Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Midterm Exam – Part 2
Professor Sanjay Chugh
Fall 2009
October 15, 2009
NAME:
Part 2 of the Exam has a total of two (2) problems and pages numbered one (1) through eight (8).
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
You may use one page (doublesided) of notes.
You may
not
use a calculator.
Problem 3
/ 28
Problem 4
/ 22
TOTAL PART 2
/ 50
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Problem 3:
“Hyperbolic Impatience” and Stock Prices (28 points).
In this problem you will
study a slight extension of the infiniteperiod economy from Chapter 8.
Specifically, suppose the
representative consumer has a lifetime utility function given by
23
123
()
( )
( ).
.
.
.
tt
t
t
uc
JE
±±±
±±
±
±
,
in which, as usual,
u
(
.
) is the consumer’s utility function in any period and
ȕ
is a number
between zero and one that measures the “normal” degree of consumer impatience.
The number
J
(the Greek letter “gamma,”
which is the new feature of the analysis here) is also a
number between zero and one, and it measures an “additional” degree of consumer
impatience, but one that ONLY applies between period t and period t+1.
1
This latter
aspect is reflected in the fact that the factor
Ȗ
is NOT successively raised to higher and
higher powers as the summation grows.
The rest of the framework is exactly as studied in Chapter 8:
1
t
a
²
is
the
representa
tive
consumer’s holdings of stock at the beginning of period
t,
the nominal price of each unit of stock
during period
t
is
t
S
, and the nominal dividend payment (per unit of stock) during period
t
t
D
.
Finally, the representative consumer’s consumption during period
t
is
c
t
and the nominal
price of consumption during period
t
is
P
t
.
As usual, analogous notation describes all these
variables in periods
t
+1,
t
+2, etc.
The Lagrangian for the representative consumer’s utilitymaximization problem (starting from
the perspective of the beginning of period
t
) is
1
11
1
1
1
1
1
1
2
22
2
2
1
2
2
2
2
3
33
3
32
.
.
.
t
t
t
t
t t
t
t
ttt
t
t
t
t
t
t
t
t
t
YSD
a
P
c
S
a
YS
D
a
P
c
S
a
D
a
P
c
S
a
D
a
P
O
JEO
JE O
²
±
±
±
±
±
±
±
±
±
±
±
±
±
±
ªº
±
²
²
¬¼
±
²
²
±
²
²
±
²
...
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 Spring '08
 chugh
 Economics, Utility, Federal government of the United States

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