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.

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