Indifference curves
• Workers care about whether their job is safe or risky
Utility = f (w, s)
• where s risk of injury
• Indifference curves reveal the trade offs that a worker prefers between
wages and riskiness
• Firms may have a risky work environment because it is less expensive to
pay higher wages than to make the environment safe
Indifference curves
(one individual)
50
U2
30
U1
20
U0
Wage
Dw
10
0
1
Probability of Injury
A risky job pays $20 per hour while a safe job pays $10
George’s indifference curves are relatively flat
George chooses the safe job paying $10 because his utility is higher at $10 than it is at $20
George prefers the risky job if it pays $50 per hour (U2 > U1)
The worker is indifferent between the two jobs if the risky job paid $30/hour instead of 10.
The worker’s reservation price is then given by Dw = 30 – 10 = 20
Indifference curves
(multiple individuals)
Wage
UA
UC
UB
$25
0.45
0.05 0.10
Probability of loosing your arm
Different workers have different preferences for risk. A is very risk-averse, while C does
not mind risk as much.
The Market for Risky Jobs
wR – wS
S
(wR – wS)*
D
E*
Number of Workers in Risky Job
The supply curve slopes up because as the wage gap between the risky job and the safe
job increases, more and more workers are willing to work in the risky job.
The demand curve slopes down because fewer firms will offer risky working conditions if
risky firms have to offer high wages to attract workers.
The market compensation differential equates supply and demand, and gives the bribe
required to attract the last worker hired by risky firms.
The Market for Risky Jobs
SR
wR – wS
100
E*
0
(wR –
N
wS)*
-50
Number of Workers in Risky Job
DR
If the
a fraction
demand
offor
all such
N workers
workers
likeisto
small,
workthe
in risky
market
jobs,
compensating
they are willing
differential
to pay is
for
the right to be injured.
negative,
meaning
More
andworkers
more workers
employed
enter
inthis
risky
labor
jobsmarket
earn less
as the
thanwage
workers
differential
employed
shrinks
in safe
from
– $50 to $0
jobs.
Isoprofit Curves
• Firms may have a risky work environment because it may be more
profitable:
Profit = h (w, s)
• where s risk of injury, which decreases as the job site becomes more safe.
• Isoprofit curves reveal the trade offs that firms make between wages and
riskiness (job safety)
• Firms may have a risky work environment because it is less expensive to
pay higher wages than to make the environment safe
Isoprofit Curves
(single firm)
Wage
$30
p0
$25
p1
0.05
0.15
Lower wages lowers firm costs,
raising profit
Less safety equipment and training
lowers firm costs, raising profit
Probability of Injury
Firms can hold profits constant by creating safer work environments, allowing them to
attract risk-adverse workers at lower wages.
Isoprofit curves are concave because production of safety is subject to the law of diminishing
returns
Lower isoprofit curves represent higher profits.
Isoprofit Curves
(multiple firms)
Wage
$25
pY
pX
0.05
pZ
0.15
0.10
Probability of loosing your arm
Different firms offer different levels of risk for a given wage rate.
Hedonic Wage Theory
UC
Hedonic Wage Function
Wage
UB
UA
pZ
pY
pX
Probability of Injury
The labor firms
Different
market
have
marries
different
workers
isoprofit
who curves
dislike risk (workers of type A) with firms
with safe work environments (firm X)
Different workers have different indifference curves.
Workers who do not mind risk as much (workers of type C) are married with firms
that find it difficult to provide a safe environment (firm Z).
Hedonic Wage Theory
Hedonic Wage Function
Wage
28,200
21,600
15,000
.002
.003
.004
Probability
of Injury
Estimating the Hedonic Wage function:
wi = a + b pi + d xi
Kip Viscusi (1993) estimated b: A .001-point increase in the probability of fatal
injury may increase annual earnings by about $6600 (in 2002 dollars)
Hedonic Wage Theory
UC
Hedonic Wage Function
Wage
UB
28,200
21,600
UA
pZ
pY
15,000
pX
.002
.003
.004
Probability
of Injury
The statistical value of life is the amount that workers are jointly willing to pay to reduce
the likelihood that one of them will suffer a fatal injury in a given year on the job
Hedonic Wage Theory
How Much is a Life Worth?
Assume Kip Viscusi (1993)’s b estimate is correct:
Dw 6600 -$6600 -$6, 600, 000



Dp .001
-.001
-1
(E = 1000)
(E = 1000)
= 20,000
= .002
= .003
= $26,600
Suppose the probability that a worker will die on the job at firm X is .002 and this
firm pays its workers 20,000 per year.
If both firms have 1000 employees, then 2 workers at firm X and 3 at firm Y are
expected to die on the job this year.
Workers at firm Y are willing to accept .001 higher risk of death because they are
each earning an additional $6600 per year.
That is, each worker at Firm Y is willing to give up $6600 to reduce the probability of
death by 0.001.
Workers are jointly willing to give up $6,600,000 in total earnings so that firm Y can
improve safety to save an additional life
Hedonic Wage Theory
Safety and Regulation
U*
Wage
Hedonic Wage Function
U0
p0
p*
w*
w0
r
r*
Probability of Injury
The workers maximize utility by choosing the job paying wage of w* and offers a
probability of injury of r*.
The government (OSHA) prohibits firms from offering a probability of injury higher
than r , lowering firm profit and worker utility.
Compensating Differentials and Job Amenities
• Amenities include:
– Monday-Friday day shift
– low probability of being laid off
– Low probability of getting hurt or dying
– not having health insurance, zero sick days, no vacation
– Job security
– Location
– Corner office with a view
– Parking
– Health insurance
• Amenities are associated with low wage rates
• With the exception of the risk of death, evidence is not clear on the link
between amenities and wage differentials.
Compensating Differentials and Job Amenities
Income
w1 = $25
w0 = $10
U0
U
1900
3500 4000
Hours of Leisure
The worker
utility by
workingschedule,
2100 hours
per year
at wthe
$10/hrwage but
Another
job maximizes
offers the worker
a seasonal
where
she gets
0 = same
works only 500 hours a year. This would make the worker worse off.
Hence, seasonal employers need to offer seasonal workers a compensating wage differential.
If the seasonal job is to attract any workers, the job must raise the wage to $25.
This makes workers indifferent between the two jobs.
Health Benefits and Compensating Differentials
VTCP = value of worker’s total
compensation package ($)
H = value of health benefits ($)
w = value of wages
25
UA
15
UB
0
10
VTCP0
If workers A and B are equally productive, their job packages lie on the same VCTP line.
Worker A chooses a package with a high wage and no health insurance benefits.
Worker B chooses a package with wage wB and health benefits HB.
Health Benefits and Compensating Differentials
VTCP = value of worker’s total
compensation package ($)
H = value of health benefits ($)
w = value of wages
25
15
0
10
Observed data may identify a trade-off between job benefits and wages.
Health Benefits and Compensating Differentials
VTCP = value of worker’s total
compensation package ($)
H = value of health benefits ($)
w = value of wages
28
UC
15
UB
0
10 15
VTCPB
VTCPC
Workers B and C have different earnings potential, so their job packages lie on different
VTCP lines.
Their choices generate a positive correlation between wages and health benefits.
Health Benefits and Compensating Differentials
VTCP = value of worker’s total
compensation package ($)
H = value of health benefits ($)
w = value of wages
28
15
0
10 15
Observed data may not identify a trade-off between wages and health benefits.