W3211 Spring 2009
Professor Vogel
Homework #3: Due Tuesday 03/31/09
°
Please write your name on the top of
every page
of your homework (in case they get
separated) and
please staple all pages together
.
°
Where appropriate, you must show all work. If you just give an answer without work,
you don°t receive credit (on a mathematical question, of course).
For a given income,
I
, and a given level of e/ort
e
±
0
, Sue°s utility is
u
(
I; e
) =
I
²
1
2
e
2
.
Suppose the ±rm°s revenue as a function of Sue°s e/ort is
R
(
e
) = 10
e
.
1.
(20 Points)
Suppose Sue earns a wage
w
±
0
no matter how much e/ort she exerts.
(a)
(10 Points)
Solve for the level of e/ort she will exert as a function of the wage.
(b)
(10 Points)
Given your answer to part
(
a
)
solve for the wage
w
±
0
that maxi
mizes the ±rm°s pro±t, which is equal to
R
(
e
)
²
w
in this case. [i.e. Suppose the
±rm knows how much e/ort Sue will exert given its choice of wage. Then solve
for the wage the ±rm would choose that maximizes its pro±t]
2.
(20 Points)
Now suppose that the ±rm can observe Sue°s e/ort and writes a contract
that stipulates that Sue°s base salary is zero and that she receives a bonus
b
±
0
for
every unit of e/ort that she exerts.
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 Spring '08
 Govel
 Business, Salary, Monotonic function, Convex function

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