Dietrich Vollrath and Bent E. Sørensen
June 27, 2005
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. (30%)
People live for two periods and maximize their lifetime utility of
U
= ln
c
1
+ ln
c
2
. They
have a discount rate of zero and there is a positive interest rate of r.
Individuals have two options for their time. They can work or they can go to school. The time
spent in school is denoted
n
, and the time they spend working is (1

n
). Time spent in school
creates human capital that can be used in the next period, according to the following formula,
h
t
+1
= (
n
t
h
t
)
α
x
1

α
, where
x
represents public education spending. Note that human capital in
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 '05
 would
 Economics, Monetary Policy, Interest Rate, education spending, base wage rate

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