Management Engineering - Leadership & Innovation

Price discrimination exercises

Other

LEZ 10 PRICE DISCRIMINATION EXERCISES Ex 1 MONOPOLY IT Cost Structure say ÈÈ FEYENTS q agg WE CAN Identify DEMAND Functions FOR THE DIFFERENT SEGMENTS Four steps analysis 1.1 monopoly situation i L mate 1.3 resale is not possible V 2 GPD prices compare and make achoice 4 Analyse performances between the two options CPD PRICES We have to maximise profit for the two markets A Pi 2.5 0.59A P ta pay Tc 2.5 0.50 moto i ggg TE F MÉEFIE fixed costs are equally divided among the two markets To maximise It we have to calculate adotta o and verify the maximum trough the second order condition It o GIF MR 2.5 Qa me o qfba.SI sasoogg 7pi71.2sfuser day We verify the maximum IIe 1 o Vox The maximum profit is It 3125 Fa Elday The consumer surplus is Csf ftp.IQ o ftp.qedg 2.5 1.2s 2so o Fthete 1562 se da y To t a l W S A VftCSa 4687 SE day B PÉ S O Iàeger P II p G FB_ 5 QB Qb Fa To maximise It we have to calculated 0 È VIT and verify the maximum trough the second Moto order condition o agli got MR S 293 me o QII a.SI sasoogg 7pfea.sfuser day We verify the maximum Iff a o Vo r The maximum profit is ITS 6250 Fa Elday The consumer surplus is cstf qqfjffgfls 2 si as 31254dm To t a l WSI VI Csa 9375 Hay CPD performance Q'PD QED QED_Sooo userslday PPD TAG TED 9375 F Eday WS 14062 SE da y CSGPD CSEPD CSID 4687 SE day uniform PRICE one product and one price Q Q A QB 5 2p 5 P 10 3 p 7 p 333 0.339 p I p Q F 3.33 0.339 Q F II O 3.33 0.660 È 5000 te pm 1 gg seedayPm VIT me golf 0.66 o voi am Me O TM 3.33 0.33 5 5000 F 8335 FEday WSM_VITA Csm 12,502 Elday CSM 4167 Eday ANALYSE PERFORMANCES GROUP PRICE DISCRIMINATION QUANTITY UNIFORM PRICE 5000 userslday 5000 userslday PRICE 1.25 A 2.5 B Fuser day V 1.667 Fuser day PROFIT 9375 F ay 8335 FEday CONSUMERSURPLUS 4687 SE day 4167 Ebay TIFARE 14062 SE day 12502 Ebay From the analysis of performances we can see that it is convenient to support Gpd since uniform price is an inferior pricing strategy lower results for both the parties company rit and customers Cs With Gpd the commercial launch of Msd is authorised The final outcome depends on different variables however we can generally say that the monopoly m strategy is worse than the group price discrimination Pd It is not always true that csm csa but it is true that A customers are favoured under apd whilst B customers have to pay a higher price However apd results to be the best trade off considering the overall effects Ex 2 PASS actual situation two types of customer two product versions solution Four steps analysis 1 verify pass conditions more than one group impossibility to reach them using GPD strategy 2 PASS pricing and feasibility 3 specialization pricing compare and make achoice 4 analyse performances between the two options We can define a Ntp table for the two groups users B E L 50 75 q q H 100 200 q q In order to apply Pass we have to translate the two constraints partecipation and incentive compatibility into actions in order to push Users to self select their version P WIPE SO E 9 partecipation constraint PE WIPE _200 E q are they feasible Wtf e pe WTA B PB PE PB WTA E NTP B incentive compat ibility constraint PE so 200 100 pel 150 setting pe 200 is not feasible because H users will switch to product B which prices do west pe 50 Effie 150 9 pe min PASS is feasible and customers reveal their category but is this strategy the best one We have to compare the profits of different strategies VITAE PE MC µ PB_me im 150 25 n 50 25 M 125N 25m we consider losers al fitkmonte number of users for gross profit houses each category but we can calculate since Fc are the Limit number for which Pass is Unknown convenient For the case of specialization we have to consider all the possible cases of the Ntp table D Vito 50 25 Ntm 25 Ntm at price so both the categories will buy the product 2 VITE 100 25 N 75N It price 100 only H users will buy the product 3 VITE 75 25 Ntm so Ntm 4 VITE 200 200 25 N 175N When is Pass convenient We need to compare ult'evith the 4 possible ult 1 uttpdsssvttfso dasntzs.ms asntasm 100N o always verified it is not worth to specialize in any case a vita VITI 7 hasnt 2s m 75N sont 25m o always verified it is never convenient to specialize 3 vita VITE 7 hasnt 2s m son som 75N 25m n m PASS is convenient only if NEIN otherwise specialization on E version and set the price 75 is more convenient sue.es III itiI IIIIIIIII onde na m otherwise So Pass is feasible and worth if M and N are comparable 2N Msn whilst it is better to maintain the actual strategy if the number of Losers is very low o very high Ms 2N Man