# You MUST show the math to receive credit and also label graphs in detail.

November 24, 2016

Question
ECP3203 – Martinez

Homework 7

You MUST show the math to receive credit and also label graphs in detail. Draw the graphs
large enough to clearly make out the changes (it is best if you use different colors to illustrate
changes). You can work in groups but each person needs to turn in their own assignment.

1. (Continued from in-class assignment 7) The figure below represents the matching
process between employers and employees that occurs when working conditions differ
across jobs. The curves labeled A1, A2, and A3 refer to indifference curves between the
wage and risk of injury for one individual. The curve OC refers to the offer curve formed
by the isoprofit curves of many different employers. The matching process shown in the
figure below assumes that the worker is perfectly mobile but imperfectly informed
about the degree of risk associated with a particular job. In particular, suppose that the
worker receives a wage of approximately \$10.60 and thinks that he or she is being
exposed to a risk level of 3 deaths per 10,000 workers when in fact the actual level of
risk is 7 deaths per 10,000 workers. Also assume that the firms know the degree of risk
actually associated with a particular job, but are not aware of the worker’s
misconception.

a. Suppose that the government does a study, learns about the worker’s misconception,
and decides to regulate a reduction in risk. What would be the optimal level of risk
exposure to allow? Why? Explain. What wage would person A receive when exposed to
the optimal level of risk?
b. What would be the lowest level of risk exposure the government could set without
actually making the worker worse off? Why? Explain

c. Assuming the results of the government study are not made public, would person A be
in favor of a regulation limiting risk exposure to 1 death per 10,000 workers per year?
Why? Explain
d. Now suppose the worker is perfectly informed and mobile. What wage/risk combination
would he or she choose?
e. Would a perfectly informed and mobile worker support a regulation limiting risk
exposure to 1 death per 10,000 workers per year? Why? Explain

2. (Continued from in-class assignment 7) The figure below represents the matching
process between employers and employees that occurs when working conditions differ
across jobs. The curve labeled A2 refers to the indifference curve between the wage and
risk of injury for one individual while the curve OC refers to the offer curve formed by
the isoprofit curves of many different employers. The matching process shown in the
figure below assumes that the worker is perfectly informed and perfectly mobile. The
utility maximizing choice for person A is a job with a wage of \$8 and a risk level of 4.
Now consider a regulation that would mandate a decrease in risk exposure to 1 death
per 10,000 workers.

a. How much per hour would person A be willing to pay for such a risk reduction? Note:
the horizontal lines through points a and c should line up with 8 and 6, respectively.
Why? Explain
b. How much per hour would it cost firms to comply with the regulation? Why? Explain
c. Would such a regulation pass a benefit/cost test? Why? Explain
d. Empirical studies of compensating differentials attempt to measure the tradeoff
between wage and risk (holding all else constant) based on people’s actual choices. In
the figure above, at person A’s actual choice, the rate at which person A (and A’s

employer) are willing to trade off wages and risk is given by the slope of the dashed line.
What is the slope of this line?
e. In actually carrying out benefit/cost studies of various safety regulations, the observed
tradeoffs between wages and risk are extrapolated to measure the benefits associated
with the regulation. If the tradeoff between wages and risk implicit at point a is assumed
to be constant for any change in risk, how much would one predict person A would be
willing to pay for a risk reduction to 1 death per 10,000 workers?
f. Does the extrapolation in (e) overstate or understate person A’s actual willingness to
pay for such a risk reduction? Why does the difference occur? What are the implications
for benefit/cost studies of safety regulations?

3. (Continued from in-class assignment 7) Consider a worker that ranks combinations of
employee benefits (E) and wages (W) according to the utility function U = Eα Wβ , where
α and β are positive constants and U is the index of satisfaction. Suppose that firms are
able to remain competitive (i.e., keep profits at zero) if they offer \$90 in wages and no
employee benefits. If they offer benefits, wages must be reduced by 75 cents for every
dollar of benefits offered. Suppose that currently, the firm is offering a compensation
package of \$40 in benefits and \$60 in wages.
a. Suppose an individual’s preferences are such that α = 1 and β = 2 (i.e., they give more
weight to wages than to benefits in the ranking process). Why might such a weighting
occur?
b. What is the utility level associated with the initial compensation package?
c. How much in wages would this individual be willing to give up for a \$20 increase in
benefits? What would such an increase in benefits cost the firm? Would the worker be
made better off by such an increase in benefits (assume the firm changed wages just
enough to cover the costs of the increased benefits)?
d. Suppose that workers are now given more freedom over the choice of benefits so that α
and β are both given an equal weight of one. Given the original compensation package,
how much would the individual be willing to give up for a \$20 increase in benefits?
What would such an increase in benefits cost the firm? Would the worker be made
better off by such an increase in benefits (assume the firm changed wages just enough
to cover the costs of the increased benefits)?

4. Consider the conditions of work in perfume factories. In New York perfume factories,
workers dislike the smell of perfume, while in California workers appreciate the smell of
perfume, provided that the level does not climb above S *. (If it rises above S *, they start
to dislike it.) Suppose that there is no cost for firms to reduce or eliminate the smell of
perfume in perfume factories and assume that the workers have an alternative wage,
W *.

Draw a diagram using isocost and indifference curves that depicts the situation. (The
New York and California isocost curves are the same, but their indifference curves differ.)
What level of perfume smell is there in the New York factories? In the California factories?
Is there a wage differential between the California and New York workers?

5.

“The concept of compensating wage premiums for dangerous work does not apply to
industries like the coal industry, where the union has forced all wages and other
compensation items to be the same. Because all mines must pay the same wage,
compensating differentials cannot exist.” Is this statement correct? (Assume wages and
other forms of pay must be equal for dangerous and non-dangerous work and consider
the implications for individual labor supply behavior.)

6. In 2005, a federal court authorized United Air Lines (UAL) to terminate its pension plan.
The government will take over pension payments to retired UAL employees, but this
action means that pension benefits will be less than promised by UAL to both its current
retirees and current workers. What future labor-market effects would you expect to
occur from this sudden and unexpected reduction of pension benefits?

7. The demand for labor in Occupation A is LD = 20 – W, where LD = number of workers
demanded for that occupation, in thousands. The supply of labor for Occupation A is LA
= -1.25 + 0.5 W.
For Occupation B, the demand for labor is similar but the supply of labor is LB = -0.5 +
0.6 W, which is indicative of a more pleasant work environment associated with that
occupation in comparison with Occupation A.
a. What is the compensating wage differential between the two occupations?
The zero-profit isoprofit curve for Company ABC is W = 4 + .5R, where W = the wage rate
that the firm will offer at particular risk levels, R, keeping profits at zero. The zero-profit
isoprofit curve for Company XY is W = 3 + .75R.
b. Draw the zero-profit isoprofit curves for each firm. What assumption about
marginal returns to safety expenditures underlies a linear isoprofit curve?
c. At what risk level will the firms offer the same wage?
d. At low-risk levels, which firm will be preferred by workers? At high-risk levels,
which firm will be preferred by workers? Explain.

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