Chapter 8

Compensating Wage Differentials

What affects occupational choice?

• wages• non-pecuniary characteristics• since jobs have both of these attributes,

people face tradeoffs between them

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?

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

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)

Holding worker characteristics constant, employees in “bad”

jobs receive higher wages than those working under more

pleasant conditions.

What are these worker characteristics?

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

We will assume:

• workers maximize utility• workers have perfect information about

their jobs• workers have mobility

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

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

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

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

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 worker’s utility is lowered if they incur an injury

Risk

Wage

U1

Risk

Wage

R0

w0

R1

U1

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...

A

Risk

Wage

R0

w0

R1

w1

U1

…his wage increases to w1.

Risk

Wage

U1

U2U2 represents a higher level of utility than U1

Risk

Wage

U1

U2

R0

w2

w1

A

B

At risk level R0, w2 > w1. Thus, A must be preferred

to B.

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

.

Risk

Wage

R0

W0

Given that risks are low, the worker requires only a small increase in wage to accept additional risk

U1

Risk

Wage

R1

W1

When risk is higher, the worker will require a larger increase in wage to accept additional risk

U1

Risk

Wage

Joe Tom

The steeper the curve, the more risk averse the worker. Joe is more risk averse than Tom.

Risk

Wage

Joe Tom

R0

w0

What is it worth to these men to have risk lowered from R0 to R1?

R1

Risk

Wage

Joe Tom

R0

w0

w1T

R1

w1J

Joe is willing to accept a much lower wage than Tom to have risk reduced from R0 to R1

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

Risk

Wage

0

Isoprofit Curve

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

Risk

Wage

0

w0

R0

w1

R1

A

B

A firm is equally profitable at A or B. Note that higher risk allows the

firm to pay higher wages.

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

Risk

Wage

0

w0

R0

w1

R1

Risk can be reduced more cheaply at R1 than R0

Risk

Wage

1w0

R0

2

Firms with steeper isoprofit curves find it more costly to reduce risks.

Risk

Wage

1w0

R0

w1

R1

2

w2

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 tolower wages to w2. Thus, Firm 1can reduce the risk at lowerrelative cost.

The zero profit isoprofit curve is most often the only relevant

isoprofit curve.

Why?

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

Risk

Wage

U0

0

Risk

Wage

U0

w*

r*

0

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

Risk

Wage

UAUB

Indifference curves for two

workers: Worker A and Worker B

Risk

Wage

Z

X

Isoprofit curves for two firms: Firm X and Firm Z

Risk

Wage

Z

wA

RA

X

UA

Risk

Wage

Z

wA

RA

X

wB

RB

UA

UB

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

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)

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

Risk

Wage

w0

R0

U0

0

Risk

Wage

w0

R0

U0

0

R*

Suppose that R* is the minimum acceptable amount of risk allowable by government standards

Risk

Wage

w0

R0

U0

0

R*

The firm will only offer a wage of w* (any higher wage would reduce profit)

w*

Risk

Wage

w0

R0

U0

0

R*

To remain equally happy, the worker would need a wage of wR

w*wR

Risk

Wage

w0

R0R*

What happens to worker utility at R*? U0

0

w*

Risk

Wage

w0

R0R*

w*

U0

U*

0

Utility falls from U0 to U*

Has government intervention helped?

No, the worker is made worse off

What happens when the worker does not know the true level of

risk?In this case, government intervention

can make the worker better off

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

Risk

Wage

w0

R0

U0The worker thinks that he is at point G

G

0

Risk

Wage

W0

R0

U0

Ra

0

But the worker is actually at point A...

AG

Risk

Wage

w0

R0

U0

Ra

Ua

…at utility level Ua

0

G A

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)

Risk

Wage

w0

R0

U0

Ra

Ua

0

Risk

Wage

w0

R0

U0

Ra

Ua

0

Rb

Risk

Wage

w0

R0

U0

Ra

Ua

Rb R*

Suppose the government chooses R* as the minimum amount of risk that is acceptable

0

Risk

Wage

w0

R0

U0

Ra

Ua

Rb R*

w*

U1

0

The firm pays the worker a wage of w* and the worker ends up on indifference curve U1