Chapter 5
Compensating Wage Differentials
“It’s just a job. Grass grows, birds fly,
waves pound the sand. I beat people
up.”
-Muhammad Ali
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Introduction
The labor market is not characterized by a single wage: workers
differ and jobs differ.
Adam Smith proposed the idea that job characteristics influence
labor market equilibrium.
Compensating wage differentials arise to compensate workers
for nonwage characteristics of the job.
Workers have different preferences and firms offer different
working conditions.
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The Market for Risky Jobs
Workers care about whether their job is safe or risky.
Utility = f(wage, risk of injury).
Indifference curves reveal the worker’s preferences between
wages and risk.
Firms may have a risky work environment because it is less
expensive to pay higher wages than to make the environment
safe.
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Indifference Curves Relating the Wage and the
Probability of Injury
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The worker earns a wage of w0
and gets U0 utils if she chooses
the safe job. She would prefer
the safe job if the risky job paid
a wage of w1’, but would prefer
the risky job if that job paid a
wage of w1’’. The worker is
indifferent between the two jobs
if the risky job pays w^1. The
worker’s reservation price is
then given by Δw = w^1 - w0.
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Determining the Market Compensating Differential
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The supply of labor to risky
jobs 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.
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Market Equilibrium When Some Workers Prefer Risky
Jobs
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If some workers like to work in
risky jobs (i.e., they are willing
to pay for the right to be
injured) and if the demand for
such workers is small, then
the market compensating
differential is negative. At
point P, where supply equals
demand, workers employed in
risky jobs earn less than
workers employed in safe
jobs.
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Hedonic Wage Theory
Workers maximize utility by choosing wage-risk combinations
that offer them the greatest amount of utility.
Isoprofit curves are upward sloping because production of safety
is costly.
Isoprofit curves are concave because production of safety is
subject to the law of diminishing returns.
Hedonic wage functions reflect the relationship between wages
and job characteristics.
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Indifference Curves for Three Types of Workers
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Different workers
have different
preferences for risk.
Worker A is very riskaverse.
Worker C
does not mind risk
very much at all.
Worker B is between
the two.
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Isoprofit Curves
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An isoprofit curve gives all the riskwage
combinations that yield the
same profits. Because it is costly to
produce safety, a firm offering risk
level ρ* can make the workplace
safer only if it reduces wages (while
keeping profits constant), so that
the isoprofit curve is upward
sloping. Note: higher isoprofit
curves yield lower profits.
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The Hedonic Wage Function
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Different firms have different
isoprofit curves and different
workers have different
indifference curves. The labor
market marries workers who
dislike risk (such as worker A) with
firms that find it easy to provide a
safe environment (like firm X); and
workers who do not mind risk very
much (worker C) with firms that
find it difficult to provide a safe
environment (firm Z). The
observed relationship between
wages and job characteristics is
called a hedonic wage function.
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Policy Application: How Much is a Life Worth?
Studies report a positive relationship between wages and work
hazards.
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.
The empirical evidence is ambiguous on the estimates of the
value of a life.
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Policy Application: How Much is a Life Worth?
Calculating the Value of Life (VoL)
wx = annual earnings in Firm X
wy = annual earnings in Firm Y
The probabilities of fatal injury in Firm X and Firm Y are given as
ρx and ρy.
If X is a safe job and Y is the risky job, then:
• VoL = (wy – wx) / (ρy – ρx)
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Policy Application: Safety and Health Regulation
OSHA is charged with the protection and health of the American
labor force.
OSHA sets regulations that are aimed at reducing risks in the
work environment.
Mandated standards reduce the utility of workers and the profits
of firms.
Safety regulations can improve workers’ welfare as long as
workers consistently underestimate the true risks.
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Impact of OSHA Regulation on Wage, Profits, and
Utility
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A worker maximizes utility by
choosing the job at point P,
which pays a wage of w* and
offers a probability of injury of
ρ*. The government prohibits
firms from offering a
probability of injury higher
than , shifting both the
worker and the firm to point
Q. As a result, the worker
earns a lower wage and
receives less utility (from U*
to U), and the firm earns
lower profits (from * to ).
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Impact of OSHA Regulations When Workers
Misperceive Risks
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Workers earn a wage of w*
and incorrectly believe that
their probability of injury is
only ρ0. In fact, their
probability of injury is ρ*.
The government can
mandate that firms do not
offer a probability of injury
higher than , making the
uninformed workers better
off (that is, increasing their
actual utility from U* to
U).
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Compensating Differentials and Job Amenities
Good job characteristics are associated with low wage
rates.
Bad job characteristics are associated with high wage
rates.
• The evidence is not clear on the link between amenities
and wage differentials, except for the risk of death.
Examples of amenities: job security, predictability of
layoffs, work schedules, work hours, safety, etc.
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Layoffs and Compensating Differentials
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At point P, a person maximizes
utility by working h0 hours at a
wage of w0 dollars. An
alternative job offers the
worker a seasonal schedule,
where she receives the same
wage but works only h1 hours.
The worker is worse off in the
seasonal job (her utility
declines from U0 to U utils). If
the seasonal job is to attract
any workers, the job must
raise the wage to (w1) so that
workers will be indifferent
between the two jobs.
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Health Benefits and Compensating Differentials
19
Workers A and B face the various
compensation packages offered by
isoprofit curve 0. 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. The observed data identifies the tradeoff
between job benefits and wages. In
contrast, workers B and B* have different
earnings potential, so their job packages
lie on different isoprofit curves. Their
choices generate a positive correlation
between wages and health benefits. The
observed data do not identify the trade-off
between wages and health benefits.