Indifference curves

1
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

2
Indifference curves(one individual)
U2
50
Wage
U1
30
Dw
20
U0
10
1
0
Probability of Injury
A risky job pays 20 per hour while a safe job
pays 10
Georges 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 gt U1)
The worker is indifferent between the two jobs if
the risky job paid 30/hour instead of 10.
The workers reservation price is then given by
Dw 30 10 20
3
Indifference curves(multiple individuals)
Wage
UC
UA
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.
4
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.

5
The Market for Risky Jobs
SR
S
wR wS
100
E
0
N
(wR wS)
Number of Workers in Risky Job
-50
DR
If a fraction of all N workers like to work in
risky jobs, they are willing to pay for the right
to be injured. More and more workers enter this
labor market as the wage differential shrinks
from 50 to 0
If the demand for such workers is small, the
market compensating differential is negative,
meaning workers employed in risky jobs earn less
than workers employed in safe jobs.
6
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

7
Isoprofit Curves(single firm)
Wage
p0
Lower wages lowers firm costs, raising profit
30
p1
Less safety equipment and training lowers firm
costs, raising profit
25
Probability of Injury
0.05
0.15
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.
8
Isoprofit Curves(multiple firms)
Wage
25
pY
pZ
pX
0.15
0.05
0.10
Probability of loosing your arm
Different firms offer different levels of risk
for a given wage rate.
9
Hedonic Wage Theory
UC
Hedonic Wage Function
Wage
UB
UA
pZ
pY
pX
Probability of Injury
Different firms have different isoprofit curves
Different workers have different indifference
curves.
The labor market marries workers who dislike risk
(workers of type A) with firms with safe work
environments (firm X) 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).
10
Hedonic Wage Theory
Hedonic Wage Function
Wage
28,200
21,600
15,000
Probabilityof Injury
.003
.004
.002
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)
11
Hedonic Wage Theory
UC
Hedonic Wage Function
Wage
UB
28,200
UA
pZ
21,600
pY
15,000
pX
Probabilityof Injury
.003
.004
.002
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
12
How Much is a Life Worth?
Hedonic Wage Theory
Assume Kip Viscusi (1993)s b estimate is correct
6600
.001
(E 1000)
20,000
.002
.003
26,600
(E 1000)
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
13
Safety and Regulation
Hedonic Wage Theory
Hedonic Wage Function
U0
U
Wage
?0
p
w
w0
r
Probability of Injury
The workers maximize utility by choosing the job
paying wage of w and offers a probability of
injury of r.
14
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.

15
Compensating Differentials and Job Amenities
Income
w1 25
w0 10
U0
U?
1900
4000
3500
Hours of Leisure
The worker maximizes utility by working 2100
hours per year at w0 10/hr
Another job offers the worker a seasonal
schedule, where she gets the same wage but 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.
16
Health Benefits and Compensating Differentials
VTCP value of workers 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.
17
Health Benefits and Compensating Differentials
VTCP value of workers 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.
18
Health Benefits and Compensating Differentials
VTCP value of workers total
compensation package ()
H value of health benefits ()
w value of wages
28
UC
15
UB
0
10
15
VTCPC
VTCPB
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.
19
Health Benefits and Compensating Differentials
VTCP value of workers 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.