14 May 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.
SHORT, PRECISE, CLEAR, AND CORRECT ANSWERS RECEIVE FULL POINTS.
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