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Lecture 6: Compensating Wage Differentials
The model of competitive labor markets implies that as long as workers or firms
can freely enter and exit the marketplace, there will be a single wage in the economy if
all jobs are alike and all workers are alike.
All jobs are not the same. Adam Smith in 1776 argued that compensating wage
differentials arise to compensate workers for the nonwage characteristics of jobs. It
is not the wage that is equated across jobs in a competitive market, but the “whole of
the advantages and disadvantages” of the job.
Workers differ in their preferences for job characteristics and firms differ in the
working conditions that they offer. The theory of compensating differentials tells a
story of how workers and firms “match and mate” in the labor market.
1. Workers’ and Firms’ Choice with Risky Jobs
E.g. Employer X: NT.$100 per hour, clean, safe work conditions
Employer Y: NT.$100 per hour, dirty, noisy factory
→ Most workers would undoubtedly choose employer X.
If employer Y decides not to alter working conditions, it must pay wage above
NT.$100 to be competitive in the labor market.
→ The extra wage it must pay to attract workers is called a compensating wage
differential because the higher wage is paid to compensate workers for the
undesirable working conditions.
After the wage rise of firm Y, if both firms could obtain the quantity and quality of
works they wanted, the wage differential would be an equilibrium differential, in the
sense that there be no forces causing the differential to change.
* The compensating wage differential serves two purposes:
(1) It serves a social need by giving people an incentive to voluntarily do dirty,
dangerous, or unpleasant work or a financial penalty on employers offering
unfavorable working conditions.
(2) At an individual level, it serves as a reward to workers who accept unpleasant jobs
by paying them more than comparable workers in more pleasant jobs. Those who
opt for more pleasant conditions have to buy them by accepting lower pay.
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→ Compensating wage differentials provide the key to the valuation of the
nonpecuniary aspects of employment.
Note: The predicted outcome of the compensating wage differential theory of job
choice is not that employees working under “bad” conditions receive more than those
working in “good” conditions. The prediction is that, holding worker characteristics
constant, employees in bad jobs receive higher wages than those working under more
pleasant conditions.
* The compensating wage differential theory is based on three assumptions:
(1) Utility Maximization
Workers seek to maximize their utility, not their income. Compensating wage
differentials will only arise if some people do not choose the highest-paying job
offered, preferring instead a lower-paying but more pleasant job.
→ Wages do not equalize in this case. The net advantage – the overall utility from the
pay and the psychic aspects of the job – tend to equalize for the marginal workers.
(2) Worker Information
Workers are aware of the job characteristics of potential importance to them.
→ Company offering a “bad” job with no compensating wage differential would have
trouble recruiting or retaining workers, trouble that would eventually force it to raise
its wage.
Note: Our predictions about compensating wage differentials hold only for job
characteristics that workers know about.
(3) Workers Mobility
Workers have a range of job offers from which to choose. It is the act of
choosing safe jobs over dangerous ones that forces employers offering dangerous
work to raise wages.
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2. The Hedonic Wage Function
A wage theory based on the assumption of philosophical hedonism that workers
strive to maximize utility.
To simplify our discussion, we shall analyze just one dimension –risk of injury on
the job – and assume that the compensating wage differentials for every other
dimension have already been established.
→ To obtain a complete understanding of the job selection process and the outcomes
of that process, it is necessary to consider both the employer and employee sides of
the market.
(1) Employee Considerations
Some combinations of wage rates and risk levels that would yield the same
level of utility can be represented by indifference curve map.
U2 slopes upward because risk of
injury is a “bad” job
characteristics. i.e., if risk
increases, wage must rise if
utility is to be held constant.
People differ in their aversion to
the risk of being injured. Those
who are very sensitive to this risk
will require large wage increases
for any increase in risk (UH),
while those who are less sensitive
will require smaller wage
increases to hold utility constant
(UL).
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(2) Employer Considerations
Assumptions:
(a) It is presumably costly to reduce the risk of injury facing employees.
(b) Perfect competition → Firms operate at zero profits.
(c) All other job characteristics are presumably given or already determined.
→ If a firm undertakes a program to reduce the risk of injury, it must reduce wages to
remain competitive.
Forces on the employer side of the market tent to cause low risk to be associated
with low wages and high risk to be associated with high wages, holding other thing
constant.
→The employer trade-offs between wages and levels of injury risk can be graphed
through the use of isoprofit curves , which show the various combinations of risk and
wage level that yield a given level of profits.
The concavity of isoprofit curves
is a representation of our
assumption that there are
diminishing marginal returns to
safety expenditures.
→ The cost of reducing risk
levels is reflected in the slope of
the isoprofit curve.
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Employers differ in the ease (cost)
with which they can eliminate
hazards.
→ Firm X can reduce risk
more cheaply than firm Y.
(3) The Matching of Employer and Employees
Graphing worker indifference curves and employer isoprofit curves together can
show which workers choose which offers.
A’s choice: (WAX, RAX)
→ value safety higher
If A took B’s offer
A1 < A2
B’s choice: (WBY, RBY)
Since X can produce safety more cheaply than Y, X will be a low-risk producer
who attracts employees, like A, who value safety highly. Y attracts people like B, who
have a relatively strong preference for money wages and a relatively weak preference
for safety.
Note: The only offers of jobs to workers with a chance of being accepted lie along
XR’Y’.
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→ The curve XR’Y’ can be called an “offer curve”, because only along XR’Y’ will
offers employers can afford to make be potentially acceptable to employees.
The more types of firms there are
in a market, the smoother this
offer curve will be. It will always
slope upward because of our
assumptions that risk is costly to
reduce and that employees must be
paid higher wages to keep their
utility constant if risk is increased.
* Major Insights:
(1) Wages rise with risk, other things equal.
→ There will be compensating wage differentials for job characteristics that are
viewed as undesirable by workers.
(2) Workers with strong preferences for safety will tend to take jobs in firms where
safety can be generated most cheaply.
→ Firms and workers offer and accept jobs in a fashion that makes the most of their
strengths and preferences.
3. Policy Application: How Much is a Life Worth?
(1) Empirical Evidences
Many studies estimate the hedonic function relating wages and the probability of
injury on the job. This literature typically estimates regressions of the form:
wi =i + other variables
Where wi gives the wage of worker i and i. gives the probability of injury on the
worker’s job. The coefficient gives the wage change associated with a one-unit
increase in the probability of injury.
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Many empirical studies report a positive relationship between wages and
hazardous or unsafe work conditions, regardless of how the hazard or the unsafe
nature of the work environment is defined.
(2) Calculating the Value of Life
The correlations of the wages and the probability of injury on the job allow us to
calculate the “value of life.”
Example:
Firm
X
Y
Probability of Fatal Injury
ρx
ρx + .001
Annual Earnings
wx
wx+ $5,000
The data suggests that each of the workers in firm Y is willing to give up $5,000 per
year to reduce the probability of fatal injury in their job by 0.001 units. Put
differently, the 1,000 workers employed in firm Y are willing to give up $5 million (or
$5,000x 1,000 workers) to save the life of the one worker who will almost surely die
in any given year. The workers in firm Y, therefore, value a life at $5 million.
This calculation instead gives the amount that workers are jointly willing to pay to
reduce the likelihood that one of them will suffer a fatal injury in any given year. It
is the statistical value of a life.