ECON G25 (MACROECONOMICS)
Macrodynamics and Growth
Class Test Sample questions
For some of the solutions please refer to the slides from live session in pdf file "MSc
Week 10 A live.pdf" or the recording of the live support session in week 10.
Short answer type
1. Consider the Solow growth model with technological progress at the rate g, popu-
lation growth at the rate n and capital depreciation rate at the rate δ. The savings rate
is s and the production function is given by F (K,AL) = Kα(AL)1−α, 0 < α < 1. Then
y = f(k) = kα where y = Y/AL, k = K/AL, f(k) = F (k, 1). The notation is standard
with Y output, K capital, A knowledge or technology and L labour. AL is effective
labour.
Answer the following questions based on this information.
a) Show that the aggregate production F (K,AL) = Kα(AL)1−α has constant returns
to scale.
b) What is the intensive form of the production function? [Plot the intensive form
of the production function!]
c) What is the steady state value of capital and output per unit of effective labour?
d) What is the marginal product of capital in the steady state? Is it positive or
negative?
e) What is the growth rate of aggregate capital and aggregate output in the steady
state?
Ans: See slides from live session in pdf file "MSc Week 10 A live.pdf" or the recording
of the live support session in week 10.
Consider the Solow growth model with technological progress at the rate g, popula-
tion growth at the rate n and capital depreciation rate at the rate δ. The savings rate
is s and the production function is given by F (K,AL) = Kα(AL)1−α, 0 < α < 1. Then
y = f(k) = kα where y = Y/AL, k = K/AL, f(k) = F (k, 1). The notation is standard
with Y output, K capital, A knowledge or technology and L labour. AL is effective
labour.
Answer the following question based on this information.
2. The steady state value for capital is
(a) k∗ =

s
n+g+δ
1
1−α
(b) k∗ =

s
n+g+δ
1
α−1
(c) k∗ =

n+g+δ
s
1
1−α
(d) None of the above.
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Ans (a).
3. Which of the following statements is correct?
a) An increase in the savings rate increases the steady state value of capital per unit
of effective labour in the Solow model.
b) An increase in the savings rate decreases the steady state value of capital per unit
of effective labour in the Solow model.
c) An increase in the population growth rate decreases output per unit of effective
labour.
d) (a) and (c).
Ans: (d)
4. Which of the following statements is correct?
a) The Ramsey model necessarily has an unique equilibrium.
b) The Solow model necessarily has an unique equilibrium.
c) The Diamond overlapping generations model necessarily has an unique equilib-
rium.
d) (a) and (b).
Ans (d)
5. Which of the following statements is correct?
a) Ricardian equivalence holds in the Ramsey model.
b) A fall in the discount rate of households increases output per unit of effective
labour in the Diamond overlapping generations model with logarithmic utility and Cobb-
Douglas production function.
c) The Diamond overlapping generations model may have multiple equilibria.
d) (a), (b) and (c).
Ans: (d)
Consider the Ramsey model for the household with logarithmic preferences i.e. θ = 1
in our notation in lecture notes. Consumption (per unit of effective labour) is denoted
by c and capital (per unit of effective labour) is denoted by k. The equation for the c˙ = 0
locus is given by
f ′(k) = ρ+ g.
where ρ > 0 is the rate of time preference and g > 0 is the rate of technological progress.
The equation for the k˙ = 0 locus is given by
c = f(k)− (n+ g)k
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The production function is Cobb-Douglas written in intensive form as y = kα.
Answer the following questions 6-7 based on the information.
6. The steady state value of k is
a) (ρ+g
α
)
1
α−1
b) ( α
ρ+g
)
1
1−α
c) ( 1
ρ+g
)
1
1−α
d) (a) and (b).
Ans: (d)
7. The steady state value of c is
a) (ρ+g
α
)
α
α−1 − (n+ g)(ρ+g
α
)
1
α−1 .
b) ( α
ρ+g
)
α
1−α .
c) ( 1
ρ+g
)
α
1−α .
d) (n+ g)(ρ+g
α
)
1
α−1 − (ρ+g
α
)
α
α−1 .
Ans: (a)
For questions 6 and 7, also see slides from live session in pdf file "MSc Week 10 A
live.pdf" or the recording of the live support session in week 10.
8. Which of the statements below may be true of c and k along the saddle path in
the Ramsey model.
a) c and k are both decreasing.
b) c is decreasing and k is increasing.
c) c is increasing and k is decreasing.
Ans a)
9. A decrease in government spending in the Ramsey model
a) shifts the k˙ = 0 locus upwards.
b) shifts the k˙ = 0 locus downwards.
c) shifts the c˙ = 0 locus leftward.
d) shifts the c˙ = 0 locus leftward.
Ans: (a)
10. Which of the following reasons is not a cause for the failure of Ricardian equiv-
alence.
a) Presence of credit constraints.
b) Presence of distortionary taxes.
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c) Presence of infinitely lived households.
d) None of the above.
Ans: c).
11. In the steady state of the Solow model, the rate of growth of output per unit of
effective labour (y) is zero. True or False.
True
12. Suppose, the rate of growth of population and the rate of depreciation is zero.
The rate of growth of technology, on the other hand, g is positive. In the steady state
of the Solow model, what is the rate of growth of aggregate output ( Y ). What is rate
of growth of output per capita (Y/L)?
Both growth rates are g.
13. Suppose there is a increase in the capital depreciation rate in the Solow model.
What happens to capital and output per unit of effective labour in the new steady state?
Explain briefly the transition of the economy towards the new steady state?
See diagram in live support session and "MSc Week 10 A live.pdf". Both capital and
output per unit of effective labour fall in the new steady state.
14. Consider the two period model of tax smoothing. It is optimal to allow tax
revenues to rise during recessions according to this model. True or False?
False. See pp. 43-45 of Fiscal policy slides.
15.
Suppose consumers live for two periods and receive endowments of Y1 and Y2 and
pay lump-sum taxes T1 and T2 (where subscripts indicate periods 1 and 2).
Consumers maximise a standard utility function U(C1, C2) (where C1 and C2 are
consumption levels). Consumers’ budget constraints in periods 1 and 2 are as follows
A1 = Y1 − T1 − C1,
C2 = Y2 − T2 + (1 + r)A1,
where A1 is the savings held at the end of period 1. Savings pay interest rate r.
The government spends G1 and G2. The government’s budget constraints in periods
1 and 2 are as follows
B1 = G1 − T1,
T2 = G2 + (1 + r)B1,
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where B1 is the stock of government debt at the end of period 1. The government pays
interest at rate r on its debt.
(a) Assume that taxes are cut in period 1 and they are raised in period 2 so as to
continue to satisfy the government’s intertemporal budget constraint. Is the consumer’s
optimal consumption choices affected as a result of this change in tax policy. Explain
briefly. [No proof is required; simply explain intuitively (in words)]
(b) Suppose consumers cannot borrow (so that consumption in period 1 must
satisfy the additional constraint C1 ≤ Y1 − T1). How would this affect your answer to
part (a)?
Ans
(a) No. This is the Ricardian result. Consumers simply save the tax cut and use
the extra savings to pay for the tax rise next period (including principal plus interest).
Optimal consumption choices are not affected. May use diagrams to illustrate.
(b) Let the optimal consumption levels (if consumers maximise utility) in the
absence of this constraint be C∗1 , C
∗
2 . If C
∗
1 > Y1−T1, then consumers are forced to choose
C1 = Y1 − T1 and C2 = Y2 − T2. The timing of taxes affect consumption so Ricardian
equivalence may not hold true.
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