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Basic Price Optimization. Lecture 5. The Price Response Curve , d(p ). How demand for a product varies as a function of price A function for each element in the PRO cube – each combination of product , market-segment and channel Similar to market demand function in economics

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Basic Price Optimization


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    1. Basic PriceOptimization Lecture 5

    2. ThePriceResponseCurve, d(p) • Howdemandfora productvariesas a functionofprice • A functionforeach element inthe PRO cube – eachcombinationofproduct, market-segment and channel • Similarto market demandfunctionineconomics • E.g. differentbooksellers – effectivenessof marketing campaigns, perceivedcustomerdifferencesinquality, productdifferences, locationetc.

    3. E.g. wheat – a commodity, indifferenceamongofferings, perfectknowledgeaboutprices and willbuyonlyfromthelowest-price seller • Each seller isrelativelysmall • Must onlyworryabouthowmuchtoproduce • No need forPricing and RevenueOptimization

    4. Propertiesofprice-responsecurve • PRO decisionshavetimeassociatedwiththem – minutes/hoursinecommerce, days/weeksinretail, longerasinlong-termcontractpricing • Nonnegative • Continuous – no gapsorjumps, thusinvertible • Differentiable – cantake a derivative • Downwardsloping

    5. Forthe rest wewillignore: • Giffengoods– a studentwithan $8 budgetperweekfordinner; burger $1 and steak $2, the latter beingeaten on Sundays; thepriceofburgergoesupto $1.1 – and itsdemandgoesupto 7; VERY rareinreality • Priceasanindicatorofquality– wine: a market withmanyalternatives and some „lazy“ buyers, whousepriceas a proxy • Conspicuousconsumption – a rock stardrinking $300 bottlesofCristalchampagne and driveBentleys

    6. Pricesensitivity: slope, a localestimator • Semiconductors, currentprice $0.13 perchip, slope 1000 chips/weekpercent; 2 centincrease -= 2000 chipsperweek; 3 centdecrease+= 3000 chipsperweek; depends on units – pounds and cents vs. tons and dollars

    7. Pricesensitivity: elasticity, a localestimator, arc and pointelasticity • Percentagechangeindemandtothepercentagechangeinprice; doesnotdepend on units

    8. Semiconductors, currentprice $0.13 perchip, at 10000 chipspermonth; thinkshispriceelasticityis 1.5 • Thus, a 15% increaseinprice, from $0.13 to $0.15, wouldleadto a decreaseindemandofabout 1.5*15%=22.5%: from 10000 to 7750

    9. Short and longrunelasticity • Gasoline – shortrun 0.2, longrun 0.7; similarmilk – 20c pricerise and longrunresponse • Durables (suchasautomobiles and washingmachines) – longrunelasticityislowerthanshort-run • Levelofanalysis – market orcompany

    10. Short and longrunelasticity

    11. Willingnesstopay • Maximumforonecustomer–thereservationprice

    12. A uniformwillingness-to-paydistributioncorrespondsto a linearprice-responsefunction

    13. Partitionsthepriceresponsefunctioninto a total-demandcomponent and a willingness-to-paycomponent • E.g. totaldemandvariesseasonally, whilethewtpdistributionremainsconstantovertheperiodoftime • Wedecomposeourgoalintoestimatingtotaldemand and estimatingthepriceresponse • Anadvertisingcampaignwillnotincreasethetotalpopulation, butwillshiftwtpdistribution • Whenweopen a newstore, thetotaldemandwillbedeterminedbythepopulationserved, butwecanusewtpfromsimilardemographicspopulations

    14. Wtpcanchange – e.g. temperaturesensitive Coca-Cola vendingmachines • A suddenwindfallor a bigraisemayincreaseanindividual’smaximumwtp – ifthese are uncorralatedpopulationwillbeunchangedas a whole, butsystematicchangeswillhavetheprice-responsefunctionshifting • Doesnotincorporateadditionalinduceddemand – pricereductionmayhaveonebuyingtwopairsofsocks • Wtpframeworkisbetterfor „bigticket“ consumeritems and industrialgoods

    15. Linearwtp • Isnot a realisticglobalmodel • If a competitoroffers a closesubstitute, itwillonlyworkclosetothe market price

    16. C is a parameter: d(1) = C Thesetwo– 3.10 fromabove, secondfromwtpslide nr 13

    17. Constantelasticityprice-responsefunctions • Not a realisticglobalmodel – inrealityweexpectelisticitytochangeaspricechanges • If e<1 (inelasticdemand) R’(p)>0, seller canincreaserevenuebyincreasingprice • If e>1, seller canincreaserevenuebydecreasingprice • If e=1 thenpricechangedoesnotchangerevenue • Wtpfunctionishighlyconcentratednearzero • Assumes, thatthedistributionofwtp drops steadilyaspriceincreases, butonlyapproaches 0

    18. Whatis a realisticprice-responsefunction? • Carwith market priceof $13000 • At $20k a fewloyalcustomerwillbuy • … and thereis no bigchangefrom $20k->$21k • Ifwe are selling at $9k, almosteveryone, whowantstobuy a compactcar, willbuyfromus (exceptthefewveryloyalto a competitor) • … and thereis no bigchangefrom $9k->$8k • But at aboutthe market price, elasticityishigh • At market price, manymorewillbuyfromus, whenwe are selling at $250 below, and evenmorewillshift, ifweask $500 belowthe market price

    19. Thelogitpriceresponsefunctions

    20. b =0.0005; 0.001; 0.01; p=$13000; • Pricesensitivityisthehighest at p^=-(a/b) • Wewillfix p^=$13000, thus a=-$13000*b • C isthe market size=20000 • As b grows, the market ismorepricesensitive, approachingperfectcompetition

    21. Empiricalresearchhasshownthelogitfunctiontobe present on a wide range ofmarkets

    22. Priceresponsewithcompetition • IncorporatingCompetitoninthePrice-ResponseFunction • Oftentheprices are notavailableat thetime • Inbusiness-to-businessmarketsthey are never made visibletothecompetition • Retailersdonothavethetimeorresourcestodoexhaustiveresearch on a dailybasis • BUT price-responsefunctionwillbebased on history and thusitalreadyincludes „typical“ competitivepricing

    23. 2) Consumer-ChoiceModeling • E.g. OnlinePetroleumInformation System • Differentgradesofpetroleumofferedbydifferentsellersin all major marketsin USA and Canada • Differentwtp’srepresentthevaluesthat are placed on features and „brandvalue“ associatedwitheachproduct • Surplusisthedifferencebetweentheprice and thewtp

    24. Let p(p1,p2,..,pn) – vectorofprices • Letμi bethe market shareofproduct i • μi=fi(p) for all i • Eachalternativehas a sharebetween 0 and 1 • Eachbuyerchoosesoneproduct • Increaseinpricedecreasesthe market share • Increasingthepriceof a productincreasesthe market sharesof all competitors (substitutes)

    25. Themultinominallogit, b beingpricesensitivity • NotethatKoshibaishighlysensitive and getsa low market sharewhencomparedtoCacophonia, whichistwiceasexpensive

    26. Themultinominallogit and thelogitprice-responsefunction • Whenotherprices are constantthe MNL reducesto LPRF • Assumethatotherprices are constant, weset: • Wherea=ln(k) and weknowthat: 1/K=e^(-lnK)

    27. Tostatetheimportant • Ifcompetitiveprices are stable MNL provideslittlepredictivevalueover LPRF • Thereis a vast literature on consumer-choicemodeling; Statisticalpackagessuchas SAS includeproceduresforestimatingtheparametersofthelogit and probitmarket-sharefunctions • Butthere are weaknesses, namely: ….

    28. Weaknesses • Assumption: everyonepurchasesonealternative; whatifsomedon’tpurchase at all – sincetheirwtpisbelow all prices? Thuswecannotsaythat market size D isindependentofthepricesoffered: anaggressivediscountnotonlysiphonscustomersawayfromcompetitors, butwillalsomakesomeonepay, whomightnothavepurchased at all

    29. Wetheoretically need information on all alternatives, whereasusuallyonlysome major competitors are considered • A solutionhereistoderive a competitiveindexpricebyweightingthepricesof major competitors and usingthisas a singlecompetitivepriceinmultinominallogit

    30. Priceresponsewithcompetition3)Anticipating competitiveresponse • Morestrategically: ifwedrop a price, willthecompetitorsmatch; ifweraise a price – onceagain, whatwillthecompetitorsdo? • Theapproachesherefallunderdecisionanalysis and gametheory – and thereis a vast literature on theuseofgametheoryinstrategicpricing, butwe are concideringtacticaldecisionsof PRO

    31. Forexampleifcustomersin a market choose a supplierbased on MNL priceresponsemodel, thenouractionistomaximizeourexpectedcontributiongiventhecompetitorspricesbysettingourprice • The philosophy of pricing and revenue optimization is to make money by many small adjustments, searching for and vacuuming up small and transient puddles of profit as they appear in the marketplace

    32. Manyofthepriceadjustmentswillfallbelowthe radar screenofthecompetition, and willnottriggeranyexplicitresponse • Butpotentialretaliationsbycompetitorsshouldstillbeconsidered: e.g. Hertzintheearly 1990s bycommunicatingitsupcomingsophisticated PRO systeminthepricewareagercarrentalindustry – itwasabletogenerateadditionalrevenuethroughthousandsofsmalladjustmentstoprices, thatthecompetitorswereunabletomatch

    33. Incrementalcosts • The incremental cost of a customer commitment is the difference between the total costs a company would experience if it makes the commitment and the total cost it would experience if it doesn’t.

    34. Examples • Anairline: additionalmeal and fuelcost + commissionsor fees paid forbooking • A retailer – buying a stockoffashiongoods: zero • A drugstore – ordering a number ofbottlesofshampooweekly: wholesaleunitcost • A distributor – biddingfor a yearlycontractwith a hospital: expectedcostofpurchases, butalsocostofcustomerservice, operatingcosts and holding costsduetovarianceinorders and thereturns

    35. Theincrementalcosts are (closelyrelatedto ABC): • Forward looking: somecosts are sunk, othershavestilltobe made • Marginal: made forthiscustomer, maynotbethesameastheaveragecostofsimilarpastcommitment • Notfullyallocated: nottheoverheadorfixedcostofstayinginbusiness • Candepend on thetype, size and durationofthecommitment: for a multiunit order setupcosts are allocatedacross all theunits • Maybeuncertain: Roadway Express, a truckingcompany – covering all thefreighttenderedbythecustomer at anagreed-ontariff

    36. Thebasicpriceoptimizationproblem, tomaximizethemargin, m(p) totalcontribution; c isincrementalcost

    37. Marginalrevenue (derivativeoftotalrevenuewithrespecttoprice) shouldequalmarginalcost (alwaysnegative) – totalcontributionismaximized

    38. Price-responsefunction d(p)=10000-800p • Incrementalcost $5 • Marginalrevenue R’(p)=10000-1600p • Marginalcost = -$4000 • P*=$8.75

    39. Ifmarginalrevenueisgreaterthanmarginalcost, contributioncanbeincreasedbyincreasingprice • Ifmarginalrevenueislowerthanmarginalcosts, priceshouldbedecreased – in order toincreasecontribution

    40. Optimalcontributionmargin and elasticity • Wecanrewrite 3.17 as 3.20, wheree(p) ispointelasticity; sincethesecond term in 3.20 isalwayspositive: • Ifelasticity at ourpriceis <1, wecanincreasetotalcontributionbyincreasingprice