UNIVERSITY OF SOUTHAMPTON ECON6023W1
SEMESTER 1 EXAMINATIONS 2018-19
ECON6023 Macroeconomics
Duration: 180 mins (3 HRS)
This paper contains 4 questions
Answer ALL questions in Section A and in Section B.
Section A carries 1/2 of the total marks for the exam paper and you should aim
to spend about 90 minutes on it.
Section B carries 1/2 of the total marks for the exam paper and you should aim
to spend about 90 minutes on it.
An outline marking scheme is shown in brackets to the right of each question.
Only University approved calculators may be used.
A foreign language direct ‘Word to Word’ translation dictionary (paper version)
ONLY is permitted. Provided it contains no notes, additions or annotations.
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2 ECON6023W1
Section A
A1 (10 points) Consider a two-period (t=0,1) version of the neoclassical
growth model: max(c0,c1,k1,k2){ln c0 + β ln c1}, where β ∈ (0, 1),
subject to c0 + k1 = k
α
0 , c1 + k2 = k
α
1 , and c0, c1, k1, k2 ≥ 0, where
α ∈ (0, 1) and k0 is given. Notation is as usual.
(a) Derive the optimal decision rules for the capital stock and con-
sumption in period t = 0. [5]
(b) Derive the value function in period t = 0. [5]
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3 ECON6023W1
A2 (15 points) Consider a Markov chain with the following transition
matrix:
P =
[
0.7 0.3
0.2 0.8
]
(a) Suppose that the unconditional distribution at time t over the 2
states of the Markov chain with this transition matrix is:
pit =
[
0.75 0.25
]
[5]Find the unconditional distribution at time t + 1, pit+1.
(b) Find the stationary distribution of this Markov chain. [10]
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4 ECON6023W1
A3 (25 points)
Consider a consumer with the following optimization problem:
max
{ct,at+1}
∞∑
t=0
βt ln(ct)
s.t. ct + at+1 = Rat + w, t = 1, 2, . . . ,
where β ∈ (0, 1), ct is the consumer’s level of consumption in period
t, at is the consumer’s asset holdings at the beginning of period t,
R is the gross interest rate, and w is the consumer’s labour earnings
in each period.
(a) Formulate the consumer’s problem as a recursive problem. [5]
(b) Use the “guess-and-verify” method to find the value function
and the corresponding decision rules. (Hint: the value function
in this problem takes the form v(a) = A+B ln(a+D), where
A, B, D are coefficients to be solved for) [10]
(c) Characterize the dynamics of the consumer’s asset holdings. Do
they converge or diverge? If they converge, to what value do
they converge? [10]
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5 ECON6023W1
Section B
Consider an economy inhabited by a continuum of identical house-
holds and each household solves:
max
{ct,ht,it,kt+1}∞t=0
∞∑
t=0
βt [u (ct) + v (1− ht)] ,
subject to ptbt+1 + ct + it = rt(1 − τk,t)kt + (1 − τw,t)wtht + bt
and kt+1 = (1 − δ)kt + it. bt+1 is government debt which the
government must pay back to the households in period t + 1. This
asset is traded at period t at price pt. All other variables have the
usual interpretation. In each period, tax revenues and government
debt are used by the government to finance some exogenously given
and constant government spending G. Perfectly competitive firms
solve each period
max
kdt ,h
d
t
[
Af (kdt , h
d
t )− rtkdt − wthdt
]
,
where kd and hd denote capital and labour demand. A ≥ 0 is a
productivity parameter. Preferences and production function f have
the usual neoclassical assumptions. β and δ ∈ (0, 1), and agents
have rational expectations.
(a) Find the first order conditions for the representative household
and firm. [10]
(b) Write down the problem of a benevolent planner. [10]
(c) Find the first order conditions of a benevolent planner and ex-
plain whether there is a market equilibrium with the same allo-
cations. [10]
(d) Write down the implementability constraints that a Ramsey plan-
ner would take as given and explain why the solution to a Ramsey
problem differs from that of a Planner problem. [10]
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6 ECON6023W1
(e) Show the long run level of capital income taxes chosen by the
Ramsey planner. [10]
END OF PAPER
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Social Sciences

Examination Feedback
2018/2019

Module Code & Title: ECON6023 Macroeconomics

Module Coordinator: Alessandro Mennuni and Serhiy Stepanchuk

Mean Exam Score: 56.08

Percentage distribution across class marks:


UG Modules
1 st (70% +)
2.1 (60-69%)
2.2 (50-59%)
3rd (40-49%)
Fail (25-39%)
Uncompensatable Fail
(<25%)





PGT Modules
70% + 25%
60-69% 25%
50-59% 25%
<50% 25%

Overall strengths of candidates’ answers:
All students answered question A2(b) correctly. Most students also answered question A2(a) correctly. This
shows their understanding of the properties of Markov chains. Most students answered correctly question
A3(a), which demonstrates their ability to formulate recursively the dynamic optimization problems.

The understanding of the Ramsey taxation was not great for many students. Besides the mathematics, some
struggled with understanding the difference between a planner problem and a government that faces market
constraints.

Overall weaknesses of candidates’ answers:
Very few students had a correct answer to question A3(c). This shows that their ability to apply the dynamic
programming tools needs more work.

Pattern of question choice:
N/A
Issues that arose with particular questions:
N/A
Further comments not covered above:
N/A

Discipline vetting completed By (Name): E Mentzakis Date:28 Feb 2019


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