Homework: Hedonic Theory
Assume
that there is a baseline risk of death on the job of q
0
percent annually. Firms can invest to
reduce this risk, so that actual risk at a job is q(
i
)=q
0
–
i
*ß.
Here i is amount invested
into reducing
the
risk
a given employee faces
.
Of course mortality is bounded below by 0, so the
maximum productive
amount that can be invested i
n reduci
ng mortality risk i
s i
Max
= q
0
/ß .
All firms produce the same good c
and this good has a price equal to 1.
All workers are equally productive and produce an output of
H
of
the consumption good.
Question 1
D
erive an expression of wages
w(q)
in this
economy that has to be satisfied by wage
–
risk combinations
that
competitive
firms would be willing to
offer to workers in equilibrium.
Question 2
Consider now individuals that have preferences over consumption and risk of death given by
(,)
Ucs
,
where
0
s
q
q
?
?
is “job safety” relative to base
–
line risk
0
q
.
Write down the maximization problem
that workers face
and illustrate the choice problem in a graph
in a two
–
dimensional graph with c and s
on the axes
.
Assume that the parameter values are such that the solution is in the interior (ie
0
sq
?
)
Question 3
Say
consumers preferences are such that a both c and s are normal goods. Assume furthermore that
individuals differ in
the
human capital
H
(but still everybody has
0
sq
?
)
.
Consider two individuals of
whom one has a higher level of H than the other. W
ho will earn higher wages and who will face greater
risk?
Will the two individuals differ in their Value of a Statistical L
ife (VSL)?
Question 4
Use your answer to question 3 to explain why it might be difficult
to empirically measure the VSL using
the relation between wages and risk.
SHORT, PRECISE, CLEAR, AND CORRECT ANSWERS RECEIVE FULL POINTS.