Compensating Wage Differentials

1
Chapter 8

• Compensating Wage Differentials

2
What affects occupational choice?

• wages
• non-pecuniary characteristics
• since jobs have both of these attributes, people
  face tradeoffs between them

3
Compare two jobs - - Both pay 7.50/hour

• Firm X is offering an office job as a file clerk
• Firm Y is an asphalt company who needs workers to
  help pave roads
• Which firm will attract more applicants at a wage
  of 7.50?
• What will have to happen at Firm Y to attract
  more workers?

4
The extra wage that is paid to attract workers
into paving roads is called the compensating wage
differential

• workers require "combat pay" for undesirable
  working conditions
• on the other hand, the pleasant atmosphere of
  desirable jobs must be bought by the workers
  through lower pay

5
Compensating Wage Differentials

• the price at which various qualitative job
  characteristics are bought and sold
• BADS result in positive differentials (higher
  wages)
• GOODS result in negative differentials (lower
  wages)

6
Holding worker characteristics constant,
employees in bad jobs receive higher wages than
those working under more pleasant conditions.
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What are these worker characteristics?

• skill
• age
• sex
• race
• marital status
• education
• geographic region
• union status

8
We will assume

• workers maximize utility
• workers have perfect information about their jobs
• workers have mobility

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Utility Maximization

• if we used income maximization, the worker would
  take the highest paying job regardless of
  attributes
• this is likely not the case with most workers

10
Perfect Information

• workers are aware of the job characteristics and
  the wages paid
• this may not always be true
• for example, workers did not use to know the
  adverse effect of asbestos

11
Worker Mobility

• workers have a range of jobs to choose from and
  can look for a new job while working
• median job tenure in the U.S. is 3.5 years

12
When graphing worker preferences for wages vs.
job characteristics, we use indifference curves

• we will put the wage on the y-axis
• we will put the risk of injury on the x-axis
• since risk is a bad, these indifference curves
  will have an unusual shape
• the indifference curves will be upward-sloping
  and convex

13
The indifference curves will be upward-sloping

• to accept more risk, an individual will require a
  higher wage to remain equally satisfied
• this is because the workers utility is lowered
  if they incur an injury

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U1
15
Suppose a person is currently at point A. If the
risk of the job rises to R1, the person will only
remain equally satisfied if...
U1
A
w0
R0
R1
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his wage increases to w1.
U1
w1
w0
R0
R1
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U2 represents a higher level of utility than U1
U2
U1
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At risk level R0, w2 gt w1. Thus, A must be
preferred to B.
U2
U1
A
w2
w1
B
R0
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The indifference curves will be convex

• at low risk of injury, the person is not as
  willing to accept a lower wage for an additional
  decrease in risk, relative to when risks are high

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.
U1
Given that risks are low, the worker requires
only a small increase in wage to accept
additional risk
W0
R0
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U1
When risk is higher, the worker will require a
larger increase in wage to accept additional risk
W1
R1
22
Tom
Joe
The steeper the curve, the more risk averse the
worker. Joe is more risk averse than Tom.
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Tom
Joe
What is it worth to these men to have risk
lowered from R0 to R1?
w0
R0
R1
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Tom
Joe
Joe is willing to accept a much lower wage than
Tom to have risk reduced from R0 to R1
w0
w1T
w1J
R1
R0
25
Isoprofit Curves

• are different across employers
• reflect the combinations of risk and wage that
  result in the same level of profit for the firm
• are upward-sloping and concave

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?0
Isoprofit Curve
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Isoprofit curves are upward-sloping

• since reducing risk is costly to the firm, it
  will be willing to pay higher wages as jobs
  become more risky
• thus, there should be a positive relationship
  between risk and wage reflected in the isoprofit
  curve

28
A firm is equally profitable at A or B. Note
that higher risk allows the firm to pay higher
wages.
?0
B
w1
A
w0
R0
R1
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Isoprofit curves are concave

• this is due to diminishing marginal returns to
  reducing risk
• at first, firms will use safety measures that can
  be done so most easily and inexpensively
• the more safety measures employed by a firm, the
  more expensive and difficult additional measures
  will be

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Risk can be reduced more cheaply at R1 than R0
?0
w1
w0
R0
R1
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Firms with steeper isoprofit curves find it more
costly to reduce risks.
?2
w0
?1
R0
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To reduce risk from R0 to R1 and keep profit
constant, Firm 1 would have to lower wages only
to w1 while Firm 2 would have to lower wages to
w2. Thus, Firm 1 can reduce the risk at
lower relative cost.
?2
w0
?1
w1
w2
R0
R1
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The zero profit isoprofit curve is most often the
only relevant isoprofit curve.

• Why?

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Equilibrium

• occurs where the isoprofit curve is tangent to
  the indifference curve
• this means that the slope of the isoprofit curve
  is equal to the slope of the indifference curve
• the rate at which the firm is able to trade wages
  for risk is equal to the rate at which workers
  are willing to trade wages for risk

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U0
?0
36
U0
?0
w
r
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Given isoprofit and indifference curves, we can
show that

• more risk averse workers will work at less risky
  jobs that pay lower wages
• firms with higher costs of reducing risks will
  pay higher wages

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UB
UA
Indifference curves for two workers Worker A
and Worker B
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Isoprofit curves for two firms Firm X and Firm Z
?X
?Z
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UA
?X
?Z
wA
RA
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UB
UA
?X
wB
?Z
wA
RA
RB
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Wages Rise With Risk

• workers with strong preferences for safety are
  willing to accept lower wages
• workers with strong preferences for safety will
  take jobs where safety can be generated at a
  lower cost

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How do government programs controlling risk
affect workers utility?

• The federal government set safety standards for
  many occupations through OSHA (Occupational
  Safety and Health Administration)

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Suppose a firm is threatened with large fines by
the government if they do not comply to safety
standards. If the firm complies with the
standards, are the workers better off?

• not if the workers know the risks
• the workers may be better off if they are unaware
  of the risks
• we can use our model to show this

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U0
?0
w0
R0
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Suppose that R is the minimum acceptable amount
of risk allowable by government standards
U0
?0
w0
R0
R
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The firm will only offer a wage of w (any higher
wage would reduce profit)
U0
?0
w0
w
R0
R
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To remain equally happy, the worker would need a
wage of wR
U0
?0
w0
wR
w
R0
R
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What happens to worker utility at R?
U0
?0
w0
w
R0
R
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Utility falls from U0 to U
U0
U
?0
w0
w
R0
R
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Has government intervention helped?
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No, the worker is made worse off
53
What happens when the worker does not know the
true level of risk?

• In this case, government intervention can make
  the worker better off

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Unknown Risk

• Suppose a worker receives a wage of w0 and thinks
  that the risk level is R0
• the worker thinks that his utility level is U0
• but, if the actual risk is Ra, the actual utility
  level is Ua

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U0
The worker thinks that he is at point G
?0
G
w0
R0
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U0
But the worker is actually at point A...
?0
A
G
W0
R0
Ra
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U0
Ua
at utility level Ua
?0
A
G
w0
R0
Ra
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Government intervention can help in this case

• if the government sets the allowable risk level
  between Ra and Rb,workers will actually end up on
  a higher indifference curve.
• the workers may perceive that they are worse off
  (because their wage will be lower) when in fact
  they have been made better off (because the level
  of risk has been reduced)

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U0
Ua
?0
w0
R0
Ra
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U0
Ua
?0
w0
R0
Ra
Rb
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U0
Ua
Suppose the government chooses R as the minimum
amount of risk that is acceptable
?0
w0
R0
Rb
Ra
R
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U0
Ua
U1
The firm pays the worker a wage of w and the
worker ends up on indifference curve U1
?0
w0
w
R0
Rb
Ra
R