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Topic #3 CompensatingWage Differentials

Compensating wage differentials are where people are paid more for dirty, dangerous,difficult, or dishonorable work. Well focus on how much more people get paid for

dangerous worker where there is a risk of death on the job. The policy implicationsof this analysis pertain to safety regulations.

If all working conditions were the same, then employees would work at the job with thehighest wage. But, jobs differ. We will eamine the way they differ in terms ofwages and the incidence of being fatally injured on the job.

!"Bob !"Bart

!#Bob !#Bart

Wages

$isk of %eath on the &ob

Indifference cur'es connect all the wage(safety combinations that yield the same utility.We assume three things about our indifference cur'es. )irst, we assume that employeesmaimi*e utility, not income. +econd, we assume they ha'e perfect information aboutthe wages and risk in'ol'ed with each job. Third, we assume that workers are mobileand can change jobs without cost.

Bob and Bart ha'e different preferences. Bob has fi'e young children, he takes care ofhis in'alid mother, and he lo'es to play sports. Conseuently Bob is more risk a'erse.Therefore, Bob is willing to gi'e up more in terms of wages to be safer. Bart is less riska'erse. Bart has no family, no hobbies, but he enjoys sa'ing money. %angerous work is

fine - Bart is willing to work dangerous jobs to earn more money.

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otice that the marginal rate of substitution between wages and risk changes along theindifference cur'e. /t point /, the worker is not willing to gi'e up much in terms ofwages to be safer because danger is practically nothing but the wage rate is relati'elylow. /t point B, the worker is willing to gi'e up a lot in terms of wages to be made saferbecause the worker is in relati'ely imminent danger. Thus, indifference cur'es should becon'e 0where the marginal rate of substitution increases as you mo'e from left to right1because of a diminishing marginal rate of substitution. That is, the wages were willingto gi'e up in order to be made safer decreases the safer we become.

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Wages bWB

a W/

$isk/ $iskB$isk of %eath on the &ob

Isoprofit cur'es identify all the wage(safety combinations that yield the same le'el ofeconomic profits. We assume three things about isoprofit cur'es. )irst, we assume thatsafety costs money. +econd, we assume that firms will earn *ero economic profits 0alongtheir *ero economic profit isoprofit cur'e1 in a long(run euilibrium. Third, we assumethat other job characteristics are the same - the only things that 'aries across jobs arewages and safety.

)irms that are able to eliminate danger relati'ely easily - at minimal cost - offer jobs thatare safer and therefore ha'e flatter isoprofit cur'es. )irms that are not able to eliminatedanger as easily - only at substantial cost - pro'ide jobs that are more dangerous andtherefore ha'e steeper isoprofit cur'es.

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+2+ 0negati'e profits1Wages +2+ 0*ero profits1

+2+ 0positi'e profits1

B345+ 0negati'e profits1

B345+ 0*ero profits1

B345+ 0positi'e profits1

$isk of %eath on the &ob

If firms offer la'ish combinations of wages and safety, theyll lose money and be dri'enout of business with negati'e economic profits. If they offer meager combinations ofwages and safety, then they will not be able to attract employees and will not be able toproduce. The economy is at an euilibrium when all firms are earning *ero economicprofits offering wage(safety combinations that are just high enough to attract workers butnot so high that negati'e economic profits are being earned.

If a firm spends more on safety, it must spend less on other things, which includes wages,to keep profits constant along the isoprofit cur'e 0and at *ero in a long(run euilibrium1.

Isoprofit cur'es are conca'e6 easy to sol'e safety problems are taken care of first becauseit is not as costly to reduce danger initially. /s diminishing returns to safety set in, it ismore costly to continue reducing the chance of injury. In fact, it may not be possible tocompletely eliminate the chance of injury on the job.

!nder *ero economic profit conditions, Belks offers a lower wage because their job issafer. The night security guard ser'ice 0+2+1 must pay a higher wage because it ismore dangerous.

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!7Bart !"Bart

!#Bart !7Bob !

"Bob

!#

Bob

Wages +2+ 0*ero profits1WBart

B345+ 0*ero profits1

WBob

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We can now match employers and employees. Bob works at Belks and Bart works as anight security guard. 8atching is nice for the workers because they maimi*e utility -Bob gets more safety and Bart gets higher wages. It is also nice for employers becausethose who ha'e dangerous jobs can attract employees. ote that wages increase withrisk. +afe firms get employees who 'alue safety because they ha'e a comparati'ead'antage in being able to reduce the risk of injury. $isk(prone firms compensate forhigher risk with higher wages to people who are not 'ery risk a'erse.

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In reality, there are many firms offering many different wage(safety combinations. Themost attracti'e wage(safety combinations make up the offer cur'e. The consumer picksthe wage(safety combination that maimi*es utility. otice that combination a does this,and it is on the :offer cur'e. ote that combination c is also on the offer cur'e, but itdoes not maimi*e utility. /nd, bundle b is under the offer cur'e, so it is possible to find

a job with either higher wages, less risk, or a combination of higher wages and less risk.Thus, combination b certainly does not maimi*e utility.

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Wages

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The theory of compensating wage differentials may not produce outcomes that areoptimal for society. That is, though indi'iduals think that they are maimi*ing utility,

their selected wage(safety combination may not be best for society. This would occur,first, when eternal people 0such as other family members or tapayers in society whosupport disability programs1 are ad'ersely affected by a workers choice of risk. +econd,sometimes workers do not know what is best for themsel'es.

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a1, when, in fact, he is really better off 0because combination c is on a higher indifferencecur'e than combination b1.

In #@A;, the >ccupational +afety and =ealth /ct was passed, creating >+=/. >+=/penali*es employees who are not sensiti'e to risk and who appreciate higher wages

because employees bear the cost of safety standards in the form of lower wages.

The figure below represents the matching process between /nna &ane and fi'e employersthat occurs when working conditions differ across jobs. The cur'es labeled !i are/nna &anes indifferences cur'es, while the cur'es labeled Ii refer to *ero(economicprofit isoprofit cur'es for fi'e firms - firm /, firm B, firm C, firm %, and firm 3.+uppose that /nna &ane is well informed about the wageDrisk combinations offered atdifferent workplaces and that she maimi*es utility. Bundles , y, and * represent someof the many wageDrisk combinations a'ailable.

)igure 7

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$5.00 x

IFirm E IFirm D IFirm C I)irm B

I)irm /

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/ssume all fi'e firms offer /nna &ane a job. /nna &ane will work for firm B at bundle ybecause it offers the wageDrisk combination on the highest possible indifference cur'e

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ow assume that >+=/ passes new regulations stating that no firm can ha'e a risk le'elgreater than ;.#E. /ccording to the figure, /nna &ane would be willing to pay less thanF;.?; for a risk le'el of ;.#E. /nna &ane will now work for firm / at bundle and willbe worse off because bundle y is on a higher indifference cur'e than bundle .$egulations potentially increase utility when indi'iduals (i)dont maimi*e utility, (ii)arent mobile, and (iii)dont ha'e perfect information.

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=edonic Wage Theory.

Were still assuming that employee benefits cost money, *ero economic profits areearned in a long(run euilibrium, and that other job characteristics are held constant.

/lso, were still assuming that consumers maimi*e utility but not income, thatconsumers are mobile, and that consumers ha'e perfect information.

Wages9;,;;;

F";,;;;

F";,;;; F9;,;;; 3mployee Benefits

3mployees choose between F9;,;;; in wages, F9;,;;; in fringe benefits 0such as acompany condo, a company car, a pension plan, health insurance, country clubmembership, etc.1, or any combination in between.

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F";,;;; F9;,;;; 3mployee BenefitsIf the go'ernment mandates that employers offer benefits and that employees take them,then mandating benefits will either ha'e no effect or will make consumers worse off. )oreample, suppose +usan maimi*es utility with F";,;;; in wages and F";,;;; inemployee benefits. If the go'ernment mandates that employers offer and employees takeF7;,;;; in employee benefits 0indicated by :mandate below1, then consumers like +usanmust mo'e to a wage(benefits combination that yields less utility on a lower indifferencecur'e.

Wages9;,;;;

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F";,;;; 8andate F9;,;;; 3mployee Benefits

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Problem Set #3 CompensatingWage Differentials

#. )igure # represents the matching process between employers and employees thatoccurs when working conditions differ across jobs. The cur'es labeled /#and B"refer to indifference cur'es between the wage and risk for two indi'iduals, while thecur'es and J refer to isoprofit cur'es for two firms. +uppose that both workers arewell informed about the wageDrisk combinations offered at different workplaces.

)igure # /# B" Wage

J

a #"."?

Hc

A b

9

J

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a) +uppose that person B is mobile, but person / is constrained to work only for firm J.If firm J offers the wage and risk combination indicated by point a 0riskKH,

wageK#"."?1 to all workers, what effect does the lack of alternati'e offers ha'e onperson /s le'el of utility 0relati'e to what could be attained if person / was mobile1.

b) 2i'en the situation in part a, what effect would a regulation that reduced risk to 9deaths per #;,;;; workers ha'e on worker /s le'el of utilityL

c) What effect would a regulation that reduced risk to 9 deaths per #;,;;; workers ha'eon person Bs le'el of utilityL Would the effect of the regulation be better or worse ifB was constrained to work for employer JL

". )igure " represents the matching process between employers and +ue that occurswhen working conditions differ across jobs. The cur'es labeled /#, /"and /7referto indifference cur'es between the wage and risk of injury for +ue. The cur'e >Crefers to the offer cur'e formed by the isoprofit cur'es of many different employers.The matching process shown in )igure " assumes that the worker is perfectly mobilebut imperfectly informed about the degree of risk associated with a particular job. Inparticular, suppose that +ue recei'es a wage of approimately F#;.G; and thinks thatshe is being eposed to a risk le'el of 7 deaths per #;,;;; workers 0point a1 when infact the actual le'el of risk is A deaths per #;,;;; workers 0point b1. /lso, assume

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that the firms know the degree of risk actually associated with a particular job, but arenot aware of the workers misconception.

a) +uppose that the go'ernment does a study, learns about +ues misconception, anddecides to regulate a reduction in risk. What would be the optimal le'el of risk

eposure to allowL What wage would +ue recei'e when eposed to the optimal le'elof riskLb) What would be the lowest le'el of risk eposure the go'ernment could set without

actually making +ue worse offLc) /ssuming the results of the go'ernment study are not made public, would +ue be in

fa'or of a regulation limiting risk eposure to # death per #;,;;; workers per yearLd) ow suppose the worker is perfectly informed and mobile. What wageDrisk

combination would +ue chooseLe) Would a perfectly informed and mobile worker support a regulation limiting risk

eposure to # death per #;,;;; workers per yearL

)igure "

/7 /"Wage

/#

#;.G; a b >C

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7. )igure 7 represents the matching process between employers and employees thatoccurs when working conditions differ across jobs. The cur'e labeled /"refers to theindifference cur'e between the wage and risk of injury for =arold while the cur'e >Crefers to the offer cur'e formed by isoprofit cur'es of many different employers. The

matching process shown in )igure 7 assumes that =arold is perfectly informed andperfectly mobile. The utility maimi*ing choice for =arold is a job with a wage ofFH.;; and a risk le'el of 9 0point a1. ow consider a regulation that would mandate adecrease in risk eposure to # death per #;,;;; workers.

a) /pproimately how much per hour would =arold be willing to pay for such a riskreductionL

b) =ow much per hour would it cost firms to comply with the regulationL

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c) Would such a regulation pass a benefitDcost testLd) 3mpirical studies of compensating differentials attempt to measure the tradeoff

between wage and risk 0holding all else constant1 based on peoples actual choices.In )igure 7, at =arolds actual choice, the rate at which =arold and =aroldsemployer are willing to trade off wage and risk is gi'en by the slope of the dashed

line. What is the slope of this lineLe) In actually carrying out benefitDcost studies of 'arious safety regulations, the obser'edtradeoffs between wages and risk are etrapolated to measure the benefits associatedwith the regulation. If the tradeoff between wages and risk implicit at point a isassumed to be constant for any change in risk, how much would one predict =aroldwould be willing to pay for a risk reduction to # death per #;,;;; workersL

f) %oes the etrapolation in part 7 o'erstate or understate =arolds actual willingness topay for such a risk reductionL Why does the difference occurL What are theimplications for benefitDcost studies of safety regulationsL

)igure 7 /"

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9. >n 8arch ";, #@@", The Wall Street Journalreported on an attempt by the Bush/dministration to change the way benefitDcost analyses of regulations are performed.+pecifically, when computing the cost of a regulation, the administration wanted

agencies to take into account the reduction in income that the regulation brings about.The theory behind this suggested change, according to 5ip Miscusi, an economist notaffiliated with the plan, was that regulations cost people money, and the poorerpeople become, the more likely they are to get ill or die early. >ne study cited bythe 4abor %epartment estimated that each FA.? million of regulatory epenses couldresult in one additional death from lowered incomes. In a letter to

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was based on a dangerous notion6 that /mericas working men and women ha'e tomake a choice between their jobs and their health.

a) Was the premise of the proposed change soundL Was it insensiti'eL

b) While the proposed change would affect calculations of the cost of regulations, thebenefit calculations would basically be unchanged. /re there any factors that aretypically left out of benefit calculations that perhaps should not beL

?. %eferred benefits such as pensions make up about 9E of total compensation. +uchplans, howe'er, can be 'ery costly to administer, particularly if they are definedbenefit pension plans. ne of the key issues in the debate o'er health care reform is the ta treatment ofemployee health benefits. Traditionally, such benefits ha'e not been counted as partof an employees taable income. /lso, since these benefits are a business epense,they tend to reduce the firms corporate ta liability. >pponents of the status uoargue that if employees had to pay taes on the benefits, and if firms could notautomatically deduct the cost of benefits from their income, both employees andemployers might shop more carefully for health co'erage. If employers andemployees pay greater attention to the cost of different plans, pro'iders of both healthinsurance and health ser'ices would face greater incenti'es to keep costs down.

a) =ow would the hedonic wage model of employee benefits change if employees hadto pay taes on health care benefitsL

b) =ow would the hedonic wage model of employee benefits change if employers couldcount only part of their health care epenses as a business epenseL

c) =ow would changes in part a and b affect the optimal combination of wage andemployee benefitsL

A. >ne of the most widely publici*ed issues of the #@@" presidential campaign was thedebate o'er the )amily and 8edical 4ea'e /ct. The legislation, mandating employers to

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pro'ide workers with up to #" weeks of unpaid lea'e to deal with special familycircumstances, was appro'ed by Congress in +eptember, #@@" and then 'etoed by

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Answers #3 Compensating WageDifferentials

/nswer to uestion #6a) The lack of alternati'es means that person / ends up on indifference cur'e /,

which goes through point a instead of being able to reach a higher indifferencecur'e. 2i'en the shape of /s indifference cur'e, it appears that /smaimum utility would be attained near point c. To reach c, howe'er, /would ha'e to be able to mo'e and work for employer .

b) +uch regulation would make the immobile person / better off by allowing /to attain the le'el of utility associated with point b.

c) The regulation would make B worse off by forcing B to point c, a pointassociated with a lower indifference cur'e. The regulation would, howe'er,be e'en worse if B were constraint to work for employer J, since that wouldreuire a mo'ement to point b.

/nswer to uestion "6a) The optimal le'el of risk is that le'el associated with point c. The wage rate,

howe'er, would fall from somewhere between F#;.;; and F##.;; to FH.;;.b) The lowest le'el of risk is that associated with point d.c) o, +ue would not be in fa'or of such a regulation since +ue percei'es that she is

on indifference cur'e /7. In this case, howe'er, mo'ement to point e does alsolead to a lower actual le'el of utility.

d) !nder perfect information and mobility, +ue should choose point c where thewage is FH.;; and the risk of fatal injury is 9D#;,;;;.

e) o, regulation to any risk le'el lower than 9 deaths per #;,;;; workers wouldmake a fully informed and mobile worker worse off.

/nswer to uestion 76

a) =arold would be willing to see the wage reduced from FH.;; to just under FG.;;from point a to point c.

b) The cost of reducing risk can be seen in the wage reductions necessary to keep thefirms competiti'e. In this case, the wage must fall from FH.;; to F9.;; for a costof F9.;; per hour.

c) o, since the cost of F9.;; eceeds the workers willingness to pay, which isslightly o'er F".;;, the regulation fails the cost(benefit test. =arold would beforced to a lower indifference cur'e.

d) The slope is #.e) Based on point a, we predict that =arold would be willing to gi'e up F7.;; in

wages for a reduction in risk from 9 deaths per #;,;;; to #.f) >'erestimates because the etrapolation ignores the con'eity of =arolds

indifference cur'es. Con'eity reflects a decreasing willingness to pay for riskreductions as the workplace becomes safer. This means that cost(benefit studiesmay be biased in fa'or of finding that benefits eceed costs.

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Wages

F?;; a

F7;; e c!#

d b F"?; F?;; FA?; 3mployee Benefits

/nswer to uestion G6a) Taing health care benefits should lead to a flattening of the indifference

cur'es in the hedonic wage model as the willingness to gi'e up wages foradditional dollars of benefits should decrease. This is shown as an eamplebelow in the shape of the indifference cur'es from !#to !".

b) /llowing firms to deduct only part of their health care epenses wouldincrease the cost of pro'iding benefits relati'e to the cost of pro'iding wages.This would lead to steeper isoprofit cur'es for firms. In the eample below,the isoprofit cur'e is shown rotating from line ab to ad. 0F?;; in wages forFA?; in benefits to F?;; in wages for F?;; in benefits after the change inpolicy1.

c) Taken by itself, the flattening of the indifference cur'e should lead to morewages and fewer benefits. The steepening of the isoprofit cur'e should lead tofewer benefits and perhaps more wages. Taken together, this predictionwould be for fewer benefits and more wages. This is shown abo'e from pointc to e. Benefits decrease and wages increase.

Wages

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/nswer to uestion A.

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a) 8andated benefits potentially make workers better off in two situations.Consider a worker who is not mobile that recei'es a compensation packagelike point c in the eample on the net page. $egulating an increase inbenefits from F#;; to F";; would lead the worker to a higher le'el of utilitye'en though wages fall from F9;; to F7;;. /lternati'ely, suppose the worker

has imperfect information about the compensation package he or she isrecei'ing. +uppose the worker belie'es the compensation package consists ofpoint d when in fact benefits are only at the le'el consistent with point c.$egulating an increase in benefits to point e would make the worker better off.8andated benefits can make a worker worse off if the mandate mo'es theworker past point f along isoprofit cur'e ab so that he or she ends up on alower indifference cur'e. 8andated benefits also make a worker worse off ifthe worker is already at his or her optimal mi of wages and benefits 0point e1.

b) The ta credit plan would reduce the cost of pro'iding benefits and cause arotation of the isoprofit cur'e from line ab to line ag. Before, the firm couldonly trade off F?;; in wages for F?;; in benefits, but now it can offer FA?; in

benefits for only F?;; in wages. This would allow all workers, e'en thosethat are perfectly informed and mobile, to mo'e to a higher indifference cur'e.The optimal point would now be point h, which in'ol'es F7;; in benefits andF7;; in wages. /n immobile or imperfectly informed worker might still notattain point h, but gi'en that the firms isoprofit cur'e has shifted out, theworkers are likely to see more benefits offered and this will mo'e the workersto higher le'els of utility.

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