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E200 MACROECONOMICS

Creation date：2024-04-11 14:12:25

Belonging category：经济Economics

Tag ECM9

MACROECONOMICS

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ECM9/ECM11

MPhil in Economics
MPhil in Finance & Economics
Candidates are required to answer one out of two questions.
Write your candidate number (not your name) on your uploaded answers.
1 of 3
E200 MACROECONOMICS
This is a two hour examination for which students are expected to begin at 12:00pm
and submit by 2:20pm. The twenty minutes are added to the standard two hour time for
answer uploadings. Detailed online examination guidelines are available on Moodle.
Students are not allowed to consult or seek help from others.
Write legibly. Illegible handwriting may be penalised.
1 Menu Costs, Sticky Prices and Covid-19 Shock
In the second quarter of 2020, the Covid-19 pandemic led to a sharp decline in UK real
gross domestic product (GDP) by nearly 20% and a rise in the GDP deflator of almost 7%,
whereas the Consumer Price Index (CPI) remained quite stable. Consider the following
menu cost model to analyze and discuss the conditions under which it is optimal for firms
to keep their prices fixed in response to this large Covid-19 shock, and the macroeconomic
implications this has.
The representative consumer i ∈ [0, 1] maximizes utility
Ui = Ci − 1
γ
Lγi
subject to the budget constraint
Ci = Πi +
W
P
Li
where Ci denotes consumption, Li employment, with constant parameter γ > 1, W the
nominal wage, P the aggregate price level, and Πi real profits.
The profit-maximizing representative firm i ∈ [0, 1] operates under monopolistic competi-
tion in the goods market and faces a small real menu cost Z ≥ 0 when it changes the price
Pi of its good. Its real profits without menu costs equal
Π˜i =
Pi
P
Qi − W
P
Li
where Qi denotes the production of good i. The production technology is described by
Qi = ALi
where A denotes productivity. The firm faces the following individual demand function
with constant parameter η > 1:
Qi = Y
(
Pi
P
)−η
where Y ≡ ∫ 1
0
Qidi denotes aggregate output, and P ≡
∫ 1
0
Pidi.
The aggregate demand relation is given by
Y =
M
P
where M denotes aggregate demand. The labour market is characterized by either (a)
perfect competition, or (b) the following real wage function with constant, strictly positive
parameters B and β:
W
P
= BLβ
where L ≡ ∫ 1
0
Lidi denotes aggregate employment.
In your answer, carefully analyse and discuss:
• The difference between the macroeconomic equilibrium with (i) flexible prices and
(ii) fixed prices, for labour market conditions (a) and (b).
• How the Covid-19 shock could be analysed in this model, and whether keeping prices
fixed in response to such a large shock is a Nash equilibrium.
2 of 3
2 Secular stagnation and rates of return
In recent decades there appears to have been a decline in trend output growth and in the
rates of return on a broad class of assets. It has been argued that these patterns might stem
from a decline in the rate of technological progress.
(a) Carefully analyse and discuss these patterns and arguments from the perspective of
the Solow model.
(b) Now analyse and discuss these patterns from the perspective of the following closed
endowment economy. Specifically, suppose a representative agent has period utility
u(ct) =
c1−σt − 1
1− σ
with consumption ct in period t, parameter σ > 1 and time discount factor 0 < β < 1,
and is endowed with a stream of income, yt, into the infinite future. Suppose further
that the deterministic endowment process is such that yt+1
yt
= G (with some given y0).
• Set up the intertemporal optimization problem of the agent and derive his/her
Euler equation when faced with a riskless gross real return on savings from t to
t+ 1 of R ≡ 1 + r.
• Show that in equilibrium there must be a connection between G and r, give
intuition for its sign (i.e. positive or negative relationship) and explain how its
magnitude depends on σ.
• Briefly discuss whether this is consistent with the insights from part (a).
(c) Some people have argued that rates of return have declined not only due to lower trend
growth, but also from an increased desire to save. Carefully discuss this argument.
END OF PAPER

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LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 FINC5090 MATH1052 SciComp Elec4622 FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 MAT 237 BISM2201 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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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