Product Costing and Pricing under Long-Term Capacity Commitment

Transcription

1 MAR Volue Foueen 00 Poduc Cosng and Pcng unde Long-e Caac Coen Ra D anke n Hwang enda K Msha he Unes of eas a Dallas Absac: We deelo a odel o anale oal oduc-cosng and cng decsons n a dnac nfoaon enonen unde long-e-caac coen he aal of new nfoaon abou deand and cos aaees each eod akes he oble cole he oal ces and caac choces n ou odel canno be decouled as n anke and Hughes 994 sngle-eod odel he oal ces ae based on oduc coss ha ae adused each eod o eflec changes n eeced aable coss as well as ulaon of fed ac esouces he chage fo each fed esouce s onooncall nceasng n he eeced deand fo ha esouce n each sae gen he oal caac choce he aeage oal ces acoss eods and saes ae sla o anke and Hughes 994 benchak ces Fnall, we nesgae a wo-eod eson of he odel o eloe he oal of cang dle caac he oal oduc-cos chage fo fed caac s scl less n he fs eod han n he second eod when he f eecs deand gowh Kewods: oduc cosng; fed coss; cng; caac RODUCO hs ae anales he ssue of oal oduc cosng and cng when a onools akes a long-e coen o he caac of ac esouces oh econoc and elean cos analses n anageal accounng conclude ha coed fed coss such as caac coss should no be chaged o oducs because hese sunk coss ae elean fo decson akng Howee, os fs chage caac coss o oducs and use he esulng coss fo cng decsons Sh and Sud 995; Gondaan and Anhon 983 Ac-based cosng adocaes ecoend chagng coed coss o oducs based on cause-andeffec elaonshs Cooe and Kalan 987 hs acce of chagng coed fed coss o oducs and hen usng such oduc coss o ce he oducs leads anageal accounng eseaches o eloe he econoc aonale fo such acces he anageal accounng leaue offes seeal easons fo allocang fed coss hese nclude ooun coss Kalan and hoson 97; Kalan and We hank sena acans a he 00 AAA Manageen Accounng Secon Confeence n Ausn, eas, he 00 Euoean Accounng Assocaon Congess n Coenhagen, and he Unes of eas a Dallas AM Reseach Woksho We ae gaeful o an anonous efeee fo consuce coens and helful nsghs

2 80 ounal of Manageen Accounng Reseach, 00 Wela 974; Mlle and uckan 987; alachandan and Sndh 987; anke e al 988, anageal ncenes Zean 979, and caac choces alachandan e al 987; Whang 989 anke and Hughes 994 sud how he coed ac esouce coss affec oal caac and cng decsons, as well as wha nfoaon decenaled decson akes need o leen hose decsons n a sngle-eod odel he show ha he oal cng ule ncooaes acbased oduc coss ha nclude chages fo coed esouces Moe ecenl, seeal aes hae eended hs lne of eseach alakshnan and Saaakshnan 996 and alachandan e al 997 consde had caac consans alakshnan and Saaakshnan 00 and anke and Hansen 00 coae he efoance of dffeen heuscs fo he on caaclannng and cng oble Gö 00 ealuaes he efoance of dffeen heusc ules n a wo-eod lannng odel ha consdes ce changes eued o achee bee ulaon of coed caac leels Ou ae s closel elaed o anke and Hughes 994, alakshnan and Saaakshnan 00, and Gö 00 alakshnan and Saaakshnan 00 consde a sngle-eod odel wh wo oducs, wo saes hgh and low deand, had caac consans, and deensc deand deand s coleel eealed afe caac decsons n he odel, he fs oduc des all deand fo caac because nesng n caac o oduce he second oduc s unofable Unde hese assuons, he show ha deand aaees us be known o desgn he oal oduc-cosng sse and ha ac-based coss ae no suffcen o se ces as n anke and Hughes 994 sngle-eod odel Gö 00 consdes he caac-lannng and cng oble unde uncean deand n a sngle-eod odel wh boh had and sof caac consans He fnds ha caac coss ae elean onl when he caac-lannng and cng decsons ae ade unde he sae nfoaon abou he sae of naue When he f has oe nfoaon a he e of he cng decson, he f uses agnal-cos cng Ou eseach eends and coleens hs eale eseach b elang soe of he assuons and odng seeal new nsghs We eend he anke and Hughes 994 faewok and deelo a geneal uloduc, uleod odel of long-e caac coen n a dnac nfoaon enonen whee new nfoaon abou deand, cos, and so ces aes each eod We anale how oal oduc coss dffe acoss eods when he f chooses caac of dffeen ac esouces a he ouse bu new nfoaon abou deand, coss, and so ces becoes aalable fo he cng decson n each subseuen eod n ou odel, esouce chages o deene oal ces deend on he shoage obabl and can be hghe, lowe, o eual o he ac-based full cos Conseuenl, deand aaee and ac-based full-cos nfoaon ogehe s no suffcen Aesh e al 990 fo he oal cng decson n ou odel We show ha he oal chage fo coed esouces dffes acoss eods b a faco ha nceases onooncall wh he eeced deand fo he esouce n each eod hs feaue dsngushes ou esuls fo hose of anke and Hughes 994 n whch ce based on full cos s oal n conas, when he f us co o a fed ce fo each oduc oe he ene hoon, we oban a benchak soluon sla o ha fo he anke and Hughes 994 sngle-eod odel Moe oanl, he aeage of he eeced oal ces when ces flucuae wh new nfoaon euals he anke and Hughes 994 benchak ce based on full coss hs esul a aonale he ecal fndng ha fs use ac-based full coss n he cng decsons We seculae ha ahe han sl basng ces on full coss,

3 anke, Hwang, and Msha 8 fs a fs coue benchak ces based on full coss, and hen adus hese ces heuscall o eflec udaed nfoaon on deand and cos condons see also, Aknson e al 995, 34 Ou sud adds o eale eseach n hee was Fs, we lnk sho-e cng and oduc-cosng decsons n a uleod dnac nfoaon enonen o long-e benchaks based on full coss Second, we show ha he oal sho-e chage fo coed caac esouces nceases wh he eeced deand Fnall, we denf when he f should ca dle caac and ode heoecal suo fo saegcall chagng less han he full cos of caac o oducs when deand gowh s eeced he eande of hs ae s oganed as follows he second secon deelos a uloduc, uleod caac-lannng and cng odel he hd secon esens he analcal esuls fo oal cng and oduc-cosng decsons n he uleod seng A secal case of he uleod odel elaed o he oal of dle caac unde deand gowh eecaons aeas n he fouh secon he las secon concludes he ae wh a bef sua of he esuls LOG-ERM CAPACY COMMME MODEL We consde a onools f oducng oducs ndeed b,,, n each of eods ndeed b,,, he f has a Leonef oducon funcon ha cones nu esouces n each eod no he ouu eco,, K, hee ae wo es of esouces, coesondng o aable and fed coss he fs e, such as soe dec aeal, dec labo, and aable oehead, s acued on an as-needed bass he cos of hese aable nus s denoed b fo each un of oduc n eod Fo he second e of esouce, he f us co a he begnnng of he lannng hoon o leels of caac,,, K,, ha wll be aalable houghou he lannng hoon a a cos e un of caac,,, K,, n each eod hese coss a flucuae acoss eod due o dffeences n anenance, nsuance, lan anageen, salaes, and ohe caac-elaed ac coss he f can acue an addonal aoun of an esouce on an as-needed bass a a eu on he so ake, esulng n a cos of e un of he esouce We eue he e ane eeced alue E[ ] oe all eods and saes o be geae han E[ ], bu unlke anke and Hughes 994, we allow o be less han n soe eods Fgue below shows he e lne of eens fo ou odel he f faces uncean abou he fuue sae of he econo ha a affec s cos and deand funcons n each of he eods A he begnnng of each eod, he FGURE e Lne of Eens egnnng 0 Peod F ses caac fo fed esouces Each eod,,, F obsees sae of ec ono F ses ces fo eod Acual deand s eale d, and so uchases ae ade o augen ac caaces f necessa Acual coss ae ealed fo eod

4 8 ounal of Manageen Accounng Reseach, 00 f obsees a sgnal on he sae of he econo, whee {,, K, }, and udaes s nal belefs abou he dsbuon of he cos and deand funcon aaees he obabl of he sgnal beng n eod s gen b a obabl easue : [ 0, ] he f ses a ce,, based on he obseed sgnal n each eod he acual deand fo each oduc s ealed n accodance wh a lnea deand funcon fo he oduc wh an adde sochasc coonen as n anke and Hughes 994: ε, fo,, K, oducs,,, K, eods, whee ε s dsbued wh ean eo and fne aance Le ε denoe E[ ε ], he esed eecaon of he esdual deand gen he sgnal such ha condonal on he obseaon of, ε s dsbued as ε ε wh E[ ε ] 0 and ε has fne aance as n anke and Hughes 994 heefoe, he eeced deand gen ha he f obsees a sgnal and selecs a ce s gen b: whee ε E[ ] We use he followng eco noaon o slf ou esenaon he ecos,, K, and,,, K ae ecos whose eleens ae he ces and eeced deand uanes of oducs gen he sae n eod he ecos,, K, and,, K, nclude all ossble ces and oducon uanes acoss all eods and all saes he cos funcon C, ncooaes aable, fed, and so eu coss as n anke and Hughes 994 he eeced cos gen a sgnal s: C, ξ E, 3 whee: > ξ f, fo,,,, 0 ohewse caac led b esouces coed o ac, eeced un aable cos of oduc gen sae n eod, eeced un cos fo esouce gen sae n eod, eeced so ake eu fo esouce gen sae n eod, uns of ac eued o suo one un of oduc, and obabl of sae occung n eod

5 anke, Hwang, and Msha 83 he fs e on he gh-hand sde of Euaon 3 eesens he eeced fed coss hese coss do no a wh acual oducon leel, bu ncease wh he ac caaces he second e s he eeced aable coss, whch ae decl ooonal o oducon uanes he hd e eflecs he eeced so eu o oban addonal caac when he ealed deand eues caac esouces eceedng he coed caac We denoe he eeced oal usage of ac fo he eeced oducon n eod gen sae as, and he acual oal usage of ac as hs allows us o slf ou analss b seaang he addonal deand due o adde sochasc coonen fo he ean aeage deand n addon, we defne, ε ψ, ε ψ, ψ ψ and s o slf ou eoson lae We denoe he dens funcon and he dsbuon funcon of as φ and, Φ esecel Each s dsbued wh fne aance as each ε has fne aance Usng he aboe defnon, we can ewe he acual ac usage as f he acual deand fo he esouce eceeds s coed caac, e,, > hen he f ncus an addonal cos of fo each addonal un of he esouce consued n ecess of he aalable caac On he ohe hand, f, < hee s ecess caac and he oal eeced cos of ac s Usng ou defnons aboe, we oban: he f s eeced of s: > ξ f, 0 ohewse fo,,, and,,, 4 [ ] π, E φ d Gen hs eeced of funcon, we ne anale he e ane oal caac and ce choces of he f

6 84 ounal of Manageen Accounng Reseach, 00 AALYSS AD RESULS We begn ou analss wh he oal e ane caac and eod-b-eod cng choces of he uloduc onools he f fs selecs he caac leel fo each esouce and subseuenl chooses a dffeen ce fo each eod based on nfoaon aalable a ha e he followng lea chaacees he oal choces of caaces and ces Lea : he oal choce of caac leels and ces soles he followng se of euaons [ Φ ] [ Φ ],, and 5 6 whee and Poof: All oofs ae n he Aend he f soles a se of sulaneous euaons o deene he oal caac leels fo he esouces and he oal ces fo he oducs n each sae n each of eods Cleal, hs s a cole oble when he nube of oducs o sae ealaons s lage he gh-hand sde of Euaon 5 s he eeced agnal cos of addng an ea un of caac aeaged oe all eods and he lef-hand sde s eual o he aeage eeced agnal cos of ocung an ea un of caac n he so ake, should he need ase Gen he ou caac, he f s ndffeen beween hese wo oons a he agn Alhough cole, hs eesson s sla n s o he anke and Hughes 994 esul Rewng Euaon 5 elds: whee w Φ w Euaon 7 ndcaes ha he f wll nes n caac onl f he aeage eeced so eu eceeds he eeced un cos of nsallng an addonal un of caac hs s analogous o anke and Hughes 994 eueen ha he so eu faco be geae han Howee, n ou odel he so eu faco can be less han n soe saes of he econo, eg, n an econoc downun Fo he cng decson he f ades off he eeced agnal loss n conbuon agn on he lef-hand sde of Euaon 6 agans he eeced agnal cos sangs hough educon n so eu fo eceedng he oal caaces 7

7 anke, Hwang, and Msha 85 shown on he gh-hand sde of Euaon 6 Rewng he ce euaon n a fo sla o anke and Hughes 994 elds: whee λ [ Φ ] s he fed cos adusen fac- o he e s he ao of he eeced agnal cos fo he nall coed caac esouce gen a cean sae of naue o s aeage eeced agnal cos Also, Φ s he eeced so eu and [ ] s he obabl of caac shoage As n anke and Hughes 994, he oal ce n Euaon 8 has wo coonens, one elaed o he deand aaees,, and he ohe elaed o oducon cos aaees based on he oal caac choce Howee, unlke n anke and Hughes 994, he oal ces deend on he oal caac choces, and he oal caac choces deend on he cos ndecl hough he eeced deand, whch deends on he oal ces, Slal, he oal caac chage used o deene ces deaes fo he ac-based full cos obaned n he anke and Hughes odel hs esul ha full-cos cng s no oal fo sho-e cng aallels sla esuls obaned n alakshnan and Saaakshnan 00 and Gö 00 unde dffeen ses of assuons n addon, we show lae n Pooson ha he aeage of hese sho-e ces s elaed o he full-cos-based ce n anke and Hughes 994 nfoaon, Euaon 8 shows ha c λ aggegaes all of he dealed nfoaon abou aable and coed ac esouces ha s eued fo he cng decson n eod gen he sae hs aggegae cos, c, esebles he ac-based oduc cos n anke and Hughes 994 c ece ha he chage e un of he coed aces,,, s he aoun λ λ nsead of sl he eeced un cos of he ac gen b hs les ha he knowledge of deand aaees and full-cos allocaon based on ac-based cosng s no adeuae fo he cng decson,, and 8 n addon, we also fnd ha he caac-lannng and cng decsons can no longe be decouled as n anke and Hughes 994

8 86 ounal of Manageen Accounng Reseach, 00 n he aboe analss, we hae allowed he f o dnacall adus he ce of s oducs n he oduc ake Alhough hs assuon eflecs he case fo an coodes and seces, such as gasolne and a ael, fs ofen do no hae hs flebl hs s esecall ue n long-e cusoe-sule elaonshs ha eue ufon ce coens b he sule, as s ealen n he auooble coonens ndus Hence, we ne eloe he oal ces when he f us co o a sngle ce fo each oduc hough all eods Lea : he oal e ane choce of caac leels unde ce coen soles he followng euaons whee and and ces,, and 0 We call hese esced oal choces he benchak caaces and ces because he ae sla n fo o he anke and Hughes 994 sngle-eod esuls ha effecel decoule he cng and caac choces hus, when he f us co e ane o a ce, he chage fo each ac s sla o ha n he anke and Hughes 994 odel Alhough hese benchak-caac and ce choces ae neesng n he own gh, Pooson ne eloes how he elae o he unesced oal choces n Lea Pooson : he benchak ce s eual o he aeage eeced oal ce of each oduc acoss all saes and eods 3 he aeage eeced deand fo each esouce oe eods s dencal fo he benchak and oal soluons he eeced shoage cos fo each esouce oe eods s dencal fo he benchak and oal soluons ˆ Φ Φ [ ] [ ] 9 hs esul also coesonds o ha n Gö 00, deonsang ha full-cos-based cng s oal when he ce and caac decsons ae based on dencal nfoaon 3 A sla esul s obaned n a hghl sled seng b alakshnan and Saaakshnan 00 he noe ha s due o deand sochasc beng caued b he nece e n he odel Howee, we show ha hs esul also holds n ou oe geneal seng

9 anke, Hwang, and Msha 87 he benchak ce s sl he aeage of he eeced oal ces oe he eods hus, when he f us co o a ce fo all eods, sl chooses he aeage of he eeced oal ces oe he eods Pas and of Pooson show ha he eeced deand fo esouces and he eeced shoage cos ae also dencal oe he eods Howee, f of wh he unesced oal ces us eceed he coesondng of usng he coon benchak ce n all eods he ncease n eeced of coes fo deand anageen he f sulaes deand b chagng lowe ces when deand s eeced o be lowe and daens he deand b chagng hghe ces when deand s eeced o be geae Lkewse, he ooun cos of he aalable coed caac s lowe when he deand s low and hghe when he deand s hgh n un, he f aduss he chage fo he coed esouces n dffeen saes based on he eeced deand and cos aaees n each sae he dffeence beween he oal ce and he benchak ce becoes: hs oal dffeence ncludes hee coonens: he base-leel deand, he aable coss, and he chage fo he coed esouces he fs wo coonens ae eogenous o he f, bu he hd esuls fo he f s accounng sse adusng he chage fo he coed esouce e, we chaacee he fed cos chage, λ, n he oal soluon and coae o he coesondng chage n he benchak soluon Pooson : λ [ ], e, he oal chage fo coed esouce s onooncall nceasng n he eeced deand fo ha esouce n each sae, gen he oal caac choce, he fed cos adusen faco, Φ [ ] Φ [ λ ] Deendng on he fed cos adusen faco e, on whehe λ >, < λ, o λ, he chage fo he coed esouce s oe han, less han, o eual o he coesondng full cos ae n he benchak case Pooson shows ha he chage fo a coed esouce deends decl on he eeced deand fo ha esouce he geae he deand, he salle he slack caac, and heefoe he geae s he coesondng chage hus, when hee s a hgh lkelhood of dle caac fo a esouce, he f should educe he chage fo he esouce, heeb educng s ce and sulang deand OPMALY OF DLE CAPACY Fs acue caac based on long-e saegc lans ha foecas fuue needs he f a acue soe caac ha s no full uled nall n ode o hae he caac o ee fuue deand gowh Fo eale, n he Soceé onleu case Shank 996 he coan nesed 8 llon fancs n a

10 88 ounal of Manageen Accounng Reseach, 00 new kln ha had a caac of 06 cubc ees e week bu was oeang a onl cubc ees a week he f chose he lage kln caac o ee ancaed gowh n oduc deand he an ueson n Soceé onleu case s how he cos of he dle kln caac should be chaged o oducon n he cuen eod A second eale s he Fab 30 lan bul b AMD Saon GbH n Desden, Gean h://wwwadco/locaons/aboufabhl Fab 30 s a sae-ofhe-a anufacung facl, cosng $9 bllon Poducon began n Decebe 998, and soe nal caac eaned dle unl AMD added new hghefoance ocessos o he oducon schedule As of Decebe 00, AMD eeced ha Fab would soon ule all he nal caac he cenal ueson n boh of hese cones s how he facl coss should be chaged o oducs oe he econoc lfe of he facl he oose suaon occus when a f s n a declnng ake fo s oduc lne Alhough he oble of oduc cosng wh saegc dle caac s coon, lle heoecal gudance s aalable n he anageen accounng leaue o addess hs ssue wh a elael sle odel, we ada ou uleod caac-lannng and cng odel o a wo-eod seng whee he f eecs fuue gowh o declne of a oduc lne o focus on he caac and cng decsons fo oduc gowh o declne, we assue ha hee s no esdual uncean n coss and ha he so eu faco,, s dencal fo boh eods As befoe, we eesen deand as: ε fo, oducs and, eods Leng fo each oduc, wh a sc neual fo a leas one oduc, sa oduc, would eesen eeced deand gowh Conesel,, < eflecs an ancaed declne n deand As befoe, he f acues caac a he begnnng of he fs eod Wh and, he cos funcon becoes: whee ξ, C, 0, he fs e on he gh-hand sde of Euaon s he coed esouce caac coss fo he wo-eod odel he second e eesens he aable coss fo he wo eods he las e s he so eu cos f he deand eceeds caac n ehe eod Usng he noaon defned n he second secon, we can eess he oal usage of ac o suo acual oducon as: f f ξ > fo, fo,

11 anke, Hwang, and Msha 89 As n he ognal odel, f he acual deand fo esouce s geae han he nall coed esouce caac, e, >, he f us a e addonal un of ac esouce, and he eeced of funcon s: whee E [ π, ] [ ], E, and ε We assue ha he eo e n he deand funcon s ndeendenl and dencall dsbued acoss oducs and eods o anale hs odel, we fs chaacee he oal caaces,, and ces,, as he soluons o he followng se of euaons: φ d [ Φ ] fo,,, 3 [ Φ ] 0 fo all and Euaon 3 euaes he aeage eeced cos of so eus oe wo eods wh he agnal cos of acung addonal caac n he fs eod Euaon 4 euaes he eeced agnal loss n conbuon agn wh he eeced agnal cos sangs n es of educon n so eus fo eceedng he oal caaces Rewng 4 elds: [ Φ ] fo all and he oal ce agan has hee coonens, he fs elaed o deand and he ohe wo elaed o oducon coss o anale he caac and cng choces, defne γ as he ao of he shoage obables n eods and : 4 5 Φ P γ Φ P 6 Ou assuon abou deand gowh hen consans he alue of he oal as follows: Lea 3: When deand gowh s eeced n eod e, and >, hen γ < fo all When deand declne s eeced n eod e, and <, hen γ fo all > γ

12 90 ounal of Manageen Accounng Reseach, 00 We can also ewe he oal caaces and ces as follows: γ Φ Φ γ γ, γ γ, and, γ oe ha γ s a funcon of he oal aoun of coed esouce and he oal eeced deand fo esouce n boh eods Gen ha he f acues caac based on ancaed deand gowh, Pooson 3 esablshes when he f should ca dle caac Pooson 3: hee ess a ccal alue of he so eu faco c c < 4 / γ γ < fo each esouce, aboe whch e, fo >, he f should ca dle caac fo esouce n he fs eod when eecng deand gowh n he second eod 4 he eesson n Pooson ndcaes ha whehe he f chooses o ca dle caac fo fuue deand gowh deends on he eeced need fo he fuue eods as well as he so eu n fac, as n anke and Hughes 994, f he so eu faco fo each esouce s geae han o eual o een f he deand s naan acoss he wo eods, he f eecs o hae dle caac esece of he deand aaees he ccal alue fo he eeced dle caac n Pooson 3 s less han he ccal alue of n he anke and Hughes 994 odel because he f ancaes fuue deand gowh n he esen odel, wheeas does no n he anke and Hughes 994 odel he geae he dffeence beween he fs and second eod eeced deands, he salle he ccal alue n Pooson 3 hus, hee ae wo easons n ou odel fo fs o ca dle caac; fs, o aod ang he so eu fo caac and, second, o accoodae ancaed deand gowh 5 he fnal ueson we addess n Pooson 4 s how he coed caac cos should be chaged o oducs o suo oal cng decsons when he f eecs deand gowh o deand declne Pooson 4: When he f eecs deand gowh n he second eod and >, he chage e un of caac esouces n he fs eod s scl less han he chage n he second eod γ, γ γ 4 alakshnan and Saaakshnan 996 show wh a nuecal eale n a wo-eod seng ha a f a ca dle caac n ancaon of gowh n ou odel, deand gowh alone does no l ha he f should ca dle caac he so eu us eceed a ccal alue, n addon o an ancaed gowh n deand, o ake oal fo he f o ca dle caac 5 Relacng he assuon ha he so eu s he sae oe boh eods wh he assuon ha he eu s an nceasng funcon of he aggegae deand fo ha esouce ρ ρ >, 0 c c elds eeced dle caac fo >, whee γ 4

13 anke, Hwang, and Msha 9 he conese holds when he f eecs deand declne n he second eod Pooson 4 suos he nuon ha cuen oducs should no be chaged he cos of dle caac when he f acues caac o ee eeced deand n subseuen eods Slal, f he f eecs he deand fo a acula oduc o declne, should educe he caac chage n he second eod o sulae he deand COCLUSO hs ae deelos a oduc cosng and cng odel unde long-e caac coen o anale he neacon beween he nal caac choce and subseuen oduc cosng and cng decsons n a dnac nfoaon enonen he esulng oal oduc coss dffe fo he ac-based coss n anke and Hughes 994 sngle-eod odel ece when he f has o co o a coon ce fo all eods Deendng on he so eu cos, he oal chages fo fed esouces could be geae han, less han, o eual o he benchak chage ha esuls unde ce coen n addon, he aeage eeced oal chage fo an ac esouce euals s eeced full cos as n anke and Hughes 994 Howee, he oal chage n each eod flucuaes aound hs benchak as he f aduss cosng and cng based on ealed deand Usng ou odel n a wo-eod cone deonsaes he oal of cang dle caac Fuhe, when he f eecs deand gowh n he second eod, he chage e un of caac esouces n he fs eod s scl less han he chage n he second eod he oose holds when he f eecs deand o declne n he second eod As n anke and Hughes 994, we hae ade cean slfng assuons such as he Leonef oducon funcon Fuue eseach a o ela soe of he esce assuons, aculal he eueen ha all oducs be oduced n all eods Ohe eseach aenues nclude adang hs odel o dffeen cones, such as whee he ealed deand need no be e n all eods and saes Ohe eensons nclude he analss of decsons elaed o he noducon of a new oduc o he dong of an esng oduc A osng aoach noles he use of sle heuscs based on he cole eessons fo oal ces and caac choces, such as hose esened hee n suo of hese aenues fo fuhe eseach, he esen sud odes nsghs no how he oal deenaon of oduc coss o faclae cng decsons n dffeen eods neacs wh eecaons abou he lkelhood of coed caac eanng dle n each eod

14 9 ounal of Manageen Accounng Reseach, 00 APPEDX Lea : Eeced of funcon gen he known aaees s: whee he fs-ode condon FOC wh esec o ges: Slal, he FOC wh esec o ges: [ ], E π φ d [ ], E π φ d 0 [ ] Φ 0 [ ], E π 0 d φ,, and [ ] Φ A3 Lea : he eeced of funcon unde ce coen s: [ ] π, E A4 A [ ] Φ A [ ] Φ φ d

15 anke, Hwang, and Msha 93 whee and Euaon A4, he fs-ode condon FOC wh esec o, ges he oal : [ ] Φ A5 On he ohe hand, he FOC wh esec o ges: [ ], E π 0 d φ denong he oal ce as, we hae: [ ], 0 Φ ha s: 0 heefoe, and,, A6 whee and Pooson : Aeagng all he oal ces n Euaon A3 ges: Φ A7

16 94 ounal of Manageen Accounng Reseach, 00 whee: Fo Euaons A and A5: [ ] Φ [ ] Φ [ ] Φ [ ] Φ A9 Sung he aboe wo deands fo each esouce ges: ha s, A8 fo Euaon A7, and,, Φ fo Euaon A

17 anke, Hwang, and Msha 95 Pooson : We hae λ [ ], Φ coed esouce s Φ λ and he chage fo he [ ] λ 0 φ > he eued esul follows decl fo he aboe elaon Lea 3: γ γ γ γ A0 A γ A γ A3 We ode a oof b conadcon Fs, we consde he case when deand gowh s eeced n eod e, and > f, hen: and [ Φ Φ ] 0 > Howee, f > fo,, hen <, whch conadcs he assuon ha heefoe, us be he case ha < ecause Φ s an nceasng funcon, γ Φ Φ < e, consde he case when deand declne s eeced n eod e, and < f, hen: [ Φ Φ ] 0, > [ ] Φ Φ 0 <,

18 96 ounal of Manageen Accounng Reseach, 00 and [ ] Φ Φ 0 < Howee, f > fo,, hen >, whch conadcs he assuon ha heefoe, us be ha > ecause Φ s an nceasng funcon, γ Pooson 3: ecause Φ Φ > Φ γ b defnon, we hae Φ Φ γ γ dle caac wll be caed n he fs eod f and onl f γ < o, γ eualenl fo all c c 4 γ > whee he fac ha c < follows because γ ohewse s cheae o acue he esouces fo he so ake ahe han c 4γ conacng fo nall he condon ha < holds f γ <, whch γ follows fo Lea 3 Pooson 4: he oal ces and uanes of he wo oducs fo he wo eods ae: γ γ γ γ γ γ A4 A5 A6 A7 he chages e un of caac esouces n eod and eod ae γ γ and γ, esecel γ γ s less han γ f and onl f γ < Fo Lea 3, when he f eecs deand gowh n he second eod, we hae γ <, and when he f eecs deand declne n he second eod, we hae γ > Hence, Pooson 4 follows decl fo a coason of chages b aealng o Lea 3

19 anke, Hwang, and Msha 97 REFERECES Aesh, A, R D anke, and S M Daa 990 Econoc suffcenc and sascal suffcenc n he aggegaon of accounng sgnals he Accounng Reew anua: 330 Aknson, A, R D anke, R S Kalan, and S M Young 995 Manageen Accounng Englewood Clffs, : Pence Hall alachandan, V, L L, and R P Magee 987 On he allocaon of fed and aable coss fo sece deaens Coneoa Accounng Reseach Fall: 6485, R alakshnan, and K Saaakshnan 997 On he effcenc of cos-based decson ules fo caac lannng he Accounng Reew Ocobe: alachandan, K R, and Sndh 987 A aonale fo fed chage alcaon ounal of Accounng, Audng, and Fnance Sng: 569 alakshnan, R, and K Saaakshnan 996 s assgnng caac coss o nddual oducs necessa fo caac lannng? Accounng Hoons Seebe:, and 00 Seuenal soluons o caac lannng and cng decsons Coneoa Accounng Reseach 6 anke, R D, S M Daa, and S Keke 988 Relean coss, congeson and sochasc n oducon enonens ounal of Accounng and Econocs: 797, and S Hughes 994 Poduc cosng and cng he Accounng Reew ul: , and S C Hansen 00 he adeuac of full-cos-based cng heuscs ounal of Manageen Accounng Reseach 4: 3358 Cooe, R, and R S Kalan 987 How cos accounng sseacall dsos oduc coss n Accounng and Manageen: A Feld Sud Pesece, eded b W uns, and R S Kalan oson, MA: Haad usness School Pess Gondaan, V, and R Anhon 983 How fs use cos daa n ce decsons Manageen Accounng ul: 3036 Gö, R F 00 he ac of cos-based cng ules on caac lannng unde uncean Wokng ae, Oo on Guecke Unes of Magdebug 00 Caac lannng and cng unde uncean ounal of Manageen Accounng Reseach 4: 5978 Kalan, R S, and G L hoson 97 Oehead allocaon a aheacal ogang odels he Accounng Reew Al: 35364, and U P Wela 974 Oehead allocaon wh efec akes and nonlnea echnolog he Accounng Reew ul: Mlle, L, and A G uckan 987 Cos allocaon and ooun cos Manageen Scence Ma: Shank, 996 Cases n cos anageen: A saegc ehass Cncnna, OH: Souh- Wesen College Publshng: 94 Sh, E, and E F Sud 995 How anufacues ce oducs Manageen Accounng Febua: 3739 Whang, S 989 Cos allocaon esed: An oal esul Manageen Scence Ocobe: 6473 Zean, 979 he coss and benefs of cos allocaons he Accounng Reew ul: 5045

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