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Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
MIDTERM EXAM
Professor Orhan Torul
Summer I – 2010
June 21, 2010
NAME:
Time: 2 Hours
Exam has a total of four (4) problems and pages numbered one (1) through thirteen (13). Each
problem’s total number of points is shown below. Your solutions should consist of some
appropriate combination of mathematical analysis, graphical analysis, logical analysis, and
economic intuition, but in no case do solutions need to be exceptionally long. Your solutions
should get straight to the point –
solutions with irrelevant discussions and derivations will be
penalized.
You are to answer
all questions
in the spaces provided, and
show all your work.
Problem 1
/ 20
Problem 2
/ 30
Problem 3
/ 35
Problem 4
/ 15
TOTAL
/ 100
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Problem 1: Consumption and Leisure in the OnePeriod Economy (20 points)
Consider the economy where the representativeagent lives
only for one period
. She enjoys both
consumption and leisure. Her utility function is defined as
( , )
2ln( ) 4ln( )
u c l
c
l
where
c
denotes consumption,
l
denotes leisure (in fractionoftheperiod units), and ln is the natural
logarithm function.
Her only source of income is her labor income. She chooses what fraction of the period to enjoy
as leisure and what fraction of the period she wants to devote to as labor.
Nature imposes the
following restriction: Sum of fraction she enjoys as leisure and fraction she devotes to as labor is
equal to 1, i.e.
1
ln
, where
n
denotes fraction of the period devoted as labor.
The nominal wage rate in the economy is given as
$
W
(i.e. if the representative agent devotes all
her time to labor, she would earn
$
W
as labor income
excluding taxes
).
There is a
proportional labor income tax,
which requires the representative agent to pay
n
t
fraction of her income as tax. (i.e. for each dollar she earns, she has to pay
n
t
dollar as labor
income tax, where
01
n
t
.)
The price of the consumption good in the economy is given as
$
P
.
There is
a proportional sales tax
, which requires the representative agent to pay an additional
c
t
fraction of her expenditure as sales tax. (i.e. for each dollar she spends, she has to pay
c
t
dollar
as sales tax, where
c
t
.)
a)
Construct the budget constraint for the representative agent in its general form.
(2 pts)
(1
)
)
)
cn
P
t
c
t
W
l
2
b)
Suppose that you are given the following information:
$10
W
,
$2
P
,
0.40
n
t
,
0.50
c
t
.
Rewrite the budget constraint using this information.
(2pts)
2 (1 0.5)
(1 0.4) 10 (1
)
or
3
6(1
)
or
2(1
)
cl
c)
Set up the Lagrangian for this problem, and derive the optimality condition.
(6pts)
( , , )
2ln( ) 4ln( )
) 3
L c l
c
l
l
c
Firstorder conditions are
2
3
0
c
c
4
6
0
l
l
Combining the two first order conditions, optimality conditions is simply
d)
Using the optimality condition you find in part c, and the budget condition you find in part b,
find the values for consumption
c
, labor
n
, and leisure
l
. (You are to find
numerical
values for
the
,,
cn
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This note was uploaded on 03/08/2011 for the course ECON 602 taught by Professor Chugh during the Spring '11 term at Johns Hopkins.
 Spring '11
 chugh
 Economics

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