Michael Rothschild
UCLA Economics 145a
October 14, 2009
1 Problem
1. The &rst homework problem asks you to do comparative statics in a prob
lem where an individual picks how much of life to spend on schooling.
Let±s write equation
(4)
of the handout for April 21²which gives the ex
pected present discounted value of earning ²correctly. With
s
years of
schooling you earn at a rate
W
(
s
) =
e
bs
while you are working. If you
start school at age
6
and work until age
T
and discount earnings at rate
r
the present discounted value of your earnings are
V
(
s
) =
W
(
s
)
e
6
r
Z
T
6+
s
exp(
rt
)
dt
.Start out by simplifying the above expression by mutliplying by the pos
itive constant
e
6
r
:
We further simplify the notation somewhat letting
~
T
=
T
6
years. Then our problem is to choose
s
to maximize
~
V
(
s
) =
W
(
s
)
Z
~
T
s
exp(
rt
)
dt:
We can now drop the tildes and just choose
s
to maximize
V
(
s
) =
W
(
s
)
Z
T
s
exp(
rt
)
dt
The &rst term is the wage that you earn; the second term is just the
discounted amount of time that you work. Integrating we see that
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 Fall '09
 BRESNOCK
 Economics, Economic system, 6 years

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