Startz, Macroeconomics, McGraw–Hill, (11th edition)
•
Mankiw, N.G. Macroeconomics, Worth, (8th edition).
Key steps to improvement
•
You need to be flexible in your ability to apply macroeconomic ideas and models in new or
unfamiliar contexts. Merely memorising the exposition of a model may not help you answer
a question. Developing your ability to apply macroeconomic ideas takes practice.
•
You need to ensure your answers remain focused and to the point of the question. Spend a
little more time initially thinking about the most relevant arguments before you actually
start writing. A shorter, but well-thought through, answer is superior to a longer answer
that does not address the question.
•
You need to manage your time well in the examination. Try to ensure you allocate your
time in proportion to the marks allocated to the questions.
Examination revision strategy
Many candidates are disappointed to find that their examination performance is poorer than they
expected. This may be due to a number of reasons. The Examiners’ commentaries suggest ways of
addressing common problems and improving your performance. One particular failing is ‘question
spotting’, that is, confining your examination preparation to a few questions and/or topics which
have come up in past papers for the course. This can have serious consequences.
We recognise that candidates may not cover all topics in the syllabus in the same depth, but you
need to be aware that the examiners are free to set questions on any aspect of the syllabus. This
means that you need to study enough of the syllabus to enable you to answer the required number of
examination questions.
The syllabus can be found in the Course information sheet in the section of the VLE dedicated to
each course. You should read the syllabus carefully and ensure that you cover sufficient material in
preparation for the examination. Examiners will vary the topics and questions from year to year and
may well set questions that have not appeared in past papers. Examination papers may legitimately
include questions on any topic in the syllabus. So, although past papers can be helpful during your
revision, you cannot assume that topics or specific questions that have come up in past examinations
will occur again.
If you rely on a question-spotting strategy, it is likely you will find yourself in difficulties
when you sit the examination. We strongly advise you not to adopt this strategy.
2
Examiners’ commentaries 2016
Examiners’ commentaries 2016
EC2065 Macroeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2016).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone A
Candidates should answer ELEVEN of the following FOURTEEN questions: all EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly
advised to divide their time accordingly.
If more questions are answered than requested, only the first answers attempted will be counted.
Section A
Answer all eight questions in this section (5 marks each).
Briefly explain whether each of the following statements is true or false.
Question 1
If consumption does not depend on income then the IS curve is vertical.
Reading for this question
Subject guide, Chapter 2.
Approaching the question
The statement is FALSE.
The IS curve represents the combinations of income and interest rates where the aggregate
demand for output is equal to national income. A change in the interest rate would still affect
the demand for investment (and possibly consumption) even when consumption does not directly
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EC2065 Macroeconomics
depend on income. This implies a different level of aggregate demand for each interest rate,
although in this special case there is no multiplier effect from income back to consumption
demand. The IS curve is still downward-sloping, but steeper than when consumption depends on
income.
Question 2
The Keynesian consumption function features a constant marginal propensity to
consume and an increasing average propensity to consume.
Reading for this question
Subject guide, Chapters 2 and 9.
Approaching the question
The statement is FALSE.
The Keynesian consumption function is C = C0 + cY , where Y is income (or disposable income
more generally), and C0 and c are constants. The marginal propensity to consume is the amount
by which consumption increases for a unit increase in income, that is, the partial derivative
∂C/∂Y . The consumption function is linear in income, so this derivative is simply equal to the
constant c. Therefore, the marginal propensity to consume is constant.
The average propensity to consume is the ratio C/Y of consumption to income. The Keynesian
consumption function implies:
C
C0
=
+c
Y
Y
and because C0 is a constant, the average propensity to consume declines with income. This
demonstrates that the average propensity to consume is not increasing.
Question 3
According to Tobin’s q theory of investment, there should be a positive relationship
between stock market valuations and investment.
Reading for this question
Subject guide, Chapter 10.
Approaching the question
The statement is TRUE.
Suppose stock market valuations of firms reflect present discounted sums of future profits. An
increase in the stock market value of a firm should then be taken as a signal for the firm to invest
more because either future profits are higher, indicating a higher marginal product of capital, or
because discount rates are lower, reflecting lower borrowing costs. It is rational for the firm to
undertake more investment in either case.
Question 4
If households and firms hold an increasing fraction of money as deposits rather than
cash then the money multiplier will be smaller.
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Examiners’ commentaries 2016
Reading for this question
Subject guide, Chapter 11.
Approaching the question
The statement is FALSE.
The broad money supply is M = C + D, where C is cash and D is deposits. The monetary base
is B = C + R, where R denotes reserves. The money multiplier m = M/B is the ratio of the
broad money supply to the monetary base. Let c = C/D and r = R/D denote the cash-deposit
ratio and the reserve-deposit ratio, respectively. The money multiplier can be written in terms of
c and r as follows:
(C/D) + (D/D)
c+1
C +D
=
=
.
m=
C +R
(C/D) + (R/D)
c+r
If households are holding more money M as deposits D then the ratio D/M = D/(C + D)
= 1/(c + 1) must have increased, which means c must have fallen. When r < 1, the money
multiplier m is negatively related to c, so the money multiplier should increase when more money
is held as deposits rather than as cash.
Question 5
The balanced growth path of the Solow model features a constant ratio of the
capital stock to GDP.
Reading for this question
Subject guide, Chapters 5 and 6.
Approaching the question
The statement is TRUE.
The Solow model assumes a constant-returns production function Y = F (K, AL) with
labour-augmenting technology A growing at a constant rate. This production function can be
converted to y = f (k), where k = K/AL and y = Y /AL are capital and output in efficiency units
of labour, and f (k) = F (k, 1). The dynamics of k are described by the equation
∆k = sf (k) − (δ + n + g)k, and there is a steady state for k because f (k) is a concave function.
In this steady state, both k and y = f (k) are constants, so K/Y = (K/AL)/(Y /AL) = k/y is also
constant. Therefore, the Solow model features a balanced growth path where the capital-output
ratio is constant.
Question 6
The presence of a real balance effect means that the IS curve will shift to the left if
the price level falls.
Reading for this question
Subject guide, Chapter 3.
Approaching the question
The statement is FALSE.
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EC2065 Macroeconomics
A real balance effect is a special case of a wealth effect on the demand for consumption, which
works through changes in the real value of the stock of money. The argument is that holdings of
real money balances are part of the economy’s aggregate real wealth because money (strictly
speaking, the monetary base) is not a liability of anyone (money is sometimes described as a
liability of the central bank, but usually this is true only in an accounting sense). Since
consumption should be positively related to wealth, anything that increases wealth should raise
consumption. A decline in the price level increases the real value of existing nominal money
balances, and hence raises real wealth. The resulting increase in consumption demand should
shift the IS curve to the right.
Question 7
Higher nominal interest rates would be expected to reduce the velocity of money
according to most theories of money demand.
Reading for this question
Subject guide, Chapters 2 and 11.
Approaching the question
The statement is FALSE.
The velocity of money is defined as the ratio of nominal spending (or nominal income) to the
nominal money supply, that is, V = P Y /M . Most theories of money demand (for example, the
Baumol–Tobin model) imply that real money demand depends positively on real income Y and
negatively on the nominal interest rate i. The resulting money demand equation is written as
M/P = L(Y, i), where the function L(Y, i) increases with Y and decreases with i. Since
V = Y /(M/P ), the velocity of money implied by the money demand equation is V = Y /L(Y, i).
With L(Y, i) depending negatively on i, velocity V should be increasing in the nominal interest
rate i.
Question 8
If the short-run aggregate supply curve is vertical then money will be neutral.
Reading for this question
Subject guide, Chapters 3 and 4.
Approaching the question
The statement is TRUE.
Money is said to be neutral if a change in the level of the money supply simply leads all nominal
prices to adjust in proportion to the money supply and has no real effects. In the AD/AS
diagram, changing the money supply shifts the aggregate demand curve. If the aggregate supply
curve was vertical in the short run as well as the long run (which requires all prices and wages to
be fully flexible), all the effects of a change in the money supply fall on the price level and none
on real output. Money would be neutral in this case.
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Examiners’ commentaries 2016
Section B
Answer three questions from this section (20 marks each).
Question 9
Consider the Baumol–Tobin model of money demand. Suppose a household receives
real income Y (nominal income = P Y ) at the beginning of a month and plans to
spend all the income during the month at a constant rate. The household has a
bank account paying interest rate i on any money deposited (interest is not
compounded for simplicity). Income is initially paid into the household’s bank
account. Spending requires cash, and each withdrawal of cash from the bank
account has a (real) transaction cost of c. Cash pays no interest. Suppose the
household makes n (equally sized) withdrawals from the bank account during the
month (for simplicity, assume that n does not need to be a whole number).
(a) [7 marks] What is the total transaction cost incurred? What is the average
amount of cash held during the month and how much extra interest could have
been received if this cash had not been withdrawn? Using your answers, find
the number of withdrawals that minimises the sum of transactions costs and
foregone interest. What is the implied level of money demand (on average)
during the month?
(b) [7 marks] By issuing money that pays no interest as opposed to bonds that pay
interest, the government is able to reduce its overall borrowing costs. The
reduction in the government’s interest costs is equal to the nominal interest rate
i multiplied by the real money supply M/P , referred to here as seigniorage
revenue. After taking account of the requirement that the real money supply
must be equal to the demand for money derived in part (a), show that
seigniorage revenue is higher when the nominal interest rate is higher. How
large is the sum of the transactions costs and foregone interest suffered by
households relative to the amount of seigniorage revenue collected by the
government?
(c) [6 marks] Suppose the government’s objective is to maximise an objective
function given by seigniorage revenues minus the transaction costs and foregone
interest suffered by households. After taking account of the requirement that
the real money supply must be equal to the demand for money derived in part
(a), find the required nominal interest rate. Give an economic intuition for your
answer.
Reading for this question
Subject guide, Chapters 4, 11 and 13.
Approaching the question
(a) Each of the n withdrawals costs an amount c, so the total transaction cost (denoted Kc ) is
cn. With n equally-sized withdrawals over the month and with income P Y spent completely
at the end of the month, each withdrawal has size P Y /n. Since cash is spent at a constant
rate and as each new withdrawal is made when holdings of cash reach zero, the average cash
balance M held during the month is P Y /(2n). The amount of foregone interest expressed as
a real cost (and denoted Ki ) is iM/P , and hence Ki = iY /(2n). The sum K of transaction
costs Kc and foregone interest Ki is:
K = cn +
iY
.
2n
The first-order condition below is used to find the number of transactions n that minimises
total costs K:
∂K
iY
= c − 2 = 0.
∂n
2n
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EC2065 Macroeconomics
This equation can be rearranged as follows to solve for the optimal number n:
r
iY
iY
2
n =
⇒
n=
.
2c
2c
Average holdings of real money balances are M/P = Y /(2n), hence real money demand is:
r
r
Y
2c
cY
M
=
=
.
P
2 iY
2i
(b) Let S = iM/P denote seigniorage revenues. Using the expression for real money demand
from part (a), seigniorage revenues are:
r
r
cY
ciY
S=i
=
.
2i
2
This is an increasing function of i, so real seigniorage revenues are larger when the nominal
interest rate is higher. Since S = Ki , this formula also gives the interest foregone by
households. Next, using the expression for the optimal value of n from part (a), total
transaction costs Kc are:
r
r
iY
ciY
Kc = c
=
.
2c
2
Therefore, the minimised sum of all costs faced by households is:
r
r
r
ciY
ciY
ciY
+
=2
K = Kc + Ki =
2
2
2
and hence the ratio of these costs to the government’s seigniorage revenue is:
K
= 2.
S
The total costs faced by households are double the amount of seigniorage received by the
government.
(c) Suppose the government wants to maximise the difference between its seigniorage revenue S
and the total costs K faced by households. Since seigniorage revenue S is identical to
foregone interest Ki , the objective is to maximise:
S − K = S − Kc − Ki = −Kc .
This means that the government must minimise total transaction costs Kc to fulfil its
objective. Using the expression for the optimal value of n from part (a), total transaction
costs Kc are:
r
r
iY
ciY
Kc = c
=
.
2c
2
This formula is increasing in the nominal interest rate i, so the interest rate that minimises
transaction costs is i = 0.
Intuitively, foregone interest is simply a transfer from holders of money to the government
(it is identical to seigniorage revenue). When private agents choose holdings of money to
minimise the sum of transaction costs and foregone interest, the outcome is not necessarily
efficient because agents might choose to incur transaction costs to avoid losing out on
interest. These transaction costs are a deadweight loss because time and resources are used
up simply to prevent one party having to make a transfer to another. After netting out
transfers, efficiency therefore requires that transaction costs are minimised. However,
private agents will do this only when there is no individual incentive to try to avoid
foregoing interest, which means that the return on bonds must be brought into line with the
return on money. Therefore, the nominal interest rate must be brought down to zero.
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Examiners’ commentaries 2016
Question 10
Consider a government with preferences represented by the loss function
L = π 2 + au
where π is the inflation rate, u is the unemployment rate, and a is a positive
constant indicating the strength of the government’s preference for low
unemployment.
There is an expectations-augmented Phillips curve that links inflation and
unemployment:
u = un − b(π − π e )
where π e denotes inflation expectations, un is the natural rate of unemployment,
and b is a positive constant. Expectations of inflation are assumed to be rational.
Assume that monetary policy is able to affect aggregate demand and thus control
the unemployment rate u.
(a) [6 marks] List and explain two costs of inflation. The term π 2 in the loss
function implicitly assumes that deflation is just as costly as inflation. Is this
true for the costs of inflation you have listed?
(b) [7 marks] Assume that the government is able to choose a monetary policy
without being restricted by any past commitments (the government acts with
discretion). This means inflation expectations π e are taken as given when
monetary policy is chosen. Find the inflation rate π that minimises the loss
function subject to the Phillips curve. Given that expectations are formed
rationally, what are the equilibrium unemployment and inflation rates?
(c) [7 marks] Now suppose the government is able to commit to a rule where
monetary policy must meet an inflation target of π = 0. Assuming this rule is
credible, find the equilibrium unemployment rate and explain the sense in which
the equilibrium found in part (b) features an ‘inflation bias’. Explain why the
zero inflation rule is not time consistent, and briefly discuss some mechanisms
by which a government might make a credible commitment to low inflation.
Reading for this question
Subject guide, Chapters 4 and 12.
Approaching the question
(a) Menu costs are one cost of inflation. A menu cost refers to a cost of reprinting a price label
or catalogue, or more generally, any cost incurred in the process of adjusting prices. When
there is inflation, there is a greater need to change prices more frequently (to maintain
desired relative prices), which means more menu costs need to be paid. The optimal rate of
inflation to minimise menu costs is zero because deflation leads to exactly the same problem
as inflation.
Another cost of inflation is relative price distortions. Inflation can distort actual relative
prices of goods and services because prices are infrequently adjusted at different times for
different products, or it can lower the informational content of prices if agents are not fully
informed about all other prices (there is a possibility of confusion between nominal and
relative price changes). This leads to a less efficient allocation of resources because the
quantities produced and consumed of different goods are now affected by the overall rate of
inflation, not only by the economy’s real fundamentals. The optimal rate of inflation to
minimise relative price distortions is zero because deflation creates exactly the same
problems.
There are other examples of costs of inflation, such as shoe-leather costs. Not all of these
imply that the optimal rate of inflation is zero (for shoe-leather costs, it would be negative).
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EC2065 Macroeconomics
(b) The loss function is minimised subject to the Phillips curve as a constraint. Substituting the
Phillips curve into the loss function to eliminate the unemployment rate:
L = π 2 + a(un − b(π − π e )) = π 2 − abπ + aun + abπ e .
Expectations of inflation π e are taken as given under discretion. The government chooses
inflation π to minimise the loss function, which requires the following first-order condition to
hold:
∂L
= 2π − ab = 0.
∂π
The solution for the inflation rate is π = ab/2.
Expectations of inflation are assumed to be formed rationally. Any π e different from ab/2
would result in a predictable error in forecasting inflation, so rational expectations requires
π e = ab/2. Since π = π e , the Phillips curve implies that the equilibrium unemployment rate
is u = un . The unemployment rate is equal to the natural rate of unemployment.
(c) If the government commits to rule with π = 0 and this is credible, rational expectations
implies π e = 0 as well. With π = π e , the Phillips curve implies u = un . The equilibrium in
part (b) features an inflation bias in the sense that compared to part (c), there is higher
inflation (π = ab/2 > 0), which is worse, but no gain in terms of lower unemployment
(u = un in both cases).
While the rule π = 0 is superior to discretion, it is not time consistent. Once the
government has succeeded in persuading private agents to expect π e = 0, the optimal choice
of inflation is π = ab/2. This is because with π e given, the Phillips curve implies the
government could achieve u < un by having π > 0 = π e . Therefore, the government would
not honour a past commitment to choose π = 0 unless it were compelled to. Of course, if
the government is not bound to deliver π = 0, this means that rational agents would expect
π e = ab/2 in equilibrium, which was the outcome in part (b).
To make the commitment credible, the government must limit its ability to interfere with
monetary policy. This might be done by making the central bank independent, and
appointing a hawkish governor, or establishing a policy framework such as inflation
targeting where the independent central bank is assigned a different set of goals from those
represented by the government’s loss function.
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Examiners’ commentaries 2016
Question 11
Consider a small open economy with fixed prices and wages.
Goods-market equilibrium is where output Y is equal to the sum of consumption C,
investment I, government spending G, and net exports N X. The consumption and
investment functions are:
C = C0 + c(Y − T ),
I = I0 − bi
where i is the domestic interest rate. Government spending and taxes are
exogenously fixed at G = G0 and T = T0 . Net exports are given by:
N X = N X0 − mY − ae
where e is the nominal exchange rate (defined as the foreign-currency price of
domestic currency).
Money-market equilibrium is where the demand for real money balances L(Y, i) is
equal to the real money supply M s /P :
Ms
P
= L(Y, i)
where L(Y, i) is an increasing function of Y and a decreasing function of i.
Balance-of-payments equilibrium is where the sum of the current account CA
(assumed equal to net exports N X) and the capital account KA is zero. Capital
mobility is imperfect, and capital flows are given by the equation:
KA = KA0 + f (i − i∗ )
where i∗ is the foreign interest rate. Throughout the question, assume the exchange
rate is fixed.
(a) [7 marks] Show how balance-of-payments equilibrium (BP = 0) requires a
positive relationship between income Y and the domestic interest rate i (for a
given exchange rate e), referred to as the BP curve. Explain how intervention
in the foreign exchange market allows an economy in internal equilibrium with
BP < 0 to reach both internal and external equilibrium.
(b) [7 marks] Suppose the government decides to establish a sovereign wealth fund.
Instead of using tax revenue to repay government debt, the sovereign wealth
fund purchases foreign assets (it effectively sells domestic assets in exchange for
foreign assets). This affects the term KA0 in the equation for the capital
account. Using the IS-LM-BP diagram, show how establishing the sovereign
wealth fund changes the economy’s equilibrium, stating the effects on the
current account, the capital account, and investment. Is there a change in
national saving? Explain your answer.
(c) [6 marks] What difference would it make to your answers to part (b) if there
were greater capital mobility? What happens in the special case of perfect
capital mobility? Explain the economic intuition for your answer.
Reading for this question
Subject guide, Chapters 7 and 8.
Approaching the question
(a) Balance of payments equilibrium requires BP = CA + KA = 0. Using the equations for the
current account (net exports) N X and the capital account KA:
(N X0 − mY − ae) + (KA0 + f (i − i∗ )) = 0.
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EC2065 Macroeconomics
This equation can be rearranged to express the domestic interest rate i as a function of
income Y , taking the exchange rate e as given:
i = i∗ +
mY + ae − N X0 − KA0
.
f
The derivative of i with respect to Y is m/f , which is positive. The BP line, representing
balance-of-payments equilibrium, is therefore an upward-sloping line. Intuitively, higher
income leads to higher imports and a lower current account. However, if the country is to
buy more goods from foreign countries without selling more goods to them, assets must be
sold to foreigners instead. This means a capital account surplus is required, but with
imperfect capital mobility, foreign investors are only willing to hold more domestic assets if
the domestic interest rate rises relative to the foreign interest rate. This is what lies behind
the positive relationship between income and the interest rate depicted as the BP line.
Suppose the economy’s internal equilibrium (the intersection between the IS and LM curves)
would lead to a balance of payments deficit (BP < 0). Since the capital account is
increasing in i, the region below the BP line corresponds to where a balance of payments
deficit occurs in the diagram, which means the intersection of IS and LM is below the BP
line. A balance of payments deficit means that there would be less demand for the domestic
currency in the foreign exchange market to purchase domestic goods or assets than the
amount agents would like to supply. This is not an external equilibrium, and there would be
pressure for the domestic currency to depreciate in value relative to the foreign currency.
A fixed exchange rate can be maintained in these circumstances by a central bank
intervention that reduces the supply of domestic currency. The reduction in the money
supply implies that the LM curve shifts to the left. The central bank continues to intervene
until the LM curve has shifted far enough left to the point where it intersects both the IS
and BP curves.
(b) Establishing the sovereign wealth fund increases domestic purchases of foreign assets funded
by increased sales of domestic assets (more domestic government bonds are in circulation
than would otherwise be the case). These transactions increase the economy’s capital
account deficit, which corresponds to a lower value of KA0 in the equation for the capital
account. The reduction in KA0 shifts the BP line upwards, so all else equal, a higher
interest rate is required for balance-of-payments equilibrium. Intuitively, if there were no
change in the current account, external equilibrium would require private investors to sell
foreign assets to the sovereign wealth fund and buy domestic assets. With imperfect capital
mobility, they are only willing to do this if i rises relative to the foreign interest rate i∗ (and
the latter is taken as given by a small open economy).
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Examiners’ commentaries 2016
The upward shift of the BP line means that the economy is no longer in both internal and
external equilibrium (establishing the sovereign wealth fund does not directly affect the
demand for goods, so the IS curve does not shift, and does not directly affect the demand
for or supply of domestic currency, so the LM curve does not shift). The economy is now in
the position described in part (a) where internal equilibrium would result in a
balance-of-payments deficit. The adjustment to internal and external equilibrium is the one
described in the answer to part (a).
The central bank intervenes by reducing the money supply, which shifts the LM curve to the
left. The economy’s equilibrium is now at a lower level of income and a higher interest rate.
The current account improves because lower income means less demand for imports
(competitiveness has not changed because of the fixed exchange rate). Given
balance-of-payments equilibrium, the capital account must deteriorate. Investment falls
because of the higher interest rate.
National saving is equal to the sum of investment and the current account, but since the
former declines while the latter increases, this equation does not provide an unambiguous
prediction. Alternatively, note that national saving is defined as the sum of private saving
and public saving. The latter is unchanged, while the former decreases because income falls
by more than consumption does (since the marginal propensity to consume is less than one).
It follows that national saving must decrease.
(c) Greater capital mobility means that international investors have a greater willingness to
seek out the highest returns internationally for their wealth. This implies that international
capital flows become more sensitive to relative interest rates, which is represented by a
higher value of the coefficient f in the capital account equation.
An increase in f reduces the gradient of the BP line, and also reduces the size of the vertical
shift of the BP line that occurs when the sovereign wealth fund is established. While the
direction of the effects described in part (b) is the same, the magnitude of all the effects is
reduced.
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EC2065 Macroeconomics
In the special case of perfect capital mobility, f becomes extremely large as the smallest
difference in interest rates is now sufficient to induce very large capital flows. This means the
BP line becomes horizontal and does not shift when the sovereign wealth fund is established.
There are no effects on the current account, capital account, investment or national saving.
Intuitively, since private investors are indifferent between domestic and foreign assets as long
as the domestic and foreign interest rates are equalised, they are willing to trade assets with
the sovereign wealth fund without the need for any change in interest rates. Private capital
simply flows in the opposite direction to the capital flows associated with the sovereign
wealth fund, and the economy’s equilibrium is unaffected.
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Examiners’ commentaries 2016
Question 12
Consider the aggregate demand-aggregate supply model in a closed economy.
(a) [6 marks] Assume that nominal wages W are contractually fixed at W = W̄ .
Firms are perfectly competitive and the price level P is flexible (both firms and
workers are fully informed about the level of prices P ). Output Y is produced
according to the production function Y = AF (L), where L is employment and
A is total factor productivity. The marginal product of labour is diminishing.
Employment is chosen by firms to maximise profits. Show how these
assumptions justify an upward-sloping aggregate supply curve.
(b) [7 marks] Assume that money demand becomes perfectly interest-elastic where
the interest rate is zero, and that the demand for consumption and investment
depends only on income and interest rates. Explain why interest rates cannot
fall below zero and show what consequences this has for the shape of the
aggregate demand curve. Analyse the effects of an increase in the money supply
when the interest rate is zero and use your answer to explain the notion of a
‘liquidity trap’.
(c) [7 marks] Consider an economy in a liquidity trap. The government is
considering a package of structural reforms that will raise total factor
productivity A as part of its plan to escape the liquidity trap. Use the AD-AS
model to evaluate the effects of the reforms on output, employment, and
unemployment.
Reading for this question
Subject guide, Chapters 3 and 4.
Approaching the question
(a) Suppose a firm hires labour L and produces output Y . The firm has revenues P Y and a
wage bill W L in nominal terms given the price level P and nominal wages W . Profits are
V = P Y − W L. Output and employment are linked by the production function Y = AF (L),
which implies that profits are V = P AF (L) − W L as a function of employment L.
Competitive firms choose employment to maximise profits taking prices and wages as given.
Hence the profit-maximising level of employment is the solution of the first-order condition:
∂V
= P AF 0 (L) − W = 0
∂L
⇒
AF 0 (L) =
W
.
P
In the above, AF 0 (L) is the marginal product of labour, and W/P is the real wage. Profit
maximisation implies firms should hire workers until the marginal product of labour has
declined to the point where it is equal to the real wage. Therefore, labour demand can be
depicted in the labour market diagram as the downward-sloping marginal product of labour
curve.
Nominal wages are assumed to be contractually fixed at W = W̄ , rather than adjusting to
clear the labour market (that is, bringing labour demand into line with labour supply).
Given a price level P , the fixed nominal wage W̄ implies a particular real wage W̄ /P . It is
assumed that labour demand falls short of desired labour supply at this real wage, in which
case firms choose employment on the labour demand curve, leaving some workers
unemployed who would like to work at the prevailing real wage.
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EC2065 Macroeconomics
In this environment, a rise in the price level P reduces the real value of the fixed nominal
wage. This leads firms to move down the labour demand curve because it is now profitable
to employ some workers who previously had a marginal product below the old real wage.
Employment rises, and the production function implies that output increases. Hence there is
a positive relationship between the price level P and aggregate output Y , namely the
short-run aggregate supply curve.
(b) The aggregate demand curve gives the levels of output at which the IS and LM curves
intersect for each price level P . A fall in the price level will increase the real supply of
money M s /P , which shifts the LM curve downwards when the nominal interest rate is
initially positive. The reason is that real money demand is increasing in income and
decreasing in the interest rate, so some combination of higher income or lower interest rates
is required to restore equilibrium in the money market. The downwards shift of the LM
curve leads to a movement along the downward-sloping IS curve, resulting in a lower interest
rate and higher output. Since a lower price level boosts demand through this mechanism, it
follows that the aggregate demand curve is downward-sloping.
At a zero nominal interest rate the money demand curve is assumed to become perfectly
interest-elastic (horizontal). The logic behind this assumption is that at a negative nominal
interest rate, money would be preferable to bonds as a store of value in addition to being
preferable as a medium of exchange. As a result, there would be a huge shift of wealth from
bonds to money when the interest rate falls to zero. Therefore, the money market cannot be
in equilibrium at a nominal interest rate less than zero.
This has implications for the aggregate demand relationship between P and Y . Lower P
raises the real money supply, but if the nominal interest rate is zero and money demand is
perfectly interest-elastic, no fall in the interest rate is required to restore equilibrium in the
money market. This means that the LM curve does not shift downwards when the price
level falls (it still shifts to the right because output would now have to rise further to reach a
point where the equilibrium nominal interest rate is positive). If the IS and LM curves
initially intersect at a zero interest rate, this remains the case after the fall in P , and hence
the level of aggregate demand is unchanged. Graphically, this corresponds to a
price-inelastic (vertical) aggregate demand curve at sufficiently low price levels (AD is still
downward-sloping for sufficiently high price levels).
An increase in the nominal money supply raises the real money supply for a given price
level. Therefore, it has the effects on the money market described above. If the nominal
interest rate is initially positive, the level of aggregate demand will rise, while if the nominal
interest rate is already zero, there will be no effect on aggregate demand. Graphically, the
downward-sloping section of the AD curve shifts to the right, while the vertical section of
the AD curve shifts upwards.
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Examiners’ commentaries 2016
If the economy’s equilibrium in the goods market (the intersection of the aggregate demand
and aggregate supply curves) is on the vertical section of the aggregate demand curve, then
an increase in the money supply has no impact on the economy. Intuitively, the additional
money is willingly held because agents are indifferent between money and bonds at the
margin when the nominal interest rate is zero. There is a huge potential demand for money
at the existing interest rate, so increasing the supply of money has no effect on the
economy’s equilibrium. This is the notion of a ‘liquidity trap’.
(c) Suppose the structural reforms succeed in raising total factor productivity A. This increases
the marginal product of labour AF 0 (L) at all levels of employment and shifts the labour
demand curve to the right. Given the real wage implied by the contractually fixed nominal
wage W̄ and the price level P , firms will choose a higher level of employment. The amount
of output supplied at this price level will be higher both because of increased productivity
and the higher level of employment chosen by firms, so the aggregate supply curve shifts to
the right.
Considering an economy in the liquidity trap (where the SRAS curve intersects the vertical
section of the AD curve), it must be the case that the new equilibrium remains on the
vertical section of the AD curve following the structural reforms. Therefore, output is
unchanged and the price level falls.
Since productivity has improved but output has remained unchanged, it follows that
employment must have fallen. This happens in spite of the rightward shift of the labour
demand curve. The reason is that the lower price level resulting from the rightward shift of
the SRAS curve raises the real wage W̄ /P implied by the contractually fixed nominal wage
W̄ , leading to a movement up along the labour demand curve. This effect actually
outweighs the rightward shift of labour demand. As the real wage has increased, workers
would actually like to increase employment, so the fall in employment leads to a rise in
unemployment.
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EC2065 Macroeconomics
Question 13
Consider a household choosing a consumption plan for two time periods (Fisher
model of consumption). In the first time period, the household has no initial assets,
receives income Y1 , and pays (lump-sum) tax T1 . The household chooses its current
consumption C1 and the amount of bonds B to carry into the future time period. In
the future, the household will receive income Y2 and pay taxes T2 , and will have
financial wealth (1 + r)B, where r is the real interest rate. Future consumption C2
will be:
C2 = Y2 − T2 + (1 + r)B
The government has current expenditure G1 and plans expenditure G2 in the
future. If the government runs a deficit D = G1 − T1 then it issues bonds that pay
interest rate r. Assume that the government has no initial debt and must repay all
debt in the future time period, hence
T2 = G2 + (1 + r)D
(a) [6 marks] Derive present-value (‘life-time’) budget constraints for the household
and for the government, and show how these life-time budget constraints can be
combined to eliminate taxes T1 and T2 .
(b) [7 marks] Suppose there is a temporary increase in government spending G1 .
Find the effects on current consumption C1 , private saving Sp = Y1 − T1 − C1 ,
and national saving Sn = Sp + (T1 − G1 ) in the following cases:
i. there is no increase in current taxes T1 ;
ii. taxes T1 are increased by the same amount as government spending G1 .
In what sense does ‘Ricardian equivalence’ hold in this example?
(c) [7 marks] Assume a closed economy and suppose that the government defaults
on some of its debts in the second time period (and that this was completely
unexpected in the first time period). Explain what effect this is predicted to
have on consumption C2 . Does your reasoning imply that government bonds are
part of the economy’s ‘net wealth’ ?
Reading for this question
Subject guide, Chapters 9 and 13.
Approaching the question
(a) In the first time period, disposable income Y1 − T1 that is not spent on consumption C1 can
be used to buy bonds B = (Y1 − T1 ) − C1 . In the second time period, consumption is given
by future disposable income Y2 − T2 plus financial wealth (1 + r)B, that is,
C2 = (Y2 − T2 ) + (1 + r)B. By substituting the expression for B from the first time period:
C2 = (Y2 − T2 ) + (1 + r)((Y1 − T1 ) − C1 )
and dividing both sides by 1 + r and rearranging:
C1 +
(Y2 − T2 )
C2
= (Y1 − T1 ) +
.
1+r
1+r
This is the household’s life-time budget constraint. The present discounted value of current
and future consumption must equal the present discounted value of current and future
income after tax.
For the government, substituting the expression for its first-period deficit D = G1 − T1 into
the formula for the level of second-period taxes T2 = G2 + (1 + r)D required to cover
spending and debt repayments:
T2 = G2 + (1 + r)(G1 − T1 ).
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Examiners’ commentaries 2016
Dividing both sides by 1 + r and rearranging leads to:
G1 +
G2
T2
= T1 +
.
1+r
1+r
This is the life-time budget constraint for the government. The present discounted value of
current and future government spending must equal the present discounted value of current
and future taxes.
The household and government life-time budget constraints can be combined as follows to
eliminate the present value of taxes:
C1 +
C2
=
1+r
Y1 +
Y2
1+r
T2
Y2
G2
− T1 +
= Y1 +
− G1 +
.
1+r
1+r
1+r
The present value of consumption is effectively constrained by the present value of life-time
pre-tax income net of the present value of government spending.
(b) Since taxes do not appear in the consolidated life-time budget constraint, the effect on the
budget constraint of the increase in government spending is the same in both cases
considered in the question. The budget constraint shifts to the left by an amount equal to
the rise in G1 . This leads the household to choose lower consumption C1 , but C1 does not
fall by as much as G1 rises (because C2 decreases as well, which is optimal if current and
future consumption are both normal goods). The same fall in C1 occurs irrespective of
whether the government borrows more or raises taxes immediately.
In case i. where there is no increase in current taxes, since disposable income is unchanged
and consumption falls, private saving Sp = Y1 − T1 − C1 must increase. National saving is
Sn = Sp + (T1 − G1 ) = Y1 − T1 − C1 + T1 − G1 = Y1 − C1 − G1 . As C1 falls by less than G1
rises, national saving must fall.
In case ii. where a rise in current taxes matches the increase in government spending,
disposable income is reduced. However, since the fall in consumption is smaller than the rise
in taxes (equal to the rise in government spending), private saving must fall. In this case,
there is no change in the government budget deficit, so the change in national saving is
equal to the change in private saving. National saving must therefore fall.
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EC2065 Macroeconomics
Although fiscal policy affects consumption in this example, the timing of taxes does not.
Ricardian equivalence holds in the sense that the different ways the government can pay for
the increase in spending (borrowing more, or raising taxes now) have equivalent effects on
consumption.
The effect on private saving does depend on how the government pays for the increase in
spending. When the government borrows more, the private sector saves more. When the
government does not borrow, the private sector borrows. However, the impact on national
saving is the same in both cases: the economy as a whole reduces saving. This is due to the
increase in government spending being temporary combined with a desire for consumption
smoothing by households, implying that current consumption falls by less than the increase
in government spending. Therefore, the sum of spending by households and the government
rises, so with no change to national income, these two groups must together be saving less or
borrowing more. When taxes rise, households are solely responsible for the decline in saving.
When taxes are not changed, the government borrows even more, and households partially
increase saving to compensate.
(c) In the second time period, consumption is given by C2 = Y2 − T2 + (1 + r)B. In a closed
economy, households must ultimately hold the bonds D issued by the government. Let B0
denote bonds issued by entities other than the government (for example, corporate bonds
issued by firms). It must be the case that household holdings of bonds are equal to
B = D + B0 . Consumption C2 is therefore:
C2 = Y2 − T2 + (1 + r)D + (1 + r)B0 .
As this equation shows, a default that reduces the government’s repayments (1 + r)D has
the effect of reducing households’ financial wealth by the same amount. However, the
equation for the required level of taxes T2 is still valid after taking account of the default in
reducing (1 + r)D:
T2 = G2 + (1 + r)D.
It follows that (1 + r)D = T2 − G2 , which can be substituted into the expression for C2 :
C2 = Y2 − T2 + (T2 − G2 ) + (1 + r)B0 = Y2 − G2 + (1 + r)B0 .
The term (1 + r)D cancels out, which suggests the default will have no effect on
consumption unless it leads to a change in government spending G2 .
Intuitively, while default reduces households’ financial wealth, it also reduces the need for
taxes. This illustrates the idea that government bonds are not part of the economy’s ‘net
wealth’. Households holding bonds are also subject to the taxes that will be used to repay
those bonds. Default eliminates a financial claim of households on government, but by
reducing the need to raise taxes, eliminates a claim of the government on households. These
two effects cancel each other out.
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Examiners’ commentaries 2016
Question 14
Consider the Solow growth model. Output Y is produced according to the
production function Y = F (K, L), where K is the capital stock and L is the labour
force. The function F (K, L) has constant returns to scale and diminishing marginal
returns to capital, and the per-worker production function is y = f (k), where
y = Y /L and k = K/L. The labour force and technology are both constant over
time (n = 0 and g = 0, and the level A of technology is set to 1 in the production
function). Investment I is equal to saving, which is a fraction s of income. Capital
depreciates at rate δ. The evolution of the per-worker capital stock k over time is
determined by the equation ∆k = sf (k) − δk. Consumption per worker is
c = (1 − s)f (k).
(a) [7 marks] The ‘Golden rule’ level of capital per worker is the value of k that
results in the highest sustainable level of consumption per worker c. Show that
the Golden rule capital stock is the solution of the equation f 0 (k) = δ, where
f 0 (k) is the marginal product of capital. Considering an economy starting from
a saving rate where the steady-state capital stock is above the Golden rule,
sketch graphs of k and c over time following an immediate decrease in the
saving rate sufficient to reach the Golden rule in the long run.
√
(b) [7 marks] Assume that f (k) = k, δ = 0.15, and s = 0.3. Find the steady-state
capital stock per worker k. Calculate whether this is more, less, or exactly the
right amount of capital required for the Golden rule.
(c) [6 marks] Assume that owners of capital save all of their income (equal to the
marginal product of capital multiplied by the capital stock), while all labour
income is consumed. Will the economy have more, less, or exactly the right
amount of capital in the long run required for the Golden rule? Explain your
reasoning.
Reading for this question
Subject guide, Chapters 5 and 6.
Approaching the question
(a) The goal is to maximise consumption c = (1 − s)f (k), but the chosen level of consumption
must be sustainable in the long run. This requires that the capital stock k must be a steady
state, that is, it must satisfy the equation sf (k) = δk given the saving rate s. Taking
account of this constraint, sustainable levels of consumption are given by:
c = f (k) − sf (k) = f (k) − δk.
The Golden rule level of capital k maximises this expression for c. The first-order condition
is:
∂c
= f 0 (k) − δ = 0.
∂k
and hence f 0 (k) = δ. The marginal product of capital f 0 (k) must equal the depreciation rate
of capital δ.
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EC2065 Macroeconomics
If the economy begins in a steady state with more capital than required for the Golden rule
then the saving rate must be reduced to reach the Golden rule. This is because a lower
saving rate implies a lower steady-state capital stock. There is a slow process of adjustment
for capital where k gradually falls from a higher steady state to a lower steady state. Since
there is no initial change in k, consumption c = (1 − s)f (k) increases when the saving rate is
reduced. Furthermore, since the economy is moving to the Golden rule, the new steady-state
level of consumption must be greater than the previous steady state. With the capital stock
and hence income falling during the transition, after the initial increase, consumption
c = (1 − s)y must decline towards its new steady state. However, consumption is always
above its initial level during this process.
√
(b) With f (k) = k, s = 0.3, and δ = 0.15, the steady-state level of capital k is the solution of
the equation:
√
0.3 k = 0.15k.
√
Dividing both sides by 0.15 k shows that:
√
2= k
⇒
k = 4.
The marginal product of capital is:
1
f 0 (k) = √
2 k
and hence at the steady state f 0 (4) = 1/(2 × 2) = 0.25, which exceeds δ = 0.15. Since the
marginal product of capital f 0 (k) is decreasing in k, the Golden-rule equation f 0 (k) = δ
requires a higher capital stock. The saving rate must be increased to achieve this.
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Examiners’ commentaries 2016
(c) The total income of owners of capital is f 0 (k)K. Since owners of capital are assumed to save
all of their income, while workers save nothing, total saving is S = f 0 (k)K. The implied
saving rate s is:
S
f 0 (k)K
kf 0 (k)
s=
=
=
Y
Y
f (k)
as K/Y = k/y and y = f (k). The resulting steady-state level of capital can be found by
substituting this into the equation sf (k) = δk:
f (k)
kf 0 (k)
= δk.
f (k)
The terms in f (k) cancel out, and both sides of the equation can be divided by k to leave
f 0 (k) = δ. This means that steady-state level of capital resulting from the saving behaviour
assumed in the question is exactly equal to the Golden-rule level of capital.
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EC2065 Macroeconomics
Examiners’ commentaries 2016
EC2065 Macroeconomics
Important note
This commentary reflects the examination and assessment arrangements for this course in the
academic year 2015–16. The format and structure of the examination may change in future years,
and any such changes will be publicised on the virtual learning environment (VLE).
Information about the subject guide and the Essential reading
references
Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2016).
You should always attempt to use the most recent edition of any Essential reading textbook, even if
the commentary and/or online reading list and/or subject guide refer to an earlier edition. If
different editions of Essential reading are listed, please check the VLE for reading supplements – if
none are available, please use the contents list and index of the new edition to find the relevant
section.
Comments on specific questions – Zone B
Candidates should answer ELEVEN of the following FOURTEEN questions: all EIGHT from
Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly
advised to divide their time accordingly.
If more questions are answered than requested, only the first answers attempted will be counted.
Section A
Answer all eight questions in this section (5 marks each).
Briefly explain whether each of the following statements is true or false.
Question 1
If the demand for money does not depend on interest rates then the LM curve is
horizontal.
Reading for this question
Subject guide, Chapter 2.
Approaching the question
The statement is FALSE.
The LM curve represents the combinations of income and interest rates at which the money
market is in equilibrium. Suppose money demand does not depend on the nominal interest rate,
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Examiners’ commentaries 2016
but does depend on income as normal. This means that money demand increases with income
moving to the right in the IS/LM diagram and decreases moving to the left, but moving up or
down in the IS/LM diagram has no effect on money demand in this special case. Consequently,
there is a single level of income consistent with money demand being equal to money supply,
irrespective of the interest rate. This corresponds to a vertical LM curve, not a horizontal LM
curve.
Question 2
The permanent income theory implies that consumption should respond more to
temporary than permanent changes in income.
Reading for this question
Subject guide, Chapter 9.
Approaching the question
The statement is FALSE.
The permanent income theory of consumption is based on the idea that households prefer
relatively smooth consumption over time. This means they will use saving or borrowing to
spread out the effects of a temporary change in income (saving more if income increases
temporarily, and running down saving or borrowing if income falls temporarily). Consequently,
consumption responds by little to temporary changes in income. On the other hand, if there is a
permanent change in income, it does not make sense to adjust saving or borrowing given that the
change in income is not expected to be reversed. Therefore, permanent changes in income should
have a large effect on consumption.
Question 3
The Fisher equation implies that higher expected inflation must result in a higher
nominal interest rate.
Reading for this question
Subject guide, Chapters 2 and 10.
Approaching the question
The statement is FALSE.
The Fisher equation states that the real interest rate r is equal to the difference between the
nominal interest rate i and the expected rate of inflation π e :
r = i − πe .
This equation shows that when expected inflation π e increases, either the nominal interest rate i
rises, or the real interest rate r declines, or some combination of both. However, the Fisher
equation itself does not give an unambiguous answer about which of these two occur.
For example, if the classical dichotomy holds (which requires fully flexible prices and wages),
there is an equilibrium real interest rate which is unaffected by inflation and monetary variables.
In this case, higher expected inflation will indeed raise the nominal interest rate (this is usually
referred to as the Fisher effect). However, the Fisher equation is also consistent with an economy
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EC2065 Macroeconomics
where real variables are not independent of nominal variables (for example, because of sluggish
adjustment of nominal prices or wages). In this case, higher expected inflation can reduce the
real interest rate to the extent that the central bank does not follow a monetary policy that
raises the nominal interest rate in response.
Question 4
The main difference between the AK and Solow models of economic growth is that
the AK model assumes increasing returns to scale, while the Solow model assumes
constant returns to scale.
Reading for this question
Subject guide, Chapters 5 and 6.
Approaching the question
The statement is FALSE.
The production function in the AK model is Y = AK, while the Solow model has Y = F (K, AL).
The Solow model assumes the function F (K, AL) displays constant returns to scale, meaning
that an equal percentage increase in capital K and labour L leads to the same percentage
increase in output Y (note that the exogenous technological factor A is held constant). Since the
AK production function is linear in capital, and labour does not appear, an equal percentage rise
in both factor inputs leads to the same percentage rise in output. This means the AK model’s
production function also displays constant returns to scale. What distinguishes the models is not
returns to scale, but marginal returns to capital. The AK model features constant marginal
returns to capital, while the Solow model has diminishing marginal returns to capital.
Question 5
According to the neoclassical theory of investment, a permanent increase in total
factor productivity will increase investment.
Reading for this question
Subject guide, Chapter 10.
Approaching the question
The statement is TRUE.
The neoclassical theory of investment has firms invest up to the point where the (diminishing)
marginal product of capital is equal to the user cost of capital, that is, the sum of the real
interest rate and the depreciation rate:
MPK = r + δ.
A permanent increase in total factor productivity will increase the marginal product of capital at
each and every level of the capital stock. This means that some investment projects where the
marginal product of capital previously fell short of the user cost now have a marginal product
above the user cost. Consequently, it is rational for firms to undertake additional investments.
Question 6
The Solow model predicts that economies with different saving rates will have
different long-run growth rates.
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Examiners’ commentaries 2016
Reading for this question
Subject guide, Chapter 6.
Approaching the question
The statement is FALSE.
The Solow model assumes a production function Y = F (K, AL) with labour-augmenting
technology A growing at a constant rate g. The production function is assumed to feature
constant returns to scale, which implies that y = f (k), where y = Y /AL and k = K/AL are
output and capital in efficiency units of labour, and f (k) = F (k, 1). The dynamics of k are
determined by the equation ∆k = sf (k) − (δ + n + g)k, where s is the saving rate and n is the
population growth rate. There is a steady state for k because f (k) is a concave function, and as
y = f (k), the level of y is constant in this steady state. Whatever is the steady-state value of y,
the definition y = Y /AL implies that income per worker Y /L must be growing at rate g, and
GDP Y must be growing at rate n + g. Changes in the saving rate s only affect the steady-state
level of y, not the growth rates of income per worker or GDP.
Question 7
Okun’s law states that there is a negative relationship between GDP growth and
unemployment.
Reading for this question
Subject guide, Chapter 4.
Approaching the question
The statement is TRUE.
Okun’s law derives from the production function linking output and employment. Lower
unemployment means that (given the size of labour force) the amount of labour input going into
the production function has increased. Holding constant both the capital stock and the level of
technology in the short run, this implies higher output, so the growth rate of GDP increases.
Okun’s law therefore implies a negative relationship between the unemployment rate and the
GDP growth rate (in the short run).
Question 8
If banks hold a higher fraction of deposits as reserves then the money multiplier will
be larger.
Reading for this question
Subject guide, Chapter 11.
Approaching the question
The statement is FALSE.
The broad money supply is M = C + D, where C is cash and D is deposits. The monetary base
is B = C + R, where R denotes reserves. The money multiplier m = M/B is the ratio of the
broad money supply to the monetary base. Let c = C/D and r = R/D denote the cash-deposit
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EC2065 Macroeconomics
ratio and the reserve-deposit ratio, respectively. The money multiplier can be written in terms of
c and r as follows:
C +D
(C/D) + (D/D)
c+1
m=
=
=
.
C +R
(C/D) + (R/D)
c+r
If banks hold a higher fraction of deposits as reserves then r increases, which implies a lower
money multiplier.
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Examiners’ commentaries 2016
Question 9
Consider the aggregate demand-aggregate supply model in a closed economy.
(a) [6 marks] Assume that nominal wages W are contractually fixed at W = W̄ .
Firms are perfectly competitive and the price level P is flexible (both firms and
workers are fully informed about the level of prices P ). Output Y is produced
according to the production function Y = AF (L), where L is employment and
A is total factor productivity. The marginal product of labour is diminishing.
Employment is chosen by firms to maximise profits. Show how these
assumptions justify an upward-sloping aggregate supply curve.
(b) [7 marks] Assume that money demand becomes perfectly interest-elastic where
the interest rate is zero, and that the demand for consumption and investment
depends only on income and interest rates. Explain why interest rates cannot
fall below zero and show what consequences this has for the shape of the
aggregate demand curve. Analyse the effects of an increase in the money supply
when the interest rate is zero and use your answer to explain the notion of a
‘liquidity trap’.
(c) [7 marks] Consider an economy in a liquidity trap. The government is
considering a package of structural reforms that will raise total factor
productivity A as part of its plan to escape the liquidity trap. Use the AD-AS
model to evaluate the effects of the reforms on output, employment, and
unemployment.
Reading for this question
Subject guide, Chapters 3 and 4.
Approaching the question
(a) Suppose a firm hires labour L and produces output Y . The firm has revenues P Y and a
wage bill W L in nominal terms given the price level P and nominal wages W . Profits are
V = P Y − W L. Output and employment are linked by the production function Y = AF (L),
which implies that profits are V = P AF (L) − W L as a function of employment L.
Competitive firms choose employment to maximise profits taking prices and wages as given.
Hence the profit-maximising level of employment is the solution of the first-order condition:
∂V
= P AF 0 (L) − W = 0
∂L
⇒
AF 0 (L) =
W
.
P
In the above, AF 0 (L) is the marginal product of labour, and W/P is the real wage. Profit
maximisation implies firms should hire workers until the marginal product of labour has
declined to the point where it is equal to the real wage. Therefore, labour demand can be
depicted in the labour market diagram as the downward-sloping marginal product of labour
curve.
Nominal wages are assumed to be contractually fixed at W = W̄ , rather than adjusting to
clear the labour market (that is, bringing labour demand into line with labour supply).
Given a price level P , the fixed nominal wage W̄ implies a particular real wage W̄ /P . It is
assumed that labour demand falls short of desired labour supply at this real wage, in which
case firms choose employment on the labour demand curve, leaving some workers
unemployed who would like to work at the prevailing real wage.
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EC2065 Macroeconomics
In this environment, a rise in the price level P reduces the real value of the fixed nominal
wage. This leads firms to move down the labour demand curve because it is now profitable
to employ some workers who previously had a marginal product below the old real wage.
Employment rises, and the production function implies that output increases. Hence there is
a positive relationship between the price level P and aggregate output Y , namely the
short-run aggregate supply curve.
(b) The aggregate demand curve gives the levels of output at which the IS and LM curves
intersect for each price level P . A fall in the price level will increase the real supply of
money M s /P , which shifts the LM curve downwards when the nominal interest rate is
initially positive. The reason is that real money demand is increasing in income and
decreasing in the interest rate, so some combination of higher income or lower interest rates
is required to restore equilibrium in the money market. The downwards shift of the LM
curve leads to a movement along the downward-sloping IS curve, resulting in a lower interest
rate and higher output. Since a lower price level boosts demand through this mechanism, it
follows that the aggregate demand curve is downward-sloping.
At a zero nominal interest rate the money demand curve is assumed to become perfectly
interest-elastic (horizontal). The logic behind this assumption is that at a negative nominal
interest rate, money would be preferable to bonds as a store of value in addition to being
preferable as a medium of exchange. As a result, there would be a huge shift of wealth from
bonds to money when the interest rate falls to zero. Therefore, the money market cannot be
in equilibrium at a nominal interest rate less than zero.
This has implications for the aggregate demand relationship between P and Y . Lower P
raises the real money supply, but if the nominal interest rate is zero and money demand is
perfectly interest-elastic, no fall in the interest rate is required to restore equilibrium in the
money market. This means that the LM curve does not shift downwards when the price
level falls (it still shifts to the right because output would now have to rise further to reach a
point where the equilibrium nominal interest rate is positive). If the IS and LM curves
initially intersect at a zero interest rate, this remains the case after the fall in P , and hence
the level of aggregate demand is unchanged. Graphically, this corresponds to a
price-inelastic (vertical) aggregate demand curve at sufficiently low price levels (AD is still
downward-sloping for sufficiently high price levels).
An increase in the nominal money supply raises the real money supply for a given price
level. Therefore, it has the effects on the money market described above. If the nominal
interest rate is initially positive, the level of aggregate demand will rise, while if the nominal
interest rate is already zero, there will be no effect on aggregate demand. Graphically, the
downward-sloping section of the AD curve shifts to the right, while the vertical section of
the AD curve shifts upwards.
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Examiners’ commentaries 2016
If the economy’s equilibrium in the goods market (the intersection of the aggregate demand
and aggregate supply curves) is on the vertical section of the aggregate demand curve, then
an increase in the money supply has no impact on the economy. Intuitively, the additional
money is willingly held because agents are indifferent between money and bonds at the
margin when the nominal interest rate is zero. There is a huge potential demand for money
at the existing interest rate, so increasing the supply of money has no effect on the
economy’s equilibrium. This is the notion of a ‘liquidity trap’.
(c) Suppose the structural reforms succeed in raising total factor productivity A. This increases
the marginal product of labour AF 0 (L) at all levels of employment and shifts the labour
demand curve to the right. Given the real wage implied by the contractually fixed nominal
wage W̄ and the price level P , firms will choose a higher level of employment. The amount
of output supplied at this price level will be higher both because of increased productivity
and the higher level of employment chosen by firms, so the aggregate supply curve shifts to
the right.
Considering an economy in the liquidity trap (where the SRAS curve intersects the vertical
section of the AD curve), it must be the case that the new equilibrium remains on the
vertical section of the AD curve following the structural reforms. Therefore, output is
unchanged and the price level falls.
Since productivity has improved but output has remained unchanged, it follows that
employment must have fallen. This happens in spite of the rightward shift of the labour
demand curve. The reason is that the lower price level resulting from the rightward shift of
the SRAS curve raises the real wage W̄ /P implied by the contractually fixed nominal wage
W̄ , leading to a movement up along the labour demand curve. This effect actually
outweighs the rightward shift of labour demand. As the real wage has increased, workers
would actually like to increase employment, so the fall in employment leads to a rise in
unemployment.
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EC2065 Macroeconomics
Question 10
Consider the Solow growth model. Output Y is produced according to the
production function Y = F (K, L), where K is the capital stock and L is the labour
force. The function F (K, L) has constant returns to scale and diminishing marginal
returns to capital, and the per-worker production function is y = f (k), where
y = Y /L and k = K/L. The labour force and technology are both constant over
time (n = 0 and g = 0, and the level A of technology is set to 1 in the production
function). Investment I is equal to saving, which is a fraction s of income. Capital
depreciates at rate δ. The evolution of the per-worker capital stock k over time is
determined by the equation ∆k = sf (k) − δk. Consumption per worker is
c = (1 − s)f (k).
(a) [7 marks] The ‘Golden rule’ level of capital per worker is the value of k that
results in the highest sustainable level of consumption per worker c. Show that
the Golden rule capital stock is the solution of the equation f 0 (k) = δ, where
f 0 (k) is the marginal product of capital. Considering an economy starting from
a saving rate where the steady-state capital stock is below the Golden rule,
sketch graphs of k and c over time following an immediate decrease in the
saving rate sufficient to reach the Golden rule in the long run.
√
(b) [7 marks] Assume that f (k) = 2 k, δ = 0.1, and s = 0.25. Find the steady-state
capital stock per worker k. Calculate whether this is more, less, or exactly the
right amount of capital required for the Golden rule.
(c) [6 marks] Assume that owners of capital save all of their income (equal to the
marginal product of capital multiplied by the capital stock), while all labour
income is consumed. Will the economy have more, less, or exactly the right
amount of capital in the long run required for the Golden rule? Explain your
reasoning.
Reading for this question
Subject guide, Chapters 5 and 6.
Approaching the question
(a) The goal is to maximise consumption c = (1 − s)f (k), but the chosen level of consumption
must be sustainable in the long run. This requires that the capital stock k must be a steady
state, that is, it must satisfy the equation sf (k) = δk given the saving rate s. Taking
account of this constraint, sustainable levels of consumption are given by:
c = f (k) − sf (k) = f (k) − δk.
The Golden rule level of capital k maximises this expression for c. The first-order condition
is:
∂c
= f 0 (k) − δ = 0
∂k
and hence f 0 (k) = δ. The marginal product of capital f 0 (k) must equal the depreciation rate
of capital δ.
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Examiners’ commentaries 2016
If the economy begins in a steady state with less capital than required for the Golden rule
then the saving rate must be increased to reach the Golden rule. This is because a higher
saving rate implies a higher steady-state capital stock. There is a slow process of adjustment
for capital where k gradually rises from a lower steady state to a higher steady state. Since
there is no initial change in k, consumption c = (1 − s)f (k) decreases when the saving rate
is increased. Furthermore, since the economy is moving to the Golden rule, the new
steady-state level of consumption must be greater than the previous steady state. With the
capital stock and thus income rising during the transition, after the initial decrease,
consumption c = (1 − s)y must increase towards its new steady state. However, there is
period of time during which consumption will be below its initial level.
√
(b) With f (k) = 2 k, s = 0.25, and δ = 0.1, the steady-state level of capital k is the solution of
the equation:
√
0.25(2 k) = 0.1k.
√
Dividing both sides by 0.1 k shows that:
√
5= k
⇒
k = 25.
The marginal product of capital at this steady state is:
1
f 0 (k) = √
k
and hence at the steady state f 0 (25) = 1/5 = 0.2, which exceeds δ = 0.1. Since the marginal
product of capital f 0 (k) is decreasing in k, the Golden-rule equation f 0 (k) = δ requires a
higher capital stock. The saving rate must be increased to achieve this.
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EC2065 Macroeconomics
(c) The total income of owners of capital is f 0 (k)K. Since owners of capital are assumed to save
all of their income, while workers save nothing, total saving is S = f 0 (k)K. The implied
saving rate s is:
S
f 0 (k)K
kf 0 (k)
s=
=
=
Y
Y
f (k)
as K/Y = k/y and y = f (k). The resulting steady-state level of capital can be found by
substituting this into the equation sf (k) = δk:
f (k)
kf 0 (k)
= δk.
f (k)
The terms in f (k) cancel out, and both sides of the equation can be divided by k to leave
f 0 (k) = δ. This means that steady-state level of capital resulting from the saving behaviour
assumed in the question is exactly equal to the Golden-rule level of capital.
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Examiners’ commentaries 2016
Question 11
Consider the Baumol–Tobin model of money demand. Suppose a household receives
real income Y (nominal income = P Y ) at the beginning of a month and plans to
spend all the income during the month at a constant rate. The household has a
bank account paying interest rate i on any money deposited (interest is not
compounded for simplicity). Income is initially paid into the household’s bank
account. Spending requires cash, and each withdrawal of cash from the bank
account has a (real) transaction cost of c. Cash pays no interest. Suppose the
household makes n (equally sized) withdrawals from the bank account during the
month (for simplicity, assume that n does not need to be a whole number).
(a) [7 marks] What is the total transaction cost incurred? What is the average
amount of cash held during the month and how much extra interest could have
been received if this cash had not been withdrawn? Using your answers, find
the number of withdrawals that minimises the sum of transactions costs and
foregone interest. What is the implied level of money demand (on average)
during the month?
(b) [7 marks] By issuing money that pays no interest as opposed to bonds that pay
interest, the government is able to reduce its overall borrowing costs. The
reduction in the government’s interest costs is equal to the nominal interest rate
i multiplied by the real money supply M/P , referred to here as seigniorage
revenue. After taking account of the requirement that the real money supply
must be equal to the demand for money derived in part (a), show that
seigniorage revenue is higher when the nominal interest rate is higher. How
large is the sum of the transactions costs and foregone interest suffered by
households relative to the amount of seigniorage revenue collected by the
government?
(c) [6 marks] Suppose the government’s objective is to maximise an objective
function given by seigniorage revenues minus the transaction costs and foregone
interest suffered by households. After taking account of the requirement that
the real money supply must be equal to the demand for money derived in part
(a), find the required nominal interest rate. Give an economic intuition for your
answer.
Reading for this question
Subject guide, Chapters 4, 11 and 13.
Approaching the question
(a) Each of the n withdrawals costs an amount c, so the total transaction cost (denoted Kc ) is
cn. With n equally-sized withdrawals over the month and with income P Y spent completely
at the end of the month, each withdrawal has size P Y /n. Since cash is spent at a constant
rate and as each new withdrawal is made when holdings of cash reach zero, the average cash
balance M held during the month is P Y /(2n). The amount of foregone interest expressed as
a real cost (and denoted Ki ) is iM/P , and hence Ki = iY /(2n). The sum K of transaction
costs Kc and foregone interest Ki is:
K = cn +
iY
.
2n
The first-order condition below is used to find the number of transactions n that minimises
total costs K:
∂K
iY
= c − 2 = 0.
∂n
2n
This equation can be rearranged as follows to solve for the optimal number n:
r
iY
iY
2
n =
⇒
n=
.
2c
2c
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EC2065 Macroeconomics
Average holdings of real money balances are M/P = Y /(2n), hence real money demand is:
r
r
Y
M
2c
cY
=
=
.
P
2 iY
2i
(b) Let S = iM/P denote seigniorage revenues. Using the expression for real money demand
from part (a), seigniorage revenues are:
r
r
cY
ciY
S=i
=
.
2i
2
This is an increasing function of i, so real seigniorage revenues are larger when the nominal
interest rate is higher. Since S = Ki , this formula also gives the interest foregone by
households. Next, using the expression for the optimal value of n from part (a), total
transaction costs Kc are:
r
r
iY
ciY
Kc = c
=
.
2c
2
Therefore, the minimised sum of all costs faced by households is:
r
r
r
ciY
ciY
ciY
+
=2
K = Kc + Ki =
2
2
2
and hence the ratio of these costs to the government’s seigniorage revenue is:
K
= 2.
S
The total costs faced by households are double the amount of seigniorage received by the
government.
(c) Suppose the government wants to maximise the difference between its seigniorage revenue S
and the total costs K faced by households. Since seigniorage revenue S is identical to
foregone interest Ki , the objective is to maximise:
S − K = S − Kc − Ki = −Kc .
This means that the government must minimise total transaction costs Kc to fulfil its
objective. Using the expression for the optimal value of n from part (a), total transaction
costs Kc are:
r
r
iY
ciY
Kc = c
=
.
2c
2
This formula is increasing in the nominal interest rate i, so the interest rate that minimises
transaction costs is i = 0.
Intuitively, foregone interest is simply a transfer from holders of money to the government
(it is identical to seigniorage revenue). When private agents choose holdings of money to
minimise the sum of transaction costs and foregone interest, the outcome is not necessarily
efficient because agents might choose to incur transaction costs to avoid losing out on
interest. These transaction costs are a deadweight loss because time and resources are used
up simply to prevent one party having to make a transfer to another. After netting out
transfers, efficiency therefore requires that transaction costs are minimised. However,
private agents will do this only when there is no individual incentive to try to avoid
foregoing interest, which means that the return on bonds must be brought into line with the
return on money. Therefore, the nominal interest rate must be brought down to zero.
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Examiners’ commentaries 2016
Question 12
Consider a household choosing a consumption plan for two time periods (Fisher
model of consumption). In the first time period, the household has no initial assets,
receives income Y1 , and pays (lump-sum) tax T1 . The household chooses its current
consumption C1 and the amount of bonds B to carry into the future time period. In
the future, the household will receive income Y2 and pay taxes T2 , and will have
financial wealth (1 + r)B, where r is the real interest rate. Future consumption C2
will be:
C2 = Y2 − T2 + (1 + r)B
The government has current expenditure G1 and plans expenditure G2 in the
future. If the government runs a deficit D = G1 − T1 then it issues bonds that pay
interest rate r. Assume that the government has no initial debt and must repay all
debt in the future time period, hence
T2 = G2 + (1 + r)D
(a) [6 marks] Derive present-value (‘life-time’) budget constraints for the household
and for the government, and show how these life-time budget constraints can be
combined to eliminate taxes T1 and T2 .
(b) [7 marks] Suppose there is a temporary increase in government spending G1 .
Find the effects on current consumption C1 , private saving Sp = Y1 − T1 − C1 ,
and national saving Sn = Sp + (T1 − G1 ) in the following cases:
i. there is no increase in current taxes T1 ;
ii. taxes T1 are increased by the same amount as government spending G1 .
In what sense does ‘Ricardian equivalence’ hold in this example?
(c) [7 marks] Assume a closed economy and suppose that the government defaults
on some of its debts in the second time period (and that this was completely
unexpected in the first time period). Explain what effect this is predicted to
have on consumption C2 . Does your reasoning imply that government bonds are
part of the economy’s ‘net wealth’ ?
Reading for this question
Subject guide, Chapters 9 and 13.
Approaching the question
(a) In the first time period, disposable income Y1 − T1 that is not spent on consumption C1 can
be used to buy bonds B = (Y1 − T1 ) − C1 . In the second time period, consumption is given
by future disposable income Y2 − T2 plus financial wealth (1 + r)B, that is,
C2 = (Y2 − T2 ) + (1 + r)B. By substituting the expression for B from the first time period:
C2 = (Y2 − T2 ) + (1 + r)((Y1 − T1 ) − C1 )
and dividing both sides by 1 + r and rearranging:
C1 +
(Y2 − T2 )
C2
= (Y1 − T1 ) +
.
1+r
1+r
This is the household’s life-time budget constraint. The present discounted value of current
and future consumption must equal the present discounted value of current and future
income after tax.
For the government, substituting the expression for its first-period deficit D = G1 − T1 into
the formula for the level of second-period taxes T2 = G2 + (1 + r)D required to cover
spending and debt repayments:
T2 = G2 + (1 + r)(G1 − T1 ).
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EC2065 Macroeconomics
Dividing both sides by 1 + r and rearranging leads to:
G1 +
G2
T2
= T1 +
.
1+r
1+r
This is the life-time budget constraint for the government. The present discounted value of
current and future government spending must equal the present discounted value of current
and future taxes.
The household and government life-time budget constraints can be combined as follows to
eliminate the present value of taxes:
C1 +
C2
=
1+r
Y1 +
Y2
1+r
T2
Y2
G2
− T1 +
= Y1 +
− G1 +
.
1+r
1+r
1+r
The present value of consumption is effectively constrained by the present value of life-time
pre-tax income net of the present value of government spending.
(b) Since taxes do not appear in the consolidated life-time budget constraint, the effect on the
budget constraint of the increase in government spending is the same in both cases
considered in the question. The budget constraint shifts to the left by an amount equal to
the rise in G1 . This leads the household to choose lower consumption C1 , but C1 does not
fall by as much as G1 rises (because C2 decreases as well, which is optimal if current and
future consumption are both normal goods). The same fall in C1 occurs irrespective of
whether the government borrows more or raises taxes immediately.
In case i. where there is no increase in current taxes, since disposable income is unchanged
and consumption falls, private saving Sp = Y1 − T1 − C1 must increase. National saving is
Sn = Sp + (T1 − G1 ) = Y1 − T1 − C1 + T1 − G1 = Y1 − C1 − G1 . As C1 falls by less than G1
rises, national saving must fall.
In case ii. where a rise in current taxes matches the increase in government spending,
disposable income is reduced. However, since the fall in consumption is smaller than the rise
in taxes (equal to the rise in government spending), private saving must fall. In this case,
there is no change in the government budget deficit, so the change in national saving is
equal to the change in private saving. National saving must therefore fall.
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Examiners’ commentaries 2016
Although fiscal policy affects consumption in this example, the timing of taxes does not.
Ricardian equivalence holds in the sense that the different ways the government can pay for
the increase in spending (borrowing more, or raising taxes now) have equivalent effects on
consumption.
The effect on private saving does depend on how the government pays for the increase in
spending. When the government borrows more, the private sector saves more. When the
government does not borrow, the private sector borrows. However, the impact on national
saving is the same in both cases: the economy as a whole reduces saving. This is due to the
increase in government spending being temporary combined with a desire for consumption
smoothing by households, implying that current consumption falls by less than the increase
in government spending. Therefore, the sum of spending by households and the government
rises, so with no change to national income, these two groups must together be saving less or
borrowing more. When taxes rise, households are solely responsible for the decline in saving.
When taxes are not changed, the government borrows even more, and households partially
increase saving to compensate.
(c) In the second time period, consumption is given by C2 = Y2 − T2 + (1 + r)B. In a closed
economy, households must ultimately hold the bonds D issued by the government. Let B0
denote bonds issued by entities other than the government (for example, corporate bonds
issued by firms). It must be the case that household holdings of bonds are equal to
B = D + B0 . Consumption C2 is therefore:
C2 = Y2 − T2 + (1 + r)D + (1 + r)B0 .
As this equation shows, a default that reduces the government’s repayments (1 + r)D has
the effect of reducing households’ financial wealth by the same amount. However, the
equation for the required level of taxes T2 is still valid after taking account of the default in
reducing (1 + r)D:
T2 = G2 + (1 + r)D.
It follows that (1 + r)D = T2 − G2 , which can be substituted into the expression for C2 :
C2 = Y2 − T2 + (T2 − G2 ) + (1 + r)B0 = Y2 − G2 + (1 + r)B0 .
The term (1 + r)D cancels out, which suggests the default will have no effect on
consumption unless it leads to a change in government spending G2 .
Intuitively, while default reduces households’ financial wealth, it also reduces the need for
taxes. This illustrates the idea that government bonds are not part of the economy’s ‘net
wealth’. Households holding bonds are also subject to the taxes that will be used to repay
those bonds. Default eliminates a financial claim of households on government, but by
reducing the need to raise taxes, eliminates a claim of the government on households. These
two effects cancel each other out.
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EC2065 Macroeconomics
Question 13
Consider a small open economy with fixed prices and wages.
Goods-market equilibrium is where output Y is equal to the sum of consumption C,
investment I, government spending G, and net exports N X. The consumption and
investment functions are:
C = C0 + c(Y − T ),
I = I0 − bi
where i is the domestic interest rate. Government spending and taxes are
exogenously fixed at G = G0 and T = T0 . Net exports are given by:
N X = N X0 − mY − ae
where e is the nominal exchange rate (defined as the foreign-currency price of
domestic currency).
Money-market equilibrium is where the demand for real money balances L(Y, i) is
equal to the real money supply M s /P :
Ms
P
= L(Y, i)
where L(Y, i) is an increasing function of Y and a decreasing function of i.
Balance-of-payments equilibrium is where the sum of the current account CA
(assumed equal to net exports N X) and the capital account KA is zero. Capital
mobility is imperfect, and capital flows are given by the equation:
KA = KA0 + f (i − i∗ )
where i∗ is the foreign interest rate. Throughout the question, assume the exchange
rate is flexible.
(a) [7 marks] Show how balance-of-payments equilibrium (BP = 0) requires a
positive relationship between income Y and the domestic interest rate i (for a
given exchange rate e), referred to as the BP curve. What happens to the BP
curve if the exchange rate depreciates? Use your answers to show how
adjustment of the exchange rate allows an economy in internal equilibrium with
BP < 0 to reach both internal and external equilibrium.
(b) [7 marks] Suppose the government decides to establish a sovereign wealth fund.
Instead of using tax revenue to repay government debt, the sovereign wealth
fund purchases foreign assets (it effectively sells domestic assets in exchange for
foreign assets). This affects the term KA0 in the equation for the capital
account. Using the IS-LM-BP diagram, show how establishing the sovereign
wealth fund changes the economy’s equilibrium, stating the effects on the
current account, the capital account, and investment. Is there a change in
national saving? Explain your answer.
(c) [6 marks] What difference would it make to your answers to part (b) if there
were greater capital mobility? What happens in the special case of perfect
capital mobility? Explain the economic intuition for your answer.
Reading for this question
Subject guide, Chapters 7 and 8.
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Examiners’ commentaries 2016
Approaching the question
(a) Balance of payments equilibrium requires BP = CA + KA = 0. Using the equations for the
current account (net exports) N X and the capital account KA:
(N X0 − mY − ae) + (KA0 + f (i − i∗ )) = 0.
This equation can be rearranged to express the domestic interest rate i as a function of
income Y , taking the exchange rate e as given:
i = i∗ +
mY + ae − N X0 − KA0
.
f
The derivative of i with respect to Y is m/f , which is positive. The BP line, representing
balance-of-payments equilibrium, is therefore an upward-sloping line. Intuitively, higher
income leads to higher imports and a lower current account. However, if the country is to
buy more goods from foreign countries without selling more goods to them, assets must be
sold to foreigners instead. This means a capital account surplus is required, but with
imperfect capital mobility, foreign investors are only willing to hold more domestic assets if
the domestic interest rate rises relative to the foreign interest rate. This is what lies behind
the positive relationship between income and the interest rate depicted as the BP line.
Suppose the economy’s internal equilibrium (the intersection between the IS and LM curves)
would lead to a balance of payments deficit (BP < 0). Since the capital account is increasing
in i, the region below the BP line corresponds to where a balance of payments deficit occurs
in the diagram, which means the intersection of IS and LM is below the BP line. A balance
of payments deficit means that there would be less demand for the domestic currency in the
foreign exchange market to purchase domestic goods or assets than the amount agents
would like to supply. This is not an external equilibrium, and there would be pressure for
the domestic currency to depreciate in value relative to the foreign currency (e falls).
As the exchange rate falls, the domestic interest rate required for balance-of-payments
equilibrium decreases (given a level of income Y ), which means that the BP line shifts
downwards. Intuitively, the depreciation of the domestic currency leads to a gain in
competitiveness for domestic goods, which increases net exports and therefore reduces the
balance of payments deficit. The increase in net exports also raises the demand for goods,
shifting the IS curve to the right. External equilibrium is restored through a combination of
the BP line shifting downwards and the IS curve shifting to the right, until both intersect
the LM curve at the same point.
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EC2065 Macroeconomics
(b) Establishing the sovereign wealth fund increases domestic purchases of foreign assets funded
by increased sales of domestic assets (more domestic government bonds are in circulation
than would otherwise be the case). These transactions increase the economy’s capital
account deficit, which corresponds to a lower value of KA0 in the equation for the capital
account. The reduction in KA0 shifts the BP line upwards, so all else equal, a higher
interest rate is required for balance-of-payments equilibrium. Intuitively, if there were no
change in the current account, external equilibrium would require private investors to sell
foreign assets to the sovereign wealth fund and buy domestic assets. With imperfect capital
mobility, they are only willing to do this if i rises relative to the foreign interest rate i∗ (and
the latter is taken as given by a small open economy).
The upward shift of the BP line means that the economy is no longer in both internal and
external equilibrium (establishing the sovereign wealth fund does not directly affect the
demand for goods, so the IS curve does not shift, and does not directly affect the demand
for or supply of domestic currency, so the LM curve does not shift). The economy is now in
the position described in part (a) where internal equilibrium would result in a
balance-of-payments deficit. The adjustment to internal and external equilibrium is the one
described in the answer to part (a).
The domestic currency depreciates, shifting the IS curve to the right and the BP curve
partially back downwards. The economy’s equilibrium is now at a higher level of income and
a higher interest rate. The current account improves because of the exchange rate
depreciation that shifts the IS curve to the right, and given balance-of-payments equilibrium,
the capital account must deteriorate. Investment falls because of the higher interest rate.
National saving is equal to the sum of investment and the current account, but since the
former declines while the latter increases, this equation does not provide an unambiguous
prediction. Alternatively, note that national saving is defined as the sum of private saving
and public saving. The latter is unchanged, while the former increases because income rises
by more than consumption does (since the marginal propensity to consume is less than one).
It follows that national saving must increase.
(c) Greater capital mobility means that international investors have a greater willingness to
seek out the highest returns internationally for their wealth. This implies that international
capital flows become more sensitive to relative interest rates, which is represented by a
higher value of the coefficient f in the capital account equation.
An increase in f reduces the gradient of the BP line, and also reduces the size of the vertical
shift of the BP line that occurs when the sovereign wealth fund is established. While the
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direction of the effects described in part (b) is the same, the magnitude of all the effects is
reduced.
In the special case of perfect capital mobility, f becomes extremely large as the smallest
difference in interest rates is now sufficient to induce very large capital flows. This means the
BP line becomes horizontal and does not shift when the sovereign wealth fund is established.
There are no effects on the current account, capital account, investment, or national saving.
Intuitively, since private investors are indifferent between domestic and foreign assets as long
as the domestic and foreign interest rates are equalised, they are willing to trade assets with
the sovereign wealth fund without the need for any change in interest rates. Private capital
simply flows in the opposite direction to the capital flows associated with the sovereign
wealth fund, and the economy’s equilibrium is unaffected.
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EC2065 Macroeconomics
Question 14
Consider a government with preferences represented by the loss function
L = π 2 + au
where π is the inflation rate, u is the unemployment rate, and a is a positive
constant indicating the strength of the government’s preference for low
unemployment.
There is an expectations-augmented Phillips curve that links inflation and
unemployment:
u = un − b(π − π e )
where π e denotes inflation expectations, un is the natural rate of unemployment,
and b is a positive constant. Expectations of inflation are assumed to be rational.
Assume that monetary policy is able to affect aggregate demand and thus control
the unemployment rate u.
(a) [6 marks] List and explain two costs of inflation. The term π 2 in the loss
function implicitly assumes that deflation is just as costly as inflation. Is this
true for the costs of inflation you have listed?
(b) [7 marks] Assume that the government is able to choose a monetary policy
without being restricted by any past commitments (the government acts with
discretion). This means inflation expectations π e are taken as given when
monetary policy is chosen. Find the inflation rate π that minimises the loss
function subject to the Phillips curve. Given that expectations are formed
rationally, what are the equilibrium unemployment and inflation rates?
(c) [7 marks] Now suppose the government is able to commit to a rule where
monetary policy must meet an inflation target of π = 0. Assuming this rule is
credible, find the equilibrium unemployment rate and explain the sense in which
the equilibrium found in part (b) features an ‘inflation bias’. Explain why the
zero inflation rule is not time consistent, and briefly discuss some mechanisms
by which a government might make a credible commitment to low inflation.
Reading for this question
Subject guide, Chapters 4 and 12.
Approaching the question
(a) Menu costs are one cost of inflation. A menu cost refers to a cost of reprinting a price label
or catalogue, or more generally, any cost incurred in the process of adjusting prices. When
there is inflation, there is a greater need to change prices more frequently (to maintain
desired relative prices), which means more menu costs need to be paid. The optimal rate of
inflation to minimise menu costs is zero because deflation leads to exactly the same problem
as inflation.
Another cost of inflation is relative price distortions. Inflation can distort actual relative
prices of goods and services because prices are infrequently adjusted at different times for
different products, or it can lower the informational content of prices if agents are not fully
informed about all other prices (there is a possibility of confusion between nominal and
relative price changes). This leads to a less efficient allocation of resources because the
quantities produced and consumed of different goods are now affected by the overall rate of
inflation, not only by the economy’s real fundamentals. The optimal rate of inflation to
minimise relative price distortions is zero because deflation creates exactly the same
problems.
There are other examples of costs of inflation, such as shoe-leather costs. Not all of these
imply that the optimal rate of inflation is zero (for shoe-leather costs, it would be negative).
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Examiners’ commentaries 2016
(b) The loss function is minimised subject to the Phillips curve as a constraint. Substituting the
Phillips curve into the loss function to eliminate the unemployment rate:
L = π 2 + a(un − b(π − π e )) = π 2 − abπ + aun + abπ e .
Expectations of inflation π e are taken as given under discretion. The government chooses
inflation π to minimise the loss function, which requires the following first-order condition to
hold:
∂L
= 2π − ab = 0.
∂π
The solution for the inflation rate is π = ab/2.
Expectations of inflation are assumed to be formed rationally. Any π e different from ab/2
would result in a predictable error in forecasting inflation, so rational expectations requires
π e = ab/2. Since π = π e , the Phillips curve implies that the equilibrium unemployment rate
is u = un . The unemployment rate is equal to the natural rate of unemployment.
(c) If the government commits to rule with π = 0 and this is credible, rational expectations
implies π e = 0 as well. With π = π e , the Phillips curve implies u = un . The equilibrium in
part (b) features an inflation bias in the sense that compared to part (c), there is higher
inflation (π = ab/2 > 0), which is worse, but no gain in terms of lower unemployment
(u = un in both cases).
While the rule π = 0 is superior to discretion, it is not time consistent. Once the
government has succeeded in persuading private agents to expect π e = 0, the optimal choice
of inflation is π = ab/2. This is because with π e given, the Phillips curve implies the
government could achieve u < un by having π > 0 = π e . Therefore, the government would
not honour a past commitment to choose π = 0 unless it were compelled to. Of course, if
the government is not bound to deliver π = 0, this means that rational agents would expect
π e = ab/2 in equilibrium, which was the outcome in part (b).
To make the commitment credible, the government must limit its ability to interfere with
monetary policy. This might be done by making the central bank independent, and
appointing a hawkish governor, or establishing a policy framework such as inflation
targeting where the independent central bank is assigned a different set of goals from those
represented by the government’s loss function.
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