AppliedMathematics,2021,12,252-261
https://www.scirp.org/journal/am
ISSNOnline:2152-7393
ISSNPrint:2152-7385
ConspicuousEthics:ExistenceofPrice
DependentEthicalUtilityFunctions
PascalStiefenhofer
NewcastleUniversityBusinessSchool,NewcastleuponTyne,UK
Howtocitethispap er:Stiefenhofer,P.
(2021) ConspicuousEthics:Existenceof Price
DependentEthicalUtilityFunctions.Applied
Mathematics,12,252-261.
https://doi.org/10.4236/am.2021.124016
Received:March4,2021
Accepted:April5,2021
Published:April8,2021
Copyright
c
2021byauthor(s)andScientific
Research PublishingInc.
This work is licensed under the Creative Com-
monsAttributionInternationalLicense(CC
BY4.0).
http://creativecommons.org/licenses/by/4.0/
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lentesquehabitantmorbitristiquesenectuset
netusetmalesuadafamesacturpisegestas.
Phasellusidmagna.Duismalesuadainter-
dumarcu.Integer metus.Morbipulvinarpel-
lentesquemi.Suspendissesedesteumagna
molestieegestas.Quisquemilorem,pulvinar
eget,egestasquis,luctusat,ante.Proinauc-
torvehiculapurus.Fusceacnisl aliquamante
hendreritpellentesque.Classaptenttacitiso-
ciosquadlitoratorquentperconubianostra,
perinceptoshymenaeos.Morbiwisi.Etiam
arcumauris,facilisissed,eleifendnon,non-
ummyut,pede.Crasutlacustempormetus
mollisplacerat.Vivamuseutortorvelmetus
interdum malesuada.
Sedeleifend,erossitametfaucibuselemen-
tum,urnasapienconsectetuermauris,quis
egestasleojustononrisus.Morbinonfelisac
liberovulputatefringilla.Maurisliberoeros,
lacinianon,sodalesquis,dapibusporttitor,
pede.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Morbi dapibus mauris condimentum
nulla.Cumsociisnatoquepenatibuset magnis
disparturient montes,nasceturridiculusmus.
Etiamsitameterat.Nullavarius.Etiamt-
inciduntduivitaeturpis.Donecleo.Morbi
vulputateconvallisest.Integeraliquet.Pel-
lentesque aliquetsodalesurna.
Nullameleifendjustoinnisl.Inhachabitasse
plateadictumst.Morbinonummy.Aliquam
utfelis.Invelitleo,dictumvitae,posuereid,
vulputatenec,ante.Maecenasvitaepedenec
dui dignissim suscipit.Morbi magna.Vestibu-
lumidpurusegetvelitlaoreetlaoreet.Prae-
sentsedleovelnibhconvallisblandit.Ut
rutrum.Donecnibh.Donecinterdum.Fusce
sed pede sit amet elitrhoncus ultrices.Nullam
atenimvitaepedevehiculaiaculis.
Classaptenttacitisociosquadlitoratorquen-
tperconubianostra,perinceptoshymenaeos.
Aeneannonummyturpisidodio.Integereu-
ismodimperdietturpis.Utnecleonecdi-
amimperdietlacinia.Etiamegetlacuseget
miultriciesposuere.Inplacerattristiquetor-
tor.Sedportavestibulummetus.Nullaia-
culissollicitudinpede.Fusceluctustellusin
dolor.Curabiturauctorvelitasem.Mor-
bisapien.Classaptenttacitisociosquadl-
itoratorquentperconubianostra,perincep-
toshymenaeos.Donecadipiscingurnavehic-
ulanunc.Sedornareleoinleo.Inrhoncus
leoutdui.Aeneandolorquam,volutpatnec,
fringillaid,consectetuervel,pede.
Nullamalesuadarisusuturna.Aenean
pretiumvelitsitametmetus.Duisiaculis.In
hachabitasseplateadictumst.Nullammo-
lestieturpisegetnisl.Duisamassaidpede
dapibusultricies.Sedeuleo.Inatmaurissit
amettortorbibendumvarius.Phasellusjusto
risus,posuerein,sagittisac,variusvel,tor-
tor.Quisqueidenim.Phasellusconsequat,
liberopretium nonummy fringilla,tortor lacus
vestibulumnunc,utrhoncusligulanequeid
justo.Nullamaccumsaneuismodnunc.Proin
vitae ipsumac metusdictum tempus.Nam ut
wisi.Quisque tortor felis, interdum ac, sodales
a,sempera,sem.Curabiturinvelitsitamet
duitristiquesodales.Vivamusmaurispede,
laciniaeget,pellentesquequis,scelerisqueeu,
est.Aliquamrisus.Quisquebibendumpede
eudolor.
Donec tempusneque vitaeest.Aenean egestas
odio sed risus ullamcorper ullamcorper.Sed in
nullaatortortinciduntegestas.Namsapien
tortor,elementumsitamet,aliquamin,port-
titorfaucibus,enim.Nullamconguesuscipit
nibh.Quisqueconvallis.Praesentarcunibh,
vehicula eget,accumsaneu,tincidunt a,nibh.
Suspendissevulputate,tortorquisadipiscing
viverra, lacus nibh dignissim tellus, eu suscipit
risusantefringilladiam.Quisquealiberov-
elpedeimperdietaliquet.Pellentesquenunc
nibh,eleifenda,consequatconsequat,hen-
dreritnec,diam.Sedurna.Maecenaslaoreet
eleifendneque.Vivamuspurusodio,eleifend
non,iaculisa,ultricessitamet,urna.Mau-
risfaucibusodiovitaerisus.Innisl.Praesent
purus.Integeriaculis,semeuegestaslacinia,
lacuspedescelerisqueaugue,inullamcorper
dolorerosaclacus.Nuncinlibero.
Fuscesuscipitcursussem.Vivamusrisusmi,
egestasac,imperdietvarius,faucibusquis,
leo.Aeneantincidunt.Donecsuscipit.Cras
idjustoquisnibhscelerisquedignissim.Ali-
quamsagittiselementumdolor.Aeneancon-
sectetuerjustoinpede.Curabiturullamcorper
ligula nec orci.Aliquam purus turpis,aliquam
id, ornarevitae, porttitor non,wisi.Maecenas
luctusportalorem.Donecvitaeligula euante
pretiumvarius.Prointortormetus,convallis
et,hendreritnon,scelerisquein,urna.Cras
quisliberoeuligulabibendumtempor.Viva-
mustellusquam,malesuadaeu,tempussed,
temporsed,velit.Doneclaciniaauctorlibero.
Praesentsednequeidpedemollisrutrum.
Vestibulumiaculisrisus.Pellentesquelacus.
Ut quisnunc sedodio malesuada egestas.Duis
amagnasitametligulatristiquepretium.Ut
pharetra.Vestibulumimperdietmagnanec
wisi.Maurisconvallis.Sedaccumsansollic-
itudinmassa.Sedidenim.Nuncpedeenim,
laciniaut,pulvinarquis,suscipitsemper,elit.
Crasaccumsaneratvitaeenim.Crassollici-
tudin.Vestibulumrutrumblanditmassa.
Sedgravidalectusutpurus.Morbilaoreet
magna.Pellentesque eu wisi.Proin turpis.In-
tegersollicitudinauguenecdui.Fuscelectus.
Vivamusfaucibusnullaneclacus.Integerdi-
am.Pellentesquesodales,enimfeugiatcursus
volutpat,semmaurisdignissimmauris,quis
consequatsemestfermentumligula.Nullam
justo lectus, condimentum sit amet, posuere a,
fringillamollis, felis.Morbinulla nibh,pellen-
tesqueat,nonummyeu,sollicitudinnec,ip-
sum.Crasneque.Nuncaugue.Nullamvitae
quamidquampulvinar blandit.Nunc sitamet
orci.Aliquameratelit,pharetranec,aliquet
a,gravidain,mi.Quisqueurnaenim,viverra
quis,suscipitquis,tinciduntut,sapien.Cras
placeratconsequatsem.Curabituracdiam.
Curabiturdiamtortor,molliset,viverraac,
tempusvel,metus.
Curabituraclorem.Vivamusnonjustoin
duimattisposuere.Etiamaccumsanligula
idpede.Maecenastinciduntdiamnecvelit.
Praesentconvallissapienacest.Aliquamul-
lamcorpereuismodnulla.Integermollisenim
veltortor.Nullasodalesplaceratnunc.Sed
tempusrutrumwisi.Duisaccumsangravi-
dapurus.Nuncnunc.Etiamfacilisisduieu
sem.Vestibulumsemper.Praesenteueros.
Vestibulumtellusnisl,dapibusid,vestibulum
sit amet,placerat ac,mauris.Maecenas etelit
uteratplaceratdictum.Namfeugiat,turpis
etsodalesvolutpat,wisiquam rhoncusneque,
vitaealiquamipsumsapienvelenim.Maece-
nassuscipitcursusmi.
Quisque consectetuer.In suscipit mauris a do-
lor pellentesque consectetuer.Mauris convallis
nequenonerat.Inlacinia.Pellentesqueleo
eros,sagittisquis,fermentumquis,tincidun-
tut,sapien.Maecenassem.Curabitureros
odio,interdumeu,feugiateu,portaac,nis-
l.Curabiturnunc.Etiam fermentum convallis
velit.Pellentesquelaoreetlacus.Quisquesed
elit.Namquistellus.Aliquamtellusarcu,
adipiscingnon,tincidunteleifend,adipiscing
quis,augue.Vivamuselementumplaceraten-
im.Suspendisseuttortor.Integerfaucibus
adipiscingfelis.Aeneanconsectetuermattis
lectus.Morbimalesuadafaucibusdolor.Nam
lacus.Etiamarcu libero,malesuada vitae,ali-
quamvitae,blandittristique,nisl.
Maecenasaccumsandapibussapien.Duis
pretiumiaculisarcu.Curabiturutlacus.Ali-
quamvulputate.Suspendisseutpurussed sem
tempor rhoncus.Utquam dui, fringillaat, dic-
tum eget,ultricies quis,quam.Etiam semest,
pharetra non, vulputate in, pretium at, ipsum.
Nunc semper sagittis orci.Sed scelerisquesus-
cipitdiam.Utvolutpat,doloratullamcorp-
ertristique,erospurusmollisquam,sitamet
ornareantenuncetenim.
Phasellusfringilla,metusidfeugiatcon-
sectetuer,lacuswisiultricestellus,quislobor-
tisnibhloremquistortor.Donecegestas
ornarenulla.Maurismitellus,portafau-
cibus,dictumvel,nonummyin,est.Ali-
quameratvolutpat.Intellusmagna,port-
titorlacinia,molestievitae,pellentesqueeu,
justo.Classaptenttacitisociosquadlitora
torquentperconubianostra,perinceptoshy-
menaeos.Sedorcinibh,scelerisquesitamet,
suscipitsed,placeratvel,diam.Vestibulum
nonummy vulputate orci.Donec et velit ac ar-
cuinterdumsemper.Morbipedeorci,cursus
ac,elementumnon,vehiculaut,lacus.Cras
volutpat.Namvelwisiquisliberovenenatis
placerat.Aeneansedodio.Quisqueposuere
purusacorci.Vivamusodio.Vivamusvar-
ius,nullasitametsemperviverra,odiomau-
risconsequatlacus,atvestibulumnequearcu
eutortor.Doneciaculistincidunttellus.Ali-
quameratvolutpat.Curabiturmagnalorem,
dignissimvolutpat,viverraet,adipiscingnec,
dolor.Praesentlacusmauris,dapibusvitae,
sollicitudinsitamet,nonummy eget,ligula.
Crasegestasipsumanisl.Vivamusvariusdo-
lorutdolor.Fuscevelenim.Pellentesque
accumsanligulaeteros.Crasidlacusnon
tortorfacilisisfacilisis.Etiamnislelit,cur-
sussed,fringillain,conguenec,urna.Cum
sociisnatoquepenatibusetmagnisdispar-
turientmontes,nasceturridiculusmus.In-
tegeratturpis.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes,nascetur
ridiculusmus.Duisfringilla,ligulasedporta
fringilla,ligulawisicommodofelis,utadipisc-
ingfelisduiinenim.Suspendissemalesuada
ultricesante.Pellentesquescelerisqueaugue
sitameturna.Nullavolutpataliquettortor.
Crasaliquam,tellusataliquetpellentesque,
justosapiencommodoleo,idrhoncussapien
quamaterat.Nullacommodo,wisiegetsol-
licitudinpretium,orciorcialiquamorci,ut
cursusturpisjustoetlacus.Nullaveltor-
tor.Quisque eratelit, viverrasit amet, sagittis
eget,portasitamet,lacus.
In hac habitasse platea dictumst.Proin at est.
Curabitur tempusvulputate elit.Pellentesque
sem.Praesent eusapien.Duiselitmagna,ali-
quet at,tempus sed, vehicula non, enim.Mor-
biviverraarcunecpurus.Vivamusfringilla,
enimet commodomalesuada,tortor metusel-
ementumligula,necaliquetestsapienutlec-
tus.Aliquammi.Utnecelit.Fusceeuismod
luctustellus.Curabiturscelerisque.Nullam
purus.Namultricies accumsanmagna.Morbi
pulvinarloremsitametipsum.Donecutjus-
tovitaenibhmolliscongue.Fuscequisdiam.
Praesent tempuserosutquam.
Donecinnisl.Fuscevitaeest.Vivamusante
ante,mattislaoreet,posuereeget,conguevel,
nunc.Fuscesem.Namvelorcieuerosviver-
raluctus.Pellentesquesitametaugue.Nunc
sitametipsumetlacusvariusnonummy.In-
teger rutrum sem egetwisi.Aenean eu sapien.
Quisqueornaredignissimmi.Duisaurnavel
risus pharetraimperdiet.Suspendisse potenti.
Morbijusto.Aeneannecdolor.Inhac
habitasseplateadictumst.Proinnonummy
porttitorvelit.Sedsitametleonecmetus
rhoncusvarius.Crasante.Vestibulumcom-
modosemtinciduntmassa.Namjusto.Ae-
neanluctus,felisetcondimentumlacinia,lec-
tusenimpulvinarpurus,nonportavelitnisl
sed eros.Suspendisse consequat.Mauris a dui
et tortormattispretium.Sednulla metus,vo-
lutpatid, aliquameget, ullamcorperut, ipsum.
Morbieununc.Praesentpretium.Duisali-
quampulvinarligula.Ut blanditegestasjusto.
Quisqueposueremetusviverrapede.
Vivamussodaleselementumneque.Viva-
musdignissimaccumsanneque.Sedatenim.
Vestibulumnonummyinterdumpurus.Mau-
ris ornarevelitid nibh pretiumultricies.Fusce
temporpellentesqueodio.Vivamusauguepu-
rus,laoreetin,scelerisquevel,commodoid,
wisi.Duisenim.Nullainterdum,nunceusem-
pereleifend,enimdolorpretiumelit,utcom-
modoligulanislaest.Vivamusante.Nulla
leomassa,posuerenec,volutpatvitae,rhon-
cuseu,magna.
Quisquefacilisisauctorsapien.Pellentesque
gravidahendreritlectus.Maurisrutrumso-
dalessapien.Fuscehendreritsemvellorem.
Integerpellentesquemassavelaugue.Integer
elit tortor, feugiat quis, sagittis et, ornare non,
lacus.Vestibulumposuerepellentesqueeros.
Quisquevenenatisipsumdictumnulla.Ali-
quam quis quam nonmetus eleifend interdum.
Nam eget sapien ac mauris malesuadaadipisc-
ing.Etiameleifendnequesedquam.Nulla
facilisi.Proinaligula.Sedidduieunibh
egestastincidunt.Suspendissearcu.
Maecenasdui.Aliquamvolutpatauctorlorem.
Crasplaceratestvitaelectus.Curabitur
massalectus,rutrumeuismod,dignissimut,
dapibus a, odio.Ut eros erat, vulputate ut, in-
terdumnon,portaeu,erat.Crasfermentum,
felis inportacongue, velit leo facilisisodio,vi-
taeconsectetuerloremquamvitaeorci.Sed
ultrices,pedeeuplaceratauctor,anteligula
rutrum tellus,vel posuere nibh lacus necnibh.
Maecenaslaoreetdoloratenim.Donecmo-
lestie dolornec metus.Vestibulum libero.Sed
quiserat.Sedtristique.Duispedeleo,fer-
mentumquis,consectetuereget,vulputatesit
amet,erat.
Donecvitaevelit.Suspendisseportafermen-
tummauris.Utvelnuncnonmaurisphare-
travarius.Duisconsequatliberoquisurna.
Maecenasatante.Vivamusvarius,wisised
egestastristique,odiowisiluctusnulla,lobor-
tisdictumdolorligulainlacus.Vivamusali-
quam, urna sed interdum porttitor,metus orci
interdum odio,sitamet euismod lectusfelis et
leo.Praesentacwisi.Namsuscipitvestibu-
lum sem.Praesent eu ipsumvitae pede cursus
venenatis.Duis sed odio.Vestibulum eleifend.
Nullautmassa.Proinrutrummattissapien.
Curabiturdictumgravidaante.
Phasellusplaceratvulputatequam.Maece-
nasattellus.Pellentesquenequediam,dig-
nissim ac, venenatisvitae, consequat ut, lacus.
Nam nibh.Vestibulum fringilla arcu mollis ar-
cu.Sedetturpis.Donecsemtellus,volut-
pat et,variuseu, commodo sed,lectus.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Quisqueenimarcu,suscipitnec,tempus
at,imperdietvel,metus.Morbivolutpatpu-
rusaterat.Donecdignissim,semidsemper
tempus, nibh massa eleifendturpis,sedpellen-
tesquewisipurussedlibero.Nullamlobortis
tortorvelrisus.Pellentesqueconsequatnulla
eutellus.Donecvelit.Aliquamfermentum,
wisiacrhoncusiaculis,tellusnuncmalesuada
orci,quisvolutpatduimagnaidmi.Nuncvel
ante.Duisvitaelacus.Crasnecipsum.
Morbinunc.Aliquamconsectetuervariusnul-
la.Phaselluseros.Crasdapibusporttitorris-
us.Maecenasultricesmiseddiam.Praesent
gravida velit at elit vehicula porttitor.Phasel-
lusnislmi,sagittisac,pulvinarid,gravidasit
amet,erat.Vestibulumest.Loremipsumdo-
lorsit amet,consectetueradipiscingelit.Cur-
abitur idsem elementum leo rutrumhendrerit.
Utatmi.Donectinciduntfaucibusmassa.
Sed turpis quam, sollicitudin a, hendrerit eget,
pretiumut,nisl.Duishendreritligula.Nunc
pulvinarcongueurna.
Nuncvelit.Nullamelitsapien,eleifendeu,
commodo nec, semper sit amet, elit.Nulla lec-
tus risus,condimentum ut,laoreet eget,viver-
ra nec, odio.Proin lobortis.Curabitur dictum
arcuvelwisi.Crasidnullavenenatistortor
congueultrices.Pellentesqueegetpede.Sed
eleifendsagittiselit.Namsedtellussitamet
lectusullamcorper tristique.Mauris enimsem,
tristiqueeu,accumsanat,scelerisquevulpu-
tate, neque.Quisque lacus.Donec etipsum sit
amet elitnonummy aliquet.Sed viverranisl at
sem.Namdiam.Maurisutdolor.Curabitur
ornaretortorcursusvelit.
Morbitinciduntposuerearcu.Crasvenenatis
estvitaedolor.Vivamusscelerisquesemper
mi.Donecipsumarcu,consequatscelerisque,
viverraid,dictumat,metus.Loremipsum
dolor sit amet, consectetuer adipiscing elit.Ut
pede sem, tempus ut, porttitor bibendum, mo-
lestieeu,elit.Suspendissepotenti.Sedidlec-
tus sitamet purus faucibusvehicula.Praesen-
tsedsemnonduipharetrainterdum.Nam
viverra ultricesmagna.
Aeneanlaoreetaliquamorci.Nuncinterdum
elementumurna.Quisqueerat.Nullamtem-
porneque.Maecenasvelitnibh,scelerisquea,
consequatut,viverrain,enim.Duismagna.
Donecodioneque,tristiqueet,tincidunteu,
rhoncusac, nunc.Maurismalesuada malesua-
da elit.Etiam lacus mauris, pretium vel, blan-
ditin, ultriciesid,libero.Phasellusbibendum
eratutdiam.Incongueimperdietlectus.
Aeneanscelerisque.Fuscepretiumporttitor
lorem.Inhachabitasseplatea dictumst.Nulla
sitametnislatsapienegestaspretium.Nunc
nontellus.Vivamusaliquet.Namadipiscing
euismoddolor.Aliquameratvolutpat.Nul-
lautipsum.Quisquetinciduntauctorau-
gue.Nuncimperdietipsumegetelit.Ali-
quamquamleo,consectetuernon,ornaresit
amet,tristique quis,felis.Vestibulum anteip-
sumprimisinfaucibusorciluctusetultrices
posuerecubiliaCurae;Pellentesqueinterdum
quamsitametmi.Pellentesquemaurisdui,
dictuma,adipiscingac,fermentumsitamet,
lorem.
Utquiswisi.Praesentquismassa.Vivamus
egestasrisusegetlacus.Nunctincidunt,risus
quisbibendumfacilisis,lorempurusrutrum
neque,necportatortorurnaquisorci.Ae-
neanaliquet,liberosempervolutpatluctus,
pedeeratlaciniaaugue,quisrutrumsemip-
sumsitametpede.Vestibulumaliquet,nibh
sediaculissagittis,odiodolorblanditaugue,
egetmollisurnatellusidtellus.Aeneanali-
quetaliquamnunc.Nullaultriciesjustoeget
orci.Phasellustristiquefermentumleo.Sed
massametus,sagittisut,semperut,pharetra
vel,erat.Aliquamquamturpis,egestasvel,
elementumin,egestassitamet,lorem.Duis
convallis,wisisitametmollismolestie,libero
mauris portadui, vitaealiquam arcuturpis ac
sem.Aliquamaliquetdapibusmetus.
Vivamuscommodoeroseleifenddui.Vestibu-
luminleoeuerattristiquemattis.Crasat
elit.Craspellentesque.Nullamidlacussit
ametliberoaliquethendrerit.Proinplacerat,
minonelementumlaoreet,eroselittincidun-
tmagna,arhoncussemarcuidodio.Nul-
laegetleoaleoegestasfacilisis.Curabitur
quisvelit.Phasellusaliquam, tortornecornare
rhoncus,purusurnaposuerevelit,etcommo-
dorisustellusquistellus.Vivamusleoturpis,
tempussitamet,tristiquevitae,laoreetquis,
odio.Proinscelerisquebibendumipsum.Eti-
amnisl.Praesentveldolor.Pellentesquevel
magna.Curabitururna.Vivamuscongueur-
na in velit.Etiam ullamcorper elementum dui.
Praesentnon urna.Sed placeratquam non mi.
Pellentesquediammagna,ultricieseget,ultri-
cesplacerat,adipiscingrutrum,sem.
Morbisem.Nullafacilisi.Vestibulumante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Nullafacilisi.Mor-
bisagittisultriceslibero.Praesenteuligula
sedsapienauctorsagittis.Classaptenttaciti
sociosquadlitoratorquentperconubianos-
tra,perinceptoshymenaeos.Donecvelnunc.
Nuncfermentum,lacusidaliquamporta,dui
tortoreuismoderos,velmolestieipsumpurus
eulacus.Vivamuspedearcu, euismod ac,tem-
pusid,pretiumet,lacus.Curabitursodales
dapibusurna.Nunceusapien.Doneceget
nuncapededictumpretium.Proinmauris.
Vivamusluctusliberovelnibh.
Fuscetristiquerisusidwisi.Integermolestie
massaidsem.Vestibulumveldolor.Pel-
lentesquevelurnavelrisusultricieselemen-
tum.Quisquesapien urna,blandit nec,iaculis
ac,viverrain,odio.Inhachabitasseplatea
dictumst.Morbinequelacus,convallisvitae,
commodoac,fermentumeu,velit.Sedinor-
ci.Infringillaturpisnonarcu.Donecinante.
Phasellustemporfeugiatvelit.Aeneanvar-
iusmassanonturpis.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;
Aliquamtortor.Morbiipsum massa,imperdi-
etnon,consectetuervel,feugiatvel,lorem.
Quisqueeget loremnec elitmalesuadavestibu-
lum.Quisquesollicitudinipsum velsem.Nul-
laenim.Proinnonummyfelis vitaefelis.Nul-
lampellentesque.Duisrutrumfeugiatfe-
lis.Maurisvelpedesedliberotinciduntmol-
lis.Phasellussedurnarhoncusdiameuismod
bibendum.Phasellussednisl.Integercondi-
mentumjusto id orciiaculis varius.Quisque et
lacus.Phaselluselementum, justoat dignissim
auctor,wisi odio lobortisarcu,sed sollicitudin
felisfeliseuneque.Praesentatlacus.
Vivamussitametpede.Duisinterdum,nunc
egetrutrumdignissim,nisldiamluctusleo,
ettinciduntvelitnislidtellus.Inloremtel-
lus,aliquetvitae,portain,aliquetsed,lectus.
Phasellussodales.Utvariusscelerisqueerat.
Invelnibheuerosimperdietrutrum.Donec
ac odio nec neque vulputatesuscipit.Nam nec
magna.Pellentesquehabitantmorbitristique
senectus et netus et malesuada fames acturpis
egestas.Nullamporta,odioetsagittisiaculis,
wisi neque fringilla sapien, vel commodo lorem
loremidelit.Utsemlectus,scelerisqueeget,
placeratet,tinciduntscelerisque,ligula.Pel-
lentesque nonorci.
Etiamvelipsum.Morbifacilisisvestibulum
nisl.Praesentcursuslaoreetfelis.Integer
adipiscingpretiumorci.Nullafacilisi.Quisque
posuerebibendumpurus.Nullaquam mauris,
cursuseget,convallisac,molestienon,enim.
Aliquamcongue.Quisquesagittisnonummy
sapien.Proinmolestiesemvitaeurna.Mae-
cenas lorem.Vivamus viverra consequat enim.
Nuncsedpede.Praesentvitaelectus.Prae-
sentnequejusto,vehiculaeget,interdumid,
facilisiset,nibh.Phasellusatpurusetlibero
laciniadictum.Fuscealiquet.Nullaeuante
placeratleosemperdictum.Maurismetus.
Curabiturlobortis.Curabitursollicitudin hen-
dreritnunc.Donecultriceslacusidipsum.
Donecanibhutelitvestibulumtristique.In-
tegeratpede.Crasvolutpatvariusmagna.
Phaselluseuwisi.Praesentrisusjusto,lobor-
tis eget, scelerisqueac, aliquet in, dolor.Proin
idleo.Nunciaculis,mivitaeaccumsancom-
modo, nequesemlacinianulla,quisvestibulum
justosemineros.Quisquesedmassa.Morbi
lectus ipsum, vulputate a, mollis ut,accumsan
placerat,tellus.Nullaminwisi.Vivamuseu
ligulaanuncaccumsancongue.Suspendisse
aclibero.Aliquameratvolutpat.Donecau-
gue.Nuncvenenatisfringillanibh.Fusceac-
cumsan pulvinar justo.Nullam semper, dui ut
dignissim auctor, orcilibero fringilla massa,b-
landitpulvinarpedetortoridmagna.Nunc
adipiscing justo sed velit tincidunt fermentum.
Integerplacerat.Pellentesquehabitantmorbi
tristique senectuset netus etmalesuada fames
acturpisegestas.Sedinmassa.Classaptent
tacitisociosquadlitoratorquentperconubi-
anostra,perinceptoshymenaeos.Phasellus
tempusaliquamrisus.Aliquamrutrumpurus
atmetus.Donecposuereodioaterat.Nam
nonnibh.Phasellusligula.Quisquevene-
natislectusinaugue.Sedvestibulumdapibus
neque.
Mauris tempus eros at nulla.Sed quisdui dig-
nissimmaurispretiumtincidunt.Maurisac
purus.Phasellusaclibero.Etiamdapibusia-
culisnunc.Inlectus wisi,elementumeu, sollic-
itudinnec,imperdietquis,dui.Nullaviverra
nequeaclibero.Maurisurnaleo,adipiscing
eu,ultricesnon,blanditeu,dui.Maecenas
duineque,suscipitsitamet,rutruma,laoreet
in,eros.Uteunibh.Fuscenecerattempus
urnafringillatempus.Curabituridenim.Sed
ante.Crassodalesenimsitametwisi.Nunc
fermentum consequatquam.
Utauctor,augueportadignissimvestibulum,
arcudiamlobortisvelit,velscelerisqueris-
usauguesagittisrisus.Maecenaseujusto.
Pellentesquehabitant morbitristique senectus
etnetusetmalesuadafamesacturpiseges-
tas.Mauriscongueligulaegettortor.Nul-
lam laoreeturnased enim.Doneceget erosut
erosvolutpatconvallis.Praesentturpis.Inte-
germaurisdiam,elementumquis,egestasac,
rutrumvel,orci.Nullafacilisi.Quisqueadip-
iscing,nullavitaeelementumporta,semurna
volutpatleo,sedportaenimrisussedmassa.
Integeracenimquisdiamsodalesluctus.Ut
eget eros a ligula commodo ultricies.Donec eu
urnaviverradolorhendreritfeugiat.Aliquam
acorcivelerosconguepharetra.Quisque
rhoncus,justoeuvolutpat faucibus,augueleo
posuerelacus,arhoncuspuruspedevelest.
Proinultricesenim.
Aenean tincidunt laoreet dui.Vestibulum ante
ipsumprimisinfaucibusorciluctusetultri-
cesposuerecubiliaCurae;Integeripsumlec-
tus,fermentumac,malesuadain,eleifendut,
lorem.Vivamusipsumturpis,elementumvel,
hendrerit ut,semper at,metus.Vivamus sapi-
entortor,eleifendid,dapibusin,egestaset,
pede.Pellentesquefaucibus.Praesentlorem
neque, dignissim in,facilisis nec, hendrerit vel,
odio.Namatdiamacnequealiquetviver-
ra.Morbidapibusligulasagittismagna.In
lobortis.Donecaliquetultricieslibero.Nunc
dictumvulputate purus.Morbivarius.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Intempor.Phaselluscommodoporttitor
magna.Curabiturvehiculaodioveldolor.
Praesentfacilisis,augueaadipiscingvene-
natis,liberorisusmolestieodio,pulvinarcon-
sectetuerfeliseratacmauris.Namvestibu-
lumrhoncusquam.Sedveliturna,pharetra
eu,eleifendeu,viverraat,wisi.Maecenasul-
tricesnibhatturpis.Aeneanquam.Nulla
ipsum.Aliquamposuereluctuserat.Cur-
abiturmagnafelis,laciniaet,tristiqueid,ul-
tricesut,mauris.Suspendissefeugiat.Cras
eleifendwisivitaetortor.Phasellusleopurus,
mattissitamet,auctorin,rutrumin,magna.
Inhachabitasseplateadictumst.Phasellus
imperdietmetusinsem.Vestibulumacenim
nonsemultriciessagittis.Sedveldiam.
Integervelenimsedturpisadipiscingbiben-
dum.Vestibulumpededolor,laoreetnec,po-
suerein,nonummyin,sem.Donecimperdiet
sapienplaceraterat.Donecviverra.Aliquam
eros.Nunc consequat massaid leo.Sed ullam-
corper,loreminsodalesdapibus,risusmetus
sagittislorem,nonporttitorpurusodionec o-
dio.Sedtinciduntposuereelit.Quisqueeu
enim.Donecliberorisus,feugiatac,dapibus
eget, posuere a,felis.Quisque vellectusut me-
tustincidunteleifend.Duis utpede.Duis velit
erat,venenatis vitae,vulputatea, pharetrasit
amet,est.Etiamfringillafaucibusaugue.
Aeneanvelitsem,viverraeu,tempusid,
rutrumid, mi.Nullamnec nibh.Proinullam-
corper,dolorincursustristique,erosaugue
tempornibh,atgravidadiamwisiatpurus.
Donec mattis ullamcorper tellus.Phasellus vel
nulla.Praesentinterdum,erosinsodalessol-
licitudin,nunc nulla pulvinarjusto, aeuismod
erossemnecnibh.Nullamsagittisdapibus
lectus.Nullamegetipsumeutortorlobortis
sodales.Etiampurusleo,pretiumnec,feu-
giatnon,ullamcorpervel,nibh.Sedvelelit
etquamaccumsanfacilisis.Nuncleo.Sus-
pendissefaucibuslacus.
Pellentesqueinterdumsapiensednulla.Proin
tincidunt.Aliquamvolutpatestvelmassa.
Seddolorlacus,imperdietnon,ornarenon,
commodoeu,neque.Integerpretiumsem-
perjusto.Proinrisus.Nullamidquam.
Namneque.Duisvitaewisiullamcorperdi-
amcongueultricies.Quisqueligula.Mauris
vehicula.
Curabiturnuncmagna,posuereeget,vene-
natiseu,vehiculaac,velit.Aeneanornare,
massaaaccumsanpulvinar,quamlorem
laoreetpurus, eusodales magnarisusmolestie
lorem.Nunceratvelit,hendreritquis,male-
suadaut,aliquamvitae,wisi.Sedposuere.
Suspendisseipsumarcu,scelerisquenec,ali-
quameu,molestietincidunt,justo.Phasellus
iaculis.Sedposuereloremnonipsum.Pel-
lentesquedapibus.Suspendissequamlibero,
laoreeta,tincidunteget,consequatat,est.
Nullamutlectusnonenimconsequatfacili-
sis.Maurisleo.Quisquepedeligula,auctor
vel,pellentesquevel,posuereid,turpis.Cras
ipsumsem,cursuset,facilisisut,tempuseu-
ismod,quam.Suspendissetristiquedoloreu
orci.Maurismattis.Aeneansemper.Viva-
mustortormagna,facilisisid,variusmattis,
hendreritin,justo.Integerpurus.
Vivamusadipiscing.Curabitur imperdiet tem-
pusturpis.Vivamussapiendolor,congueve-
nenatis,euismodeget,portarhoncus,magna.
Proincondimentumpretiumenim.Fusce
fringilla,liberoetvenenatisfacilisis,erosen-
imcursusarcu,vitae facilisisodioauguevitae
orci.Aliquamvariusnibhutodio.Sedcondi-
mentumcondimentumnunc.Pellentesque
egetmassa.Pellentesquequismauris.Donec
utligulaacpedepulvinarlobortis.Pellen-
tesqueeuismod.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentelit.Utlaoreet
ornareest.Phasellusgravidavulputatenulla.
Donecsitametarcuutsemtempormalesua-
da.Praesenthendreritaugueinurna.Proin
enimante,ornarevel,consequatut,blandit
in,justo.Donecfeliselit,dignissimsed,sagit-
tisut,ullamcorpera,nulla.Aeneanpharetra
vulputateodio.
Quisqueenim.Proinvelitneque,tristiqueeu,
eleifendeget,vestibulumnec,lacus.Vivamus
odio.Duisodiourna,vehiculain,elementum
aliquam,aliquetlaoreet,tellus.Sedvelit.Sed
velmiacelitaliquetinterdum.Etiamsapi-
enneque,convalliset,aliquetvel,auctornon,
arcu.Aliquamsuscipitaliquamlectus.Proin
tinciduntmagnasedwisi.Integerblanditla-
cusutlorem.Sedluctusjustosedenim.
Morbimalesuadahendreritdui.Nuncmauris
leo, dapibus sitamet, vestibulum et, commodo
id,est.Pellentesquepurus.Pellentesquetris-
tique,nuncacpulvinaradipiscing,justoeros
consequatlectus, sitamet posuerelectusneque
velaugue.Cras consectetuerlibero aceros.Ut
egetmassa.Fuscesitametenimeleifendsem
dictum auctor.In eget risusluctus wisiconva-
llis pulvinar.Vivamus sapien risus,temporin,
viverra in, aliquetpellentesque,eros.Aliquam
euismodliberoasem.
Nunc velit augue,scelerisquedignissim, lobor-
tiset,aliquamin,risus.Ineueros.Vestibu-
lumanteipsumprimisinfaucibusorciluctus
etultricesposuerecubiliaCurae;Curabitur
vulputateelitviverraaugue.Maurisfringilla,
tortorsitametmalesuadamollis,sapienmi
dapibusodio,acimperdietligulaenimeget
nisl.Quisquevitaepedeapedealiquetsus-
cipit.Phasellustelluspede,viverravestibu-
lum,gravidaid,laoreetin,justo.Cumsoci-
isnatoquepenatibusetmagnisdisparturient
montes,nasceturridiculusmus.Integercom-
modoluctuslectus.Maurisjusto.Duisvar-
iuseros.Sedquam.Craslacuseros,rutrum
eget,variusquis,convallisiaculis,velit.Mau-
ris imperdiet, metus at tristique venenatis, pu-
rusnequepellentesquemauris,aultriceselit
lacusnectortor.Classaptenttacitisociosqu
adlitoratorquentperconubianostra,perin-
ceptoshymenaeos.Praesentmalesuada.Nam
lacuslectus,auctorsitamet,malesuadavel,
elementumeget,metus.Duisnequepede,fa-
cilisiseget,egestaselementum,nonummyid,
neque.
Proinnonsem.Donecnecerat.Proinlibero.
Aliquamviverraarcu.Donecvitaepurus.
Donecfelismi,semperid,scelerisqueporta,
sollicitudinsed,turpis.Nullainurna.Integer
variuswisinonelit.Etiamnecsem.Mau-
risconsequat,risusnecconguecondimentum,
ligulaligula suscipiturna,vitaeportaodioer-
at quissapien.Proinluctus leoid erat.Etiam
massametus,accumsanpellentesque,sagittis
sitamet,venenatisnec,mauris.Praesentur-
na eros, ornarenec, vulputate eget, cursussed,
justo.Phasellus nec lorem.Nullam ligula ligu-
la,mollissitamet,faucibusvel,eleifendac,
dui.Aliquameratvolutpat.
Fusce vehicula,tortor etgravidaporttitor, me-
tusnibhconguelorem,uttempuspurusmau-
risapede.Integertinciduntorcisitamet
turpis.Aeneanametus.Aliquamvestibulum
lobortisfelis.Donecgravida.Sedsedurna.
Maurisetorci.Integerultricesfeugiatligu-
la.Seddignissimnibhamassa.Donecorci
dui,temporsed,tinciduntnonummy,viverra
sit amet, turpis.Quisque lobortis.Proin vene-
natistortornecwisi.Vestibulumplacerat.In
hachabitasseplateadictumst.Aliquampor-
tamiquisrisus.Donecsagittisluctusdiam.
Nam ipsumelit, imperdiet vitae,faucibus nec,
fringillaeget,leo.Etiamquisdolorinsapien
porttitorimperdiet.
Craspretium.Nullamalesuadaipsumut
libero.Suspendissegravidahendrerittellus.
Maecenas quislacus.Morbifringilla.Vestibu-
lumodioturpis,temporvitae,scelerisquea,
dictumnon,massa.Praesenteratfelis,por-
tasitamet,condimentumsitamet,placer-
atet,turpis.Praesentplaceratlacusaen-
im.Vestibulumnoneros.Utcongue.Donec
tristiquevariustortor.Pellentesquehabitant
morbi tristique senectus et netus et malesuada
famesacturpisegestas.Namdictumdictum
urna.
Phasellusvestibulumorcivelmauris.Fusce
quamleo,adipiscingac,pulvinareget,mo-
lestiesitamet,erat.Seddiam.Suspendisse
erosleo,tempuseget,dapibussitamet,tem-
puseu,arcu.Vestibulumwisimetus,dapibus
vel,luctussitamet,condimentumquis,leo.
Suspendissemolestie.Duisinante.Utso-
dales sem sit amet mauris.Suspendisseornare
pretiumorci.Fuscetristiqueenimegetmi.
Vestibulumeroselit,gravida ac,pharetrased,
lobortisin,massa.Proinatdolor.Duisac-
cumsanaccumsanpede.Nullamblanditelit
inmagnalaciniahendrerit.Utnonummyluc-
tuseros.Fusceegettortor.
Utsitametmagna.Crasaligulaeuurna
dignissimviverra.Nullamtemporleoporta
ipsum.Praesentpurus.Nullamconsequat.
Maurisdictumsagittisdui.Vestibulumsol-
licitudinconsectetuerwisi.Insitametdiam.
Nullammalesuadapharetrarisus.Proinlacus
arcu, eleifendsed, vehiculaat, conguesit amet,
sem.Sedsagittispedeanisl.Sedtincidunt o-
dioapede.Seddui.Nameuenim.Aliquam
sagittislacusegetlibero.Pellentesquediam
sem,sagittismolestie,tristiqueet,fermentum
ornare,nibh.Nullaet tellusnon felisimperdi-
etmattis.Aliquameratvolutpat.
Vestibulumsodalesipsumidaugue.Integer
ipsumpede,convallissitamet,tristiquevi-
tae,temporut,nunc.Namnonligulanon
lorem convallis hendrerit.Maecenas hendrerit.
Sedmagnaodio,aliquamimperdiet,portaac,
aliqueteget,mi.Cumsociisnatoquepenati-
busetmagnisdisparturientmontes,nascetur
ridiculusmus.Vestibulumnislsem,dignissim
vel,euismodquis,egestasut,orci.Nuncvi-
taerisusvelmetuseuismodlaoreet.Crassit
ametnequeaturpislobortisauctor.Sedali-
quamsemacelit.Crasvelitlectus,facilisis
id,dictumsed,portarutrum,nisl.Namhen-
dreritipsumsedaugue.Nullamscelerisque
hendreritwisi.Vivamusegestasarcusedpu-
rus.Utornarelectussederos.Suspendisse
potenti.Maurissollicitudinpedevelvelit.In
hachabitasseplateadictumst.
Suspendisseeratmauris,nonummyeget,
pretiumeget,consequatvel,justo.Pellen-
tesqueconsectetuereratsedlacus.Nullam
egestasnullaacdui.Doneccursusrhoncus
ipsum.Nuncetsemeumagnaegestasmale-
suada.Vivamusdictummassaatdolor.Mor-
biestnulla,faucibusac,posuerein,interdum
ut,sapien.Proinconsectetuerpretiumurna.
Donecsit ametnibhnecpurus dignissimmat-
tis.Phasellusvehiculaelitatlacus.Nullafa-
cilisi.Crasutarcu.Sedconsectetuer.Integer
tristiqueelitquisfelisconsectetuereleifend.
Crasetlectus.
Utcongue malesuadajusto.Curabiturcongue,
felisathendreritfaucibus,maurislacusport-
titor pede, nec aliquam turpis diamfeugiat ar-
cu.Nullamrhoncusipsumatrisus.Vestibu-
lumadolorseddolorfermentumvulputate.
Sednecipsumdapibusurnabibendumlobor-
tis.Vestibulum elit.Namligula arcu, volutpat
eget,laciniaeu,lobortisac,urna.Nammol-
lisultricesnulla.Crasvulputate.Suspendisse
atrisus atmetuspulvinarmalesuada.Nullam
lacus.Aliquamtempusmagna.Aliquamut
purus.Prointellus.
Vestibulumanteipsum primisinfaucibusorci
luctus et ultrices posuere cubilia Curae; Donec
scelerisquemetus.Maecenasnonmiutmetus
portahendrerit.Nuncsemper.Crasquiswisi
utloremposueretristique.Nuncvestibulum
scelerisquenulla.Suspendissepharetrasollic-
itudinante.Praesentatauguesitametante
interdum porta.Nunc bibendumaugue luctus
diam.Etiam nec sem.Sed eros turpis,facilisis
nec,vehiculavitae,aliquamsed,nulla.Cur-
abiturjustoleo,vestibulumeget,tristiqueut,
tempusat,nisl.
Nullavenenatisloremidarcu.Morbicur-
susurnaaipsum.Donecporttitor.Integer
eleifend,estnonmattismalesuada,minulla
convallismi,etauctorlectussapienutpu-
rus.Aliquamnullaaugue,pharetrasitamet,
faucibussemper,molestievel,nibh.Pellen-
tesquevestibulummagnaetmi.Sedfringilla
dolorveltellus.Nuncliberonunc,venenatis
eget,convallishendrerit,iaculiselementum,
mi.Nullamaliquam,felisetaccumsanvehic-
ula,magnajustovehicula diam,eucondimen-
tumnislfelisetnunc.Quisquevolutpatmauris
avelit.Pellentesquemassa.Integeratlorem.
Nammetuserat,laciniaid,convallisut,pul-
vinarnon,wisi.Crasiaculismaurisutneque.
Crassodales,semvitaeimperdietconsequat,
pede purussollicitudin urna,ac aliquammetus
orciinleo.Utmolestieultricesmauris.Viva-
musvitaesem.Aliquameratvolutpat.Prae-
sentcommodo,nislacdapibusaliquet,tortor
orci sodales lorem, non ornare nulla lorem quis
nisl.
Sedatsemvitaepurusultricesvestibulum.
Vestibulumtinciduntlacusetligula.Pel-
lentesquevitaeelit.Vestibulumanteipsum
primisinfaucibusorciluctusetultricespo-
suerecubiliaCurae;Duisornare,erateget
laoreetvulputate,lacusipsumsuscipitturpis,
etbibendumnislorcinonlectus.Vestibu-
lumnecrisusnecliberofermentumfringilla.
Morbinonvelitinmagnagravidahendrerit.
Pellentesquequislectus.Vestibulumeleifend
lobortisleo.Vestibulumnonaugue.Vivamus
dictumtempordui.Maecenasatligulaidfe-
liscongueporttitor.Nullaleomagna,egestas
quis,vulputatesitamet,viverraid,velit.
Utlectuslectus,ultriciessitamet,semper
eget,laoreetnon,ante.Proinatmassaquis
nuncrhoncusmattis.Aliquamlorem.Cur-
abiturpharetraduiatneque.Aliquameutel-
lus.Aeneantempus,felisvitaevulputateia-
culis,estdolorfaucibusurna,inviverrawisi
nequenonrisus.Fusceveldolornecsapien
pretiumnonummy.Integerfaucibusmassaac
nulla ornarevenenatis.Nullaquissapien.Sed
tortor.Phasellusegetmi.Crasnunc.Crasa
enim.
Quisque nisl.In dignissim dapibus massa.Ae-
neansemmagna,scelerisquenec,ullamcorper
quis,porttitorut,lectus.Fuscedignissimfa-
cilisistortor.Vivamusgravidafelissitamet
nunc.Nampulvinarodiovelenim.Pellen-
tesquesitametest.Vivamuspulvinarleonon
sapien.Aliquameratvolutpat.Utelementum
auctormetus.Maurisvestibulumnequevitae
eros.Pellentesquealiquamquam.Donecve-
nenatistristiquepurus.Innisl.Nullavelit
libero,fermentumat,portaa,feugiatvitae,
urna.Etiamaliquetornareipsum.Proinnon
dolor.Aeneannuncligula,venenatissuscipit,
porttitorsit amet, mattissuscipit, magna.Vi-
vamusegestasviverraest.Morbiatrisussed
sapiensodalespretium.
Morbicongueconguemetus.Aeneansedpu-
rus.Nampedemagna,tristiquenec,porta
id,sollicitudinquis,sapien.Vestibulumblan-
dit.Suspendisse ut augue ac nibh ullamcorper
posuere.Integereuismod,nequeateleifend
fringilla,augueelitornaredolor,veltincidunt
purusest idlacus.Vivamusloremdui, commo-
doquis,scelerisqueeu,tinciduntnon,magna.
Cras sodales.Quisque vestibulum pulvinar di-
am.Phasellustincidunt, leovitaetristique fa-
cilisis,ipsum wisiinterdum sem,dapibus sem-
pernulla velit vel lectus.Crasdapibus mauris
etaugue.Quisquecursusnullainlibero.Sus-
pendisseetloremsitametmaurismalesuada
mollis.Nullamidjusto.Maecenasvenenatis.
Doneclacusarcu,egestasac,fermentumcon-
sectetuer,tempuseu,metus.Proinsodales,
seminpretiumfermentum,arcusapiencom-
modomauris,venenatisconsequataugueur-
nainwisi.Quisquesapiennunc,variuseget,
condimentumquis,laciniain,est.Fuscefacil-
isis.Praesentnecipsum.
Suspendisseadolor.Namerateros,congue
eget,sagittisa,laciniain,pede.Maecenas
inelit.Proinmolestievariusnibh.Vivamus
tristiquepurussedaugue.Proinegestassem-
pertortor.Vestibulumanteipsumprimisin
faucibusorciluctusetultricesposuerecubil-
iaCurae;Classaptenttacitisociosquadl-
itoratorquentperconubianostra,perincep-
toshymenaeos.Vestibulumorcienim,sagittis
ornare,eleifendut,mattisat,ligula.Nulla
molestieconvallisarcu.Uterostellus,condi-
mentum at,sodalesin,ultricesvel,nulla.
Duismagnaante,bibendumeget,eleifend
eget,suscipitsed,neque.Vestibuluminmi
sedmassacursuscursus.Pellentesquepulv-
inarmollisneque.Fusceutenimvitaemauris
malesuadatincidunt.Vivamusaneque.Mau-
rispulvinar,sapienidcondimentumdictum,
quamarcurhoncusdui,idtemporlacusjusto
etjusto.Proinsitametorcieudiameleifend
blandit.Nunceratmassa,luctusac,fermen-
tumlacinia,tinciduntultrices,sapien.Prae-
sentsed orci vitae dolorsollicitudin adipiscing.
Crasaneque.Utrisusdui,interdumat,plac-
eratid,tristiqueeu,enim.Vestibulumante
ipsum primisin faucibusorci luctus etultrices
posuerecubiliaCurae;Etiamadipiscingeros
vestibulumdolor.Pellentesquealiquam,diam
eget eleifendposuere, augueeros porttitorlec-
tus,acdignissimduimetusnecfelis.Quisque
lacinia.Vestibulumtellus.Suspendissenec
wisi.Aeneanacfelis.Aliquamultricesmetus
etnulla.
Praesentsedestnonnibhtempusvenenatis.
Praesentrhoncus.Curabitursagittisestsit
ametneque.Sedcommodomalesuadalectus.
Phasellusenimtellus,temporut,tristiqueeu,
aliquameu,quam.Aeneanquisquamquis
wisigravidavehicula.Pellentesqueamassa
aleopretiumrhoncus.Suspendisseultrices.
Doneclaciniamalesuadamassa.Classapten-
ttacitisociosquadlitoratorquentperconu-
bianostra,perinceptoshymenaeos.Donec
pretiumornaremauris.Phasellusauctorer-
ategetenim.Integerscelerisque,feliseucon-
sequatfringilla,loremwisiultriciesvelit,id
vehiculapurusnullaegetodio.Nullammat-
tis,diamarutrumfermentum,odiosapien
tristiquequam,idmollistellusquaminodi-
o.Mauriseusapien.Donecaliquamloremsit
ametlorempharetralobortis.
Donecacvelit.Sedconvallisvestibulumsapi-
en.Vivamustemporlacussedlacus.Nunc
utlorem.Utettortor.Nullamvariuswisiat
diam.Etiamultricies,dolorsitametfermen-
tumvulputate,nequeliberovestibulumorci,
vitaefringillanequearcualiquetante.Lorem
ipsumdolorsitamet,consectetueradipiscing
elit.Quisquevenenatislobortisaugue.Sed
tempor,tellusiaculispellentesquepharetra,
pededuimalesuadamauris,velultricesurna
maurisacnibh.Etiamnibhodio,ultriciesve-
hicula,vestibulumvitae,feugiateleifend,fe-
lis.Vivamuspulvinar.Aliquamerat volutpat.
Nullaegestasvenenatismetus.Namfeugiat
nuncquiselitegestassagittis.Sedvitaefe-
lis.Inliberoarcu,rhoncusin,commodoeget,
auctorin,enim.Vivamussuscipitest.Nul-
ladapibus,magnavelaliquetegestas,massa
massahendreritlacus,acrutrumtellustellus
sitametfelis.Crasviverra.
Suspendisseeununc.Aliquamdignissimurna
sit ametmauris.Cras commodo, urna ut port-
titor venenatis, arcu metussodalesrisus, vitae
gravidasapienligulainest.Donecvulputate
sollicitudinwisi.Donecvehicula,estidinter-
dumornare,nibhtellusconsectetuerjusto,a
ultrices felis erat at lectus.In est massa, male-
suadanon,suscipitat,ullamcorpereu,elit.
Namnullalacus,bibendumsitamet,sagit-
tissed,temporeget,libero.Praesentligula.
Suspendissenulla.Etiamdiam.Nullaante
diam,vestibulumet,aliquetac,imperdietvi-
tae,urna.Fuscetinciduntlacusvelelit.Mae-
cenasdictum,tortornoneuismodbibendum,
pedenibhpretium tellus,atdignissim leoeros
egetpede.Nullavenenatiseleifenderos.Ae-
nean ut odio dignissim augue rutrum faucibus.
Fusceposuere,tellusegetviverramattis,er-
attellusportami,atfacilisissemnibhnon
urna.Phasellusquisturpisquismaurissus-
cipitvulputate.Sedinterdumlacusnonvelit.
Vestibulumanteipsum primisinfaucibusorci
luctusetultricesposuerecubiliaCurae;
Vivamus vehicula leoa justo.Quisquenec au-
gue.Morbimauriswisi,aliquetvitae,dignis-
simeget,sollicitudinmolestie,ligula.Indic-
tumenim sitametrisus.Curabiturvitaevelit
eudiamrhoncushendrerit.Vivamusutelit.
Praesentmattisipsumquisturpis.Curabitur
rhoncusnequeeudui.Etiamvitaemagna.
Namullamcorper.Praesentinterdumbiben-
dummagna.Quisqueauctoraliquamdolor.
Morbieuloremetestporttitorfermentum.
Nuncegestasarcuattortorvariusviverra.
Fusceeunulla utnulla interdum consectetuer.
Vestibulumgravida.Morbimattisliberosed
est.
Abstract
Thepurposeofthispaperistomodelethicalconsumptionbehaviour
basedonprice-dependentpreferences.Wemotivateethicalcon-
sumptionfoundedontheideathatethicalconsumerscompetefor
moralsuperiorityrelativeto theirpeersby purchasingmore expen-
sive ethicalconspicuous goods.An ethical consumermodel in which
consumers display moral consumption choices by purchasing ethical
conspicuousgoodsisdeveloped.Thisrequiresdefiningethicalcon-
spicuousgoods,sociallabels,andformalizingasetofassumptions
onprice-dependentethicalpreferences.Weshowthatanethical
utilityfunctionexistswithoutrelyingontheusualtransitivityas-
sumption.WeutiliseBlashke’sRollingTheoremtoshowourmain
result.
Keywords
Existence,Balshke’sRollingThoerem,EthicalUtility
1.Introduction
In “The Theory of the Leisure Class”, Veblen( [1], chapter 4, p.35-36)
recognizesthattheconsumptionof“moreexcellentgoods
1
”isevidence
ofwealthandthatfailuretodosobecomesamarkofinferiorityand
demerit.Veblen’stheoryofindividualconsumptionisatheorybased
onindividualsmaximizing“esteem”bydisplayingwealthinorderto
distinguishthemselvesfromothermembersofsociety.Onamacroe-
conomiclevel,hedescribestheevolutionofasociety(socialclasses)
basedontheideathatindividualscarveforesteemthroughthecon-
sumptionof conspicuousgoods.Veblenargues thatautility function,
which,isindependentofpricesisnotasuitableframeworkforthe
analysisofconsumptionbehaviorofconspicuousgoods.Implicitin
hisformulationoftheconsumer,hebelievesthatpricesdonotonly
1“Moreexcellentgoods”referstoproductqualityandluxurygoodsinthis
context.
DOI:10.4236/am.2021.124016Apr.8,2021252AppliedMathematics
P.Stiefenhofer
signal the scarcity of goods in thecoordination of consumptionalloca-
tions,buttheyalsoaffecttheindividual’spreferences.Veblen’stheo-
ryisoneofthemostinfluentialcritiquesoftheneoclassicaleconomic
model,partiallycriticizingitforitsrestrictionoftheutilityfunc-
tiontothecharacteristicsofgoods.Veblen’scritiqueinspiresanew
developmentofpricedependentutilityfunctionwithintheneoclassi-
calmodel.HisviewswerefirstanalyticallyintroducedinSamuelson
( [2],p.119-121),who formulates amodelof conspicuousconsumption
withpricedependent utilityfunctions.Inthismodel,Samuelson con-
sidersaprice-parameterizedutilityfunctionandaconspicuousgood
representedbygold.Samuelson’sseminalworkinitiatestworesearch
directionsofprice dependent preferences.Oneresearch linecontinues
to search for the motivation of pricedependent preferences in the con-
textof consumptionof conspicuousgoods,andthe otherresearchline
focusesonthedemandformoneyandotherfinancialassets.
Herewepursue anew developmentof pricedependentpreferences in
the context of ethically conspicuous goods.At variance to the existing
literatureonpricedependentutilityfunctions,weconsiderVeblen’s
originalphilosophyofesteemmaximization,whichyetlacksarigor-
ousformulationwithintheneoclassicalmodel.Thesearchforprice
dependentutilityfunctionsinthecontextoftheneoclassicaltheory
beginswithScitovsky[3]providingtherationalefortakingpricesas
an index ofproduct quality.He states thatjudging qualityby itsprice
isrationalifconsumersareinformedaboutproductqualities.How-
ever,Scitovsky doesnotestablishtheconditionsofrationalbehavior,
insteadfocusingonpriceeffects,alsoknownasVebleneffects,where
prices and quantity demandedare positively correlated.Veblen effects
arealsoanalyzedinLeibstein[4]andAlcalyandKlevorick[5]with
Kalman[6]andPollak[7]beingmathematicallythemostrigorous.
Thisliteratureprincipallyfocusesonthemotivationforpricedepen-
dentutilityfunctionsandthederivationandimplicationsofwealth
effects by considering variations of theSlutsky equation.Pricedepen-
dentutilityfunctionshavealsobeenintroducedintothe“NewCon-
sumer Theory”,alsoknownas theLancaster model[8],in thecontext
of judgingquality by priceand snobappeal[5], wherethe priceenters
theutilityasoneofthecharacteristicsofthegoods.Thesepaper-
sestablishanalyticallytheconditionsofpositivecorrelationbetween
pricesanddemandforgoods.
Inthispaper,however,weareprimarilyinterestedinmotivating
ethicalconsumptionbyhypothesizingasocietyinwhichethicalcon-
sumersderiveesteemfromdisplayingtheirmoralconsumption choices.
We show that a price dependent ethical utility function exists.InSec-
tiontwowecharacteriseethicalconspicuousgoodsandformalisethe
conceptofasociallabelandtheideaofconspicuousethics.Section
three introduces the axioms of rational ethical consumption behaviour
andstatesthemainresults.Sectionfourisaconclusion.
2.TheEthicalConsumptionModel
Thetheoryonpricedependentpreferencesissparse.Thevarious
hypothesesmotivatingthestudyofpricedependentpreferencesare:
judging thequality ofagoodbyits price[1],“Snob appeal”of agood
[3],andtreatmentofmoneyandotherfinancialassetsintemporal
equilibriummodels [2].In thispaper, weconsidera newhypothesis for
introducingpricedependentpreferencesintoconsumertheory.Inour
model,pricesperformtheroleofinformingconsumersaboutethical
DOI:10.4236/am.2021.124016253AppliedMathematics
P.Stiefenhofer
production.Weassumethereexistsagroupofsociallyresponsible
consumersrepresentedbyanindexi=1,...,mwhodonotonlycare
abouttheirownconsumptionofgoodsl=1,...,n,withconsumption
bundlex
i
R
n
+
,buttheyalsocareaboutcertainethicalandsocial
conditionsj=1,...,kregardingproductionanddistributionofthese
goods.Associatedwithaconsumptionbundlethereisapricesystem
pR
n
+
.Lettheethicalconsumerpricepbedefinedbytheglobal
marketpricep
M
plusapremiump
E
suchthat
p= p
M
+p
E
p
min
,(1)
wherep
min
> 0andP
E
0isapremium(R.Dragusanuand
Nunn[9]),Figure1onp.219-220).Itisassumedthattheethi-
calpricesystemp=(p
1
,...,p
n
)R
n
++
satisfiesthenormalization
S:= {pR
n
++
: p
n
= 1}as the numeraire convention.This price nor-
malization is usefulin the calculation of derivatives.Moreover relative
pricesleadtodemandfunctionswhicharehomogeneousofdegreeze-
ro.Such functionsprovide meaningfulwelfareanalysis [7][10].Inour
modelpricesdonotonlysignalthescarcityofresourcesintheireffi-
cientallocationprocessbutalsoallthesethingsourconsumerscare
aboutregardingethicalproductionanddistribution.Associatedwith
anethicalpricesystemptherearel= 1,...,nethicallyproducedand
distributedconsumptiongoods.Wenowcharacterizeaconsumption
goodx
l
i
R
+
intermsofethicalvaluessuchasnochildlabor,envi-
ronmental friendlyproduction,minimum wages, safeworkconditions,
gender equality, humanrights, etc..While some of these ethicalvalues
arequantifiable,othersareclearlynot.Hence,weintroduceaninfor-
mationarraye
l
collectingthewordsandsymbolsaboutproduction
conditionsassociatedwithagoodx
l
i
.Weassumethateachgoodlis
characterizedbyj=1,...,kethicalvaluese
lj
=(e
l1
,...,e
lk
)
2
.Each
ethicalvalueisindexedbyj1,...,kandisassumedtobeknownto
aninformedconsumer.Thecollectionofallethicalvaluesassociated
withaconsumptionbundlex
i
isaninformationarraygivenby
e=
e
11
...e
1k
.
.
.
.
.
.
.
.
.
e
n1
...e
nk
.(2)
Itfollowsthataconsumptiongoodischaracterizedbyaquantifi-
ablephysicalpropertyx
l
i
andanassociatedsetofethicalvaluese
l
,
providingadescriptionofproductionanddistributionconditionsre-
gardingenvironment,health,gender,animalwell-being,etc.Aneth-
icallyproducedgoodishencedenotedbyx
l
i
|
e
l
R
++
.Notethat
x
l
|
e
l
6=x
l
|
e
l
0
fore
l
6=e
l
0
.Ourcharacterizationofgoodsstatesthat
twophysicallyidenticalgoodsproducedunderdifferentethical condi-
tions are“nearly-identical”goods.The physically identicalgoods only
differinthewaytheyareproduced.Ethicalconsumersareinformed
consumerswhocandistinguishbetweensuchgoods.Asociallabel
conveysthisinformationtoconsumers.Ourdefinitionofaconsump-
tiongoodisageneralizationofthecharacterizationofgoodsby[11],
whicharedefinedbytheirphysical,temporal,andspatialnature,to
2Notethate
l
isnotaquantityinR
k
asintheLancastermodel,butade-
scriptivelistofcharacteristics.Hence,itshouldnotbeconfusedwiththe
mathematicaldefinitionofavector,i.e.,theinnerproductoperationdoes
notapply.Inessencee
l
isastringofinformation.
DOI:10.4236/am.2021.124016254AppliedMathematics
P.Stiefenhofer
goodswhichalsodependonasetofethicalvalues.Wedenotean
ethicalconsumptionbundlex
i
|
e
by
χ
i
∈X
i
,(3)
whereX
i
R
n
+
istheconsumptionspacecharacterizedbyethical
attributese.Welabelgoodsχ
i
∈X
i
satisfyingsuchcharacteristics
asethicalconspicuousgoods.Weformalizetheideaofconspicuous
goodsinthesubsequentthreedefinitions.
Definition1(Ethicalconspicuousgoods).Anethicalconspicuous
consumptionbundleχ
i
∈X
i
isdefinedbyaconsumptionbundlex
i
R
n
+
characterizedbyanarrayofdescriptiveethicalvaluese.
Ontheproductionsideproducersseekforsociallabelcertification
inordertoconveyinformationaboutethicalproductionanddistri-
butionstandards.Using(1)and(3)weintroduceadefinitionofa
voluntarysociallabelthatisbasedonapricesignalp(p
M
,p
E
)which
informsconsumersi=1,...,maboutethicalproductionanddistri-
butionprocesses,andaclassofethicallycharacterizedcommodities
χ
i
∈X
i
,whichfurther informsconsumers descriptively aboutthe way
goodsareproduced.
Definition2(Voluntarysociallabel).AvoluntarysociallabelSis
definedbyapair(p
i
)consistingofanethicalpricesystemp∈S
andcommoditybundlex
i
R
n
characterizedbyasetofethicals-
tandardserepresentedinwordsandsymbols,which,isintendedto
inform consumersabout ethical production and distributionstandard-
s.Aconsumeri=1,...,mwho’sconsumptionchoicesareinformed
byasociallabelS,i.e.,
S
i
:= (p
i
) ∈S×X
i
(4)
belongstotheclassofethicalconsumers.
AvoluntarysociallabelS
i
consistsofanethicalpriceandethical
conspicuouscommoditypair(p
i
)whichbelongstothesetS×X
i
.
Definition2allowsustoconsideragroupofinformedconsumers,
where S
i
represents that Sis known to i= 1,...,m.These consumers
haveethicalpreferencesinthesensethattheycareabouttheway
goodsareproducedanddistributed.Consumerssatisfyingdefinition
2areclassifiedasethicalconsumers.Itremainstocharacterizetheir
consumptionbehavior.Webeginbymotivatingethicalconsumption
behavior.
Definition3(Conspicuousethics).Conspicuousethicsreferstoan
ethicalconsumptionbehaviorwhereaninformedconsumerS
i
,for
i=1,...,n,expressessuperiorethicalresponsibilitytowardssociety
relativeto othermembersofsociety by purchasing ethicallyproduced
anddistributedgoodsχ
i
atethicalpricesp.Itisassumedthatethi-
cal consumers derive esteem from displaying their social responsibility
through the consumptionof ethically conspicuous goods.Positive eth-
icalconsumptionissatisfiedforallpairs
(p
i
) S
i
.(5)
Anethicalconsumeralsoexpressessuperiorethicalresponsibilityto-
wardssocietybyboycotting theconsumptionofunethically produced
anddistributedgoods.Negativeethicalconsumptionissatisfiedif
eitherp6= porx
i
6= χ
i
.(6)
DOI:10.4236/am.2021.124016255AppliedMathematics
P.Stiefenhofer
Ethicalconsumersbasetheirconsumptiondecisionsonthebasis
ofethicalvalues,suchashumanrights,environmentallyfriendlyand
sustainableproduction,andanimalwell-being.Wehypothesizethat
theyexpressmoralsuperioritytowardssocietyviapositiveandneg-
ativeconsumptionofethicalconspicuousgoods.Weconsiderethical
consumerswhoderiveesteemfromtheconsumptionof“moreexpen-
sive”ethicalconspicuousgoods.ThisrelatesourmodeltoVeblen[1]
whodiscusses theevolution ofsociety basedonthecompetitionofes-
teem.Veblenalsointroducestheideaofpricedependentpreferences.
This is similar toour model, the motivation for priced dependent pref-
erences,however,isdifferentandanexistencetheoremisabsent.
Wecharacterizetheconsumer’spreferenceordering
q
byanethi-
calpriceindexqassociatedwithanethicalmarketpricepricep.Itis
assumedthatthepricedependingpreferenceordering
q
isunaffect-
edbyaproportionalchangeinallpricesp[7].Moreover,weconsider
normalizedprices q,hence,our characterization oftheconsumer pref-
erence is atvariance to Kalman,who assumes a preferenceordering of
theform
p
overaconsumption-marketprice space(x,p) R
n
+
×R
n
++
,
wherexisacommoditybundle([6]:A.1,p.498).Stiefenhoferand
Zhang [12] consider aclass of price dependent ethical utility functions.
Wewanttorepresentpreferences,whichdonotonlydependon
ethicalconsumptionbundlesbutalsoonrelativeprices,whichinform
consumersaboutthewaygoodsareproduced.Wearegoingtocon-
siderutilityfunctionsoftheformu
i
(χ
i
,q).Lettheopennormalized
pricesimplexbedenotedby
S:= {pR
n
++
:
n
X
k=1
p
k
= 1},(7)
withitsclosuresimplexdefinedby
¯
S:= {pR
n
+
:
n
X
k=1
p
k
= 1}.(8)
Wenowformalizethehypothesisthatconsumersdonotonlyhave
preferencesforthephysicalpropertiesofgoods,buttheyalsocare
aboutthewaygoodsareproduced.Henceby(3)and(8)wedefined
apreferencerelationoftheform
(q,χ)
overthepreferenceordering
space(q,χ
i
)
¯
S×X
i
,where
u
i
:
¯
S×X
i
R(9)
istheprice-dependentethicalutilityfunction.Stiefenhofer[13]es-
tablishesthegeometricconditionsofsmoothethicalutilityfunction-
s.StiefenhoferandZhang[12]provideanexampleofapricede-
pendentethicalutilityfunction.Wecannowformulateanethi-
calconsumptionmodel,whereproductionisimplicitlyformulated
throughareallocationofinitialendowments.Letanethicalcon-
sumeri=1,...,mbeendowedwithavectorofinitialendowments
ω
i
|
e
= (ω
1
i
|
e
1
,...,ω
n
i
|
e
n
)
i
|
e
R
n
++
.Wedenoteω
i
|
e
byω
i
andΩ
i
|
e
byΩ
i
3
.
Definition4.Thedisentanglement ofthe ethicalcommodity market
pricepintoapriceindexqisgivenbyamap
s: S→S(10)
3Wedonotintendtoexplicitlymodelethicalproductioninthispaper.We
are,however,awarethatthisisanotherinterestingproblem.
DOI:10.4236/am.2021.124016256AppliedMathematics
P.Stiefenhofer
definedbys(p) :=
p
k
P
n
k=1
p
k
fork= 1,...,n.
3.ExistenceofanEthicalUtilityFunction
Assumption1(Ethicalpreferences).
a)(i)Forallx|
e,p
,y|
e,p
,eitherx|
e
p
y|
e
ory|
e
p
x|
e
.(ii)
x|
e,p
,y|
e,p
,z|
e,p
with x|
e,p
6= z|
e,p
implies αx|
e
+(1α)y|
e
p
y|
e
for0<α<1.(iii)Thepreferencerelation
p
iscontinuousin
x|
e
andp∈S.(non-transitivity,Sonnenschein(1971).
b)If x|
e
p
y|
e
then x|
e
p
y|
e
for allλ>0, (preference orderings
dependonrelativeprices).
c)(i) x|
e
p
y|
e
x|
e
p
FT
y|
e
, and(ii) x|
e
p
y|
e
x|
e
p
FT
y|
e
(non-negativepriceeffectonpreferences).
(a)(iii)SimilarlytoSonnenschein[14]weintroducetheconcept
ofprice-continuouspreferences.WefollowSonnenschein’sapproach,
which,togetherwithastrictconvexityassumption(ii)andacom-
pletenessassumption(i)onthepricedependentpreferencerelation
issufficienttoestablishrationalbehaviorintheconsumptionspace
X
i
.Hence,inourmodelofethicalconsumption,weareabletodis-
penseoftheusualtransitivitycondition.(b)statesthatpreferences
dependonarelativepricesystem.ThisisatvariancetoKalman[6].
However,asimilarconditionwithitswelfareimplicationsisalsodis-
cussedinPollak[7].(c)isaveryspecificassumptionwhichallows
modelingofconspicuousconsumptionofethicallyproducedgoods.It
allows for a positive correlation between prices and demand for ethical
consumptiongoodsandtheboycottofunethicallyproducedgoods.
Theassumptions1allowustomodelasociallabelS
i
asintro-
ducedindefinition2intheutilityoftheethicalconsumer.First,we
observethatbythecharacterizationofconsumptiongoodsthrough
thecharacterizationofX
i
ethicalvaluesentertheutilityofthecon-
sumerthroughacharacterizationofethicalpreferencesdistributed
overanethicalconsumptionspace.Second,thepricesignalprovid-
edbytheethicalmarketpricepenterstheutilityoftheconsumer
throughtheassumptiononthepreferencerelationallowingforthe
positivecorrelationbetweentheethicalpricesignalanddemandfor
ethicalconsumptiongoods.Wenowintroduceourmodel.
Definition5(Theethicalconsumermodel).Consideragroupof
informedconsumersS
i
,fori=1,...,msatisfyingdefinition2.Let
anethicalconsumeri=1,...,mbeendowedwithavectorofinitial
endowmentsω
i
i
,andlethissetoffeasibleconsumptionallocations
bedefinedbyB
i
(p
i
):={(p
i
)∈S×R
n
+
:p·χ
i
p·ω
i
}.Then
foranyethicalmarketpricesystemp∈Sandpricedisentanglement
s(p)intoanethicalpriceindexqgivenindefinition4,theobjective
oftheconsumerisformalizedas
argmax
(χ
i
∈B
i
(p
i
))
u
i
(χ
i
;s(p),p).(11)
Lemma2.Theindifferenceset
I(
p
) := {((x|
p
,y|
p
) X×S: x
p
yy
p
x},where XR
n
+
×R
n
+
isclosed.
Fromnow,wesimplifynotationwherenotconfusionarises.We
assumethatpricesandethicallycharacterizedgoodsareunderstood
fromthecontext.
DOI:10.4236/am.2021.124016257AppliedMathematics
P.Stiefenhofer
Proof.WedecomposetheindifferencesetIintothetwosetsA(
p
)
andA(
p
)where
A(
p
) := {(x|
p
,y|
p
) X×S: x
p
y}(12)
isaconsumptionbundlepairallocationsetassociatedwiththeprice
dependentpreferencerelation
p
andsimilarly
A(
p
) := {(x|
p
,y|
p
) X×S: x
p
y}(13)
isassociatedwiththepricedependentpreference
p
.
Step1:Pickanypoint(ˆx|
p
,ˆy|
p
)notinA(
p
).Thenthereisaset
B(
p
) := {(x|
p
,y|
p
) X×S: y
p
xx
p
y}(14)
andaset
ˆ
B(
p
) :=
y|
p
R
n
+
×S: y
p
xx
p
y
(15)
associatedwith
p
suchthatˆy|
p
ˆ
B(
p
).Byopennessoftheset
ˆ
B(
p
)wecanconstructaneighborhoodB
y|
p
)
=ky|
p
ˆy|
p
k≤ε
forsmallεR
++
.ByBlaschke’stheorems(p.113-117,[15]),wenow
show that B
y|
p
)
is the largestset contained in some finiteconvex set
in
ˆ
B(
p
).Thetheoremsimplyaconstructionof aregularizedconvex
setin
ˆ
B(
p
)by
Conv(f
1
(y|
1
p
),...,f
m
(y|
m
p
))
=
(
m
X
i=1
λ
i
f
i
(y|
i
p
) : λ
i
0,
m
X
i
λ
i
= 1
)
(16)
where fis smooth andconvex function withthe imageof
P
m
i
f
i
com-
plete.Blaschke’srollingtheoremsthenimplythereexistsalargest
SConv(f
1
(y|
1
p
),...,f
m
(y|
m
p
))withradiusr=(supk)
1
wherekis
the curvature such thatk(S) <k(Conv(f
1
(y|
1
p
),...,f
m
(y|
m
p
))) atsome
pointP.Hencewechooseεrandobtain
B
y|
p
)
S
y
ˆ
B(
p
)(17)
For each iwe have that f
i
(y|
i
p
)
y|
p
R
n
+
×S: y
p
ˆxˆx
p
y
.
Alternativelywehavethatˆx|
p
belongstoanopensetC(
p
)=
x|
p
R
n
+
×S: f
i
(y|
i
p
)
p
ˆx
.Thenforeachiweconstructaneigh-
borhood B
i
x|
p
)
=kx|
p
ˆx|
p
k≤εwith centerˆx|
p
andradius εR
++
.
ByasimilarconstructionasaboveusingBlaschke’srollingtheorems
and
m
i=1
B
i
x|
p
)
= B
x|
p
)
weobtainforalli
ˆx|
p
∈B
x|
p
)
⊂B
i
x|
p
)
S
x
C(
p
),(18)
which shows that for each iwe have that f
i
(y|
i
p
)
ˆ
B(
p
) by the strict
convexityassumption.Weconstruct
Bx|
p
,ˆy|
p
) = B
x|
p
)
×B
y|
p
)
.(19)
Consideranypair(x|
p
,y|
p
)∈Bx|
p
,ˆy|
p
)thefromabove,wehave
thatˆy|
p
∈B
y|
p
)
ˆ
B(
p
)andthusx,y)isnotinA(
p
).Itfollows
thatBx|
p
,ˆy|
p
)doenotsatisfy
p
.Needtoshowthe oppositerelation.
This follows from asimilar analysisas above.SinceA and Bare closed
sets itfollowsthat its intersection Iisalso closed.Thiscompletes the
proof.
DOI:10.4236/am.2021.124016258AppliedMathematics
P.Stiefenhofer
Theorem3(Existenceofanesteemfunction).Letassumptions1
hold.Thereexistsacontinuouspricedependentethicalutilityfunction
u
i
:R
n
++
R,forall(p
i
)S
i
andi=1,...,m,suchthatif
χ
i
∈B
i
(p,w
i
),thenu
i
(p
i
)=maxu
i
(p
i
)ifandonlyifχ
i
=
f(p,s(p),w
i
),wherefisderivedfromR(p).
Proof.Step1Weshowthatthereexistsacontinuousmap-
pingk:XRderivedfromthepreferencerelation
p
.
LetX:= R
n
+
×R
n
+
×Sbe aBanachspace equippedwith aquasi
metricd(x|
p
,y|
p
):=
y|
p
ky|
p
k
kx|
p
,y|
p
k.Aconsumerisindifferent
forallpointsI:= R(p)R
1
(p).Wenowdefine
m(x|
p
,y|
p
) :=
(x|
p
,y|
p
) argmin
y|
p
ky|
p
k
k(x|
p
,y|
p
),(z|
p
,w|
p
)k(20)
forall(z|
p
,w|
p
) ∈I.m(x|
p
,y|
p
)iscontinuessinceIisaclosed
set.Closednessof Ifollowsimmediately fromthe continuity and
closednessofR(p)andR
1
(p).Hencedefining
k(x|
p
,y|
p
) = m(x|
p
,y|
p
)(21)
itfollowsthatthemappingkiscontinuous.Moreover,itholds
thatforall(x|
p
,y|
p
) X\I
k(x|
p
,y|
p
) 6= 0.(22)
(i)To showthatk(x|
p
,y|
p
) >0weonlyneed torestrict Equation
(20)topointx|
p
P(y).(ii)Toshowthatk(x|
p
,y|
p
)<0we
onlyneedtorestrictEquation(20)topointy|
p
P(x).(iii)
ItfollowsthattherestrictionofEquation(20)forallpoints
(x|
p
,y|
p
)notinP(y)×P(x)impliesthat
k(x|
p
,y|
p
) = 0.(23)
Hence this holds for all (x|
p
,y|
p
) ∈I.(iv) We need to show that
Equation (20) is a quasi metric.Hence, we translate the original
coordinatesystemthroughthepointx|
p
suchthatunderthe
translationx|
p
isanullvector.ThenitfollowsthatEquation
(20)generatesnegativevaluessince
y|
p
ky|
p
k
= 1.
Step2Weshow that acontinuous parameterized utility function ex-
istsandthatthemodeloftheconsumeriswelldefined.To
showthis let’sdenoteby B
i
=
x|
p
R
n
+
×S: p·x|
p
w
i
the
consumer’ssetoffeasibleconsumptionallocationsanddefine
u(x|
p
;s(p)) := min
y|
p
B
k(x|
p
,y|
p
)(24)
BycontinuityofkandtheconstructionofB
i
itfollowsthatu
iscontinues.Wecannowformulatethemodeloftheconsumer.
Weneedtoshowthatifx|
p
B
i
(p),thenu
i
(x|
p
;s(p))=
maxu
i
(x,x|
p
)ifandonlyifx|
p
=f(p;s(p),w
i
).Supposethat
DOI:10.4236/am.2021.124016259AppliedMathematics
P.Stiefenhofer
x|
p
=f(p;s(p),w
i
).Thenitholdsthatk(x|
p
,y|
p
)0forall
y|
p
B
i
(p)bystep1.Bydefinition24weobtain
u(x|
p
;s(p)) := min
y|
p
B
k(x|
p
,y|
p
) = 0(25)
forally|
p
= x|
p
sincek(x|
p
,x|
p
) = 0bystep1.Oncontraryx|
p
maximizesu
i
(x|
p
;s(p))forallx|
p
B(p)since
u(x|
p
;s(p)) := min
y|
p
B
k(x|
p
,y|
p
) = k(x|
p
,x|
p
) = 0.(26)
Supposeu(x|
p
;s(p))=max
xB(p)
u(x|
p
;s(p))andthatx|
p
B(p).Wewillshowthatx|
p
=x|
∗∗
p
,assumingthatx|
∗∗
p
=
f(p;s(p),w
i
).Fromabove,sincex|
∗∗
p
=f(p;s(p),m),wehave
that
u(x|
∗∗
p
;s(p)) =max
xB(p)
u(x|
p
;s(p)) = u(x|
p
;s(p)) = 0.(27)
Itthenfollowsthatk(x|
p
,y|
p
)0foreachy|
p
B(p)and
k(x|
∗∗
p
,y|
p
)0foreachy|
p
B(p).Thiscanbereformulated
asx|
p
R(y)andx|
∗∗
p
R(y)foreachy|
p
B(p)sothat
bothx|
p
andx|
∗∗
p
satisfythedefinitionoff(p;s(p),w
i
).Hence
x|
p
= x|
∗∗
p
.
4.Conclusion
Inthispaperweestablishtheconditionsofrationalethicalconsump-
tionbehaviourand show thataprice dependentethical utility function
exists.Weproposeamodelofconspicuousethicsinwhichconsumers
arenotutilitymaximisersintheusualsensebutcompeteforesteem
relativeto othermembersinsociety.Weformulatea modelofesteem
maximization,whereesteemisderivedfromdisplayingmoralsuperi-
oritytowardssocietythroughtheconsumptionofethicalconspicuous
goods.Ethical consumersbelongto aclass ofinformedconsumers who
retrieveinformationviasociallabelsandethicalpricesystemswhich
donotonlyperformtheroleofefficientresourceallocationbutalso
informconsumers aboutthe waygoodsare producedanddistributed.
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