Lecture 7
Compensating Wage Differentials
Utility for w and D
Wage, w
U3
U2
U1
Because D is a bad,
indifference curves slope up
Prefer combinations of higher w
and less D.
Probability of Injury, D
Utility for w and D
Wage, w
U1
Z is the difference in wages
between a safe and dangerous
job that makes the worker just
indifferent between the two
jobs.
w*
Z
w0
0
1
Probability of Injury, D
Utility for w and D
Wage, w
U2
U1
w1
Here W>Z so the worker
works at job 1.
W
w*
Z
w0
0
1
Probability of Injury, D
Distribution of Z
Choose D=1
Choose D=0
E(Z)
W
Z
Distribution of B
Choose D=1
Choose D=0
W
E(B)
B
Demand and Supply of Dangerous Jobs
W=w1-w0
Supply of workers willing to
work in a dangerous job
E
W*
Demand by firms for
workers in dangerous jobs.
D*
Number of Workers in
Dangerous Jobs
Utility for w and Probability of Injury
Wage, w
Person A dislikes risk the most.
Requires the largest wage increase
to work at a slightly riskier job.
UA
UB
Probability of Injury
UC
Iso-profit curves
Wage, w
π1
Iso-profit curve slopes up
because it is more expensive
to produce safe jobs.
π2
π3
Lower iso-profit curves represent
higher profits.
Probability of Injury
Utility for w and Probability of Injury
Wage, w
Firm C has the highest costs of
producing a safe job.
πC
πB
πA
Probability of Injury
The Hedonic Wage Function
Wage, w
UC
UB
PC
πC
Hedonic Wage
Function
UA
PA
PB
πB
πA
Probability of Injury
Prior to OSHA regulation
Wage, w
U*
Hedonic Wage
Function
w*
π*
P
Initial equilibrium at P with
wage w* and probability of
injury ρ*.
ρ*
Probability of Injury
After OSHA regulation
Wage, w
U*
π´
P
Hedonic Wage
Function
π*
U´
w*
w´
Q
ρ´
New equilibrium given by Q.
Involves lower risk of injury,
ρ´, and lower wage, w´.
ρ*
Probability of Injury
Worker Misperceives Risk
Wage, w
U0
U*
U´
w0
Hedonic Wage
Function
ρ0
ρ´
ρ*
Probability of Injury
Summary
¾We have built a model which incorporates
differences in job attributes.
¾In this model the actual wage has two
parts
– First part is the worker’s value of marginal
product.
– Second part reflects the price paid for
attributes of the job (price can be negative).
¾Second part called the compensating
wage differential.
Summary
¾A firm must pay a worker to accept a job
with attributes the worker does not like.
¾A firm can sell workers, in the form of
lower wages, attributes of a job the worker
does like.
¾When workers differ in their desire for an
attribute, and firms differ in their costs of
supplying the attribute, we will have a
demand and supply curve for the attribute.
Summary
¾The equilibrium compensating wage
differential for the attribute and the supply
of the attribute will be determined by the
intersection of the demand and supply
curves.
¾The actual wage matches workers and
firms.
– Workers with the greatest desire for the
attribute will work for firms that can provide
the attribute at the lowest cost.
Summary
¾The Hedonic wage function shows the
market price for an attribute.
– In this case the price of risk.
¾Actual wage will be the sum of the
worker’s value of marginal product and the
price of all the attributes of the job
¾Can use this theory to find the value of a
statistical life.
Summary
¾Can use the model we developed to
understand the costs and benefits of
regulating workplace safety.