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.

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.