Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Problem Set 1
Professor Sanjay Chugh
Spring 2009
Due: Wednesday, February 25, 2009
Instructions
:
Written (typed is strongly preferred, but not required) solutions must be
submitted no later than 11:00am on the date listed above (either in class or in the
Economics Department Main Office, Tydings Hall 3105).
Your solutions, which likely
require some combination of mathematical derivations, economic reasoning, graphical
analysis, and pure logic, should be thoroughly presented and not leave the reader (i.e.,
your TAs and I) guessing about what you actually meant.
You must submit your own independentlywritten solutions.
You are permitted (in
fact, encouraged) to work in groups to think through issues and ideas, but your “writing
up” of solutions should be done independently of anyone else.
Under no circumstances
will multiple verbatim identical solutions be considered acceptable.
There are three problems in total, each with multiple subparts.
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Problem 1:
Optimal Choice in the ConsumptionSavings Model During a Credit
Crunch:
A Numerical Analysis (60 points).
Consider a twoperiod economy (with no
government
and
hence
neither
government
spending
nor
taxation),
in
which
the
representative consumer has no control over his income.
The lifetime utility function of the
representative consumer is
!"
1
2
1
2
,
ln
ln
u c c
c
c
#$
, where
ln stands for the natural logarithm.
We will work here in purely real terms:
suppose the consumer’s real income in period 1 is
y
1
= 10 and the consumer’s real income in period 2 is
y
2
= 22.
Suppose that the real interest rate
between period 1 and period 2 is ten percent (i.e.,
r
= 0.10), and also suppose the consumer
begins period 1 with
real
net wealth (inclusive of interest) of (1+
r
)
a
0
= 2.
Set up the lifetime Lagrangian formulation of the consumer’s problem, and use it to answer
part a, b, and c.
Show all steps in your logic/arguments.
a.
(8 points)
I
s
it possible to numerically compute the consumer’s optimal choice of
consumption in period 1?
If so, compute it; if not, explain why not.
b.
(8 points)
Is it possible to numerically compute the consumer’s optimal choice of
consumption in period 2?
If so, compute it; if not, explain why not.
c.
(6 points)
Is it possible to numerically compute the consumer’s real asset position at the
end of period 1?
If so, compute it; if not, explain why not.
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 Spring '08
 chugh
 Economics, Public Finance, Period, FISCAL STIMULUS, optimal choice

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