Chapter 4 Price discriminationECNU Oriental Real Estate College英文版产业经济学教程价格歧视4.1 Definition A prevalent marketing skill and economic phenomena. preferential price or quantity discount. eg.Sometimes people will think that if firms charge different price on different consumers for the same goods, it means price discrimination. But this understanding is incomplete. In much case, discrete price maybe only reflect traffic cost and sales cost fee. And in certain case, universal price means discrimination on the contrary (fixed fee in bus eg.). 英文版产业经济学教程价格歧视Price discrimination means one firm sales the identical goods to different consumers with different net price.(Philips,1983) Net price, subtract product difference from goods price. If price differentiation just reflects the cost difference of supplying to different consumers, we deem price discrimination doesnt exist. Ratio test Harry potterin painly packed edition vs. deluxe edition ,eg.英文版产业经济学教程价格歧视At the same time, we cant say providing different quality goods to different consumers means no discrimination.Reason of providing service in different quality (such as classed cabin in aircrafts and trains) partly is to get consumers surplus by segmenting consumers into different groupsThe concept of “identical” goods： BMW in USA is the same to in German?General equilibrium theorist may point out with some excuse，goods delivered in different time, different location and different state or different quality is different goods, so scope of pure price discrimination is very limited.英文版产业经济学教程价格歧视Conditions of price discrimination1、firms must has market power. We often confine it in monopoly or oligopoly market, only when firms can price higher than marginal cost, can they charge different price on different consumers. Locay and Rodriguez,1992：competitive firms is possible to practice price discrimination, if consumers purchase in group unit.2、the ability of effective market segmentation.3、ensure of no arbitrage. 英文版产业经济学教程价格歧视Market segmentation Can we find a right way to conduct market segmentation（the result must be related to price elasticity and WTP(willing to pay) statusgenderageLocationtimeusePurchasing amount英文版产业经济学教程价格歧视Kinds of arbitrages Possibility of price discrimination is related with possibility of arbitrage.One kind of arbitrage is related with transferability of goods.If transaction cost is low, price discrimination will encounter arbitrage, namely low-price consumers will buy for reselling to high-price consumers. Transaction cost provides one clue to feasibility of price discrimination. Absolute arbitrage or no arbitrage is only two extreme case. Generally, some limited arbitrage will occurs, it depends on relative cost and income.英文版产业经济学教程价格歧视The other kind of arbitrage is related with transferability of different consume packages or bundles provided to consumers.That not means physical transfer of goods among consumers. That means firms try to make every buyer really select consume package designed for him, not for others.Incentive compatibility and self-selection.英文版产业经济学教程价格歧视Influence of arbitrageInfluence of two kinds of arbitrage is different.Transferability of goods is inclined to prevent discrimination.Transferability of demand may cause firms increase discrimination.英文版产业经济学教程价格歧视Three kinds of price discriminationPerfect price discrimination suppliers get all consumer surplus in condition of holding perfect information of willing payment.Second-degree price discriminationsuppliers extract consumer surplus incompletely using self-selection when information of individual preference is incomplete.Third-degree price discrimination Market segmentation using direct information about demand such as age, profession and location etc. and set different price for each group.英文版产业经济学教程价格歧视4.2 Perfect price discrimination(1)simplest case：single consumer (or some identical consumers) has one unit of demand. Monopoly make price equal to reserve price, getting all consumer surplus.A classical example：a doctor is a little village similar with everybody in there and their economic information. He estimates how much everyone is willing to pay for and then charge for that amount.Another case：airline company pay for each aircraft in different price.英文版产业经济学教程价格歧视(2) Complex caseassumption：n consumers hold the same demand curve, and monopoly know about it.q = D(p)/n, so D(p)=nqT gross of consumers payment Two pricing projects：linear pricing and two part tariffLinear pricing：T=pqTwo part tariff：T=A+pq英文版产业经济学教程价格歧视Profit maximizationIn linear pricing, monopoly price：p=Two part tariff：set as net consumer surplus in competitive price p = , set “license fee” A = , so pricing project as below T(q)=Profit compare： Monopoly pricing： = Two part tariff： 0If q0If q=0英文版产业经济学教程价格歧视Profit compareDMCABC=ABCObviously, all the consumer surplus is grabbed in two part tariff.英文版产业经济学教程价格歧视(3) Universal caseAssumption：consumers hold different demand curves, and monopoly know about them.Optimal project：set p = , and ask each consumer pay its net surplus as “license fee” , namelyProblem of information reveal when consumer has unit demand and supplier only know distribution of estimation among them but no about everyones estimation, it will set single price means no price discrimination. 英文版产业经济学教程价格歧视How to make Perfect price discriminationIn fact its a question of information emergingCompretively use coupon or accumulated consuming volumesAuction or bidPricing in bindBargaining directly英文版产业经济学教程价格歧视优惠券的使用(Journal of Marketing Research, 1978)就业状态产品种类铝箔蜡纸头痛药清洁液面巾纸就业29.0%(62)17.7%(62)25.0%(76)32.6%(92)22.4%(116)失业38.3%(128)23.5%(153)28.6%(161)37.4%(214)29.2%(226)表中条目是有使用优惠券倾向的全职主妇购买商品的比例括号中的数字表示所表示比例的抽取样本中人数英文版产业经济学教程价格歧视4.3 Third-degree price discrimination（Multi-market）assumption：Monopoly can segment consumers in some groups according to some exogenous information, and know about each of their demand curves.No arbitrage among groups, and monopoly cant practise price discrimination in one group.A special example of multiple products monopoly pricing：independent demand and interdependent cost英文版产业经济学教程价格歧视How to prevent arbitrage 持卡、凭证担保（转售限制，尤其是对于中间商）掺杂交易费用合约垂直一体化 专栏：航空公司如何防止套利？英文版产业经济学教程价格歧视Profit maximizationGeneral demand Profit function According to Inverse elasticity rule (Lerner index), in every market should existsOptimal pricing means setting comparatively high price in market with lower elasticity.英文版产业经济学教程价格歧视MR1D1MR2D2MCp1p2Q1Q2英文版产业经济学教程价格歧视Welfare compareCompare it with the result of uniform pricingAssume that scale reward fixed：C is constant 英文版产业经济学教程价格歧视Profit and surplusIn case of price discrimination, price in market i is pi, profit as belowGeneral consumer surplus isIn case of uniform pricing, price is ,sales amount in market I is , profit as belowGeneral consumer surplus is 英文版产业经济学教程价格歧视Difference on welfareGeneral difference equals to change of surplus plus profit To set up limit and down limit, makeFunction of NSW is convex function of market price, and S (p) = -D (p) , according to Lagrange median theory,we can getSo, if price discrimination cannot increase sales volume, welfare will be reduced. That is the necessary condition of existence of price discrimination in the social angle.英文版产业经济学教程价格歧视Conclusion Generally, the welfare effect of the third-degree price discrimination is uncertain. It depends on the compare between loss of low-elasticity comparison and gain of high-elasticity consumers and suppliers.One of the central question in policy is its influence to income distribution. Price discrimination transfers benefit of low-elasticity consumers partly to high-elasticity consumers and suppliers.It may be not appropriate, but as we know , low-elasticity consumers are generally (not always) richer group.英文版产业经济学教程价格歧视三级价格歧视实例1Office2000在新加坡的定价 常规价格学术机构价格Excel579199Power Point579199Word579199三件产品的组合759219中国大使馆在新加坡的签证费签证提前时间1天3天7天单次入境756025双次入境857035英文版产业经济学教程价格歧视三级价格歧视实例2：迪斯尼世界门票价格，2006成人门票的类型非佛罗里达居民佛罗里达居民所有主题公园、水上乐园和欢乐岛优惠年票5394294个主题公园的年票415325淡季佛罗里达居民四个主题公园季票 不提供2154天，4个主题公园季票1951711天，1个主题公园季票6356.7英文版产业经济学教程价格歧视4.4 Second-degree price discriminationAssumption：consumer demand is heterogeneous.If monopoly know about tastes of all consumers, it can make perfect price discrimination through providing personal consume packages or bundles.But monopoly generally cannot classify consumers according to some explicit information, and it can provide a menu for selection. Then possibility of arbitrage must be considered, namely consumers belonging to one group may choose consume package designed for other groups.The restriction of self-selection or incentive-compatible. 英文版产业经济学教程价格歧视4.4.1 indirect price discrimination based on time航空公司基于订票时间的价格歧视p起飞时间预售时间票价与提前订票时间的关系提前订票时间2-3天英文版产业经济学教程价格歧视4.4.2 Indirect price discrimination based on qualityProduct lines with different quality statusDifferent kinds of consumers：high value type,low value typeCommon strategy：“harmed” goods，IBM,Sony, IntelpProduct status400350300600486SX486英文版产业经济学教程价格歧视质量歧视的三个决策：厂商应该确定几种不同的等级？ 实践表明，三个而不是两个等级是最优的。各个等级水平如何选择？如何为每个等级的产品制定相应的价格？ 参与约束&激励相容约束英文版产业经济学教程价格歧视例：参考价格对高价位产品的影响微波炉型号选择率（%）第一组（60人）第二组（60人）松下型13松下型4360爱默生5727英文版产业经济学教程价格歧视4.4.3 Indirect price discrimination based on quantityquantity discount. taxi feeelectric power usePackage strategy（quantityprice portfolio）英文版产业经济学教程价格歧视（P、F）组合类型One2one铜服务价格One2one金服务价格月租费17.50英镑36.00英镑工作日白天通话费29便士18便士英国移动通信公司的二部定价套餐此外还有，移动的动感地带短信套餐等。英文版产业经济学教程价格歧视4.5 Comparision among several methods in nonlinear pricingTwo-part tariff (T(q)= A+ pq) provides a menu of consume bundles in a line. Generally the line does not pass origin.Simplicity is its primary attraction, and sometimes it depends on possibility of limited arbitrage.Full arbitrage is prevented, namely only one buyer pays for fixed fee A, and then resale goods to other consumers.Notice：actually two-part tariff corresponds to quantity discount, average price decrease with increase of consume quantity.英文版产业经济学教程价格歧视Profit and welfareAssumption：consumers reference as below U=V(0)=0,V(q)0,V(q)1 ,monopoly produce in fixed cost c, and c 1 2 . for simplicity, assume so V(q)=1-q 英文版产业经济学教程价格歧视Utility functionNotice：fixed cost only influence the decision of buying or not. Once consumers decide to buy, it is out of consider.Consumer utility maximization：U=iV(q)- pqFirst-order condition：iV(q) = pAccording to assumption before,i(1-q) = pSo , demand function is educed as q = Di(p) = 1-p/ iNet consumer surplus is英文版产业经济学教程价格歧视General demand functionIn this case, consumer surplus isNotice that ,and 2 type consumers always hold higher surplus.Make as harmonic mean of 1 and 2 Then general demand in price p is 英文版产业经济学教程价格歧视2 1pP1=cD1D2S2(p)S1(p)英文版产业经济学教程价格歧视Case1：perfect price discriminationAssume that monopoly can observe i directly. Then it can set marginal price as p1=c, and set personal fixed feeManufacturers monopolistic profit isLeave distribution question out of account, welfare here is optimal.英文版产业经济学教程价格歧视Case2：Monopoly pricingAssume that consumers have complete arbitrage, so that monopoly can only set uniform price： T(q) = pqProfit is (p-c)D(p), and D(p) =1- p/ Monopoly price is Monopolistic profit isHere we assume that monopoly decides to provide goods to two kinds of consumers. It need (c+2)/21, or is large enough.英文版产业经济学教程价格歧视Case3：Two-part tariffAssume also that monopoly provides goods to two kinds of consumers.Set marginal price p. Maximal fixed fee that can make 1 type consumers buy goods is A=S1(p). Then 2 type consumers will purchase, because So profit function of monopoly isPrice of profit maximization isSimply, we can see that profit of two-part tariff is as good as in linear pricing at least (the late can be seen as the special case of the former ). 英文版产业经济学教程价格歧视Comparison in welfare effectIts simple to judge that And also, in the case of supplying two kinds of consumers at the same time, marginal of two-part tariff is between competitive price and monopoly price, namelyNotice：welfare under two-part tariff is higher than in linear pricing, because marginal price decreasing will bring purchasing more by two kinds of consumers, so distortion is reduced. To monopoly, it can make up loss by fixed fee when decreasing price. So fixed fee will induce monopoly decrease price so that welfare is gained.英文版产业经济学教程价格歧视ConclusionWe can make a more complex project to get more profit through complete nonlinear pricing. (process omitted)Conclusion 1：low-demand consumers do not get net surplus, while high-demand consumers can get positive net surplus. Conclusion 2：effective restriction to personal arbitrage will prevent high-demand consumers buy low-demand bundles.Conclusion 3：high-demand consumers buy socially optimal quantity; and low-demand consumers buy quantity lower than optimal quantity.英文版产业经济学教程价格歧视4.6 Quality discriminationMonopoly can also practise discrimination through providing different quality goods to different tasty consumers. It is very similar to quantity discrimination.Assume that consumers have unit demand to goods, quality noted as s, taste noted as parameter , consumer utility is U = Assume that price and cost both rest with quality, p=p(s), cost of monopoly producing one unit product is c(s), and c(*) is increasing function, and is convex.s p if they buy 0 if they do not buy英文版产业经济学教程价格歧视Comparability in stylized model and conclusionSet sign over again, we can transfer quality model in quantity model, so these two are the same in stylized meaning.Conclusion4：consumers prefer quality more(2 type) purchase optimal quality; and consumers prefer not so much (1 type) purchase quality lower than optimal level.In fact, monopoly broaden quality level, and providing low-quality goods as means of segmenting markets.英文版产业经济学教程价格歧视Concluding wordsThough we talk about monopolistic case here, most price discrimination occur in oligopoly market. If competitors has difference in one aspect (brand loyalty, location, information, etc) only, manufacturer will practise price discrimination on their residual demand curve.So research on tools of price discrimination, such as depreciate selling, coupon, advertising, bundles selling, is being interesting and important. The theoretic extension to oligopoly market is an important research domain.If loosen the assumption of being not correlative among consumers demand, we get another research aspect, such as the case of providing in the order of priority in electric and telephone service. 英文版产业经济学教程价格歧视