Indifference curves

• Workers care about whether their job is safe or risky

Utility = f (w, )

• where 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

U0

Wage

10 Probability of Injury

10

U1

50

w

U2

George chooses the safe job paying $10 because his utility is higher at $10 than it is at $20

30

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 w = 30 – 10 = 20

A risky job pays $20 per hour while a safe job pays $10George’s indifference curves are relatively flat

Indifference curves(one individual)

UCUBUA

Wage

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.

0.05 0.10 0.45

$25

Indifference curves(multiple individuals)

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.

S

E*Number of Workers in Risky Job

wR – wS

(wR – wS)*

D

The Market for Risky Jobs

SR

N

wR – wS

(wR – wS)*

0E*

Number of Workers in Risky Job

S

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.

The Market for Risky Jobs

• Firms may have a risky work environment because it may be more profitable:

Profit = h (w, )

• where 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

Isoprofit Curves(single firm)

1

0

Wage

Probability of Injury

Lower isoprofit curves represent higher profits.

0.05 0.15

$25

$30

Less safety equipment and training lowers firm costs, raising profit

Lower wages lowers firm costs, raising profit

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

Z

Wage

Probability of loosing your arm

Different firms offer different levels of risk for a given wage rate.

0.05 0.10 0.15

$25

Isoprofit Curves(multiple firms)

YX

UC

UB

UA

Probability of Injury

Z

Y

X

Hedonic Wage Function

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).

Hedonic Wage Theory

Wage

Wage

Probabilityof Injury

Hedonic Wage Function

Kip Viscusi (1993) estimated : A .001-point increase in the probability of fatal injury may increase annual earnings by about $6600 (in 2002 dollars)

Estimating the Hedonic Wage function:

wi = + pi + xi

.002

15,000

.003

21,600

.004

28,200

Hedonic Wage Theory

Z

UC

UB

UA

Y

X

Probabilityof Injury

Hedonic Wage Function

.002

15,000

.003

21,600

.004

28,200

Hedonic Wage Theory

Wage

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

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.

Suppose the probability that a worker will die on the job at firm X is .002

Assume Kip Viscusi (1993)’s estimate is correct:

How Much is a Life Worth?

$6600 $6,600,000

.001

6600

.001 1

w

p

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

= 20,000= .002= .003 = $26,600

(E = 1000)

(E = 1000)

Hedonic Wage Theory

6600

.001

and this firm pays its workers 20,000 per year.

Hedonic Wage Theory

The workers maximize utility by choosing the job paying wage of w* and offers a probability of injury of *.

U0 U*

*

Hedonic Wage Function

0

w*

Wage

Probability of Injury

w0

*

The government (OSHA) prohibits firms from offering a probability of injury higher than , lowering firm profit and worker utility.

Safety and Regulation

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.

The worker maximizes utility by working 2100 hours per year at w0 = $10/hrAnother job offers the worker a seasonal schedule, where she gets the same wage but works only 500 hours a year.

U

U0

3500 40001900 Hours of Leisure

Income

w0 = $10 w1 = $25

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.

Compensating Differentials and Job Amenities

Health Benefits and Compensating Differentials

UA

10

H = value of health benefits ($)

UB

15

25

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.

w = value of wages

VTCP = value of worker’s total compensation package ($)

0

Health Benefits and Compensating Differentials

H = value of health benefits ($)

Observed data may identify a trade-off between job benefits and wages.

w = value of wages

VTCP = value of worker’s total compensation package ($)

10

15

25

0

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

H = value of health benefits ($)

UB

UC

VTCPBVTCPC

w = value of wages

VTCP = value of worker’s total compensation package ($)

10

15

28

0 15

Observed data may not identify a trade-off between wages and health benefits.

Health Benefits and Compensating Differentials

H = value of health benefits ($)

w = value of wages

VTCP = value of worker’s total compensation package ($)

10

15

28

0 15