Dietrich Vollrath and Bent E. Sørensen
January 15th, 2008
Comprehensive Exam in Macroeconomic Theory–Procedural Instructions
(1) Write your answers only on the paper we will provide.
(2) We will be distributing a numbered sign–in sheet in a moment.
The number next to your
signature will be your
student number
.
(3) Every sheet of paper you turn in to us
must
have your
student number
written at the
top–center
of the sheet and
circled
.
(4) Every sheet of paper you turn in to us
must
have a
page number
written at the
top–right
corner
of the sheet.
(5) When you have finished, or when it is 1:00 pm (whichever comes first), prepare a cover sheet for
your exam. This cover sheet should not have a page number, but must have the following things
on it:
(a) Your
student number
at the top–center, circled.
(b) The phrase “Macroeconomics Comprehensive Exam”.
(c) The sentence “My last page is page number X”, where X is your total number of pages of
answers.
1
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1. (25%)
Individuals live for two periods. They earn labor income of
w
t
in the first period of their
life, and consume in both periods. Their utility function is
U
= (1

β
) ln
c
1
+
β
ln
c
2
, and they
take the interest rate of
r
as exogenous to their consumption decision.
(a) What is the optimal amount of savings (
s
t
) done by an individual?
Production in this economy uses both physical and human capital.
The production function is
y
t
=
k
α
t
h
1

α
t
. The wages of a young person are thus
w
t
= (1

α
)
k
α
t
h
1

α
t
.
There is a tax on savings at the rate of
τ
.
The proceeds of this tax are used to finance the
accumulation of human capital. There is no population growth. Physical capital accumulates as
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 '05
 would
 Economics, Steady State, steady state level, state growth rate

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