Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Problem Set 1 Suggested Solutions
Professor Sanjay Chugh
Fall 2010
Instructions
:
Written (typed is strongly preferred, but not required) solutions must be
submitted no later than 2:00pm on the date listed above.
You must submit your own independentlywritten solutions.
You are permitted (in
fact, encouraged) to work in groups to think through issues and ideas, but you must
submit your own independentlywritten solutions.
Under no circumstances
will
multiple verbatim identical solutions be considered acceptable.
Your solutions, which likely require some combination of mathematical derivations,
economic reasoning, graphical analysis, and pure logic, should be
clearly, logically, and
thoroughly presented;
they should not leave the reader (i.e., your TAs and I) guessing
about what you actually meant.
Your method of argument(s) and approach to problems
is as important as, if not more important than, your “final answer.”
Throughout, your
analysis should be based on the frameworks, concepts, and methods we have developed
in class.
There are three problems in total, each with multiple subparts.
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2
Problem 1:
Elasticity of Labor Supply and Fiscal Policy. (40 points).
Consider the static
(i.e., oneperiod) consumptionleisure framework.
In quantitative and policy applications
that use this framework, a commonlyused utility function is
!
"
1 1/
168
1
1/
( , )
ln
u
l
c l
c
#
$
#
%
&
%
’
&
,
in which
c
denotes consumption,
l
denotes the number of hours (in a week) spent in leisure,
and
#
and
$
(the Greek letters “psi” and “theta,” respectively) are
constants
(even
though we will not assign any numerical value to them) in the utility function.
The
representative individual has no control over either
#
or
$
, and both
0
#
(
and
0
$
(
.
Labor
is measured as
n
= 168 –
l
, the
real wage
is denoted by
w
, and the laborincome tax
rate is denoted by
t.
The
takehome rate
(the fraction of labor income that an individual
keeps) can thus be defined as
S
= (1
t
).
Finally, expressed in real terms, the representative
individual’s budget constraint is
(1
)
c
t wn
’
&
.
Thus, this is
exactly
the consumptionleisure framework studied in Chapter 2, with now a
particular functional form for
u
(
c,l
).
a.
(5 points)
For the given utility function, set up the consumptionleisure optimality
condition, and then solve it for
n
,
expressing the solution in terms of (among other
things)
S
,
rather than
t
.
(that is, your final expression here should be of the form
n
= …,
and on the righthand side the takehome rate
S
should appear, but the tax rate
t
should
not appear.).
(
Note:
You do
not
need to set up a Lagrangian in order to analyze this
problem; you may go straight to the consumptionleisure optimality condition.
Be very
careful in deriving the result, because the rest of the analysis is based on this.)
Clearly
present the steps and logic of your work.
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 Fall '08
 chugh
 Economics, Utility, representative, Natural logarithm, Labor Supply, consumptionleisure optimality condition

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