# Homework: Hedonic Theory

Homework: Hedonic Theory
Assume that there is a baseline risk of death on the job of q0 percent annually. Firms can invest to
reduce this risk, so that actual risk at a job is q(i)=q0 – 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 in reducing mortality risk is iMax = q0/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
Derive 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
U c s ( , ),
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
s q ?
)
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
s q ?
). Consider two individuals of
whom one has a higher level of H than the other. Who will earn higher wages and who will face greater
risk? Will the two individuals differ in their Value of a Statistical Life (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.