Sem 1 Tutorial

Question 1

how do you calculate gross capital income?

Answer 1

GDP at market price - labour income - (taxes - subsidies)

Question 2

how do you calculate net capital income?

Answer 2

gross capital income - depreciation

Question 3

what is net domestic product?

Answer 3

GDP adjusted for depreciation
NDP @ market price = GDP - depreciation rate K

Question 4

British PPP. The Office for National Statistics reports that GDP per capita in the UK was about £26
000 in 2013, whereas GDP per capita in the United States in 2013 was about $53 000. On a purchasing
power parity (PPP) basis, GDP per capita is listed as about $36 000 in the UK, and $53 000 in the USA.
The average exchange rate in 2013 was about $1.58 per pound.
(a) What is US GDP per capita at market exchange rates (expressed in dollars)? Is this higher or lower
than the PPP measure?
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(b) What is UK GDP per capita at market exchange rates (expressed in dollars)? Is this higher or lower
than the PPP measure?
(c) Based on your answers above, do you think that the price level is higher or lower in the UK? By
how much?
(d) In percentage terms, how much poorer are Brits than Americans when measured at market exchange
rates? What about at PPP? Which measure do you think is better?

Answer 4

This is given in the question: GDPPCUS,$ = $53 000. This is equal to the PPP
measure. The US is the reference country for PPP calculations, so these numbers will always be
equal to one another.

GDPPCUK,$ = GDPPCUK,£ ×ϵ$/£ = 26000 ×1.58 = $41 080 ≈$41 000. This is
higher than the PPP measure.

Prices are higher in the UK. To see how much, take 41 000−36 000
36 000 , which is about
14%. This means that if you took $114 and converted it to £s at market exchange rates, then
the £72 (and change) you would get can buy about as many goods as $100 spent within the
United States.

diff (market rates)= 22.6
diff PPP = 32.07

PPP is generally a better measure for standard-of-living comparisons, because they measure the
real purchasing power of incomes.

Question 5

Cost minimization. A firm’s production function is given by: Q= K ^1/2 L^1/4 where Q is output in
thousands of units, K is capital input measured in machine-hours and L is labour input measured
in worker-hours. The firm is perfectly competitive and the factor prices are r = £2.50 per hour and
w= £7.50 per hour. The total costs are given by TC= rK+ wL.
Use the method of Lagrange multipliers to find the combination of K and L that minimises the cost of
producing Q= 4.5.

Answer 5

4.5 = (6L)0.5L0.25 ⇐⇒4.5 = 6
1
2 L3
4 = ⇒L=
4.54
62
3
= 2.25; K = 6L= 13.5.

Question 6

Woodwork. A carpenter plans to make a rectangular wooden box with no lid (that is, open on its top
side) and with a capacity of 108 cubic metres. The necessary wood costs £25 per square metre. Find the
dimensions of the box that will minimize the cost of wood. Find also the minimized cost.

Answer 6

Substitute x= 2z and x= y into (4) to get 108 = 2z·2z·z= 4z3 ⇒z = 3.
Therefore, x = y= 6.
The minimised cost is
TC(x,y,z) = TC(6,6,3) = 50·6·3 + 50·6·3 + 25·6·6 = 2700

Question 7

Which of the following will affect this year’s UK GDP (and how)? Suppose that a UK owned & operated automotive manufacturer…
…builds a car and sells it to the UK government – this will increase UK GDP
…builds a car and sells it to a Russian – this will increase UK GDP
…builds a car and puts it in inventory to sell next year – this will not affect UK GDP
…imports steel to expand its factory – this will decrease UK GDP

Answer 7

true, true, false, false

Explanation: GDP = C + I + G + X -M. i. adds to G, so is true, ii. adds to X, and so is also true, iii. adds to I, so is false. The only other statement (which students were most likely to be confused about) is iv. – although imports are subtracted from GDP, in this case the steel was also counted in investment. So overall, the steel (being produced abroad) has no effect on UK GDP (but does not reduce it).

Question 8

Consider the following statements about Gross Domestic Product (GDP) and Gross National Income (GNI). Which (if any) of the statements are true?
|GDP -GNI| = net current transfers from the rest of the world.
For a country where many companies which produce domestically are foreign-owned, we expect GNI > GDP
On average, GNI is about 10% to 15% higher than GDP
Both GDP and GNI are already adjusted for the consumption of capital

Answer 8

FALSE
FALSE
FALSE
FALSE

False - the difference is not net current transfers, but net primary income ii. False (because net primary income will be negative for such a country – e.g. Ireland) iii. False – the average difference should be zero (because worldwide net primary income must add to zero), and a typical gap is just a few percent one way or the other. iv. False – the “gross” in the name of each means that they are not adjusted (the adjusted versions have “net” in the name).

Question 9

In some country, the capital stock is twice as large as GDP at market price in one year. The depreciation rate is 7%, net exports are negative and equal to minus 5% of GDP, net primary income from the rest of the world is 3% of GDP and net transfers from the rest of the world are 1% of GDP at market price.
Calculate net national disposable income at market price as a percent of GDP at market price.

Answer 9

The first thing to note is that net exports is already in GDP, so we don’t need that number. The first thing we need is to calculate net GDP at market price (net of depreciation). This is 100 − 2 × 0.07 = 86%. To get net national income at market price, we need to adjust this figure for net primary income from the rest of the world, which gives us 86 + 3 = 89%. Finally, to get net national disposable income at market price, we need to add net transfers from the rest of the world, which gives 89 + 1 = 90%

Question 10

Given the national accounts data below for some country, calculate net national disposable income at market price as a percentage of GDP (rounded to the nearest 1%)
GDP at market price …………………………………… 1000
Deprecation of capital …………………………………. 100
Labour income …………………………………………… 600
Net transfers from abroad ……………………………. -10
Net primary income from abroad …………………… 20
Indirect subsidies (subsidies on products) ………. 30
Indirect taxes (taxes on products) ………………….. 40

Answer 10

As seen in the textbook, the definition of net national disposable income at market price is: GDP + net primary income and net transfers from the rest of the world – consumption of capital. In this case, that’s 1000 + 20 − 10 − 100 = 910 = 91%.

Question 11

Reusing the data from the previous question, what is gross value added at basic price as a percentage of GDP (rounded to the nearest 1%)
GDP at market price …………………………………… 1000
Deprecation of capital …………………………………. 100
Labour income …………………………………………… 600
Net transfers from abroad ……………………………. -10
Net primary income from abroad …………………… 20
Indirect subsidies (subsidies on products) ………. 30
Indirect taxes (taxes on products) ………………….. 40

Answer 11

As seen in the textbook, the definition of gross value added at basic price is: GDP – taxes less subsidies on products. In this case, that’s 1000 − 40 − 30 = 990 = 99%.

Question 12

Consider the national income identity. According to the theory developed in the textbook, which of the following must be true in any given year?
C < GDP
G < GDP
X < GDP
M < GDP

Answer 12

Notice that the question emphasised the theory and not the data. In practice, all four of these inequalities are normally true, but in theory any of them can be false. How? The national income identity is: 𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝑋 − 𝐼𝑀. Each variable has a value greater than zero, but because imports enter negatively, it means that we can in theory have extreme examples like: 𝐺𝐷𝑃 = 10, 𝐶 = 11, 𝐼 = 11, 𝐺 = 11, 𝑋 = 11, 𝐼𝑀 = 34. A situation like this cannot be sustained for long, but might be true in a given year. For example, during World War II, Malta was a major military outpost for the allies, and imports of military and other equipment were huge relative to domestic production. There are no reliable GDP figures for the time, but it would not be surprising if several of the inequalities above were violated (though not perhaps the one on exports, but as we saw in the tutorial sheet, small trans-shipment states like Singapore can regularly export more than 100% of GDP).

Question 13

Assume that the real interest rate and the subjective rate of discount are both zero. A person is 20
years old and expects to live to 80 – working for an after-tax salary of £50,000 per year until the age
of 60, then retired with a state pension of £5,000 per year from age 60 until death (and no pension
from work – only whatever savings they have). To simplify, we assume that the person acts as if future
incomes and the length of life were known with certainty. What is his optimal level of consumption and
how much do they save?

Answer 13

From the first order condition u
′ (Ct)
u′ (Ct+1 )= 1+r
1+ρ
we see that if r= ρ, real consumption must
be constant over time, so we have C=
£50k×40+£5k×20
£2100k
=
60
60
= £35k (note: if there is inflation,
it may be that nominal consumption is rising, but we are concerned with real values). Optimal
consumption is thus £35,000 per year in all years – the person will save £15,000 per year while they
work, and dissave £30,000 per year while retired.

Question 14

A consumer expects to live forever and he/she has a constant labour income of £30,000 per year, no
assets, and a loan of £40,000. The nominal interest rate on the loan is 4% and inflation is 0%.
(a) What is the consumers’ sustainable level of consumption?

Answer 14

Solution: C = 30 000− (0.04− 0.00) × 40000 = 30 000− 1600 = £28 400

Question 15

Assume that velocity is determined by the function 𝑽 = 𝑽o𝒆𝒃𝒊, where Vo is the ‘base’
velocity, b is a parameter, and t, the nominal interest rate i is determined by 𝒊 = 𝒓𝒏 + 𝝅,
where the natural (real) rate of interest, 𝒓𝒏, is taken as given.
(a) Write down an expression for seignorage as a fraction of GDP. You can assume that
there is no population growth (𝒏 = 𝟎).

b) Calculate an expression for the rate of inflation that maximises seignorage. How
does the result depend on the parameters b and g? Explain the result

Answer 15

S = change in M/PY

but with the things given in the question just sub in

b) inflation = 1/b - g

Question 16

Suppose that the velocity of the monetary base is 20, real GDP grows 3% per year and
inflation is 2%.
(a) Calculate seignorage relative to GDP

Answer 16

𝛥𝑀/ 𝑃𝑌 = %𝛥 𝑁𝐺𝐷𝑃/ 𝑉
0.03 + 0.02/ 20 = 0.0025 = 0.25% 𝑜𝑓 𝐺𝐷𝑃

Question 17

Q11. The money supply increases 10% in a year. What is the inflation rate if…
(a) …real production and velocity are constant

(b) …real production grows 4 percent and velocity is constant

(c) …real production is constant and velocity decreases from 2 to 1.8

Answer 17

Using our rule of thumb 𝜋 = 𝛥𝑀 + 𝛥𝑉 − 𝛥𝑌𝑛
, we have 𝜋 = 10% + 0% − 0% = 10%
𝑀 𝑉 𝑌𝑛

b)

𝜋 = 10% + 0% − 4% = 6%

c) Velocity decreases by 10 percent so inflation will be 𝜋 = 10% − 10% − 0% = 0%

Question 18

Q7.
(a) What is the monetary base?

(b) Is it possible to make purchases without using monetary base?

(c) Is it possible to make loans and pay interest without using monetary base?

(d) Does the central bank have perfect control of the monetary base?

Answer 18

Currency in circulation plus banks’ deposits at the central bank.

Yes. You can barter, for example. Or you can make purchases with the monetary base
(e.g. by using cash).

Yes if you do it in terms of goods and services: I lend you potatoes and you pay back with more potatoes (or with lots of sheep or whatever).

Yes, if the central bank sells a government bond for one million it withdraws one million of monetary base.

Question 19

Q2. What is the effect on credit markets of each of the following? Make sure to specify
and explain who (if anyone) wins, and who loses.
(a) Unexpected inflation

(b) Unexpected disinflation

c) Expected inflation

d) Expected disinflation

Answer 19

Unexpected inflation will redistribute from lenders to borrowers, since it has the effect
of reducing the value of any payment stream which is fixed in nominal terms (such as a
mortgage, or any other loan).
Many families who took out mortgages with fixed interest rates in the 1960s benefited
from this effect in the 1970s when inflation increased throughout the developed world –
wages and house prices rose with prices, but mortgage payments remained fixed in
nominal terms, hurting banks and helping leveraged homeowners.

Unexpected reductions in inflation (disinflation) have the opposite effect of unexpected
inflation – disinflations redistribute from borrowers to lenders.
Japan in the 1990s and the United States in the 1930s both experienced extended
disinflations (leading to deflation in both cases). Each of these episodes had the effect of
reducing the real wealth of borrowers by increasing the real value of their loan
repayments. Lenders (e.g. banks) correspondingly benefitted from the disinflation
(though both cases were associated with financial crashes, so banks were not doing well
overall).

In general, expected inflation shouldn’t create any winners or losers – financial contracts
will be written taking account of the inflation given the Fisher identity 𝑖 = 𝑟 + 𝜋 for any
target real interest rate r.
One possible caveat is that for governments (such as the UK government) who tax
interest earnings in nominal terms, higher inflation will lead to higher nominal rates and
higher taxes, increasing tax revenues at the expense of participants in the credit market

Like expected inflation, expected disinflation shouldn’t create any winners or losers,
except that the same caveat from above applies in reverse – the tax burden should be
lower in countries where taxes are denoted in nominal terms.

Question 20

Finding the finding rate. To keep things simple, the textbook model focuses on a situation where
employment and the labour force are constant, and assumes that the employed and the unemployed have
the same probability of finding a job in a given month, and this probability is denoted f. We would like to find the value of f.

(a) The textbook model also makes use of the variables s, Z, N, U, L and u. What are these?

(b) How many job openings are there each month?

(c) How many people are seeking a job?

(d) What is the probability f that a job seeker finds a job in a given month?

(e) How does the value of f that you just found depend on s, u, and Z? Give an intuitive interpretation
for each variable.

Answer 20

s the share of employed workers who apply for other jobs and leave, independently of
whether or not they find another job
Z the share of employed workers who apply for other jobs and quit if they find one
N the number of workers employed
U the number of workers unemployed
L N + U
u U/L

Solution: The number of job openings left by those who leave for exogenous reasons is N · s.
The number of job openings left by those who quit only if they get another job is N · Z · f .
Thus the total number of job openings is N s + N Zf .

Solution: This consists of the workers unemployed at the beginning of the month, U , plus
those who quit exogenously N · s, plus those searching on the job N · Z. Thus, the total number
of people looking for work is given by U + N s + N Z.

Solution:
f = number of openings
number of seekers
f = N s + N Zf
U + N s + N Z
f (U + N s + N Z) = N s + N Zf
U f + N sf + N Zf = N s + N Zf
U f + N sf = N s
f = N s
U + N s
f ≈ s
u + s
Note that the last step uses the approximation L ≈ N . In fact, L = N + U , but since N is
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generally about 15 to 20 times larger than U , the approximation is not too far wrong, and it
simplifies the math quite a bit.

Solution:
∂f
∂s > 0: as the rate of exogenous separation increases, there are more job openings and it is
easier to find a job.
∂f
∂u < 0: as the unemployment rate increases, there are more people seeking work, so the
probability of a given job seeker finding work declines.
∂f
∂Z = 0: the share of employed workers who apply for other jobs and quit if they find one does
not affect the job finding rate; this is because these people create exactly one job opening for
every job they take, and so their effect cancels out.

Question 21

In contrast to the finding rate which you derived in an earlier question, the finding rate is
sometimes written as f = s/(λu + s). What does λ represent? Who does this finding rate apply to? Give
some intuition for the effect of λ on the job finding rate

Answer 21

Here, λ represents the willingness and ability of the unemployed workers to compete for
jobs. λ is a proportion (i.e., 0 ≤ λ ≤ 1), and so we should think of λU as effective unemployed job
seekers looking for work, rather than the actual number U of job seekers.
When only a proportion λ of the unemployed can search effectively for jobs, f = s/(λu + s) represents
the probability of an employed worker finding a job, whereas the chance of an unemployed worker
finding a job is λf .
When λ decreases, the job finding rate of the employed will rise (because they face less effective
competition), whereas the job finding rate of the unemployed will fall (because they are less effective).
This, in turn, puts upward pressure on wages, so the wage-setting schedule shifts up and the natural
rate of unemployment increases.

Question 22

Consider the wage setting equation W d/W = 1 + a − bu. What is the effect on wage setting and the natural rate of unemployment of the following shocks:

a) An increase in hiring costs.

(b) A new unemployment agency is created that helps unemployed workers to search more effectively.

(c) A new law limiting the possibilities of unions to call a strike.

Answer 22

Solution: An increase in the hiring cost makes firms more anxious to keep their workers so
they set higher wages; a increases, and the natural rate of unemployment increases.

Solution: If unemployed workers search more effectively, this reduces the chances that employed
workers find other jobs. Firms become less worried about losing their workers so they set lower
wages; a decreases and the natural rate of unemployment decreases.

Solution: If unions become weaker, wages will be lower for a given level of unemployment; a
decreases or b increases, and the natural rate of unemployment decreases.

Question 23

Efficiency wages and unemployment. The firm’s cost per worker is the direct wage cost plus the
turnover cost per worker:
Wi + h · W ·[s + Z ( Wi/W) · f ]
Where h is the cost of hiring and training a new worker as a fraction of the wage. The firm should (of
course) set wages to minimize this total cost.

(a) When the wage is set so that this cost is minimized, the derivative with respect to the wage is zero. Derive this condition. (Hint: Note that according to the chain rule, the derivative of Z(Wi/W ) with
respect to Wi is Z′ ( Wi/W) /W .

(b) Assume that we are in a symmetric equilibrium where all firms set the same wage. Solve for the
job-finding rate in equilibrium and explain the result.

(c) Set the job finding rate as f = s/(λu + s) and solve for the equilibrium rate of unemployment. What
factors affect unemployment and why?

d) Numerically, what happens to unemployment if λ doubles? Explain intuitively.

(e) Numerically, what happens to unemployment if s becomes twice as high? Explain intuitively.

Answer 23

b) Setting Wi = W we get

1 + hZ′(1)f = 0

Solving for f we get
f = − 1 / hZ′(1)

A few points:
– Z′(·) is negative, because workers at firm i are less likely to look for a new job when Wi/ W is higher.

– f is the proportion of folks finding jobs in a given time period, so 0 < f < 1.

– This implies that |hZ′(1)| > 1, which will be useful later.
– Commenting on the effects of h and Z′(1) on f :
an increase in hiring costs reduces the finding rate.
but note that because Z′(·) is already negative, an increase in Z′(·) means that it becomes closer to zero (from below), so this means that as the negative
slope of the Z function becomes flatter, the finding rate will decrease. Intuitively, as workers become less sensitive to inter-firm wage differentials (Z becomes flatter), they’re less likely to look for other work and so the hiring rate falls

Solution: If λ doubles, unemployment will be halved. (For example, the unemployment rate
will fall from 6 to 3 percent.) If unemployed workers compete twice as well for the jobs, the
unemployment “needed” to prevent wages from rising is reduced.

Solution: If twice as many workers leave their jobs, there will be twice as many job openings
and then we must have twice as many unemployed workers competing for jobs or else there
would be upward pressure on wages.

Question 24

Shocks to the steady state. Illustrate the effects on the steady state capital stock of the following shocks
and explain the results:
(a) An increase in the depreciation rate

b) An increase in the mark-up.

c) Consumers become more impatient

Answer 24

An increase in the depreciation rate will reduce the net return on investments (given by
f ′(k)/(1 + μ) − δ) for any given level of the capital stock. This is represented by a downward
shift of the net returns curve.
But since the equilibrium value of the net return should still be equal to r, and r has not
changed, something other than the net return must adjust. In this case, the marginal product
of capital – f ′(k) – will increase so as to keep the net return equal to the original value of r.
Given that capital is subject to the law of diminishing returns, the way to get the marginal
product of capital to rise is for the stock of capital to fall, and this is the result of the downward
shift of the net returns curve

The intuition here is very similar to the previous part of the question. When the
mark-up μ rises, then the net return to capital will be lower for any given level of capital, and
this is represented by a downward shift in the net returns curve.
Because the required rate of return r has not changed, a downward adjustment will be made to
the stock of capital.
Intuitively, an increase in the mark-up means that firms set higher prices and invest less so the
steady state capital stock is reduced.

Unlike the previous parts of the question, here we are not changing the net return
for a given level of capital (i.e. we are not shifting the net returns curve), but instead we are
changing the required return r. The required long run return is given by r = ρ + g. If consumers
become more impatient, they require a higher return on lending, and this is represented by
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moving to a higher point on a given net returns curve. Once again, the way to achieve higher
returns in practice is to decrease the stock of capital so as to increase the marginal product of
capital and therefore the gross (and net) returns. Intuitively, greater impatience, reduces the
amount of investment and so the steady state capital stock is reduced

Question 25

Consider the following statements about the effects of various factors on the optimal capital stock: When the interest rate (r) increases, the optimal capital stock increases. When the stock of labour (N) increases, the optimal capital stock increases. When the depreciation rate (delta) increases, the optimal capital stock increases. When the mark-up (mu) increases, the optimal capital stock increases

Answer 25

when the real interest rate 𝑟 rises, capital is more expensive to acquire, and so the optimal capital stock falls (i is false). When the number of workers 𝑁 increases, capital becomes more valuable (ii. is true). When the depreciation rate on capital rises, it is more expensive to maintain, so the optimal capital stock falls (iii. is false). When the markup increases, firms produce less output and so need less capital (iv. is false) ALL FALSE

Question 26

According to the theory presented in the textbook, there are four main factors that affect consumption, so that C equals C left parenthesis Y comma space Y to the power of e comma space r comma space A right parenthesis. Which of the claims below about how these factors affect consumption is always true? d C divided by d Y space less than space 0 d C divided by d Y to the power of e less than 0 d C divided by d r less than 0 d C divided by d A less than 0

Answer 26

false, false, false, false This comes directly from both the textbook and the tutorial sheet. i. ii. and iv. are the opposite of the truth, because an increase in current or expected income tends to increase consumption, as does an increase in assets. Case iii. is ambiguous, as the effect may depend upon whether the person is a saver or a borrower. So all statements are false.

Question 27

According to the theory presented in the textbook, the natural rate of interest will increase when ... ... inflation increases. ... part of the capital stock is destroyed. ... firms because more optimistic about future demand for their products.

Answer 27

FALSE TRUE TRUE was noted in the text, the natural interest rate is a real interest rate, so it does not change when inflation changes (i is false). The rest of the question comes directly from the week 5 tutorial sheet: ii. is true because capital destruction raises the demand from investment, iii. is true because investment depends positively on expected future income

Question 28

Consider a consumer who lives for two periods. What can we say about the effect on his consumption in the first period if the interest rate suddenly increases? The substation effect is ambiguous (it could be positive or negative) The income effect is ambiguous (it could be positive or negative) The total effect is ambiguous (it could be positive or negative)

Answer 28

FALSE TRUE TRUE The substitution effect from an increase in the interest rate will always be negative, so statement i. is false. But the income effect (and therefore the total effect) could be positive or negative depending on whether the consumer is a saver or a borrower before the change (so ii. and iii. are true).

Question 29

A rational, selfish consumer lives for two periods. Her subjective discount rate and the real interest rate are both 5% per period. If her first period income increases by £1000, by how much will her first period consumption rise? If her second period income increases by £1000, by how much will her first period consumption rise?

Answer 29

explanation: First, we should notice from the first order condition fraction numerator u apostrophe left parenthesis c subscript 2 right parenthesis over denominator u apostrophe left parenthesis c subscript 1 right parenthesis end fraction equals fraction numerator 1 plus r over denominator 1 plus rho end fraction we see that if 𝑟 = 𝜌, consumption must be constant over time, so it doesn’t actually matter for either part if we’re talking about first-­‐ or second-­‐period consumption. If it were the case that 𝑟 = 𝜌 = 0%, then a £1000 boost to income in either period would boost consumption by £500 in each period. But since interest rates are positive, a boost in income in the first period is worth more (because some money can be saved and earn interest, or at least less can be borrowed) so that consumption can rise by more than £500 in each period, whereas a boost to income in the second period is worth less (because some money must be borrowed, or at least less saved), so consumption can only rise by less than £500 in each period.

Question 30

Analyse how the following shocks will affect the natural rate of interest (r subscript n) Firms become more pessimistic about future demand for their products. A temporary reduction in production due to a bad harvest. A hurricane destroys a substantial share of the capital stock but miraculously no one dies.

Answer 30

r^n will fall will rise will rise

Question 31

Inflationary expectations are an important driver of the Phillips curve relationship. What are three different ways inflationary expectations might be modelled? Depict each graphically.

Answer 31

This is basically section 9.5 of the textbook. Three ways presented there include: (i) expectations of constant prices, (ii) expectations that this period’s inflation will be equal to last period’s, and (iii) expectations that inflation will equal the bank’s target rate.

Question 32

Consider the standard Cobb-Douglas model presented in the lectures and the textbook. Suppose the rate of depreciation falls. What happens in the long term to the following variables (relative to their trends before the change)? The steady-state value of the capital stock will rise The steady-state value of output will rise The steady-state growth rate of the capital stock will rise The steady-state growth rate of output will rise

Answer 32

true, true, false, false The equation for the steady state capital stock is given by [𝑓′(𝑘)/(1+𝜇)]−𝛿=𝑟. If 𝛿 falls and other variables stay the same, then the gross return to capital 𝑓′(𝑘) must also fall. Because the return to capital is diminishing in the stock of capital, this means that the capital stock will rise. So i. is true. Furthermore, because more capital will increase output, ii. is also true. But the steady-state growth rates are determined by population and technological growth, so they will not change. Thus iii. and iv. are false.

Question 33

Consider two countries which do not borrow from, or lend to, the rest of the world. Both countries have the same population, technology, and the same preferences, but in country A, markets are more competitive (and so the mark-up is lower) than in country B. Assume both countries are in their long run steady state and evaluate the following statements: Y grows faster in country A Y will be higher in country A K grows faster in country A K will be higher in country A

Answer 33

false, true, false, true Explanation: the long-run growth rate of both 𝑌 and 𝐾 is (𝑛+𝑔) and is not affected by the degree of competition in the country, so i. and iii. are both false. But the level of 𝑌 and 𝐾 is rising in the degree of competition, so ii. and iv. are true.

Question 34

Consider the standard Cobb-Douglas model presented in the lectures and the textbook. Poor countries have lower output and less capital than rich countries. But is the ratio of capital to output (𝐾/𝑌) higher or lower in poor countries? Why? The K/Y ratio is higher in poor countries than in rich countries. The K/Y ratio differs because of differences in E. The K/Y ratio differs because of differences in N. The K/Y ratio differs because of differences in pi.

Answer 34

FALSE FALSE FALSE FALSE K/Y = a/ (r + depreciation)(1 + markup)

Question 35

In a hypothetical closed economy, population grows at 3% per year, technology improves at 2% per year, and depreciation is 1% per year. What is the long run growth rate of consumption per capita? What is the long run growth rate of the aggregate capital stock?

Answer 35

2%, in the long run, consumption per capita will grow at the same rate as income per capita. Income per capita grows at a rate g (which is 2%), because in the long term the only thing that can raise living standards is technological progress 5% The capital stock per capita will also grow at a rate g and this means that the aggregate capital stock (which must also keep up with increases in the population) grows at n + g, which is 5%.

Question 36

In the textbook, the following expression is given for the steady-state level of production per person in the labor force as a function of parameters: Y/L = ( a/ (r + depreciation)(1 + markup) ) to the power of a/1-a x E x (1 - u) Assume a = 1/3 markup = 0.1, depreciation = 0.06, E= 1000, r = 0.06, u = 0.1. Calculate the steady state production per person. Now assume that the government introduces a tax to collect half of capital income and then redistributes the money evenly through the economy. What happens to output per capita? (Round your answer to the neares 5%)

Answer 36

The income level without tax is 1430 (r=0.06). Once tax is introduced, the pre-tax rate of return rises from 6% to 12% (because the after tax rate must remain the same), so the income level decreases to 1168, which implies a fall of 20 BECAUSE: When capital is taxed at 50%, investors demand a higher pre-tax return to get the same after-tax return. So to maintain the original after-tax return of 6%, the pre-tax return r must double to 12%.

Question 37

For the typical G7 country ... ... inflation between 1960 and 1980 was ... ... inflation between 1980 and 2000 was .. clearly rising clearly falling or roughly constant?

Answer 37

clearly rising, clearly falling 🔹 1960–1980: Clearly Rising This period saw persistent inflation increases, especially in the 1970s. Key causes: Oil shocks in 1973 and 1979 Expansionary fiscal and monetary policies Wage-price spirals Example: US inflation: ~1–2% in early 60s → ~13% by 1980 Similar trends in UK, Germany, France, etc. 🔹 1980–2000: Clearly Falling Marked by disinflation policies: Central banks (esp. Fed under Volcker) raised interest rates sharply in early 1980s. Focus shifted to inflation targeting and credibility. Inflation steadily declined in most G7 countries throughout the 80s and 90s.

Question 38

Assume that velocity of the monetary base is constant and equal to 20, and that inflation is 4% per year, population grows at 3% per year, technology improves at 2% per year, and depreciation is 1% per year. What is Seignorage as a percent of GDP?

Answer 38

The formula for seigniorage is (𝜋 + 𝑔 + 𝑛)/𝑉, which in this case is (.04 + .03 + .02)/20 = .09/20 = 0.0045 = 0.45%.

Question 39

Assume the total labour cost per worker for firm 𝑖 includes the direct wage cost and the cost of turnover, which is 𝑊𝑖 + ℎ ∙ 𝑊 ∙ [𝑠 + 𝑍(𝑊𝑖/𝑊) ∙ 𝑓]. Now consider the following statements: If the unemployment rate increases, the per-worker total cost must rise If more people quit exogenously, the per-worker total cost must rise If hiring costs increase, then the per-worker total cost must rise If firm 𝑖’s wages increase, then their per-worker total cost must rise

Answer 39

false, true, true, false The unemployment rate does not enter this formula directly, but because 𝑓 = 𝑠/(𝑢 + 𝑠), an increase in the unemployment rate will decrease f and thus decrease total costs. The exogenous quit rate is 𝑠; when it rises, it increases both 𝑓 and itself, raising costs through both channels. Hiring costs are ℎ, and when these go up then – as you might expect – so do costs. Finally, the firm’s wage 𝑊𝑖 has a u-shaped effect on total costs. The direct effect of increasing wages is of course to raise costs, but there is also an indirect effect of reducing the wage-related quit rate via 𝑍. For low wages, the indirect effect will dominate, so it is false to say that costs must rise.

Question 40

Consider the following statements about Japan’s “lost decade” of low growth: It began just after the year 2000 It is associated with a clear break in the trend growth rate of GDP per capita It is associated with a clear break in the trend growth rate of GDP per hour It is associated with a rise in both the employment-population ratio and in hours worked per employee

Answer 40

false, false, true, true

Question 41

Which (if any) of the following statements about the Zero Lower Bound (ZLB) are sometimes true? The ZLB stops policy-makers from getting the output gap as negative as they’d like The ZLB stops policy-makers from getting the inflation rate as negative as they’d like The ZLB stops policy-makers from getting real interest rates as negative as they’d like The ZLB stops policy-makers from getting nominal interest rates as negative as they’d like

Answer 41

FALSE FALSE TRUE TRUE The ZLB is a limit which prevents central banks from setting nominal interest rates much below 0% (so iv. is true). Because policy-makers cannot cut nominal rates as much as they’d like, they also cannot set real rates as low (possibly negative) as they’d like (so iii. is also true). But i. and ii. are false – policy makers generally don’t want a negative output gap or negative inflation (deflation), but to the extent that policy-makers do want these things, they are achieved by high interest rates, not low ones.

Question 42

Evaluate the following statements about the natural rate of unemployment u^n . When 𝑢 = u^n, no firm has an incentive to change its relative wage. If unemployed workers search less intensively for jobs u^n will increase. 𝑢 < u^n is impossible. 𝑢 > u^n is associated with upward pressure on inflation.

Answer 42

true, true, false, false Statements i. and ii. are direct quotes from Chapter 6 – they are both true. The latter two statements come from Chapter 7: statement iii. is false – if it wasn’t, one half of the Phillips curve wouldn’t make sense. Statement iv. is false because it is backwards – high unemployment is associated with downward pressure on inflation.

Question 43

Suppose that production is initially on the natural level. Now there is an increase in the price level because of an increase in the value added tax. If the central bank wants to avoid an output gap, what should it do? Hold the money supply constant. Hold the interest rate constant. Hold inflation constant.

Answer 43

🔍 What’s Happening in the Scenario? Initial condition: Output is at the natural level (i.e. full employment, no output gap) Shock: An increase in the value-added tax (VAT) causes the price level to rise This is a supply-side shock → it increases prices directly (not from demand) 🧠 Key Concept: Avoiding an Output Gap An output gap happens when actual output ≠ natural output: Positive gap = output > natural level → overheating Negative gap = output < natural level → recession The central bank’s job here is to keep output at the natural level, despite the temporary increase in the price level due to VAT. 🏦 What Should the Central Bank Do? Let’s look at your options: 1. Hold the money supply constant ❌ This could cause interest rates to rise, reducing aggregate demand That might worsen the output gap (likely creating a recessionary gap) So not ideal 2. Hold the interest rate constant ✅ This is the best option if the goal is to keep output steady The VAT increase is a price-level shift, not a persistent increase in inflation Holding the interest rate constant avoids overreacting to a one-off price increase This allows the temporary price spike without choking off demand 3. Hold inflation constant ❌ If the central bank tries to keep inflation constant, it may tighten policy (raise rates) to offset the VAT-driven inflation blip This could reduce demand, causing a negative output gap ✅ Correct Answer: Hold the interest rate constant This allows the temporary price level increase to pass through without triggering unnecessary changes in demand or output.

Question 44

Evaluate the following statements about the relationship between interest rates and output. Higher interest rates necessarily mean lower output Lower interest rates necessarily mean higher output Higher output necessarily means higher interest rates Lower output necessarily means lower interest rates

Answer 44

All four statements are not necessarily true. They reflect typical patterns, but other factors (e.g. expectations, confidence, supply shocks) can affect outcomes. Central bank actions also depend on context (e.g. zero lower bound, inflation targets). Key takeaway: ❌ None of the relationships are guaranteed — they are tendencies, not rules.

Question 45

Other things being equal, the multiplier will be larger if… … governments increase marginal tax rates … the marginal propensity to consume rises … the central bank keeps the interest rate fixed instead of keeping the money supply fixed

Answer 45

❌ False Higher taxes → less disposable income → lower consumption This reduces the multiplier ✅ True Higher MPC → more spending from each £ of income This increases the multiplier ✅ True Fixed interest rate → no crowding out of investment Demand rises more → larger multiplier

Question 46

Consider the IS-LM model presented in the text. Suppose we start in a situation where expected and actual inflation are equal to the inflation target of the central bank and production is on the natural level. In the short-run equilibrium… …if consumers become more pessimistic about future income, the nominal interest rate will decrease …if consumers expect future inflation to be lower than the target, the nominal interest rate will decrease …if there is an increase in the price level because of an increase in the VAT, the nominal interest rate will decrease

Answer 46

✅ True Pessimism → ↓ consumption → IS curve shifts left Output falls → central bank cuts nominal interest rate to boost demand ✅ True Lower expected inflation → ↑ real interest rate (if nominal rate unchanged) Demand drops → central bank lowers nominal interest rate to maintain output ❌ False VAT hike = supply-side price increase, not demand-driven Central bank typically does not cut the nominal rate May hold it constant to avoid output gap

Question 47

Suppose we start in a situation where expected and actual inflation are equal to the inflation target of the central bank and production is on the natural level. In the short-run (assuming other things remain equal)… …if consumers become more pessimistic about future income, 𝑖 will fall. …if consumers expect future inflation to be lower than the target, 𝑖 will fall. …if there is an increase in the price level because of an increase in the sales tax (or value added tax), 𝑖 will fall.

Answer 47

✅ True Pessimism → ↓ consumption → IS curve shifts left Output ↓ below natural level Central bank responds by lowering 𝑖 to restore demand/output ✔️ Correct — 𝑖 falls in response to a negative demand shock ✅ True Expected inflation ↓ → real interest rate (𝑟 = 𝑖 – expected inflation) rises Higher real rate → ↓ demand → output ↓ Central bank lowers 𝑖 to bring real rate and output back to normal ✔️ Correct — lower expected inflation leads to a drop in nominal 𝑖 ❌ False VAT increase = one-off supply-side price shock, not demand-driven Output may temporarily fall if real wages drop, but central bank typically holds 𝑖 constant No reason to cut rates in response to a temporary price level increase ✔️ Incorrect — 𝑖 usually stays constant, not falls

Question 48

Consider the version of the Phillips Curve (PC) which relates inflation (on the vertical axis) to output growth (on the horizontal axis). Which (if any) of the following changes will make the Phillips curve steeper? Expected inflation rises Firms start to change their wages more frequently Firms' desired wages become more sensitive to unemployment

Answer 48

❌ No It shifts the curve upward But it does not change the slope ✅ Yes Less nominal rigidity Inflation responds more strongly to changes in output → Steeper Phillips Curve ✅ Yes Wage-setting responds more to economic conditions Inflation becomes more responsive to the output gap → Steeper Phillips Curve

Question 49

Consider the following statements: The nominal exchange rate is the price of domestically produced goods in terms of goods produced abroad. If the real exchange rate increases, domestic goods become relatively more expensive compared to foreign goods. The real exchange rate is always greater than the nominal exchange rate.

Answer 49

❌ False The nominal exchange rate is the price of one currency in terms of another currency (e.g., euros per pound), not a price of goods. ✅ True A higher real exchange rate means domestic goods cost more relative to foreign goods → exports less competitive, imports more attractive ❌ False There is no fixed relationship — the real exchange rate depends on relative price levels. It can be higher or lower than the nominal exchange rate.

Question 50

In 2000 Denmark decided not to join the euro area but has maintained a fixed exchange rate with the euro. Given this position, which (if any) of the following statements is (are) true? Denmark has eliminated the prospect of speculation against the value of its currency. Denmark has maintained day-to-day control over monetary policy. Denmark has maintained the option to devalue its currency.

Answer 50

❌ False Even with a fixed exchange rate, speculation is still possible — especially if markets believe the peg might break. History shows that speculative attacks can occur under fixed exchange regimes (e.g., UK's exit from ERM in 1992). Denmark’s central bank must be ready to defend the peg, making speculation a real risk. ❌ False By pegging to the euro, Denmark gives up independent monetary policy. The Danish central bank must adjust interest rates to maintain the peg, aligning with ECB policy. This means it cannot set rates freely based on domestic needs. ✅ True (in theory) Since Denmark did not adopt the euro, it retains its own currency (krone). This means it can devalue, although it would require breaking the peg — a serious move. So the option exists, even if not actively used.

Question 51

Consider the following statements: To join the Eurozone a country needs to satisfy only the nominal convergence criteria, the fiscal discipline criteria are just guidelines which are often violated by the member states themselves Before joining the Euro, countries are required to stay within the European Exchange Rate Mechanism (ERM) band for two consecutive years, which is enough to ensure convergence of the inflation rates at a low level Under the Bretton Woods system, which was in effect until 1971, most major currencies effectively had a fixed value in gold

Answer 51

❌ False (or at best, misleading) Eurozone entry requires meeting the Maastricht criteria, which include: Nominal convergence: inflation, interest rates, exchange rate stability Fiscal criteria: deficit ≤ 3% of GDP, debt ≤ 60% of GDP While fiscal rules have been violated post-entry (e.g. Stability and Growth Pact breaches), they are not just guidelines — they are part of the formal accession requirements. ❌ False It's true that a country must stay in ERM II for at least 2 years with no severe tensions. BUT: This alone is not enough to ensure low inflation convergence. Inflation depends on more than just exchange rate stability (e.g., wage dynamics, fiscal policy, monetary credibility). There’s also a separate inflation convergence criterion. ✅ True (with clarification) Under Bretton Woods (1944–1971): Currencies were pegged to the US dollar. The US dollar was convertible into gold at $35/ounce. So, indirectly, other currencies had fixed gold values via the dollar. This system ended in 1971 when the US ended dollar-gold convertibility (Nixon Shock).

Question 52

Two countries, Country A and Country Z, produce chocolate and sausages. Labour is the only input. Country A has 100 units of labour. It takes 5 units of labour to produce 1 ton of chocolate. It takes 20 units of labour to produce 1 ton of sausages. Country Z has 1000 units of labour. It takes 10 units of labour to produce 1 ton of chocolate. It takes 10 units of labour to produce 1 ton of sausages. Which country has: Absolute advantage in chocolate? Absolute advantage in sausages? Comparative advantage in chocolate? Comparative advantage in sausages?

Answer 52

A country has absolute advantage in a good if it uses less labour per unit. ✔️ Country A has an absolute advantage in chocolate ✔️ Country Z has an absolute advantage in sausages ✅ Step 2: Comparative Advantage Use opportunity cost to determine. 🔹 Country A: 1 ton of chocolate = 5 labour 1 ton of sausages = 20 labour So: Opportunity cost of 1 chocolate = 5/20 = 0.25 sausages Opportunity cost of 1 sausage = 20/5 = 4 chocolates 🔹 Country Z: 1 chocolate = 10 labour 1 sausage = 10 labour So: Opportunity cost of 1 chocolate = 10/10 = 1 sausage Opportunity cost of 1 sausage = 10/10 = 1 chocolate ✔️ Country A has lower opportunity cost in chocolate ✔️ Country Z has lower opportunity cost in sausages Country A has an absolute advantage in chocolate production, while Country Z has an absolute advantage in sausage production. Country A has a comparative advantage in chocolate production, while Country Z has a comparative advantage in sausage production.

Question 53

Which if the following statements is/are true? The European Central Bank has instrument but not goal independence. The nominal convergence criteria for joining the euro requires that a country stays within its ERM band for two consecutive years without a devaluation or revaluation. The nominal convergence criteria for joining the euro imposes conditions on a country’s inflation rate and nominal interest rate.

Answer 53

❌ False The ECB has both instrument and goal independence. Goal independence: Its mandate (price stability) is set in EU treaties. Instrument independence: It chooses how to achieve its mandate (e.g., interest rates). ✅ True To meet the exchange rate stability criterion, a country must: Stay in ERM II for at least 2 years Avoid devaluation or revaluation of its currency during that time ✅ True The Maastricht criteria require: Inflation close to the lowest in the EU (within 1.5 percentage points) Long-term interest rate close to low-inflation countries (within 2 percentage points)

Question 54

Consider an increase in government spending. Compared to a closed economy with a fixed money supply, a small open economy with a fixed exchange rate has: A) A smaller multiplier and less crowding out of investment B) A smaller multiplier and more crowding out of investment C) A larger multiplier and less crowding out of investment D) A larger multiplier and more crowding out of investment E) A larger multiplier and more or less crowding out of investment Which is correct, and why?

Answer 54

✅ Correct Answer: A – A smaller multiplier and less crowding out of investment Explanation: Small open economy: part of government spending leaks abroad via imports, reducing the size of the multiplier. Fixed exchange rate: the central bank adjusts the money supply to keep the interest rate constant, so there's no crowding out from higher interest rates. In contrast, in a closed economy with fixed money supply, interest rates rise → crowding out occurs.

Question 55

Assess the following statements for a small open economy with a floating exchange rate and endogenous exchange rate expectations e^e (e), where the Marshall-Lerner condition holds: Under the assumption that ∂e^e/∂e >0, the IS curve is steeper than in an economy where e^e is exogenous. When e^e =e an increase in money supply generates a smaller short-run increase in output compared to an economy where e^e is exogenous. When e^e =e fiscal policy is more effective in stimulating output in the short run compared to an economy where e^e is exogenous. Which of these statements are true?

Answer 55

❌ All statements are false Explanation: False – The IS curve is flatter, not steeper. Endogenous expectations create a feedback loop: any change in the exchange rate triggers further expectation-driven depreciation or appreciation, magnifying exchange rate movements and reducing the impact of output on the exchange rate. False – When e^e = e the IS curve becomes flat. Output is determined by the LM curve. Monetary policy becomes more effective, not less, because any shift in the LM curve leads to a larger change in output when IS is flat. False – Fiscal policy is less effective. With a flat IS curve and interest parity holding (i = i*), any change in government spending is offset by immediate exchange rate adjustment, keeping output constant.