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Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Final Exam Suggested Solutions
Professor Sanjay Chugh
Fall 2009
NAME:
The Exam has a total of four (4) problems and pages numbered one (1) through nine (9).
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 two pages (doublesided) of notes.
You may
not
use a calculator.
Problem 1
/ 25
Problem 2
/ 25
Problem 3
/ 25
Problem 4
/ 25
TOTAL
/ 100
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Problem 1:
Consumption and Savings in the TwoPeriod Economy (25 points).
Consider a
twoperiod economy (with no government), in which the representative consumer has no control
over
his
income.
The
lifetime
utility
function
of
the
representative
consumer
is
±²
12
1
2
,l
n
l
n
ucc
c
c
³
, where
ln stands for the natural logarithm.
We will work here in purely
real terms:
suppose the consumer’s
present discounted value of ALL lifetime REAL income
is 26.
Suppose that the real interest rate between period 1 and period 2 is zero (i.e.,
r
= 0), and
also suppose the consumer begins period 1 with zero net assets.
a.
(17 points)
Set up the lifetime Lagrangian formulation of the consumer’s problem, in order
to answer the following:
i)
is it possible to numerically compute the consumer’s optimal
choice of consumption in period 1?
If so, compute it; if not, explain why not.
ii) 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.
iii) 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.
Solution:
We know that with zero initial assets, the LBC of the consumer is
22
11
,
cy
rr
³
³
³
³
where the notation is standard from class.
The Lagrangian is thus
1
1
(, )
yc
uc c
y
c
O
ª
º
³³´
´
«
»
³³
¬
¼
,
where
of course is the Lagrange multiplier (note there’s only one multiplier since this is the
lifetime formulation of the problem not the sequential formulation of the problem).
The first
order conditions with respect to
1
c
and
2
c
(which are the objects of choice) are, as usual:
112
212
1
0
0
1
r
´
´
³
(And of course the FOC with respect to the multiplier just gives back the LBC.)
Also as usual,
these
FOCs
can
be
combined
to
give
the
consumptionsavings
optimality
condition,
1
1
r
³
.
With the given utility function, the marginal utility functions are
1/
uc
and
, so the consumptionsavings optimality condition in this case becomes
21
1
/1
cc
r
³
.
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This document was uploaded on 11/01/2011 for the course ECON 325 at Maryland.
 Spring '08
 chugh
 Economics

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