Poverty Effects of the Minimum Wage: The Role of Household Employment Composition

Transcription

1 Corne University ILR Scoo Working apers ILR Coection -007 overty Effects of te Minimum Wage: Te Roe of Houseod Empoyment Composition Gary S. Fieds Corne University, Baran Han Corne University, Ravi Kanbur Corne University, Foo tis and additiona orks at: ttp://digitacommons.ir.corne.edu/orkingpapers Tank you for donoading an artice from Support tis vauabe resource today! Tis Artice is brougt to you for free and open access by te ILR Coection at It as been accepted for incusion in Working apers by an autoried administrator of For more information, pease contact

2 overty Effects of te Minimum Wage: Te Roe of Houseod Empoyment Composition Abstract A cange in a country s minimum age i in genera affect te number of orkers in covered sector empoyment, uncovered sector empoyment, and unempoyment. Te impact of tese abor market adjustments on absoute poverty i depend on o te pattern of empoyment composition canges itin ouseods and on o income is sared itin ouseods. An earier paper Fieds and Kanbur, 007 focused on te income-saring dimension of te probem. Te present paper focuses on ouseod empoyment composition. For a particuar structure of te abor market one it good jobs, bad jobs, unempoyment, and adut and yout orkers and it a particuar mode of o te sectora patterns of empoyment are transated into ouseod empoyment composition, e anaye te impact of minimum ages on a cass of absoute poverty measures. Te precise caracteriations demonstrate te need for a nuanced appreciation of te impacts of a minimum age increase, since tey depend intricatey on te vaues of key parameters te poverty ine, poverty aversion, abor demand easticity, and te starting eve of te minimum age. Moreover, te reationsip beteen poverty and te minimum age is in genera nonmonotonic, so tat oca effects can be quite different from te effects of arge canges in te minimum age. Keyords poverty, empoyment, unempoyment, minimum age, ouseod composition Comments Suggested Citation Fieds, G. S., Han, B., & Kanbur, R overty effects of te minimum age: Te roe of ouseod empoyment composition [Eectronic version]. Retrieved [insert date], from Corne University, ILR Scoo site: ttp://digitacommons.ir.corne.edu/orkingpapers/56/ Required ubiser Statement Copyrigt ed by te autor. Tis artice is avaiabe at DigitaCommons@ILR: ttp://digitacommons.ir.corne.edu/orkingpapers/56

3 overty Effects of te Minimum Wage: Te Roe of Houseod Empoyment Composition * Gary S. Fieds gsf@corne.edu Baran Han b84@corne.edu Ravi Kanbur sk45@corne.edu Corne University Itaca, NY November, 007 Abstract A cange in a country s minimum age i in genera affect te number of orkers in covered sector empoyment, uncovered sector empoyment, and unempoyment. Te impact of tese abor market adjustments on absoute poverty i depend on o te pattern of empoyment composition canges itin ouseods and on o income is sared itin ouseods. An earier paper Fieds and Kanbur, 007 focused on te income-saring dimension of te probem. Te present paper focuses on ouseod empoyment composition. For a particuar structure of te abor market one it good jobs, bad jobs, unempoyment, and adut and yout orkers and it a particuar mode of o te sectora patterns of empoyment are transated into ouseod empoyment composition, e anaye te impact of minimum ages on a cass of absoute poverty measures. Te precise caracteriations demonstrate te need for a nuanced appreciation of te impacts of a minimum age increase, since tey depend intricatey on te vaues of key parameters te poverty ine, poverty aversion, abor demand easticity, and te starting eve of te minimum age. Moreover, te reationsip beteen poverty and te minimum age is in genera non-monotonic, so tat oca effects can be quite different from te effects of arge canges in te minimum age. * An earier version of tis paper as presented at te Annua Convention of te Society of Labor Economists, Cicago, IL, May, 007.

4 overty Effects of te Minimum Wage: Te Roe of Houseod Empoyment Composition Gary S. Fieds Baran Han Ravi Kanbur I. Introduction Minimum ages are commony evauated by abor economists in one of to ays. Some anaysts pay primary attention to te fact tat a iger minimum age increases te abor market earnings of tose empoyed, ie oters empasie tat a iger minimum age oud normay be epected to reduce te number empoyed Bron, 999; Erenberg and Smit, 006; Borjas,005. Hoever, an anaysis of te effects of tese abor market consequences on poverty, ic is te utimate focus of muc of te poicy discourse, requires to furter steps. First, te empoyment composition of te abor market as to be transated into te empoyment composition of eac ouseod. Second, a metod of income saring itin te ouseod must be specified. In a previous paper Fieds and Kanbur, 007, in a mode it ony to types of orkers - empoyed and unempoyed - e focused primariy on different ays tat incomes migt be sared itin ouseods and o eac affected te impact of minimum ages on poverty. In te present paper e assume perfecty equa income saring itin te ouseod, and focus instead on empoyment composition. We deveop te ouseod distribution of income from te abor market outcomes for a mode it good jobs, bad jobs and unempoyment, and aduts and youts searcing for jobs. Suc a structure aos us, for eampe, to incorporate te fact tat in countries suc as te United States, many minimum age orkers ive in non-poor ouseods Burkauser, Couc, and Wittenburg, 000. Te impact of a minimum age on poverty ten depends cruciay on te empoyment composition of ouseods at different eves of income. We ask, en eacty does a iger minimum age raise poverty, en does it oer poverty, and en is poverty uncanged?

5 Te remainder of te paper is structured as foos. Section II presents te main features of te mode. Section III derives te effect of a sma increase in te minimum age. Section IV etends te anaysis to arge canges in te minimum age. Section V summaries and concudes. II. Te Mode A. Te Labor Market and Houseod Empoyment Composition In tis paper, it is assumed tat tere is a fied number of ouseods, normaied at. Eac ouseod consists of to ouseod members: one adut and one yout. Tus, te tota abor suppy is. Te abor market as to types of jobs. Hig age jobs,, pay a age. Te age of tese good jobs is assumed to be invariant to any canges taking pace eseere in te abor market. Empoyment in te ig age sector, denoted, is determined according to a standard donard-soping abor demand curve f ŵ ŵ, f'0. Lo age jobs,, pay a minimum age, ic is determined as a matter of pubic poicy. Empoyment in tese bad jobs in te o age sector is aso determined according to a standard donard-soping abor demand curve ŵ g, g 0. It is assumed tat ony aduts can be empoyed in te ig age sector. Aduts o fai to find empoyment in te ig age sector, togeter it youts, form an undifferentiated poo of appicants for o age jobs. Te o age ŵ is of course ess tan te ig age, and ouseods in ic bot members are empoyed earn more tan ouseods in ic ony one is empoyed. In addition, e assume tat te o age is greater tan af te ig age. Togeter, tese assumptions impy tat 0. Tese inequaities i be maintained trougout tis paper. We no discuss te number of persons earning eac of tese amounts and te per capita ouseod incomes. Empoyment in te ig age and o age sectors are respectivey and. Given tat te ig age sector empoys ony aduts, te number of om is normaied at,

6 3 te number of aduts seeking o age jobs is. In addition, a yout te number of ic is normaied at aso seek o age jobs. Tus, te number of appicants for o age jobs is, and te probabiity tat a o age appicant gets a job is. An adut can be empoyed in a ig age job it probabiity, empoyed in a o age job it probabiity, or unempoyed it probabiity. A yout can be empoyed in a o age job it probabiity or unempoyed it probabiity. utting tese respective ages and empoyment probabiities togeter, e ave si possibe types of ouseods, ere A i, i,, u is te empoyment state of te adut and Y j, j, u is te empoyment state of te yout; see Tabe. A ouseod members are assumed to sare teir earnings. Hence ouseod earnings per capita is te reevant measure of te ebeing of eac individua in te ouseod. Ceary te poorest individuas are tose o ive in ouseods ere nobody orks H6. Net come individuas in ouseods ere one member is unempoyed but te oter member is empoyed in te minimum age sector H4 and H5. Given our assumption tat te ig age is ess tan tice te o age, te case ere te adut as a ig age job but te yout is unempoyed H3 gives oer per capita income tan te case ere bot te adut and te yout are empoyed in te o age sector H. Finay, te igest ouseod per capita income occurs en te adut as a good job and te yout is empoyed in te minimum age sector H. Tabe sets out, terefore, te income distribution in tis society. We turn no to te measurement of poverty based on tis income distribution. B. Ho overty Is Measured overty in tis paper is measured in absoute terms. Te anaysis consists of determining o poverty in te abor market varies it canges in. overty is gauged by comparing te ouseod s abor market earnings to a fied poverty ine. Te poverty ine is $ per person, i.e., $ per ouseod. ŵ

7 4 Ho ig te fied poverty ine is itsef aoed to vary. Five cases are anayed in tis paper. Moving from te oest poverty ine to te igest, tey are: Case : 0. Case : 0. Case 3: 0. Case 4: 0. Case 5: 0. Case is ere te poverty ine is so o tat ony ouseods it a members unempoyed are poor. Case brings into te poverty net tose ouseods ere one member is unempoyed but te oter member as a minimum age job. Tese ouseods i benefit from a rise in te minimum age if tey od onto te minimum age job. Case 3 idens te poverty net sti furter to incude ouseods ere te adut is empoyed in te ig age sector but te yout is unempoyed. Case 4 sets te poverty ine at a sufficienty ig eve tat income from to minimum age jobs is not enoug to pu te ouseod out of poverty. Finay, Case 5 is te etreme case ere te poverty ine is so ig tat everybody is in poverty. Observers o argue tat te minimum age does not target poverty very e are ceary tinking of Cases troug troug 4, in ic non-poor ouseods ave minimum age earners. But in Cases troug 5, poor ouseods aso ave minimum age orkers. Hence in Cases, 3 and 4, minimum age orkers are to be found in bot poor and non-poor ouseods. In a cases, poverty is gauged using te cass of absoute poverty indices deveoped by Foster, Greer, and Torbecke 984. Te FGT inde, denoted, takes eac poor person's poverty deficit as a percentage of te poverty ine, raises it to a poer, and averages over te entire popuation. Letting y i be te income of te i-t person, te poverty ine, q te number of poor persons, and n te tota number of persons, te poverty measure is given by:

8 5 n q i yi. Tree specific vaues of are of particuar interest. As is e knon, en 0 tis measure coapses to te eadcount ratio, te fraction of peope beo te poverty ine. Oter interesting vaues of are en is greater tan or equa to one. Bencmark vaues in tis range are, in ic case e ave te income gap measure of poverty, and, ic is knon as te squared poverty gap measure. Te iger is, te greater is te sensitivity of poverty to canges in te incomes of te poorest compared to te incomes of te not so poor. For tese reasons, is knon as te poverty aversion parameter. To ao for te socia oss from poverty to increase at an increasing rate as incomes fa reative to te poverty ine, must be greater tan. Because of te intuitive appea of integer vaues of, it is common for empirica poverty researcers to coose. Different degrees of poverty aversion i be seen to be important in deineating te consequences of te minimum age for poverty. We turn no to te poverty effects of iger minimum ages in tis mode. III. Te overty Effects of a Higer Minimum Wage Witin Eac of te Five Cases We ave set fort five cases above. For eac of tese five cases, different types of tradeoffs are invoved in raising te minimum age. Te resuts are summaried in Tabe. Te detaied derivations are given in te Appendi. Here e i provide an intuitive discussion of te resuts. Te resuts fa into tree groups and i be discussed accordingy: Te resuts for 0, in ic d d > 0. Te resuts for Case, aso in ic > 0. 3 Te resuts for d d d > in Cases troug 5, in ic > 0 d 0 if te easticity of abor demand in te minimum age sector η is sufficienty ig o. Te first set of resuts for 0 can be understood in a simiar ay for a five cases. Wen 0, te poverty measure being used is te poverty eadcount ratio. A iger minimum age causes more peope to become unempoyed, ic raises te number of ouseods in

9 6 d poverty, i.e., 0 > 0. Given tat te 0 poverty measure focuses ony on te numbers in d poverty and not on o poor te poor are, te gains to te incomes of poor orking ouseods is not counted, and poverty measured by te number in poverty aays rises. Te ony reason tat d 0 0 in Case 5 is tat te poverty ine is so ig tat everybody is in poverty to begin it, d and so no furter increase in poverty is possibe. Te second set of resuts is for Case, i.e., te case in ic te ony poor ouseods are tose for ic bot ouseod members are unempoyed. Tus an increase in te minimum age cannot possiby affect teir incomes, but teir numbers i increase it te rise in unempoyment. Tus, no matter at te vaue of, in tis case, an increase in te minimum age i increase poverty, i.e., d > 0. d Te tird set of resuts is for > in Cases troug 5. In eac of tese ces, d d > 0 en η is sufficienty ig and 0 en η is sufficienty o. Tat is, en te d d easticity of abor demand is greater tan te critica vaue corresponding to tat particuar case, as te minimum age increases, poverty i increase. overty i rise en te unempoyment effect of a minimum age increase dominates te earnings effect. Of course, tis is more ikey te greater te easticity of demand for abor. On te oter and, en te easticity of abor demand is ess tan te critica vaue, as te minimum age increases, poverty i decrease: te earnings effect dominates te unempoyment effect. Tis competes our anaysis of o poverty canges ocay it te minimum age itin eac of te five cases. Let us no anaye at appens en canges in te minimum age are so arge tat e move across cases. IV. Te overty Effects of a Large Increase in te Minimum Wage Section III anayed te effects of an infinitesima increase in te minimum age. In tis section, e ask at appens if te minimum is increased discretey. On te one and, te

10 7 discrete jump in te minimum age can occur itin a case. Wen tis appens, te effect of te minimum age on poverty is te integra of a te infinitesima canges. No ne anaysis is needed en tis appens. On te oter and, te discrete jump in te minimum age can cause te economy to sitc from one case to anoter. We so in tis section tat en suc a sitc occurs, te cange in poverty may be discontinuous and, moreover, may go in te opposite direction from at appens on eiter side of te discontinuity. A. To Eampes It is possibe to gain furter insigts by ooking at specific numerica eampes. Tese eampes i ten be used to derive more genera resuts. Te to eampes e present are simiar in most respects. Tey ave te same ig age 5, te same empoyment at te ig age 0., te same range of possibe minimum ages from 7.5 to ŵ 5, te same constant easticity of demand for abor in te o age sector η 0.7, and te same demand for abor curve in te o age sector n. Te to eampes differ in one important respect, oever: in Eampe, te poverty ine is in te range, ie in Eampe, te poverty ine is in te range >. Note: In Cases and,, ie in Cases 3 troug 5, >. For te cacuations beo, 5 in Eampe and.5 in Eampe. To anaye o poverty as measured by canges it, our strategy is to fi and raise ŵ from te oest possibe vaue to te igest possibe vaue. We do tis first en and ten en >. B. Anaysis for te overty Headcount Ratio 0 We start it te situation ere is cosen to equa 0, i.e., te poverty measure is te eadcount ratio. Te eadcount ratio is sensitive ony to te number of peope beo te poverty

11 8 ine but not to te severity of teir poverty. Tis means tat canging te minimum age induces ony an unempoyment effect but no earnings effect. Wen 0, te unempoyment effect operates in te same ay in Cases troug 4: an increase in te minimum age reduces empoyment in te o age sector, tereby increasing poverty as ong as e remain itin any of tese four cases. In Case 5, oever, everyone is poor and remains so, and terefore a cange in te minimum age as no effect on te poverty eadcount. Wat appens itin a case is not te same as at appens in moving from one case to te net. To iustrate tis point, consider Figures and. Figure graps te poverty eadcount ratio 0 in Eampe. We see tat 0 increases as te minimum age rises itin Case. Hoever, tere is a discontinuous fa in 0 at 0. Wy 0? Because tat is tice te poverty ine 5 in Eampe, ic is te boundary beteen Case and Case. Wen te minimum age rises above 0, a of te peope iving in ouseods it just one member empoyed at te minimum age suddeny escape from poverty. We are no in te range of Case. In tat range, a furter increase of te minimum age decreases empoyment and terefore raises te poverty eadcount. Tis range ends just before te minimum age equas te ig age, i.e., as. Suppose e continue to maintain tat 0 but no >. Tese conditions od in Eampe. Figure graps te poverty eadcount ratio 0 in Eampe. Te figure sos tat as te minimum age rises, 0 is constant at in Case 5 and increases itin Cases 4 and 3. It aso sos discontinuous drops at te boundaries of te Cases. Te reason is anaogous to Eampe. At te boundary beteen Cases 5 and 4, a of te ouseods it te maimum possibe earnings tat is, tose in ic te adut is empoyed in a ig age job and te yout in a o age job suddeny escape poverty. Simiary, at te boundary beteen Cases 4 and 3, tose ouseods in ic bot te adut and te yout are empoyed in o age jobs suddeny escape poverty. Tese eampes iustrate resuts tat are quite genera: ŵ

12 9 roposition : Wen 0 and, an increase in te minimum age raises 0 itin a case but may oer 0 if te economy crosses from Case to Case. roof: In Appendi Turning no to te case eempified by Figure, e ave te fooing genera resut: roposition : Wen 0 and >, an increase in te minimum age eaves 0 uncanged if te minimum age remains itin Case 5, raises 0 if te minimum age remains itin Case 4 or Case 3, and may oer 0 if te economy crosses from Case 5 to Case 4 or from Case 4 to Case 3. roof: In Appendi minimum age Tis competes our anaysis of o te poverty eadcount ratio 0 varies it te. te squared poverty gap. We turn no to te anaysis of te situation ere poverty is measured by C. Anaysis for te Squared overty Gap Te squared poverty gap is sensitive bot to te number of peope beo te poverty ine and to te severity of teir poverty. Canging te minimum age i induce bot an unempoyment effect and an earnings effect. As detaied in Section III, poverty as measured by may increase or decrease depending on te reative sie of tese to effects. Figure 3 graps te squared poverty gap in Eampe. In tis particuar eampe, as te minimum age increases, increases in bot Cases and. Tis is not a genera resut:

13 0 coud be increasing, decreasing, or cange sign itin eiter of te to Cases. Figure 4 graps te squared poverty gap in Eampe. In tis particuar eampe, e ave a U-saped pattern: as te minimum age increases, decreases in Case 5, decreases and ten increases in Case 4, and increases trougout Case 3. Tis U sape is not a genera resut: coud be decreasing trougout, increasing trougout, or cange sign depending on parameter vaues. Te genera resut is: roposition 3: Wen 0, is a continuous function of te minimum age. roof: In Appendi Atoug te beavior of it respect to te minimum age is continuous, it can be non-monotonic, as son in Figure 4. Tis once again means tat oca findings, eter teoretica or empirica, are not necessariy a good guide to te impications of discrete canges. Tus, in Figure 4, ie a sma increase in te minimum age for o vaues of te age may oer poverty, a sufficienty arge increase may ave te opposite effect. On te oter and, just because an increase in te minimum age from a particuar starting point is observed to increase poverty is no guarantee tat an increase in te minimum age i ave te same effect as an increase in te minimum age from some oter starting point. V. Concusion Fieds and Kanbur 007 brougt te issue of income-saring itin te ouseod to te forefront of te debate on te poverty impact of minimum ages. Tat paper soed o tis poverty impact depends cruciay on te income-saring rue.

14 In tis paper, te fooing mode as been used. We ave assumed equa saring itin te ouseod to igigt te importance of te ouseod empoyment composition. Eac ouseod consists of one adut and one yout. Tere are to types of jobs, ig age jobs and o age jobs. Te minimum age appies to o age jobs. Ony aduts may be ired for te ig age jobs. Tose aduts not ired for te ig age jobs and a yout compete for te o age jobs. Of tese, te ones not ired in te o age jobs are unempoyed. Tis structure determines te empoyment composition of eac ouseod, ic in turn determines its income. A ouseod is poor if and ony if its per capita earnings are beo a pre-estabised poverty ine. We soed tat a minimum age increase can raise poverty, oer poverty, or eave poverty uncanged. Te particuar outcome depends on te specific baance beteen te ig age, te o age, empoyment in ig-age and o-age jobs, te easticity of demand for abor it respect to te minimum age, and te vaue of cosen. Tabe summaries te patterns tat arise depending on o ig te poverty ine is and ic vaue of is cosen. Te fifteen ces of Tabe refect at appens itin a case. In addition, minimum age canges may be arge enoug to cause movements across cases. We proved tree propositions reating to movements across cases, soing tat 0 necessariy canges discontinuousy en crossing cases and tat necessariy canges continuousy en crossing cases. Furtermore, e demonstrated tat tere may be non-monotonicities in te reationsip, ic means tat oca resuts teoretica or empirica are not necessariy a good guide to te effects of discrete canges. Te resuts derived ere reinforce te genera concusion from Fieds and Kanbur 007 tat no simpe statement can be made about eter an increase in te minimum age raises poverty, oers poverty, or eaves poverty uncanged. A detaied anaysis is needed before concusions can be dran. Tis strongy suggests tat te nature of te poicy debate soud sift from te simpistic yes versus no format tat is current to a more nuanced discussion of te precise conditions under ic a minimum age i or i not reduce poverty.

15 References Borjas, George, Labor Economics. Ne York: McGra-Hi Irin, 005. Bron, Cares, Minimum Wages, Empoyment, and te Distribution of Income, in Orey C. Asenfeter and David Card, eds., Handbook of Labor Economics, voume 3B. Amsterdam: Esevier, 999, pp Burkauser, Ricard V., Kennet A. Couc, and David C. Wittenburg, A Reassessment of te Ne Economics of te Minimum Wage Literature it Monty Data from te Current opuation Survey, Journa of Labor Economics 8: , October, 000. Erenberg, Ronad G. and Robert S. Smit, Modern Labor Economics. Boston: earson Addison Wesey, 006. Fieds, Gary S. and Ravi Kanbur, Minimum Wages and overty it Income Saring, Journa of Economic Inequaity 5, 35-47, 007. Foster, James, Joe Greer, and Erik Torbecke, A Cass of Decomposabe overty Measures, Econometrica 53: , 984.

16 3 Tabe. Types of Houseods and Distribution of Earnings. Type of ouseod Number of occurrences Tota ouseod earnings Houseod earnings per capita H. H. A, Y ŵ ŵ H3. u H4. A, Y u ŵ H5. u ŵ H6. u u 0 0

17 4 Tabe. Summary of Resuts Concerning te Effect of a Minimum Wage Increase on overty as Gauged by. Case Case Case 3 Case 4 Case 5 d 0 > 0 d > d 0 > d d 0 > 0 0 d d d d d d Wen η is Wen η is Wen η is Wen η > 0 d sufficienty sufficienty sufficienty, ig o, ig o, ig o, d > 0 d 0. > 0 d d 0 0. > 0 0. d 0. d d d d Wen η is Wen η is Wen η is Wen η is > > 0 d sufficienty sufficienty sufficienty sufficienty ig o, ig o, ig o, ig o, d > 0 d 0. > 0 d 0. > 0 d 0. > 0 0. d d d d Note: Te parameter η is te age easticity of abor demand in te minimum age sector. Moving from te oest poverty ine to te igest, te five cases are: Case : 0. Case : 0. Case 3: 0. Case 4: 0. Case 5: 0.

18 5

19 6

20 7

21 8

22 9 Appendi : Derivations of Resuts in Tabe A. Case : 0. In tis case, ŵ and ŵ are sufficienty ig reative to tat ony te ouseods it bot individuas unempoyed are poor. Te vaue of in tis case is 0. Let us no see o is affected by an increase in ŵ. We ave d d d d For a standard abor demand function it 0, is aays positive tat is, poverty d d. 3 aays increases as te minimum age increases. If, furtermore, e assume a constant d easticity of abor demand η > 0, can be manipuated to produce d d d η, d d in ic it is apparent tat d > 0 if and ony if η > 0 for a. d B. Case : 0. In Case, te poor ouseods are tose ere bot individuas are unempoyed or ere ony one ouseod member is empoyed and tat person earns te minimum age. In tis case,. 4 Te effect of a iger minimum age is obtained to be

23 0. ] [ d d d d 5 If in 5, e assume constant easticity of abor demand as before, e ave:, ] [ d d d d ic can be manipuated to yied. ] [ d d η 6 Te first term in 6 can be tougt of as te unempoyment effect; it tes us o an increase in te minimum age brings about a reduction in empoyment. Tis term may be son to be aays positive as foos. Te epression in brackets in te first term ] [ is aays positive since 0 for a. Tis term is mutipied by a number of positive terms, ic proves tat te entire first epression is aays positive. Te second term in 6 can be tougt of as te earnings effect; it tes us o an increase in te minimum age affects via te gain in earnings for tose empoyed. To sign tis epression, note tat in Case,, ence, 0 > and terefore a terms are positive ecept for. Te product of tese terms is terefore negative. To anaye te sign of, d d et us dea no it some particuar vaues of. First, it may be son tat en 0, for any η, 0 > d d. Equation 6 becomes 0 d d η,

24 ic is positive for any positive η. It may aso be son tat en, 0 d d if and ony if. ] [ η C. Case 3: 0. In tis case, te poverty group consists of ouseods in ic bot individuas are unempoyed and tose in ic ony one ouseod member is empoyed regardess of te sector of empoyment. Te etent of poverty in tis case is given by. 7 Differentiating 7 it respect to te eve of te minimum age yieds. d d d d d d d d d d 8 If te abor demand easticity η is assumed to be constant, equation 8 can be furter manipuated to yied a condition in terms of η:, d d d d d d d d d d ic in turn produces

25 . ] [ d d η 9 Again, te first term is te unempoyment effect ic is aays positive, and te second term is te earnings effect ic is aays negative. Let us ook at particuar vaues of. It may be verified tat en 0, for any η, 0 > d d. Furtermore, en, 0 d d if and ony if. ] [ ] [ η D. Case 4: 0. In Case 4, ouseods in ic bot individuas are unempoyed and in ic ony one ouseod member is empoyed are beo te poverty ine. Moreover, if bot ouseod members are empoyed and earn te minimum age, tat ouseod fas beo te poverty ine. On te oter and, a ouseod it a ig age earner and a o age earner is above te poverty ine. Tis coud be a possibe styiation of te US abor market ere about 80% of minimum age earners ive it a ig age earner Burkauser, Couc, and Wittenburg, 000. Te poverty measure in tis case becomes:. 0

26 3 Differentiating 0 it respect to to get te effect on of increase in, d d d d d d d d d d d d If te abor demand easticity η is assumed to be constant, equation can be reritten as:, d d d d d d d d d d d d ic can be epressed as:. ] [ d d η Again, te first term on te rigt and side is te unempoyment effect. ic can be son to be aays positive. Group te first to terms in brackets togeter and te tird and fift terms togeter, from ic e can see tat te bracketed term is aays positive. Te rest of te terms

27 4 of te equation form te earnings effect, ic is aays negative. Looking at different vaues of, en 0, for any η, 0 > d d. Wen, it may be son tat 0 d d if and ony if. ] [ ] [ η E. Case 5: 0. For Case 5, a ouseods fa beo te poverty ine regardess of te empoyment status of te ouseod members. Te poverty measure can be epressed in tis case as:. 3 Differentiating 3 it respect to yieds ŵ. d d d d d d d d d d d d d d 4 If te easticity of abor demand is assumed constant, 4 can be reritten as:

28 5, d d d d d d d d d d d d d d ic in turn can be reritten as. ] [ d d η 5 Again, e ave te unempoyment effect aays positive in te first term of te rigt and side of te equation and te earnings effect aays negative in te rest of te equation. Anaying 5 for specific vaues of, en 0, for any η, 0 d d. Tis is because everyone is under te poverty ine, and tat does not cange as increases. ŵ Wen, it is straigtforard to so tat for η, 0 d d. Finay, for >, e ave te condition tat: 0 d d if and ony if

29 6 ] [ ] [ η.

30 7 Appendi : roofs of ropositions -3 roposition roof:.a From 6, d > 0 itin Case. d.b From 3, d > 0 itin Case. d.c Te boundary beteen Cases and occurs at. From 4, in Case ; from, in Case. Evauated at 0 and setting 0, 6 0 in Case and 7 in Case. Because 6 > 7, 0 fas discontinuousy at Combining resuts.a-c, roposition is proved.. roposition roof:.a From 5, d 0 itin Case 5. d.b From, d > 0 itin Case 4. d.c From 9, d > 0 itin Case 3. d

31 8.d Te boundary beteen Cases 5 and 4 occurs at. From 3, in Case 5; from 0, in Case 4. Evauated at and setting 0, 0 8 in Case 5 and 0 9 in Case 4. Because 8 > 9, 0 fas discontinuousy at..e Te boundary beteen Cases 4 and 3 occurs at. From 0, in Case 4; from 7, in Case 3. Evauated at and setting 0,

32 9 0 in Case 4 and 0 0 in Case 3. Because 9 > 0, 0 fas discontinuousy at. Combining resuts.a-e, roposition is proved. roposition 3 roof for : Te continuity of itin eac case is evident. As for te boundary, te dividing ine beteen Cases and occurs at. From 4, in Case ; from, in Case. Evauated at, in Case, ic is identica to at equas in Case at tat point. Continuity is tereby proved. roof for > : 4.a-c Te continuity of itin eac case foos eacty as in.a-c. 4.d Te boundary beteen Cases 5 and 4 occurs at. From 3, in Case 5; from 0,

33 30 in Case 4. Evauated at and setting, in Case 5 and in Case 4. Tese are identica, and terefore is continuous at te boundary beteen Cases 5 and 4. 4.e Te boundary beteen Cases 4 and 3 occurs at. From 0, in Case 4; from 7, in Case 3. Evauated at and setting, in Case 4 and in Case 3. Tese are identica, and terefore is continuous at te boundary beteen Cases 4 and 3. Combining resuts 4.a-e, roposition 4 is proved.