ECON10262
THE UNIVERSITY OF MANCHESTER
ECON10262 Macroeconomics 2
Semester two 2017/18
1 HOURS and 30 MINUTES
Date: MOCK EXAM
Time:
XXX
DO NOT REMOVE FROM EXAMINATION ROOM
• You must correctly enter your registration number and the course code on the answer
sheet.
• Answer ALL Questions in both section A and section B.
• Please enter your answers for section A in the Multiple Choice Sheet and for section B
in the Answer Book provided. Your answer sheet must be completed before the end of
the exam time. You will not be permitted to complete your answer sheet after the exam
has finished.
• In section A, each of the 30 questions in this paper has 5 possible answers (a, b, c, d,
e). In each case only one is correct. Each question has an equal weight of 1.66 marks; a
mark of ZERO is given for an incorrect answer, or if multiple answers selected, or if the
question is not attempted.
• In section B, each of the 4 questions has an equal weight of 12.5 marks.
• Hand in your MCQ answer sheet, answer book and this question paper.
The four pages of this exam paper after page 18 have been left blank for your ‘working out’.
Electronic calculators may be used, provided they cannot store text.
The questions in this mock exam paper and in the tutorials are
only similar but not identical to the questions in the final exam.
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Section A
1. (1.66 points) Over the past 50 years, Brazil’s population growth rate has averaged about
2.3 percent. According to the rule of 70, Brazil’s population will double in about
years.
(a) 3
(b) 30
(c) 33
(d) 161
(e) 1.6
2. (1.66 points) Between 1970 and 1976, Israel’s average inflation rate was about 65 percent
years,
per year. With that rate of inflation, prices would double about every
using the rule of 70.
(a) 93
(b) 107.7
(c) 0.95
(d) 1.1
(e) 9.3
3. (1.66 points) Suppose that in 1965 Japan had an initial per capita GDP of $12,000 per year
and China had a per capita GDP of $5,000. But China is growing at 5 percent per year and
would have been richer in 2015 with a
Japan is growing at 3 percent per year.
per capita GDP of approximately
.
(a) Japan; $5,000
(b) Japan; $31,500
(c) China; $7,500
(d) China; $57,337
(e) Not enough information is given.
Solution:
China
Japan
Initial
GDP per capita
Growth rate
Year
$5,000
$12,000
5%=0.05
3%=0.03
50
50
Calculation
Result
$5, 000 · 1.0550 = $57,337
$12, 000 · 1.0550 = $52,607
4. (1.66 points) Suppose k, l, and A grow at constant rates given by ḡk , ḡl and ḡA . What is the
growth rate of y if y = Aka l1−a , a > 0?
(a) gy = ḡA + a(ḡk + ḡl )
(b) gy = ḡA + aḡk + (1 − a)ḡl
(c) gy = aḡA + aḡk + aḡl
(d) gy = aḡA + ḡak + ḡal
(e) gy = ḡA × aḡk × (1 − a)ḡl
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5. (1.66 points) Assume that Mexico’s average annual per capita GDP growth rate is 3 percent per year, while Argentina’s is 2.5 percent. Next, assume that both countries began
with an initial per capita GDP of $1,000 in 1965. By 2015, per capita GDP would have
in Mexico and
in Argentina.
been
(a) $228; $291
(b) $3,437; $4,384
(c) $4,515; $3,523
(d) $4,384; $3,437
(e) Not enough information is given.
Solution: Similar calculation to the answer for question 3 is required.
6. (1.66 points) Which of the following production functions exhibits constant returns to
scale?
(a) Y = K 2/3
(b) Y = K 1/3 L1/3
(c) Y = K a L1−a
(d) Y = K 1/2 L1/3
(e) All of these answers are correct.
Solution: To understand better why Y = K a L1−a , recall the definition of constant returns to scale: if we double the amount of each input, we will double the amount of
output.
Consider the production function F(K, L) = K a Lb with a > 0 and b > 0. Let’s double
inputs,
F(2K, 2L) = (2K)a (2L)b = 2a K a 2b Lb
⇒
F(2K, 2L) = 2a+b K a Lb
⇒
F(2K, 2L) = 2a+b F(K, L)
It follows now that
• if a + b = 1, then F(2K, 2L) = 2F(K, L), therefore F(K, L) exhibits constant
returns to scale.
• if a + b < 1, then F(2K, 2L) = 2a+b F(K, L) < F(K, L), therefore F(K, L) exhibits
decreasing returns to scale.
• if a + b > 1, then F(2K, 2L) = 2a+b F(K, L) > F(K, L), therefore F(K, L) exhibits
increasing returns to scale.
Hence to answer the question, you only have to remember that for constant returns to
scale, the exponents of the of capital and labour has to sum up to 1.
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7. (1.66 points) Consider the production function below.
The shape of this production function suggests:
(a) not enough information is given.
(b) a diminishing marginal product of labor.
(c) a constant marginal product of capital.
(d) an increasing marginal product of capital.
(e) a diminishing marginal product of capital.
Solution:
This figure shows that Cobb-Douglass production function Y = ĀK 1/3 L2/3 where L is
held constant. We can see that each additional unit of K increases output less and less.
This is the diminishing marginal product of capital.
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8. (1.66 points) The solution to the firm’s profit maximization is:
(a) MPL = w.
(b) MPL = w and MPK = r
(c) MPL < w and MPK = r
(d) MPL = w and MPK = 0
(e) MPL > w and MPK = r
9. (1.66 points) You are an economist working for the International Monetary Fund. Your
boss wants to know what the total factor productivity of China is, but all you have is data
on per capita GDP, y, and the per capita capital stock, k. If you assume that capital’s share
of GDP is one–third, what would you use to find total factor productivity?
1k
(a) Ā =
3y
(b) Ā = y × k1/3
k1/3
y
y
(d) Ā = 1/3
k
(e) None of these answers is correct.
(c) Ā =
Solution: The production function for output per person is y = Āk1/3 where k is output
per person. The question states that we have data about y and k. If we rewrite the
production function as
y
Ā = 1/3
k
and use the data about y and k, we can calculate Ā.
10. (1.66 points) In models with perfect competition:
(a) economic profits are always positive.
(b) accounting profits are zero.
(c) income paid to labor is the same as is paid to capital.
(d) the real interest rate is equal to the nominal interest rate.
(e) economic profits are zero.
11. (1.66 points) In the Solow model, in every period, a fraction of total output
which
next period’s capital stock.
,
(a) is saved; reduces
(b) depreciates; adds to
(c) is saved; adds to
(d) is consumed; adds to
(e) is consumed; reduces
12. (1.66 points) The endogenous variables in the Solow model are:
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(a) the capital stock, labor, and output.
(b) consumption, investment, the capital stock, labor, and the saving rate.
(c) consumption, investment, the capital stock, labor, and output.
(d) productivity and the depreciation and saving rates.
(e) the capital stock, labor, output, and the saving rate.
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13. (1.66 points) In the Solow model, if capital is in the steady state, output
(a) will continue to grow.
(b) is also in the steady state.
(c) will continue to grow, but its rate of growth will slow down.
(d) will decline, but its rate of growth will be positive.
(e) will begin to contract.
14. (1.66 points) In the figure below,
at K1 , the difference between s̄Y and d̄K
is
, and the difference between Y and s̄Y
(a) output; investment
(b) net investment; consumption
(c) gross investment; consumption
(d) output; consumption
(e) depreciation; gross investment
15. (1.66 points) According to the Solow model, in the steady state, countries with high saving
rates should have a
(a) low labor-output ratio.
(b) low capital-output ratio.
(c) high capital-output ratio.
(d) high depreciation rate.
(e) high Ā.
Solution: In the steady state, investment equals depreciation.
s̄Y ∗ = d̄K ∗ .
Rearranging yields
s̄
K∗
= .
∗
Y
d̄
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16. (1.66 points) In economics, a rival good is one that
(a) cannot be consumed by more than two people at a time.
(b) can be consumed by more than one person at a time.
(c) is congested if used by more than one person at a time.
(d) cannot be consumed by more than one person at a time.
(e) one of these answers is correct.
17. (1.66 points) If Y is a good’s output, X is spending to produce a good, F̄ is the fixed cost
associated with production, and C is the average cost of production, which of the following
production functions exhibits increasing returns?
(a) Y = (CX − F̄)
(b) Y = X + F̄ − C
(c) Y = (F̄ − X)/C
(d) Y = (X − F̄)/C
(e) Y = (X − F̄C)
Solution: If C is the average cost, there is no fixed cost, and the producer spends X
on produce output, then she/he will produce X/C units of output. Hence (a), (b) and
(e) cannot be correct because X is not divided by C in those formulas. If there is fixed
cost, the produce first has to spend F̄ before any output can be produced. Thus, X > F̄
for Y > 0. Therefore (c) cannot be a production function because it is decreasing in X,
hence the only production function is (d). And it is exhibits increasing returns. To see
this, use the expression to express the average product
!,
F̄
Y
= 1−
C.
X
X
The right hand side is clearly increasing in X, hence the average product increasing
which means the technology exhibits increasing returns.
18. (1.66 points) In the Romer model, output is increasing in the
in the
.
and decreasing
(a) saving rate; depreciation rate
(b) research share; growth rate of knowledge
(c) growth rate of knowledge; fraction of population in the ideas sector
(d) growth rate of knowledge; depreciation rate
(e) saving rate; growth rate of knowledge
Solution: In the Romer–model we assume that total labour available L̄ can be allocated either to produce output, Lyt or produce ideas, Lat . We also assume that Lat = `¯L̄
where `¯ is the fraction of population in the research sector. Note that this implies that
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¯ L̄. Finally, output is given by Yt = At Lyt . Since At is growing at a constant
Lyt = (1 − `)
rate ḡ, At = A0 (1 + ḡ)t . Putting these together allows us to rewrite output as
¯ L̄.
Yt = A0 (1 + ḡ)t (1 − `)
This corresponds to (c), At the more intuitive level, output depends on labour producing
output. Since labour is either producing output or ideas, output must be decreasing in
the fraction of labour in the ideas sector. In addition, At this periods depends on the
initial level of At via A0 . Hence higher growth rate of knowledge increases output.
19. (1.66 points) In the Romer model, if Canada and Taiwan have the same fraction of researchers and the same knowledge efficiency parameter but Canada’s population is larger,
then
(a) Taiwan has a higher per capita output growth rate.
(b) Canada has a higher per capita output growth rate.
(c) each country’s per capita output grows at the same rate.
(d) Canada has higher per capita income than Taiwan.
(e) Canada’s level of income is greater than Taiwan’s.
Solution: In the Romer model per capita output grows at the rate of the growth rate of
knowledge. Hence we only have to focus the knowledge accumulation equation
∆At+1 = z̄At Lat = z̄At `¯L̄,
which can be solved for the growth rate of knowledge
ḡ ≡
∆At+1
= z̄`¯L̄
At
The formula clearly states that even if z̄ and `¯ are the same across Taiwan and Canada,
but the population, L̄ is larger in Canada, knowledge creation will be faster, hence GDP
per capita growth be higher in Canada,.
20. (1.66 points) In the Romer model, with decreasing returns to the knowledge sector:
(a) the number of researchers is irrelevant to long-term per capita income.
(b) more researchers produce more ideas, raising the long-run growth rate of per
capita income.
(c) more researchers produce fewer ideas, raising the long-run growth rate of per
capita income.
(d) more researchers produce more ideas, raising the long-run level of per capita
income.
(e) more researchers cause the knowledge stock to contract.
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Solution: If there is a decreasing returns to the knowledge sector, increases in ideas
run into diminishing returns. In this alternative version of the Romer model, an increase
in the research share or the size of the population increases the growth rate in the short
run, but in the long run the growth rate returns to its original value. This is much like
the transition dynamics of the Solow model, and it occurs for much the same reason.
More researchers produce more ideas, and this raises the long- run level of per capita
GDP, a result known as a level effect.
The long- run growth rate is positive in this model, but it is unchanged by a one time
increase in the number of researchers. However, the temporary increase in the growth
rate leads to a higher stock of ideas, hence higher per capita GDP in the long run.
21. (1.66 points) In the labor market depicted in the figure below,
an increase in oil prices
(a) shifts labor demand from L2D to L1D .
(b) shifts labor supply from L2S to L1S .
(c) shifts labor demand from L1D to L2D .
(d) produces no change in either the labor supply or demand curve.
(e) None of these answers is correct.
Solution: Increase in oil prices is generally viewed as an event which increases the
cost of production in general. If does so, then firms will hire fewer labour as a response.
This reduces the demand for labour at all levels wages which corresponds to shifts labor
demand from L1D to L2D .
22. (1.66 points) Structural unemployment is the unemployment that results from
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(a) workers leaving the labor force.
(b) workers changing jobs in a dynamic economy.
(c) workers losing jobs during seasonal changes.
(d) workers losing jobs during recession.
(e) prevailing labor market institutions.
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23. (1.66 points) Consider the data in table below.
Separation
rate
Finding
rate
Labor
force
0.2%
0.3%
3.5%
4.0%
153
157
2010
2015
In
, the natural rate of unemployment was the higher of the two years at
percent.
(a) 2015; 7.0
(b) 2010; 94.6
(c) 2010; 8.6
(d) 2015; 7.5
(e) 2015; 5.0
Solution: The natural rate of unemployment, ū is determined by the job separation
rate, s̄, and the job finding rate, f¯ as
ū =
Hence
ū(2010) =
s̄
.
s̄ + f¯
0.3%
0.2%
= 0.054 <
= 0.07
0.2% + 3.5%
0.3% + 4%
24. (1.66 points) The present discounted value equation, $386 = $1, 000/(1.1)10 , means you
(a) would prefer to receive $386 today rather than $1,000 in 10 years.
(b) are indifferent between receiving $386 today and $1,000 in 10 years.
(c) would prefer to receive $1,000 in 10 years rather than $386 today.
(d) are indifferent between receiving $386 today and $1,000 in 100 years.
(e) Not enough information is given.
25. (1.66 points) Wage rigidity:
(a) helps the labor market achieve equilibrium.
(b) prevents the capital market from realizing equilibrium.
(c) prevents the labor market from realizing equilibrium.
(d) prevents unemployment.
(e) None of these answers is correct.
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26. (1.66 points) In 2015, The Avengers: Age of Ultron generated about $191.2 million on
its opening weekend. In 2007, Spider Man 3 generated $151.1 million on its opening
weekend. If the CPI in 2000 was 100, the CPI in 2007 was 113.4, and the CPI in 2015 was
is the larger single-day grossing movie, with about
million
137.6,
in revenues in 2000 dollars.
(a) Spider Man; $168.6
(b) Spider Man; $133.8
(c) Avengers; $139.0
(d) Spider Man; $171.3
(e) Avengers; $263.2
Solution: The Avengers: $191.2/1.376≈$139.0. Spider Man 3: $151.1/1.134≈133.2
27. (1.66 points) The velocity of money can be calculated from the quantity equation with:
(a) Pt Yt
(b) Pt Yt Mt
(c) Mt /Pt Yt
(d) Pt Yt /Mt
(e) Mt
28. (1.66 points) According to the classical dichotomy, in the long run there is:
(a) accelerating economic growth.
(b) perfect connectivity between the nominal and real sides of the economy.
(c) complete separation of the nominal and real sides of the economy.
(d) no growth after the economy reaches the steady state.
(e) zero inflation.
29. (1.66 points) If not all price setters are convinced that high inflation rates will end soon,
there is/are:
(a) price staggering.
(b) a transfer of wealth from one group to another.
(c) substantial menu costs.
(d) a coordination problem.
(e) negative real interest rates.
Solution: One difficulty in ending high inflation is what’s known as a coordination
problem. Imagine you are a business owner and you have to choose how to set your
prices in the coming week. If the rate of inflation has been high and perhaps rising for
the past year, you will build a high and rising rate of inflation into your prices. Other
firms will do this as well, as will workers as they bargain over wages. This coordination
injects a certain inertia into the inflation process. At some level, all the price setters
in the economy have to be convinced that the high inflation of recent years is going to
end, and this coordination problem can be hard to solve.
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30. (1.66 points) According to the quantity equation, the cure for hyperinflation is
(a) higher taxes.
(b) reducing government spending.
(c) reducing money growth.
(d) All of these answers are correct.
(e) None of these answers is correct.
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Section B
1. (12.5 points) Given a production function Yt = ĀKt1/3 L̄2/3 if Ā = 2, L̄ = 4, s̄ = 0.2 and
d̄ = 0.05.
(a) Calculate the steady-state level of capital and output.
(b) Does the above production function exhibit constant returns to scale, or does it exhibit
diminishing marginal returns? Explain, and define the difference between these two
concepts.
Solution:
(a) The steady-state level of capital is given by:
s̄Y = d̄K ∗
s̄Y ĀK ∗1/3 L̄2/3 = d̄K ∗
⇒
implying
s̄Ā
K =
d̄
!3/2
∗
0.2 · 2
L̄ =
¯
0.05
!3/2
· 4 = 22.627 · 4 = 90.5
∗
Steady-state level of output is given by:
Y = ĀK
∗
∗1/3 2/3
L̄
= Ā
3/2
s̄ 1/2
d̄
L̄ = 2
∗
3/2
0.2
0.05
!1/2
4 = 22.627
(b) The production function is CRS; double the inputs and you double the output.
It also exhibits diminishing returns to each input, so as you increase one input
without changing the other, output rises but at a decreasing rate (for example
fK > 0, fKK < 0.
2. (12.5 points) You have been asked to calculate real GDP growth rates for four countries
from 1985–2014: China, Hungary, South Korea, and Mexico. You decide to reach for the
Solow growth model to do your calculations, specifically the Cobb-Douglas production
function: Yt = At Kt1−a Lyta . Using the data available in the table below, which shows the
average labor share and growth rates of labor composition, capital per capita, and TFP
from 1985–2014, find the output growth rate for each country. Given what you know about
each country, what may explain your results?
China
Hungary
South Korea
Mexico
Labor share
Y/L
Labour Comp
K/L
0.60
0.65
0.55
0.45
6.9%
1.0%
5.7%
2.4%
1.1%
-0.7%
1.8%
2.5%
9.5%
2.1%
7.3%
3.4%
Solution: Suppose that the production function has the form
Yt = At Kt1−a (Ht Lyt )a
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where Yt is output, At is total factor productivity, Kt is capital stock, Lt is the population,
and Ht is a term we call labor composition. Ht may reflect the hours a member of the
population works, the average level of education or average age distribution of the
population. We therefore call Ht “labor composition”. Please see section 6.5 in the
textbook in more detail.
We can rewrite it in per capita form as
Kt
Yt
= At
Lyt
Lyt
!1−a
Hta
Now we can apply the rules how to calculate growth rates
ḡY/L = ḡA + (1 − a)ḡK/L + aḡH .
implying
ḡA = ḡY/L − (1 − a)ḡK/L − aḡH .
Using this formula, we can calculate ḡA , the growth rate of TFP.
China
Hungary
South Korea
Mexico
Labor share
Y/L
Labour Comp
K/L
TFP
0.60
0.65
0.55
0.45
6.9%
1.0%
5.7%
2.4%
1.1%
-0.7%
1.8%
2.5%
9.5%
2.1%
7.3%
3.4%
2.4%
0.7%
1.4%
-0.6%
• Answers depend on students:
◦ China: for Maoist country, undergone market reforms beginning in mid1980s; a lot of state-sponsored investment, export-led growth
◦ Hungary: former command-style economy, began market reforms after the
collapse of communism in 1989; joined NATO in 1999; joined EU in 2004
◦ Korea: began export-led growth policy in 1960s; experienced Southeast
Asian Crisis (1997); continued market reforms
◦ Mexico: import substitution, lots of natural resources, corruption, drug
wars, Latin American debt crisis (early 1980s), Mexican peso crisis (1994),
maquiladora production, market reforms
3. (12.5 points) Explain the reasons Henry Ford decided to pay higher than normal wages
(hint: efficiency wages). How do these higher wages impact the labor market? How might
you use this example to argue for and against a “living wage”.
Solution: The efficiency wage theory has three basic themes:
(i) Moral hazard: the wage is high enough to prevent people from shirking because
the opportunity cost of losing a job is high, as is the cost of monitoring and
reducing turnover costs associated with searching for and hiring new workers;
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(ii) Productivity: better-paid workers are healthier and so can work harder;
(iii) Worker quality/adverse selection: higher wages attract higher–quality workers.
First, the topic of wage floors is not explicitly discussed in the text; the text uses the
language “wage rigidity”–the same thing, but the efficiency wage reflects a fixed wage
floor, denoted by W in the figure below. W ∗ is the equilibrium wage. This creates an
excess supply of labor, E S > E D ; the difference would be structural unemployment:
U S = ES − E D.
Thus, while the wage benefits those that receive the higher wage, it creates unemployment for those who cannot, as LD (W) < LS (W). If the living wage is above the market
clearing wage, there could be the unintended consequence of a higher (fixed) wage.
Note, there is still considerable discussion about the benefits and costs of higher wages.
One argument is that higher wages lead to greater aggregate demand and hence reduce
the level of unemployment, rather than exacerbate it.
4. (12.5 points) Below is the three-year bond real interest rate from 2000–2015. Explain why
the real interest rate is positive for most of the 2000s and what explains it being negative
in 2008–2009 and 2010–2015. What explains the near-zero real interest rate in 2015?
Assuming this interest rate was used to make loans, who benefits from interest rates post–
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2010?
Solution: The real interest rate, Rt , is given by the Fisher equation Rt = it −πt , where it
is the nominal interest rate and πt is the rate of inflation. If it ≶ πt , the real interest rate
is positive/negative. Clearly, throughout most of the 2000s, πt < it , but this flipped in
2008?2009 when inflation accelerated due to rising oil prices. The information is not
present, but the negative rates mid–2010–2015 are due to low bond yields and “normal”
rates of inflation. Throughout 2015, inflation was close to zero and roughly equal to
the bond yield; this means the real interest rate is effectively zero.
Benefits accrue to borrowers, as they are essentially being paid to take a loan. This is
the unique position the U.S. federal government finds itself in: lenders are essentially
paying the government to hold their money for them (i.e., the federal government is
being ?paid? to borrow).
END OF EXAMINATION
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