Economics of Strategy (ECON 4550) Maymester 2015 Advanced Topics in Pricing: Multi-Product Pricing, Price Discrimination, Versioning, and Bundling

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1 Eonomis of Strtegy (ECON 455) Mymester 5 Advned Tois in Priing: Multi-Produt Priing, Prie Disrimintion, Versioning, nd undling eding: Versioning: The Smrt Wy to Sell Informtion (ECON 455 Coursek, Pge 8) Definitions nd Conets: Prie Disrimintion the rtie of hrging different rie for different units sold of n essentilly identil good (with the differene in rie not eing result of differenes in ost of rodution) First Degree Prie Disrimintion or Perfet Prie Disrimintion rtie in whih firm hrges every onsumer n mount etly eul to uyer s reservtion rie for every unit sold Seond Degree Prie Disrimintion or Menu Priing rtie in whih firm resents ll onsumers with different riing menus nd llows eh onsumer to hoose the menu whih they refer Third Degree Prie Disrimintion or Segmented Priing rtie under whih firm sertes onsumers into different mrket segments, nd then hrges eh different segment of onsumers different onstnt er unit rie for eh unit urhsed Versioning the rtie of selling different vritions of rodut Emles of versioning: ir trvel first lss vs. oh ; omuter softwre/s full feture version vs. re ones version ; omuter rinters IM LserPrinter vs. LserPrinter E Produt Differentition differenes in the hrteristis of two similr roduts tht result in onsumer hving different vlues of reservtion rie for the two roduts Vertil Produt Differentition rodut differentition for whih ll onsumers gree on whih hrteristis re more desirle ut differ with reset to how muh they vlue the more desirle hrteristi e.g., Ki Forte versus MW 38i Horizontl Produt Differentition rodut differentition for whih ll onsumers do not gree on whih hrteristis re more desirle (due to fundmentl differenes in tstes/referenes ross onsumers) e.g., Cherry Co-Col, versus Vnill Co-Col, versus Co-Col with Lime

2 Issues to kee in mind when versioning. The est ries re not lwys ovious s in the emle ove, you often n t simly hrge eh intended segment of onsumers rie eul to their reservtion rie for the intended version. The firm often hs hoie over how mny different versions to offer nd hoie over the seifi hrteristis/fetures of eh different version => the est hoies in these mtters deend ritilly uon how ostly it is to rete n dditionl version my t first seem ounterintuitive (see free version nd vlue sutrted version elow) 3. It my mke sense to offer free version => rtiulrly if hving network of users mtters (e.g., Adoe gives wy free version of Arot eder so tht more eole use PDF files ) enefits of your rodut re diffiult for onsumers to know efore onsuming/using the rodut (e.g., offer free version of video gme with only initil levels unloked, nd then hrge for ll levels ) there is the otentil for follow-on sles (offer low frills version for free, with the intention of selling etensions, ugrdes, susrition fees, nd/or suort servies down the rod => e.g., AOL used to give wy the softwre to run their we servies for free on CD) 4. It my mke sense to rete vlue sutrted versions, even if ositive osts must e inurred to do so IM LserPrinter ( ges er minute) vs. LserPrinter E (5 ges er minute) LserPrinter E essentilly mnuftured y tking LserPrinter nd inserting n etr hi to slow down the rinting seed => it tully ost MOE to rodue the LOWE QUALITY version! if we think out wht firm needs to do in order to hve different segments of onsumers self-selet different versions, these emles mke sense. Intuitive emle: n irline tht offers first lss servie nd oh servie fiing the ulity differene etween first lss nd oh, eh onsumer ould determine remium he would e willing to y for first lss Wht ould we do to mke more eole fly first lss? o lower the rie of the first lss tiket or rise the rie of the oh tiket o inrese ulity of the first lss eeriene (e.g., offer wider seletion of remium snks, serve drinks in glsswre) or derese ulity of the oh eeriene (e.g., sets loser together, no hoie of snk) To get eole to fly first lss, on some level the irline hs to mke oh suffiiently unerle for segment of otentil onsumer undling the rtie of selling multile distint roduts together s kge Pure undling the rtie of undling, while not llowing onsumers the otion of urhsing the undled items sertely (i.e., outside of the undle) Mied undling the rtie of undling, while lso llowing onsumers the otion of urhsing the undled items sertely (i.e., outside of the undle)

3 Multi-Produt Priing: Consider firm roduing two different roduts. If we ssume onstnt mrginl osts for eh rodut, then: If we onetully think out mimizing rofit y hoosing ries, then there re now two first order onditions for rofit mimiztion.. Fous on Condition (y the symmetri nture of the rolem, similr insights would follow from n emintion of Condition ) Three distint ses: I. => indeendent demnds to mimize rofit the firm must oerte where:, tht is, when riing roduts with indeendent demnds (long with our ssumtion of indeendent osts ) the firm simly lies the reviously derived IEP [intuitive result] II. => sustitutes to mimize rofit the firm must oerte where:, when riing sustitutes (gin, with indeendent osts ) the firm must oerte t oint where rie/ost mrku s erentge of rie is greter thn the solute vlue of the inverse of own rie elstiity of demnd Intuitive result: you should e more willing to hrge higher thn otherwise rie on Produt, sine some of the ustomers you lose from doing so re lost to yourself (sine they urhse Produt A )

4 ( Multi-Produt Priing ontinued) III. => omlements to mimize rofit the firm must oerte where:, when riing omlements (gin, with indeendent osts ) the firm must oerte where rie/ost mrku s erentge of rie is less thn the solute vlue of the inverse of own rie elstiity of demnd Intuitive result: you should e less willing to hrge higher thn otherwise rie on Produt, sine when you do so you re not only losing sles of Produt ut lso losing sles of Produt A

5 First Degree or Perfet Prie Disrimintion: Agin, the knowledge reuired y the seller to tully engge in suh ehvior n lmost never e known => no good rel world emles of st Degree P.D. However, it is still insightful to figure out wht firm would do if they were le to engge in suh riing Strt y relling wht trditionl monoolist (i.e., one who sets ommon rie for ll ustomers) would do: $ MC() Demnd untity For the trditionl monoolist, in order to sell the net unit he must dro rie on ll ( ) PD ( ) nd therefore units sold => M( ) ( ) P D ( ) PD ( ) PD ( ) (i.e., mrginl revenue is LESS THAN rie ) $ MC() P* Demnd Q* M() untity (Consumers Surlus)=(urle) (Produer s Surlus)=(ornge) (Dedweight-Loss)=(yellow)

6 ( First Degree Prie Disrimintion ontinued) If the monoolist n engge in First Degree (or Perfet ) Prie Disrimintion, then they will sell to eh onsumer t rie etly eul to his reservtion rie => to sell to the net unit they do NOT need to dro rie on ll units sold Tht is, the firm hrges eh onsumer n mount etly eul to reservtion rie => Mrginl evenue is simly eul to height of demnd $ MC() Demnd = M Q FDPD untity Firm would sell (Q FDPD ) units => etrt the entire re elow the demnd urve, u to the untity sold s evenue => (evenue)=( lue + yellow ) ( yellow ) = (Vrile Costs) => (PS) = ( lue ) Note tht (CS) = () => Consumers re worse off (omred to trditionl monooly ) (DWL) = () => Soil Surlus is lrger (omred to trditionl monooly ) Prie Disrimintion n tully inrese oth Produers Surlus nd Soil Welfre!

7 Seond Degree Prie Disrimintion or Menu Priing: Firm offers multile riing menus => ll menus re ville to ll onsumers => eh onsumer is free to self selet the menu whih they most refer At lest some of the riing menus must e more omlited thn simly onstnt er unit rie, or else ll onsumers would simly hoose the otion with the lowest rie Very often the riing menus onsist of different mrginl ries t different levels of onsumtion Emle: onsider ell hone omny tht offers two lns s follows o Pln A: $49.99 er month;,8 minutes for free ; er minute for eh dditionl minute o Pln : $9.99 er month; 6 minutes for free ; er minute for eh dditionl minute Firm simly needs to know tht there re fundmentl differenes ross onsumers, ut need not e le to identify the rtiulr tye of ny seifi onsumer Pln A tilored towrd ell hone junkies nd Pln tilored towrd emergeny users => eh onsumer self-selets the ln tht est fits their own needs Offering the two lns (insted of only Pln A ) llows the seller to: Attrt emergeny users s ustomers Without hving to srifie the lrge revenue whih is eing olleted from eh of the ell hone junkies Other emles (whih re losely relted to versioning, whih we will disuss lter in this toi): (i) first lss irfre versus oh, (ii) remium le kge versus si le Third Degree P.D. or Segmented Priing: Firm sertes ll otentil onsumers into different segments, nd then sets uniue onstnt er unit rie for eh segment Must e diffiult (or reltively ostly ) for resle to tke le ross segments Segments re ommonly geogrhi mrkets (in whih se the onsumers re hysilly serted from one nother) or sed uon oservle (or esily verifile) hrteristis of onsumers Segmented Priing is roly the most ommon form of rie disrimintion Two imortnt insights whih n e gined from emining the ehvior of firm engging in Segmented Priing.... Prie Disrimintion my llow firm to ern ositive rofit when trditionl riing does not. Consumer s Surlus n ossily e higher when firms re le to engge in rie disrimintion

8 ( Third Degree Prie Disrimintion ontinued) Emle : w Segment A onsists of welthy onsumers, eh with reservtion rie of r 5 for unit of the good; Segment onsists of 5 oor onsumers, eh with reservtion rie of r for unit of the good Suose tht the roduer must inur Fied Costs of $, in order to develo the rodut These osts n e voided if rodut is not develoed These re the only rodution osts => oth Mrginl Costs nd Vrile Costs re zero Suose the firm ws leglly reuired to hrge ommon rie ross oth segments (Prie)=(5) => sell only to Segment A onsumers => (evenue) = (5)() =, => would led to rofit of (,) (,) = () => est to NOT develo rodut (Prie)=() => sell to oth segments => (evenue) = ()(7) = 7 => would led to rofit of (7) (,) = (5) => est to NOT develo rodut Thus, PS = CS = (Soil Surlus) = () If llowed to engge in Segmented Priing (Prie)=(5) in Segment A nd (Prie)=() in Segment => sell to oth segments => (evenue) = (5)()+()(5) =,5 => would led to rofit of (,5) (,) = (3) => est to develo rodut Thus, PS = (Soil Surlus) = (3) Prie Disrimintion llowed the firm to ern ositive rofit when trditionl riing did not!

9 ( Third Degree Prie Disrimintion ontinued) Emle : Segment A hs demnd given y the liner inverse funtion P A D ( ) Segment hs demnd given y the liner inverse funtion P D ( ) Firm hs onstnt mrginl osts of MC 4 If these two segments were treted s one single mrket, then $ Demnd 5 MC() untity 6 M() Profit mimized y setting rie of $5, selling 48 units in Segment A nd omletely ignoring Segment Segment A : (CS) nd (PS) oth ositive Segment : (CS) nd (PS) oth zero If the firm is llowed to engge in Segmented Priing : set rie of $5 in Segment A => sell 48 units in Segment A set rie of $ in Segment => sell 8 units in Segment Outome in Segment A is identil to wht is ws efore ut now, in Segment : (CS) nd (PS) re oth ositive insted of zero Thus, in this emle, when the firm is le to rtie Segment Priing (s oosed to restriting the firm to hrging ommon rie ross oth segments): Produer s Surlus is lrger Totl Consumers Surlus is lrger Therefore, Totl Soil Surlus is lrger (DWL is smller) Noody is worse off nd some eole re stritly etter off Prie Disrimintion led to n inrese in Totl Consumers Surlus!

10 Emle to illustrte how versioning inreses rofit onsider simle senrio in whih softwre omny is otentilly serving two different tyes of onsumers: students vs. usinesses => develoed high end version nd low end version of their rodut suose onsumer reservtion ries re Students usiness Users low end version $6 $ high end version $75 $9 note: vertil differentition (oth le higher vlue on the high end version thn on the low end version ) suose there re n eul numer of students nd usiness users ( of eh) $ mrginl ost for roduing ny unit of either version Otions ville to firm: offer only low end, offer only high end version, or offer oth versions I. If the firm offers only the low end version, they n either: Sell to oth tyes, y hrging rie of $6 => rofit of: (6-)() = $ Sell to only usiness users, y hrging rie of $ => Profit of: (-)() = $9 Of these two, the etter hoie is lerly to hrge rie of $6 nd sell to oth tyes II. If the firm offers only the high end version, they n either: Sell to oth tyes, y hrging rie of $75 => rofit of: (75-)() = $3 Sell to only usiness users, y hrging rie of $9 => Profit of: (9-)() = $8 Of these two, the etter hoie is lerly to hrge rie of $9 nd sell to only usiness users Further, this ( sell only the high end version t rie of $9 ) is the est of the four otions onsidered thus fr III. Wht if the firm sells oth versions? Would wnt the students to uy the low end version nd the usiness users to uy the high end version Chrge rie of $6 for the low end version => selling this version to the students t this rie gives rofit of: (6-)() = $5 Wht rie to hrge for the high end version? Wht if we hrged $9 for the high end version? Chrge the highest rie you n for the high end version for whih the intended segment (i.e., usiness users ) refers to uy tht version o usiness users n get surlus of (-6) = $4 from uying the low end version for $6 o The most you ould hrge for the high end version nd still sell to the usiness users is $5 (so tht their surlus from this urhse is (9-5) = $4) Thus, set ries of $6 for the low end version nd $5 for the high end version o students will uy the low end version o usiness users will uy the high end version Profit is: (6-)+(5-) = 5+4 = $9 Offering two versions llowed the firm to relize greter rofit

11 Determining onsumer urhsing deisions under Simle Monooly Priing (i.e., no undling), Pure undling, nd Mied undling Consider firm selling two different goods ( good nd good ) Denote Consumer i s reservtion rie for the two goods e denoted y i nd (ssume unit demnd for eh) Eh onsumer is t seifi oint in, ) ( i i i I. Simle Monooly Priing firm offers good for sle t rie of nd offers good for sle t rie of Eh onsumer ssesses the urhse of eh good sertely => uy good if nd only if i ; uy good if nd only if i Thus, the ehvior of ll onsumers n e illustrted s =(uy oth goods) =(uy good ut not good ) =(uy good ut not good ) =(uy neither good)

12 ( undling ontinued) II. Pure undling firm offers the undle for sle t rie of (nd onsumers do not hve the otion of uying the goods sertely) i i Consumer i s surlus from urhsing the undle is => urhse i i undle if nd only if this is ositive (i.e., if nd only if ) Thus, the ehvior of ll onsumers n e illustrted s =(uy undle) =(do not uy undle) III. Mied undling firm offers the undle for sle t rie of, ut onsumers lso hve the otion of sertely uying good t rie of nd good t rie of For nyone to ever uy the undle, the firm must set Consumer i s surlus from urhsing i i o the undle is o only good is i o only good is i o neither good is =(uy undle) =(uy only good ) =(uy only good ) =(uy neither good)

13 ( undling ontinued) Potentil dvntge of mied undling => llows the seller to: etrt very high rie of from those onsumers with reltively high i reltively low etrt very high rie of from those onsumers with reltively high i reltively low i ut i ut while still ontinuing to serve those onsumers with intermedite vlutions for oth i i goods (i.e., those eole who don t hve high vlue of or, ut still hve high i i vlue of ) y selling them the undle t lower omined rie of Some intuition on rofitility of the different otions => eognize, mied undling n over oth of the otions of simle monooly nd ure undling Tht is: Mied undling with would give the sme outome s Simle Monooly riing with nd (sine ny ustomer tht wnted oth goods would still never uy the undle ) Mied undling with min{, } would give the sme outome s Pure undling with rie of (sine uying the undle is less eensive thn uying either good individully) Thus The mimum rofit from Mied undling hs to e t lest s lrge s the mimum * * rofit from Simle Monooly => M SM The mimum rofit from Mied undling hs to e t lest s lrge s the mimum * * rofit from Pure undling => M P ut these ineulities need not e strit (i.e., the est Mied undle might e the one * * tht relites Simle Monooly riing, in whih se ) * * we ould hve either or SM P * * SM P M SM

14 ( undling ontinued) Emle : (simle emle to illustrte tht Pure undling n yield greter rofit thn Simle Monooly) firm tht sells movies on DVD: (good ) = Movie F (good ) = Movie W two tyes of onsumers, with reservtion ries of: Movie F Movie W sum Tye A Tye 3 35 undling is most dvntgeous when the different tyes of onsumers hve reservtion ries tht re negtively orrelted with eh other suose mrginl osts of $5 strightforwrd to verify tht the est Simle Monooly ries re 3 nd 3 => sell only Movie F to Tye A nd only Movie W to Tye => w * SM 45 wht if we offer undle tht inludes oy of eh? Chrge $35 nd sell undle to * eh onsumer => (35 )() 5 P Emle : monoolist selling two goods suose onstnt mrginl ost of $ for eh good three different onsumers with reservtion ries of Good Good Sum Consumer A Consumer 5 6 Consumer C 8 Grhilly illustrte reservtion ries s: f C 8 6 A 5 A 75 C 5

15 ( undling ontinued) Otiml Simle Monooly ries? o For good : ( )(3) 5 (5 )() 75 (75 )() o For good : 5 (5 )(3) 6 (6 )() => 3 => 8 => 65 => 5 => => (8 )() 7 nd 6 8 o Thus, the est Simle Monoolist hoie is 5 * SM 8 8 Otiml Pure undling rie? o Prie of undle: 9 => ( 9 )(3) => ( )() 6 => ( )() 9 => * o Thus, the est Pure undle hoie is 9 => P o In this emle, Pure undling results in greter rofit thn Simle Monooly riing Otiml Mied undling ries? ell: est hoie est hoie est hoie C 8 6 A 5 A 75 C 5

16 ( undling ontinued) The otiml Mied undle ries re suh tht: =( uys the undle) * C 8 6 =( C uys only good ) =( A uys only good ) A 5 C A * 75 5 o Thus, the est Mied undle ries re for the undle, 75 for good, nd 8 for good uys the undle, A uys only good, nd C uys only good o This hoie yields rofit of: * M ( ) (75 ) (8 )

17 Multile Choie Questions:. refers to the generl rtie of hrging different rie for different units sold of n essentilly identil good. A. Versioning. Prie Disrimintion C. undling D. Produt Differentition. Alh Industries sells two goods: good nd good y. The ross rie elstiity of demnd for good with reset to the rie of good y nd the ross rie elstiity of demnd for good y with reset to the rie of good re oth ositive. It follows tht when mimizing rofit, this firm should e oerting where A..,.,. C.,. D., 3. Vnill Co-Col, Cherry Co-Col, nd Co-Col with Lime re emles of goods tht re A. vertilly differentited.. horizontlly differentited. C. sold y firm with no mrket ower. D. None of the ove nswers re orret. 4. Consider firm tht sells two roduts ( rodut nd rodut ) with interdeendent demnds. The rofit of the firm is generlly given y the funtion F. Inverse demnd for rodut nd rodut re resetively given y nd 3. Further, nd 4. As result, when the firm mimizes rofit y hoosing untities 3 of outut, they otin the two first order onditions: nd Whih of the following levels of outut mimize rofit? A. nd nd. C. 6 nd 3. D. 4 nd 8.

18 5. John hs reservtion ries for good nd good of 46 nd 8. He hs the otion to uy good t rie of 4, uy good t rie of, or undle onsisting of oth good n good t rie of 55. Given this otions, John should hoose to A. urhse only good.. urhse only good. C. urhse the undle onsisting of oth good nd good. D. None of the ove nswers re neessrily orret (sine dditionl informtion is needed in order to determine his otiml urhsing deision). 6. Edn sells sunglsses. She offers ustomers % disount if they show her vlid student I.D. t the time of urhse. This ehvior y Edn is n emle of A. First Degree Prie Disrimintion (or Perfet Prie Disrimintion).. Seond Degree Prie Disrimintion (or Menu Priing) C. Third Degree Prie Disrimintion (or Segmented Priing). D. Fifth Degree Prie Disrimintion (or Wlter Murhy Priing). 7. Consider firm tht sells two different roduts. If this firm engges in Pure undling, then eh onsumer A. only hs the otion of urhsing the two goods sertely.. hs the otion of either urhsing the two goods sertely or urhsing together (s kge). C. only hs the otion of urhsing the two goods together (s kge). D. must urhse ositive untity of oth goods (even if doing so gives him negtive Consumer s Surlus). 8. Whih of the following sttements regrding the rofitility of different tyes of undling is orret? A. The mimum rofit from Mied undling must lwys e t lest s lrge s the mimum rofit from Simle Monooly riing.. The mimum rofit from Pure undling must lwys e t lest s lrge s the mimum rofit from Simle Monooly Priing. C. The mimum rofit from Pure undling must lwys e etly eul to the mimum rofit from Mied undling. D. More thn one (erhs ll) of the ove nswers is orret. 9. Consider firm roduing two goods tht re omlements to eh other. When mimizing rofit, they should rie in wy so tht A. for eh good rie/ost mrku s erentge of rie is less thn the solute vlue of the inverse of own rie elstiity of demnd.. for eh good rie/ost mrku s erentge of rie is greter thn the solute vlue of the inverse of own rie elstiity of demnd. C. for eh good rie/ost mrku s erentge of rie is eul to the solute vlue of the inverse of own rie elstiity of demnd. D. rie/ost mrku s erentge of rie is eul to one for eh good.

19 . Consider monoolist selling good for whih inverse demnd is given y P D ( ) 4 nd ost of rodution re C ( ) 8 9, 75. If this seller is le to engge in Perfet Prie Disrimintion, then she would A. sell 64 units of outut.. hrge er unit rie of $4 for every unit sold. C. hoose to rodue less thn the effiient untity of outut. D. More thn one (erhs ll) of the ove nswers is orret. Prolem Solving or Short Answer Questions:. Justin owns omny lled Old Skool We, whih offers dil-u Internet servie in the Toek, KS metro re. Old Skool We offers three different monthly servie lns s follows: Fied Fee Free Minutes Prie for Additionl Minutes Pln A $ 9 Pln $ 5 Pln C $4 unlimited (not lile) A. If Kendr eets to use the Internet for totl of etly minutes er month, whih of these three lns would e est for her?. If Amnd eets to use the Internet for totl of etly 6 minutes er month, whih of these three lns would e est for her? C. If Dvid eets to use the Internet for totl of etly 8 minutes er month, whih of these three lns would e est for him? D. Determine n et rnge of monthly usge for whih onsumer eenditures re lowest under Pln.. Consider firm fing inverse demnd of P D ( ) 5. Suose tht the rodution osts of this firm re C ( ), 35,. A. Suose tht this firm must hrge ll onsumers ommon rie. Determine the resulting: rofit mimizing untity of outut, rofit mimizing rie, vlue of Dedweight-Loss, vlue of Totl Consumers Surlus, vlue of Produer s Surlus, nd vlue of Profit.. Suose tht this firm n engge in Perfet Prie Disrimintion. Determine the resulting: rofit mimizing untity of outut, vlue of Dedweight-Loss, vlue of Totl Consumers Surlus, vlue of Produer s Surlus, nd vlue of Profit. C. How do the vlues of Dedweight-Loss, Totl Consumers Surlus, Produer s Surlus, nd Profit omre to eh other ross the two senrios of Simle Monooly Priing nd First Degree Prie Disrimintion?

20 3. Consider firm selling two goods in mrket in whih there re three different tyes of onsumers. The tle elow rovides summry of the reservtion rie of eh tye of onsumer for eh good (s well s nottion denoting the numer of eh tye of onsumer in the mrket). Consumer Tye eservtion Prie for Good X eservtion Prie for Good Y Numer of Consumers Tye A A Tye 5 5 Tye C C The mrginl ost of roduing eh unit of Good X nd eh unit of Good Y is onstnt $, while Fied Costs re eul to zero. Consider three different senrios (in regrds to the size of eh mrket segment) s follows: Senrio Senrio Senrio 3 A C A. Suose tht the seller is restrited to Simle Monooly Priing (i.e., hoosing nd y, in order to sell eh good sertely). Determine the rofit mimizing rie for eh good nd the resulting rofit of the seller in eh of the three different senrios. 3. Suose tht the seller is restrited to Pure undling (i.e., selling the two goods together s kge, for rie of ). Determine generl ondition in terms of A,, nd C whih seifies when the seller would wnt to sell the undle to ll three onsumer tyes (versus selling the undle to only tyes A nd C ). In whih of the three senrios will the seller set rie of for whih ll three onsumer tyes urhse the undle? 3C. Does Pure undling led to greter rofit thn Simle Monooly Priing? Elin. 4. Sterling Mirosystems hs develoed new iee of softwre tht is of vlue to oth Professionl Finnil Anlysts nd Finne Students. The otentil mrket for this softwre onsists of N Professionls nd N Students. Eh Professionl user hs vlue of $5,675 for the softwre, while eh Student user hs vlue of only $75. The mrginl ost of roduing eh unit of the rodut is $5 (ll other rodution osts re sunk osts). 4A. Wht rie should Sterling Mirosystems hrge for this rogrm? When setting this rie, whih segment of onsumers urhse the rodut nd how muh rofit is Sterling Mirosystems le to ern? 4. Sterling Mirosystems reently hired two eeedingly intelligent MAs nmed Heidi nd Sener. Sener is in hrge of new rodut develoment, nd Heidi is in hrge of mrket reserh nd rodut riing. Heidi thinks tht Sterling Mirosystems ould inrese its rofit y offering two versions of their softwre

21 Delue Edition (with ll of the fetures ville in the originl version, trgeted t Professionl users) nd si Edition (with fewer fetures, trgeted t Student users). Sener hs roosed suset of fetures tht ould e inluded in suh vlue sutrted version (whih would lso hve mrginl ost of $5), nd Heidi hs estimted the following reservtion ries for eh version for eh tye of user. eservtion Prie for Delue Edition eservtion Prie for si Edition Numer of eh tye of ustomer Student Users $75 $5 N Professionl Users $5,675 $,7 N In order to sell the Delue Edition to Professionls nd the si Edition to Students, wht rie should Heidi set for eh version? 4C. When setting the ries determined in rt (4), how muh rofit is Sterling Mirosystems le to ern? Is this rofit greter thn wht they erned efore introduing the seond version? 4D. Now suose tht in order to introdue this seond version, Sterling Mirosystems would hve to inur rodut develoment osts of $63, (these osts must e inurred if the new version is develoed, ut n e omletely voided if the new version is not develoed). Should Sterling Mirosystems develo the seond version? Elin. 5. Consider firm selling rodut in two different mrkets, Mrket A nd Mrket. The firm hs rodution osts of CQ 8, (where Q denotes the totl untity of outut rodued, nd C is ositive onstnt). Demnd in Mrket A is D A ( ),, while demnd in Mrket is D ( ) 4,8 8. 5A. Derive nd grhilly illustrte funtion whih seifies Totl Demnd ross the two mrket segments. 5. Derive the Inverse Demnd Funtion whih orresonds to the Demnd Funtion whih you derived in rt (5A). 5C. Suosing tht the firm must hrge the sme onstnt er unit rie ross the two mrkets, determine n eression for Mrginl evenue of the firm. 5D. Suose tht C 48. If the firm must hrge the sme onstnt er unit rie ross the two mrkets, wht rie will the firm set, how muh outut will they sell, nd how muh rofit will they ern? 5E. Continuing to suose C 48, if the firm n engge in Third Degree Prie Disrimintion, wht rie will they set nd how muh outut will they sell in eh mrket? How muh rofit is the firm le to ern? How does this outome omre to tht from rt (5D) in terms of relized Consumer Surlus in eh mrket? Elin. 5F. Suose tht C 8. If the firm must hrge the sme onstnt er unit rie ross the two mrkets, wht rie will the firm set, how muh outut will they sell, nd how muh rofit will they ern? 5G. Continuing to suose C 8, if the firm n engge in Third Degree Prie Disrimintion, wht rie will they set nd how muh outut will they sell in

22 eh mrket? How muh rofit is the firm le to ern? How does this outome omre to tht from rt (5F) in terms of relized Consumer Surlus in eh mrket? Elin. 6. Consider firm selling two goods in mrket in whih there re three different tyes of onsumers. The tle elow rovides summry of the reservtion rie of eh tye of onsumer for eh good, long with seifition of the numer of eh tye of onsumer in the mrket. Consumer Tye eservtion Prie for Good X eservtion Prie for Good Y Numer of Consumers Tye A 3 9 Tye Tye C 8 The mrginl ost of roduing eh unit of Good X nd eh unit of Good Y is onstnt $5, while Fied Costs re eul to $5,. 6A. Suose tht the seller is restrited to Simle Monooly Priing (i.e., hoosing nd y, in order to sell eh good sertely). Determine the rofit mimizing rie for eh good nd the resulting rofit of the seller. 6. Suose tht the seller is restrited to Pure undling (i.e., selling the two goods together s kge, for rie of ). Determine the otiml vlue of nd the resulting rofit of the seller. 6C. Suose tht the seller is le to engge in Mied undling (i.e., set rie of for urhsing the goods s kge, in ddition to ries of nd y for urhsing the goods sertely). If the seller wishes to hve tye A onsumers urhse only Good Y, tye onsumers urhse the undle, nd tye C onsumers urhse only Good X, wht ries should he set? At these ries, how muh rofit does the seller ern? 6D. How do the mimum rofits from Simle Monooly Priing, Pure undling, nd Mied undling omre to eh other? Elin.

23 Answers to Multile Choie Questions:.. A D 5. C 6. C 7. C 8. A 9. A. A Answers to Prolem Solving or Short Answer Questions: A. Let m denote minutes used er month. In generl, onsumer eenditure under Pln if m 9 A is E A. Similrly, eenditure under Pln (.)( m 9) if m 9 if m 5 is E. Finlly, eenditure under Pln C is (.)( m 5) if m 5 simly E 4 (for ll m ). For m : E (.)( 9) 6, C E, nd E C 4. Thus, Pln A is est for this onsumer.. For m 6 : E A (.)(6 9), E (.)(6 5) 3, nd E C 4. Thus, Pln is est for this onsumer. C. For m 8 : E A (.)(8 9) 5, E (.)(8 5) 5, nd E C 4. Thus, Pln C is est for this onsumer. D. For very low vlues of m, onsumer eenditures re lowest under Pln A. For very very high vlues of m, onsumer eenditures re lowest under Pln C. For intermedite vlues of m, onsumer eenditures re lowest under Pln. The seifi vlue of m ove whih eenditures re lower under Pln thn under Pln A is the vlue for whih: EA E (.)( m 9) ( m 9). m 4 The seifi vlue of m elow whih eenditures re lower under Pln thn under Pln C is the vlue for whih: E E C (.)( m 5) 4 A

24 ( m 5). m 7 Thus, onsumer eenditures re lowest under Pln so long s 4 m 7. A. If this firm must hrge ll onsumers the sme rie, then the revenue of the firm is ( ) 5. It follows tht mrginl revenue is M( ) 5. eognize tht mrginl osts re MC ( ) 5. Thus, the rofit mimizing untity must stisfy: * 3, 3, Further, the firm will hrge rie of * PD ( *) 5 4 to eh ustomer. Grhilly, *=4 MC(3,)=8 $ *=3, M() MC() Demnd untity =PS =CS =DWL Note tht the effiient untity of trde is the level t whih MC ( ) 5 re eul to P D ( ) 5. Tht is, E 4, 5. From here it follows tht: Dedweight-Loss is eul to DWL (4,5 3,)(4 8) 4, 5 Totl Consumers Surlus is eul to CS (3,)( 4) 9, Produer s Surlus is eul to PS (3,)(8 ) (3,)(4 8) 7, nd Profit is eul to PS F 7, 35, 8,. If insted the firm n engge in Perfet Prie Disrimintion, then they re le to sell eh unit for n mount etly eul to uyer s reservtion rie. Profit is mimized y selling u to the level t whih uyer s reservtion rie is eul to mrginl osts of rodution. For the given funtions, this is 4,5 units of outut. The seller is le to etrt the entire re elow the demnd urve s revenue. Thus, Dedweight-Loss is eul to DWL Totl Consumers Surlus is eul to CS

25 Produer s Surlus is eul to PS (4,5)( ) 4, 5 nd Profit is eul to PS F 4,5 35, 5, 5 C. Comred to Simle Monooly Priing, under Perfet Prie Disrimintion: Dedweight- Loss is smller; Totl Consumers Surlus is smller; Produer s Surlus is lrger; nd Profit is lrger. Further note tht Profit is not ositive under Simle Monooly Priing ut is ositive under Perfet Prie Disrimintion. 3A. For Simle Monooly Priing, the firm essentilly hs three different ries to onsider for eh good. This is euse one the firm deides whih tyes of onsumers to sell to, they will wnt to hrge the highest rie ossile in order to sell to these hosen onsumers. For emle, for Good X, the firm will wnt to hrge rie of either $65 (nd sell only to Tye A), $5 (nd sell to oth Tye A nd Tye, ut not Tye C), or $35 (nd sell to ll three tyes). Fousing on Senrio, these three different ries would yield rofits from Good X of 35 ( 35 )(5 5 45) 5(5) 6, 5 5 ( 5 )(5 5) 4(75), 5 65 ( 65 )(5) 55(5) 3, 875 Clerly the est hoie is 35, whih leds to rofit of 6, 5. y similr logi, it n e shown tht in eh of the two mrkets, ross ll three senrios, the est hoie of ries nd resulting rofits re: y y Senrio ,5 7,65 9,5 Senrio ,875 7,5 83,375 Senrio , 9, 8, 3. If restrited to Pure undling, the mimum rie tht the seller ould set nd still sell to ll three tyes of onsumers is. If he insted wnted to sell to only tyes A nd C, he ould hrge rie u to. The former rie leds to rofit of P ( )( A C) 8( A C), while the ltter rie leds to rofit of P ( )( A C) 9( A C). Thus, selling to ll three onsumer tyes is the etter hoie if nd only if P P 8( A C) 9( A C) 8 ( A C) ( A C) 8 Alying this ondition to eh of the three senrios, if restrited to Pure undling, the seller would sell to ll onsumer tyes in Senrios nd 3 (ut not in Senrio ). 3C. Pure undling results in rofit of P 8( A C) 8(5) 9, in Senrio, whih is not lrger thn the rofit of $9,5 from Simle Monooly Priing. y

26 Pure undling results in rofit of P 9( A C) 9(475) 9, 5 in Senrio, whih is lrger thn the rofit of $83,375 from Simle Monooly Priing. Pure undling results in rofit of P 8( A C) 8(5) 9, in Senrio, whih is lrger thn the rofit of $8, from Simle Monooly Priing. 4A. If they serve oth Professionl users nd Student users, then they would wnt to hrge rie of $75. If insted they hoose to only serve Professionl users, then they would wnt to hrge rie of $5,675. Setting rie of $75 gives rofit of ( 75 5)( N N) (7)(N), 97N While setting rie of $5,675 gives rofit of ( 5,675 5)( N) 5, 67N. Sine 5,67N, 97N for ll N, rofit is mimized y selling to only the Professionl users. 4. When selling the si Edition to Student users, Heidi would wnt to hrge rie of $5, in order to etrt ll surlus from these onsumers. ut note, t this rie, Professionl user ould relize surlus of,7 5, 55 y urhsing the si Edition. Therefore, in order to sell the Delue Edition to rofessionl users, Heidi must set rie for the Delue Edition for whih Professionl user would relize surlus of t lest,55 from urhsing this version. Tht is, 5,675 D,55 D 3, 6 Thus, the rofit mimizing ries re 5 for the si Edition nd D 3, 6 for the Delue Edition. 4C. When hrging 5 nd D 3, 6, Professionl users hoose to urhse the Delue Edition nd Student users hoose to urhse the si edition. As result, the firm erns rofit of ( 5 5)(N ) (3,6 5)( N ),N 3,65N 5, 75N Sine 5,75N 5, 67N for ll N, rofit is greter from offering the two different versions. 4D. The differene in rofit from offering the two versions versus offering only one version (nd otimlly selling only to Professionl users) is 5,75N 5,67N 45N. If they need to inur rodut develoment osts of $63, to rete this seond version, then they would only wnt to do so if 45N 63,. This ondition n e simlified to N 4,. Thus, when fing these u front rodut develoment osts, they should rete nd sell the seond version if nd only if N 4,. 5A. Totl Demnd (ross the two mrket segments) n e otined y summing the untities demnded in eh mrket t every ossile rie. In terms of the given demnd funtions, this mount to D( ) D ( ) D ( ). The given demnd A

27 funtions re D A ( ), nd D ( ) 4,8 8. However, sine untity demnded is never negtive, wht we tehnilly hve in Mrket A is, for D A ( ) for nd wht we tehnilly hve in Mrket is 4,8 8 for 6 D ( ) for 6 Thus, Totl Demnd is 6,8 for 6 D( ) DA ( ) D ( ), for 6 for Grhilly: $ 6 Demnd 8 6,8 untity 5. The orresonding Inverse Demnd Funtion is P D (.5) ( ) 68 (.) for for for 8 8 6,8 6,8

28 5C. If the firm must hrge the sme rie for ll units sold ross oth mrket segments, then Mrginl evenue is Grhilly 6 58 $ (.) M ( ) 68 (.) for for for Mrginl evenue Demnd 8 8 6,8 6,8 5D. First note tht for CQ 8,, mrginl osts re eul to C. As n e seen from the grh ove, for ny vlue of C 58, there will e two intersetion of mrginl revenue nd mrginl ost (nd further, t eh intersetion mrginl revenue intersets mrginl ost from ove, so tht eh intersetion is identifying lol mimum for rofit). With C 48, these two intersetions our t 5 nd,. The orresonding ries re 74 nd 58, nd the orresonding levels of rofit re 3,5 8, 5, 5 nd, 8,,. Thus, the est hoie for the firm is to hrge rie of * 74, sell * 5 units of outut (ll in Mrket A ), nd relize rofit of * 5, 5. 5E. If insted the firm n set different ries in eh mrket, they would hoose to hrge 74 in nd sell 5 units (in order to ern Produer s Surlus of A A PS 3,5 ) in Mrket A nd would hoose to hrge 54 in nd sell A 8 6,8 6,8 untity 48 units (in order to ern Produer s Surlus of PS, 88 ) in Mrket. This results in rofit of * 3,5,88 8, 8, 4. Note tht the firm is not ltering its ehvior in Mrket A, so tht the relized Consumers Surlus in this mrket is etly wht it ws in rt (5D). However, the firm now hooses to sell some outut in Mrket (wheres reviously Mrket ws omletely ignored). Thus,

29 Consumers Surlus in Mrket is now ositive (more reisely, it tkes on n et * vlue of CS (48)(6 54), 44 ) insted of eing eul to zero. 5F. ell, for ny vlue of C 58, there will e two intersetion of mrginl revenue nd mrginl ost (nd further, t eh intersetion mrginl revenue intersets mrginl ost from ove, so tht eh intersetion is identifying lol mimum for rofit). With C 8, these two intersetions our t 7 nd,. The orresonding ries re 64 nd 48, nd the orresonding levels of rofit re 5,9 8, 7, 9 nd 4, 8, 3,. Thus, the est hoie for the firm is to hrge rie of * 48, sell *, units of outut ( * A, 4 in Mrket A nd * 96 in Mrket ), nd relize rofit of * 3,. 5G. If insted the firm n set different ries in eh mrket, they would hoose to hrge 64 in nd sell 7 units (in order to ern Produer s Surlus of A A PS 5,9 ) in Mrket A nd would hoose to hrge 44 in nd sell A,8 units (in order to ern Produer s Surlus of PS, 48 ) in Mrket. This results in rofit of * 5,9,48 8, 38, 4. Note tht when engging in Third Degree Prie Disrimintion (in omrison to Simle Monooly Priing), the firm now hooses to hrge higher rie nd seller lower untity in Mrket A nd hooses to hrge lower rie nd sell higher untity in Mrket. Thus, relized Consumers Surlus will e lower in Mrket A nd higher in Mrket thn under Simle Monooly Priing. 6A. When restrited to Simle Monooly Priing, for Good X the firm will wnt to hrge either: 3 PS ( 3 5)(,) 5, 5 PS ( 5 5)(9) 4, 5 8 PS ( 8 5)() 5, The est hoie is 5 (t whih the firm sells to tyes nd C, ut not tye A), whih results in Produer s Surlus of PS 4, 5 from Good X. Similrly, for Good Y the firm will wnt to hrge either: PS ( 5)(,) 5, y y 6 PS ( 6 5)(8) 44, y y y 9 PS y ( 9 5)() 8, 5 The est hoie is y 6 (t whih the firm sells to tyes A nd, ut not tye C), whih results in Produer s Surlus of PS y 44, from Good Y. Together, these ries yield rofit of 4,5 44, 5, 34, 5. M

30 6. If the seller is only le to sell y wy of Pure undling, then he would wnt to set either: PS ( )(,) 9, PS ( )(8) 8, PS ( )(), The est of these otions is to hrge nd sell the undle to ll three of the different ustomer tyes. This leds to rofit of P 9, 5, 4,. 6C. With Mied undling, if the seller wnts to set ries for whih tye A onsumers urhse only Good Y, tye onsumers urhse the undle, nd tye C onsumers urhse only Good X, the est ries to set re 8, 9, nd. These ries result in rofit of M ( )(7) (9 5)() (8 5)() 5, ( )(7) (85)() (75)() 5, 7, 8,5 5, 5, 43,5. 6D. Comring the rofits from the nswers to rts (6A), (6), nd (6C), we see tht in this se, M P M. Tht is, Mied undling results in stritly greter rofit thn Pure undling, whih in turn results in stritly greter rofit thn Simle Monooly Priing. y