ECO 310, Fall 2007
Problem Set 2: Consumer Theory
Due in class on October 9
Question 1
You have just emerged from medical school with a debt service burden of $25,000
per year, and have set up practice.
You have to decide how hard to work.
For each hour of work, you expect to earn $50 (after subtracting expenses of
maintaining your oﬃce, taxes, etc.). Your utility function for a full year is
U
(
I,H
)=ln
I
+ 2 ln(5000
−
H
)
,
where
H
is the number of hours you work during the year, and
I
is what is left
of your annual income after expenses, taxes, and debt service.
(a) What is your budget constraint linking
I
and
H
?
(b) Find your optimal number of hours of work.
(c) If taxes go up so you are left with only $40 per hour of work, will you
work more or fewer hours? Explain the economic intuition for the result.
Question 2
There are two goods, whose quantities are denoted by
X
and
Y
, each being a
real number. An individual’s consumption set consists of all (
X, Y
) such that
X
≥
0 and
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 Fall '08
 StephenE.Morris
 $50, $40, demand functions, $25,000

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