How To Price Internet Access In A Broaban Service Charge On A Per Unit Basis

Transcription

1 iqui Pricing for Digital Infrastructure Services Subhajyoti Banyopahyay * an sing Kenneth Cheng Department of Decision an Information Sciences Warrington College of Business Aministration University of Floria Gainesville, F * Corresponing author. Phone (352) Fax (352) shubho.banyopahyay@cba.ufl.eu Authors are in alphabetical orer.

2 iqui Pricing For Digital Infrastructure Services Abstract Broaban access proviers toay have an overcapacity in infrastructure, while their service penetration remains low. This has le to the introuction of intermeiate service levels, so that first-time consumers start experiencing the benefits of these new services. We analyze the effect of a novel pricing scheme, calle liqui banwith, whereby customers can upgrae their services for a small perio of time when they want to utilize broaban services for newer types of online content, by paying per-unit access charges. The results inicate that introuction of such pricing schemes can significantly boost the profits of the service provier. Further, effective penetration of broaban services in a monopolist market might require regulatory intervention or some form of subsiy. Keywors: liqui pricing; broaban access pricing; igital infrastructure services; market segmentation; universal access; public policy; market regulation 2

3 Introuction The large-scale eployment of broaban services has brought about a glut in the infrastructure capacity of the service proviers. While 94% of the zip coes in the Unite States have the capability for broaban, the number of broaban users stoo at a relatively moest 28.2 million in December [2]. In terms of broaban penetration among its population, the Unite States is currently ranke eleventh in the worl. In the arena of wireless services, the proviers are expecte to start offering services like wireless Internet at broaban spees, but their aoption remains an open question [18]. In a bi to utilize the available infrastructure, broaban service proviers are thus testing new strategies to attract new customers. In the Unite Sates, given the low penetration of broaban services an the wiesprea infrastructure overcapacity, service proviers have starte offering lite or intermeiate versions of their offerings at lower prices. 2 The unerlying strategy is to gain a foothol into the househols of hitherto ialup customers, who can presumably be later convince to upgrae to higher broaban spees, after they experience the benefits of these services. Further, the rise of igital services like music ownloas, vieo streaming an even full-length feature film ownloas might even lea to the rise of new segment of consumers who might not be heavy users of the traitional internet, but who might value these new services much more. Many cable an DS Internet service proviers, therefore, now regularly offer ownloa spee offerings typically in the range of kbps, at monthly prices that are lower than 1 The FCC efines any spee exceeing 200 kbps as a broaban connection 2 In the authors neighborhoo, for example, the cable broaban service provier introuce an introuctory 256kbps ownloa spee, as compare to the existing 4Mbps an 5Mbps ownloa spees (i.e. roughly 15 an 19 times higher spees). A similar offering structure exists for the local DS broaban proviers. 3

4 their stanar offerings. In short, a confluence of several factors have le the broaban services proviers to experiment with new pricing moels that iffer significantly from the flat-rate pricing that has been common from the early ays of commercial internet access. A relate issue is the very availability of broaban services (this is ifferent issue from capability for broaban, as a service provier might choose not to roll out broaban services in an area that with limite eman for such services even though the basic telecommunications infrastructure might be in place). Access to online information through the internet has now entere public policy ebates. Several broaban service proviers have been charge (with one class-action lawsuit in Floria against AT&T Broaban) with rolling out their services only in high-income areas, an a high-ranking member of the U.S. ouse telecommunications subcommittee has expresse concern with these evelopments [9]. Some analysts argue that there is now nee for government intervention to ensure universal broaban access [10], one iea being that there is a subsiy akin to the Universal Service Funs tax that telecommunications companies toay charge their subscribers to subsiize increase telephone access to schools an rural areas [21]. We analyze the effect of various internet pricing strategies with this backrop. The basic river of this analysis is a promising an innovative service, alreay available in some Scaninavian countries, that allows DS subscribers to boost their connection spees for a limite perio for a small fee, a concept that has been ubbe liqui banwith [1]. 4

5 The unerlying iea is that some consumers might sometimes want to ownloa a large file (for example, a new software, a song or a meia clip, or even a full-length feature film), an woul prefer the higher spees for those limite timeframes. These users woul prefer to pay lower costs for the service for their typical usage (like checking , online buying, or regular web surfing), but woul fin that service too limite for ownloaing large files. Currently, the service levels provie by the service proviers fail to catch this opportunity for these classes of users, who either o not sufficiently utilize the high-banwith content, or o not use them at all after consiering the agonizing wait at their service level. With the rapi growth of online content (in the form of ownloaable songs, real-time entertainment an graually full-length feature films), an the overwhelmingly large population of users still using narrowban access, the size of this misse opportunity gets larger by the ay. 3 These users might not value their traitional Internet access very highly, but woul be willing to pay more for the new online igital content. In the corporate segment, liqui banwith is alreay a functional concept in some places a company in the Unite Kingom, Neos Networks 4, provies upgraes to corporate customers that range from 30 MB/s to 100 MB/s within ten minutes. [4] argues that the lack of segmentation in broaban services is a irect result of the fact that service proviers o not offer quality of service guarantees, an therefore customers o not value ifferent levels of services. They point to the lack of empirical evience of customers paying more for relatively better performances. In recent times, however, 3 In fact, the content service proviers have a possible revenue-sharing opportunity with the proviers of these nascent high-banwith services

6 several broaban access proviers have starte to introuce ifferent levels of service, an anecotal evience seems to suggest that consumers are graually ifferentiating between ifferent classes of service insofar as their service offerings are sufficiently ifferent, an are willing to pay ifferent prices for them epening on the elay they incur while waiting for their service. 5 In this paper, we therefore moel the consumers choice emanating irectly from their ifferent levels of isutility of waiting for the service. In other wors, consumers who woul not min the congestion create by others woul have a lower elay cost as compare to consumers who o not like waiting for their Internet ownloa to take place, regarless of the type of usage. This paper looks at the various moels of market segmentation in broaban internet access, an analyzes the viability of the new pricing strategies. In particular, we try to analyze whether the concept of liqui pricing of broaban access services increases the profits of the service proviers. These pricing strategies are in no way limite to just broaban internet access, an can be in fact moifie for pricing of igital infrastructure services in general. It also consiers the public policy implications in such pricing strategies e.g. uner what market conitions woul there be a nee for subsiies in orer to ensure market coverage [3]? The INDEX project trial at the University of California at Berkeley [7] emonstrate clearly that flat-rate pricing of internet service proviers (or ISPs) is very inefficient an hiners eployment of broaban access. Further, it showe that quality-ifferentiate 5 For example, other than the example in Footnote 2, several DS service proviers, like BellSouth, SBC or Earthink, regularly offer three levels of broaban services ifferentiate by the ownloa spees 256 kbps, 1.5 Mbps an 3.0 Mbps. 6

7 service levels provie higher levels of surplus for both the consumers an service proviers. Market segmentation base on consumers utility levels an willingness to pay is a well-known concept. While proviing ifferent ownloa spees for a fixe fee is efinitely a more efficient strategy than one price fits all, the concept of liqui banwith provies the opportunity of better customer segmentation an the ability to cater to customers who value traitional static informational online access ifferently from the newer online content. A consumer toay can call her service provier an immeiately get upgrae to a higher banwith, an the entire process is controlle through software. 6 Thus, from a technological point of view, the problem is relatively simple, an the marginal cost of implementation especially at current levels of infrastructure utilization is very close to zero. What is require is a simple billing interface that the consumers can interact with either by calling the customer service or by orering from the Internet (the latter allowing further lowering of the transaction costs). Our paper iffers from the current literature in the way it explicitly allows for moeling the above-mentione opportunity. We moel the Internet traffic an its pricing in terms of congestion costs for various types of users. We consier the pricing for Internet access on a per-unit basis (the unit being of course time), an fin conitions for equilibrium uner ifferent scenarios of service offerings an consumer types. iterature review 6 One of the authors got his service upgrae to 5.0 Mbps, teste the ownloa spee, an then owngrae the service to 4.0 Mbps, teste it again, all within the uration of one phone call. 7

8 Market segmentation is an effective tool to extract consumer surplus when there is sufficient heterogeneity among customers, see for example, [6, 13, 17, 19, 22]. Several existing literature on tiere pricing for Internet services focus on the quality of service at the level of an iniviual packet. For example, [14] an [15] propose a smart market for Internet pricing, whereby the iniviual packets contain a bi value that is set by the originator of the packet, an packets with higher bi values are given priority to clear the (congeste) network. [20] proposes a Paris Metro Pricing framework, where the network consists of several subnetworks that are ientical in terms of operation, but iffer in price. Users therefore self-select the networks base on the valuation of their packets an expecte congestion. Several papers aress the main architectural criticism of this framework, namely its inability to provie quality of service (QoS) guarantees, an a summary of that literature can be foun in [4]. [4] proposes a novel quality-contingent pricing scheme an consiers two mechanisms a proportional rebate base on number of packet losses or full rebate if the quality falls below a certain threshol (see also [5] for a etaile iscussion on the full-price rebate moel). [4] assumes that users in a community receive the same level of service, an therefore suggest ifferentiating between them on the level of service guarantee. They therefore suggest a monitoring equipment for recoring QoS between the service provier an the en-users that is maintaine by an inepenent auiting boy. They then go on to suggest the two aforementione pricing schemes. The moel therefore provies an interesting an novel variation on access pricing in terms of quality of services 8

9 guarantees. owever, it is base on the premise that all users receive the same class of service, an therefore cannot be applicable when the provier specifically introuces multiple classes of service. In contrast, our moel specifically assumes that the service provier introuces ifferent classes of service that caters to ifferent types of user nees. Our moel extens the congestion pricing moel suggeste by [16], whereby a pricing moel is propose by taking into consieration the value of the users time. It also has stylistic similarities to the moeling of [11]. We assume that there are ifferent classes of users, who value their cost of elay (in terms of ollars per unit time) in a congeste network ifferently, which in turn provies for the opportunity to segment the consumers. The moel takes cognizance of the fact that currently there are ifferent classes of service, an ifferent classes of users who value their access elays ifferently. It also takes into account the fact that there are new types of igital content that might make current pricing implementations limiting for a large number of users. Finally, since the technology for implementing its pricing scheme alreay exists, there is no nee for any ae harware to implement it. Moel assumptions For simplification purposes, we assume that there are two levels of consumer eman, enote by an, although there can be more than two service offerings. In other wors, if the service in question were a broaban Internet service, there woul be two possible classes of consumers. Consumers who woul want the higher spee regarless of usage are classifie the high-type (), an the consumers who woul regularly want 9

10 the lower spee are classifie the low-type (). In our moel, the service provier is assume to be exclusively a high-banwith provier. Thus, other than the ecision regaring introuction of liqui pricing of on-eman services, the provier has to ecie whether to cater to just the high-type customers or both types of customers. We assume that most of the consumers are of the latter type, i.e. the consumers who want speey access at all times are relatively small in number. We also assume that the low-type consumers feel the nee for high-banwith services for a relatively small fraction of the time. We will later specify in greater etail what these relatively small quantities mean in the context of the moel. We assume a fixe size of a packet regarless of the type of usage, an the usage levels iffer only in the arrival rates of the packets, which is a reasonable assumption for Internet traffic. The two types of customers are ifferentiate in terms of the arrival rates of these packets: the high-type customers have a much higher arrival rate of these packets as compare to the low-type customers. We assume that the service provier has ifferent fixe fees per unit of time for the two levels of services, an a per-unit charge (i.e. liqui pricing) for on-eman access. Finally, for tractability purposes, we make the simplifying assumption that the two types of users have the entire channel banwith eicate to themselves when they are using a particular channel. 7 The Moel We consier two scenarios for our moel in orer to istinguish the effect of offering the low-type users to utilize banwith on eman. In both scenarios, we make the same assumptions regaring the service offerings an the two types of consumers. The first 7 In terms of the two most common forms of broaban internet access toay (cable an DS), it nees to be clarifie that we moel the congestion at the back en of the service provier (between the provier an the Internet). We thank one anonymous reviewer for suggesting this clarification. 10

11 scenario iscusses the moel that is more prevalent until now a broaban provier who provies a single level of service, regarless of the user type, just like the assumption of [4]. In the secon scenario, the broaban service provier has two classes of service, an has the option of proviing liqui pricing for on-eman access to the low-type customers as an when they request it. Moel 1 We apply a M/M/1 queuing system to escribe the service system where the high-type customers are characterize by a Poisson arrival rate of requests (packets) per unit of time λ, while the low-type customer s Poisson arrival rate of requests (packets) per unit of time is λ an λ λ. The service provier has the capacity of processing μ requests per unit time. et N an N represent the numbers of high type an low type customers respectively. Further, let be the elay cost per unit of time of high-type customers an the elay cost per unit of time of low-type customers is. Naturally, >. The gross value function of using the service for the two types of customers is escribe by v( λ k ), k {, }. The v( λ k ) v( λ ) v( λ ). s are twice ifferentiable an concave, an Thus, in this scenario, we assume that the service provier has one channel of service to serve all her customers. The capacity is enough to serve μ service requests (packets) per unit of time. As is to be expecte, the high-type customers place a premium on their service, an therefore their isutility of waiting is higher ( > ). Further, since the 11

12 valuation of a service is likely to increase with the number of packets sent, an the arrival rate of packets is significantly higher at broaban spees, we assume that v( λ ) v( λ ). Analysis A provier who has the technology to provie high banwith services can ecie on whether to sell to the high-type customers only or cater to both types. She can also ecie whether she wants to introuce liqui pricing, or go for only fixe fee pricing. These strategies are summarize in Table 1: Table 1: Prouct Strategies of the Digital Infrastructure Services Sell to igh type only Sell to both types No on-eman Option 1 Option 2 Π = N F 1 1 Π = ( N + N ) F 2 2 Introuce on-eman Option 3 Π = N pλ 3 1 Option 4 Π = N F + N p λ The F i, i {1,2,3}, in Table 1 refers to the various fixe prices in Options 1, 2 an 4 respectively, while p, j {1,2}, represents the liqui pricing, i.e. usage charge per unit j of time in Options 3 an 4. 8 It nees to be clarifie that the two perios of time for 8 Since the provier has just one level of service in this moel, the implicit assumption in option 4 is that the low-type customer utilizes its services only uring the times he nees broaban access, an therefore has some other provier for its usual internet access requirements. The setting of moel 1 is somewhat artificial that way, since there is only one channel. In this setting, if the low-type user is given a (presumably lower) fixe access charge for his usual nees, he will have no nee to pay per unit access charges for his broaban nees (since he gets to use that same channel through his fixe fee). Further, the high-type user woul have no incentive to pay a higher fixe cost for the same service, an thus Option 4 woul reuce to Option 2. This artificiality is taken care of in Moel 2, which expectely gets more 12

13 charging the fixe price an the liqui pricing are ifferent the fixe pricing can be thought of as the monthly charges that is common toay, while the unit time for the liqui pricing woul probably be a slot of a few hours. The profit maximization principle of the provier in each of the above options is as follows: Option 1: max Π = N F F1 1 1 s.t. v( λ ) F1 0 μ N λ (1) Option 2: max Π = ( N + N ) F F2 s.t. 2 2 v( λ) F2 0 μ ( N λ + N λ ) (2) v( λ ) F2 0 μ ( N λ + N λ ) (3) Option 3: involve. Similarly, the high-type user will have no nee to pay on-eman access charges along with a fixe fee in Option 3, since he alreay has access to the same channel (an its lower congestion) though Option 1, an therefore Option 3 will reuce to Option 1. Our iea was to introuce first a simplifie Moel 1 to give a general flavor of the problem an its implications, an then follow it up with the more realistic Moel 2. 13

14 max Π = N pλ p1 3 1 s.t. v( λ) p1λ 0 μ N λ (4) Option 4: max Π 4 = N F3 + Np2λ F3, p2 s.t. v( λ ) p λ v( λ ) F 2 3 μ ( Nλ + Nλ) μ ( Nλ + Nλ) v( λ ) F v( λ ) p λ 3 2 μ ( Nλ + Nλ) μ ( Nλ + Nλ) v( λ) p2λ 0 μ ( N λ + N λ ) v( λ ) F3 0 μ ( N λ + N λ ) (5) (6) (7) (8) In option 1, the single constraint (1) is bining, as the provier will raise the price of the service such that it is just worthwhile for the high-type consumers to participate. Similarly, in option 3, the single conition is bining. Thus, we get in option 1, An in option 3, F = 1 v( λ ) μ N λ (9) v( λ) / λ p1 = (10) λ μ N λ The profit to the provier is the same in both cases, so that 14

15 Π 1 =Π 3 = N v( λ) μ Nλ (11) Given the fact that option 1 an 3 yiel the same profit, we comment that in practical terms, the service provier woul probably introuce just option 1, given the possible complexities of billing for liqui pricing, especially when it oes not yiel any extra profit. We also note that the consumer surplus in both these two options is zero, as the single conitions are bining. In option 2, the two constraints are essentially the participation constraints of the low- an high-type users respectively. Since v( λ ) v( λ ), constraint (3) becomes strictly positive, an therefore the high-type consumer has a strictly positive surplus. The service provier raises the price of the service so that it is just worthwhile for the low-type to participate for the service, so that the first constraint becomes bining (the low-type consumer thus has zero surplus). Therefore, v( λ ) F2 0 μ ( N λ + N λ ) =, or an F2 = v( λ) (12) μ ( N λ + N λ ) Π 2 = ( N + N) v( λ) μ ( Nλ + Nλ) (13) We note that the consumer surplus of the high-type consumer is given by the expression v( λ) v( λ). μ ( Nλ + Nλ) μ ( Nλ + Nλ) 15

16 Option 4 gives us the stanar formulation of the mechanism esign of the two-menu, two-customer moel, where (5) an (6) are the incentive compatibility constraints an (7) an (8) are the participation constraints of the low- an high-type users respectively. It is common for service proviers to price their services higher when they charge on a perunit basis, as compare to when they charge a fixe fee, especially at higher usage levels. 9 Following this common practice, the service provier in our moel will increase the (fixe) price of the high-type user to such an extent that he fins it just worth his while to pay the fixe price. In other wors, constraint (6) will be bining. Thus, v( λ ) F = v( λ ) p λ. 3 2 μ ( Nλ + Nλ) μ ( Nλ + Nλ) This leas to F 3 = p 2 λ, an substituting this value of F 3 in (5) shows that constraint (5) will not be bining. Also, since v( λ ) v( λ ), we can assume that the net utility of the of high-type user is higher than that of the low-type user, i.e. v( λ ) F v( λ ) p λ. 3 2 μ ( Nλ + Nλ) μ ( Nλ + Nλ) Since the right-han sie of the above inequality is the net utility of the low-type user, his participation constraint ensures that the participation constraint of the high-type user is not bining. The service provier increases the liqui price of the low-type user so that he just participates. Therefore, v( λ) p2λ = 0. μ ( N λ + N λ ) 9 For example, cell phone service proviers charge higher for the so-calle pre-pai options (where the subscribers pay by the minute) than for services that have a fixe service cost per month. The same phenomenon is observe in broaban Internet access services in the authors local area for example, the cable broaban connection service offers a 256kbps ownloa service at approximately $25 per month, an 4Mbps an 5Mbps ownloa services at $40 an $55 per month respectively (the uploa spees also vary consierably for these services). 16

17 Thus, F = p λ (14) 3 2 an p 2 v( λ) / λ = (15) λ μ ( N λ + N λ ) Therefore, the total profits of the provier in option 4 is given by v( λ ) / λ Π 4 = p2 N + N = N + N λ μ ( Nλ + Nλ) ( λ λ ) ( λ λ ) (16) As is to be expecte, given the bining participation constraint, this profit epens on the elay cost of the low-type customer, an not that of the high-type customer. Further, as expecte, the low-type consumer oes not have any surplus, while the high-type consumer has a strictly positive surplus, given by v( λ) / λ v( λ) λ. μ ( Nλ + Nλ) λ μ ( Nλ + Nλ) Depening on the functional form of the gross value function v( λ ), the relative magnitues of the two types of customers, an their elay costs, the provier will rank the various profit functions, an choose the strategy that gives her the highest profits. Given the large number of parameters, an the functional form of the equilibrium, it is ifficult to make an analytical comparison between the various expressions of profit, so instea we consier a numerical example. 17

18 a Following [16], we assume an isoelastic eman function, such that v ( λ ) = k λ, so k that 1 a kλ v( λk ) =. In our stylize framework, the absolute values of the parameters are 1 a not so important as the relative magnitues of the parameters of the two ifferent types of customers. We therefore normalize λ, N an at their respective unit values to simplify analysis. The U.S. Census Bureau [8] estimates the number of U.S. househols in 2003 to be about million, an given the number of broaban access lines of about 28.2 million househols, currently about a quarter of the U.S. househols receive some form of broaban access. We therefore vary N in the range [0.1, 0.4]. We assume that true broaban access ranges between 1.5 to 5 Mbps, while lite broaban access is suppose to be 256 kbps. Therefore, we vary λ in the range [6, 30] as compare to the normalize unit value of λ. Finally, without reliable ata to serve as proxy for costs of elays for the two ifferent classes of users, we somewhat arbitrarily vary between the values 5 an 10, keeping normalize. Figure 1 shows the change in the profit functions with = 5, while Figure 2 shows the change in the profit functions with = 10. In both the figures, the relatively flat meshe surface shows the profit Π 2 uner Option 2, the smooth upwar-sloping surface represents the profit Π 1 or Π 3 uner Options 1 an 3, an the meshe upwar-sloping surface represents the profit Π 4 uner Option Insert Figures 1 an 2 About ere

19 As the figures inicate, option 2 (i.e. selling to both types of customers charging a single fixe fee) gives the provier highest profits when the relative magnitues of N N an λ λ are low. Thus, introucing on-eman access oes not make sense when the number of high-spee users an their relative banwith requirements are low. Option 1 (i.e. selling to high-type users only) make sense at intermeiate values of N N an λ, while at higher values of these ratios, introucing liqui pricing for low-type λ users becomes the most preferre option. Thus, in the early stages of introuction of broaban services, service proviers woul probably be best off by serving both types of customers with one fixe access charge per month. As broaban services become more popular, we run into an interesting situation where the monopolist provier might not want to service the low-type users (option 1 or 3), a situation that regulators might want to be aware of. To ensure that the low-type users are not left uncovere, regulators might want to subsiize the monopolist provier, which might manifest itself in the form of universal service funs (USF) that many telecom proviers nowaays charge for expaning telephone services to schools an rural areas. This subsiy shoul be roppe as broaban penetration rates increase an access spees get faster. We make the observation that at current penetration rates for broaban (aroun 25%) an the graual introuction of broaban access at 3 Mbps or higher, option 2 woul 19

20 probably not be the preferre route for most service proviers toay except in very nascent market segments. Moel 2 In the secon scenario, we assume that the low-type customers nee their normal lowbanwith services most of the time, an access to high-banwith services for α fraction of their time. We also assume that the provier employs two eicate service capacities, μ 1 an μ 2 where μ 1 μ 2. In terms of notation, we have the following: N : number of high-type customers N : number of low-type customers λ : igh-type customer s arrival rate of requests per unit of time, an that of the lowtype s for α fraction of the time. λ : ow-type customer s normal arrival rate of requests (packets) per unit of time α : proportion of the time of the low-type customers whose arrival rate of requests is λ, so that in the other (1 α) proportion of the time the arrival rate is λ. : elay cost per unit of time of igh type customers an the high traffic of low-type customers : elay cost per unit of time of the normal traffic of low-type customers, where >. μ 1 : service capacity of the channel for the high-type customers (channel 1), per unit of time μ 2 : service capacity of the channel for the low-type customers (channel 2), per unit of time, where μ 1 μ 2. F i : fixe fee per unit of time, where i {5,6,7,8,9} for selecting the two service capacities in the options 5, 6 an 8 we escribe below 20

21 p : usage charge per unit of time, j {3,4} in options 7 an 8 that we escribe below j v( λ k ) : gross value function of using the service for the two types of customers, k {, }, twice ifferentiable an concave Analysis Once again, we assume that the service provier has a matrix of strategies, epening on whether she wants to cater to both type of customers, or just to the high-type, as well as her ecision to introuce on-eman services. The various possible strategies for the provier are summarize in Table 2. Table 2: Prouct Strategies of the Digital Infrastructure Services Sell to igh type only Sell to both types No on-eman Option 5 Option 6 Π = N F 5 5 Π = N F + N F Introuce on-eman Option 7 Π = N p λ 7 3 Option 8 Π = N F + N p αλ + N F Option 5 refers to the ecision where the provier caters just to the high-type customers for a fixe fee. Option 6 refers to the ecision where the high-type customers are serve through the high-banwith capacity μ 1, an the low-type customers are serve through the low-banwith capacity μ 2. In option 7, the provier serves the high-type customers only for a per-unit access charge. In option 8, we moel the real-worl scenario, where the high-type customers are serve through the high-banwith capacity μ 1, an the lowtype customers are serve through the low-banwith capacity μ 2 ; in aition, for an 21

22 α fraction of the time, the low-type customers have a requirement for high-banwith services, with an arrival rate of λ, for which they pay a per-unit access charge of p 4. The profit maximization principle of the provier in each of the above options is as follows: Option 5: max Π = N F F5 5 5 st.. v( λ ) F5 0 μ N λ 1 (17) Option 6: max Π = ( N F + N F ) (18) F6, F st.. α v( λ) + (1 α) v( λ) F μ2 Nλ μ2 Nλ α v( λ) + (1 α) v( λ) F μ1 Nλ μ1 Nλ 7 6 (19) α v( λ) + (1 α) v( λ) F7 0 μ2 Nλ μ2 Nλ v( λ) F v( λ ) F μ λ μ λ N 2 N v( λ ) F6 0 μ N λ 1 (20) (21) (22) Option 7: 22

23 max Π = N p λ p3 7 3 st.. v( λ) p3λ 0 μ N λ 1 (23) Option 8: max F8, p4, F9 st.. Π = N F + N p αλ + N F α v( λ ) p λ + (1 α) v( λ ) F 4 9 μ1 Nλ μ2 Nλ α v( λ ) p4λ + (1 α) v( λ) p4λ μ1 Nλ μ1 Nλ (24) α v( λ ) p λ + (1 α) v( λ ) F 4 9 μ1 Nλ μ2 Nλ α v( λ) + (1 α) v( λ) F μ1 Nλ μ1 Nλ 8 (25) α v( λ ) p λ + (1 α) v( λ ) F 4 9 μ1 Nλ μ2 Nλ α v( λ) + (1 α) v( λ) F μ2 Nλ μ2 Nλ 9 (26) α v( λ) p4λ + (1 α) v( λ) F9 0 μ1 Nλ μ2 Nλ v( λ ) F v( λ ) p λ 8 4 μ1 Nλ μ1 Nλ v( λ) F v( λ ) F μ λ μ λ N 2 N v( λ ) F8 0 μ N λ 1 (27) (28) (29) (30) 23

24 The etails of the erivations are provie in the Mathematical Appenix. For options 5 an 7, we get, Π =Π = N 5 7 v( λ) μ1 Nλ (31) Equations (A1) an (A2) in the mathematical appenix essentially inicate that the service provier extracts all the rent in options 5 an 7, an therefore the consumers have a zero surplus. In option 6, constraints (19) an (20) are the incentive compatibility an participation constraints of the low-type customer, (21) an (22) are the incentive compatibility an participation constraints of the high-type customer. For tractability purposes, we assume that most of the users are the low banwith users, so that not only N > N but also Nλ Nλ >, i.e. in terms of total banwith usage, the low-type users cumulatively consume more of the banwith than the high-type users. We further assume that F6 > F7, i.e. the fixe charge for the low-type users is lower than that of the high-type users, something which is reaily observable an expecte in real life. Now, with μ1 > μ2, one can verify that (19) is a strict inequality, an therefore the incentive compatibility constraint of the low-type user is not bining. From the analysis etaile in the mathematical appenix, we see that the profit in option 6 is given by 24

25 α v( λ) + (1 α) v( λ) μ2 Nλ μ2 Nλ Π 6 = N μ2 Nλ μ1 Nλ. (32) + N α v( λ) + (1 α) v( λ) μ2 Nλ μ2 Nλ The surplus of the low-type consumer is zero, while that of the high-type is given by the expression α 1 2 (1 α) v( λ) + v( λ) + +. μ2 Nλ μ2 Nλ μ2 Nλ μ1 Nλ In option 8, for tractability purposes, we make a simplifying assumption that the two types of users have the entire eicate channel banwiths to themselves when they are using a particular channel. Further, as before, we assume that most of the users are the low banwith users, so that not only N > N but also N λ > N λ, i.e. in terms of total banwith usage, the low-type users cumulatively consume more of the banwith than the high-type users. The erivations in the mathematical appenix shows that the profits in this option is given by 1 α v( λ) + (1 α) v( λ) 1+ α μ2 Nλ μ2 Nλ Π 8 = μ2 Nλ μ1 Nλ 1 + N α v( λ) + (1 α) v( λ) 1 α μ2 Nλ μ2 Nλ + ( N α N ) (33) 25

26 Equation (A8) inicates that the per-unit charge for the high-channel is such that it just issuaes the high-type of user from choosing per-unit charges. Equation (A9) shows that the fixe price ifferential between the high-channel an the low-channel, which is the ifferential that high-type user pays for his service (as compare to the low type), is equal to the ifference in the elay cost of the high-type of user between using the low-channel an him using the high-channel. In other wors, the premium over the price of the lowchannel that the high type-user is willing to pay for the high-channel is equal to the extra elay cost he incurs in using the low-channel. Thus, equation (A10) gives us the maximum fixe price that the provier can extract for the low-channel, which can then be inserte in equation (A9) to get the price premium that the provier can charge for the high-channel. This price premium provies the basis for the provier to ecie on the maximum per-unit charge that he can comman from the low-type users for the highchannel in equation (A8). Once again the consumer surplus of the low-type user is zero, while that of the high type is given by the following expression: 1 v( λ) α v( λ) + (1 α) v( λ) + 1+ α μ2 Nλ μ2 Nλ μ2 Nλ μ1 Nλ As before, we plot the profit functions in the various options available to the service provier. The specific values of the parameters are kept the same as before, except that in orer to keep the relative magnitues of the available banwiths as per our assumption μ μ, we stipulate that μ 1 = 500 an μ 2 = 50. We further assume that the fraction of 1 2 time that the low-type users feel the nee for high banwith services, α = 0.1. Figures 3 an 4 show the change in the profit functions uner the various options as the ratios 26

27 N N an λ λ change. In both the figures, the relatively flat meshe surface shows the profit Π 6 uner Option 6, the smooth surface represents the profit Π 5 or Π 7 uner Options 5 an 7, an the meshe upwar-sloping surface represents the profit Π 8 uner Option Insert Figures 3 an 4 About ere --- It is interesting to note that within the range of variation of the ratios of the parameters N N an λ, option 6 (selling to both types of users with ifferent fixe prices) λ never yiels the highest profits for the monopolist service provier. Thus, at least uner the conitions of this moel, a service like AO Broaban to coexist with the regular ialup AO service is counter-prouctive. For relatively lower values of the two ratios, the monopolist will service only the high-type of users, an at higher values of the two ratios, serving both types of customers with the option of liqui pricing on eman for the low-type of users the becomes the most attractive option. As in Moel 1, the results of this stylize moel inicate that the monopolist provier might have to be subsiize or regulate in some fashion so that she provies highbanwith services at the initial stages, when the number of early aopters is low. Once the service gets more establishe among the consumers, an the service provier begins 27

28 to provie higher access rates, the liqui pricing option becomes the most lucrative, an the subsiy (or regulation) shoul then be remove. Conclusion This paper looks at the effect of introucing on-eman access with liqui pricing for igital infrastructure services, like broaban Internet, wireless communication, etc. The twin effects of infrastructure overcapacity an relatively low penetration of highbanwith services has prompte the introuction of intermeiate level services to the general population, with the hope that in the long term, these consumers woul graually upgrae their services. This paper shows that introucing liqui pricing for on-eman access to broaban services can increase the profits of the service provier. Introuction of such a service woul have practically zero costs, especially in an environment of infrastructure overcapacity, but can significantly increase revenue an profits. The results also inicates that the monopolist might sometimes prefer to service only the high-type of user, which might therefore prompt regulators to either force her to service both types of users, or otherwise subsiize her in some other fashion (assuming of course that universal access to broaban services is the esire goal of the society). As mentione in the introuction, banwith service proviers have an opportunity of revenue-sharing with proviers of broaban content. Organizations like Movielink (ownloaable feature films), Real Networks (broaban entertainment), an the rapily growing igital music inustry woul greatly benefit from increase aoption of broaban services by users who might value the traitional Internet access very 28

29 ifferently from the new online content. A similar phenomenon is graually taking shape in the mobile telecommunications inustry. An interesting extension of this research woul be to moel the effect of the availability an aoption of broaban content. In South Korea, which has the highest per-capita penetration of broaban services in the worl, broaban service proviers are graually moving into proviing broaban content in orer to rive revenues [12]. One coul therefore moel this environment as a content provier-access provier-consumer supply chain an analyze whether these content proviers shoul subsiize broaban access in orer to grow the market, as oppose to intervention by a regulatory boy that we inicate in our moel. 29

30 References 1. Between a rock an a har place, The Economist, Vol. October, October 9 (2003), Special Supplement. 2. New figures show broaban eployment accelerating in the US, Feeral Communications Commission, September (2004). 3. Banyopahyay, S., an Cheng,.K., Broaban pricing, universal access an implications for public policy. 2005, Warrington College of Business, University of Floria: Bhargava,.K., an Sun, D. Quality-contingent pricing for broaban services, in Proceeings of ICSS-38, awaii, Bhargava,.K., an Sunaresan, S. Contingency pricing for information goos an services uner inustrywie performance stanar. Journal of Management Information Systems, 20, 2 (2003) Dobson, G., an Kalish, S. Positioning an pricing a prouct line. Marketing Science, 7, 2 (1988) Eell, R.J., an Varaiya, P.P. Proviing Internet Access: What we learn from the INDEX trial, INDEX Project Report #99-010W, University of California at Berkeley, (1999). 8. Fiels, J. American families an living arrangements, U.S. Census Bureau, November (2004). 9. Garner, W.D. Broaban 'Relining' Issue Raise In Fiber Deployment, (2005) Gomes,. Despite Opposition, Might the Web Nee New Government Jolt? The Wall Street Journal, February , B aruvy, E., an Prasa, A. Optimal prouct strategies in the presence of network externalities. Information Economics an Policy, 10 (1998) ong, M.Y., an Kim, S. Broaban's future: lessons from South Korea. The McKinsey Quarterly, 4, (2004) ilien, G..; Kotler, P.; an Moorthy, K. Marketing moels. Prentice all, Mackie-Mason, J.K., an Varian,.R. Pricing the Internet, in Proceeings of Public Access to the Internet, JFK School of Government, Mackie-Mason, J.K., an Varian,.R. Some economics of the internet. e. W. Sichel, University of Michigan Press, Ann Arbor, MI,

31 16. Menelson,. Pricing computer services: queueing effects. Communications of the ACM, 28, 3 (1985) Moorthy, K.S. Market segmentation, self-selection an prouct line esign. Marketing Science, 3, 4 (1984) Mossberg, W. Verizon evices use high-spee network for voice, web, , The Wall Street Journal, December , C Mussa, M., an Rosen, S. Monopoly an prouct quality. Journal of Economic Theory, 18, 2 (1978) Olyzko, A. Paris Metro pricing for the internet, in Proceeings of ACM Conference on Electronic Commerce, Squeo, A.M. In Tiny Towns, New Call Options Shake Up an Ol Phone System, The Wall Street Journal, February , A Tirole, J. The theory of inustrial organization. Prentice-all,

32 Mathematical appenix Options 5 an 7: Analytically, options 5 an 7 are relatively simple, with the only participation constraints (17) an (23) being bining. Therefore, F5 = v( λ ) μ N λ 1 (A1) an p 3 v( λ) λ = λ μ N λ 1 (A2) Option 6: We re-write the right-han sie of inequality (21) as α v( λ) F7 + (1 α) v( λ) F7 μ2 Nλ μ2 Nλ (A3) an compare it with the left-han sie of the inequality (20). Since F6 > F7, μ1 > μ2 an N λ > N λ, one can verify that the former quantity is greater than the latter. But since the left-han sie of (21) is the net utility of the high-type user, an the left-han sie of (20) is the net utility of the low-type user, which by the participation constraint of the low-type user is non-negative, it follows therefore that the net utility of the high-type user is strictly positive, or in other wors, the participation constraint of the high-type user (22) is non-bining. Thus, the only participation constraint that the provier is concerne with is that of the low-type, an the provier will increase the fixe cost F 7, so that it is just worthwhile for the low-type to participate (thus the low-type has zero surplus). In other wors, inequality (20) is bining. The high-type will therefore extract a strictly positive surplus, an the provier will o such that it is just sufficient for the high-type to 32

33 not choose a contract that encourages him to choose the low-channel for a fixe fee. In other wors, inequality (21) will be bining. We therefore solve for F 6 an F 7 from these two bining constraints, F6 = α v( λ) + (1 α) v( λ) μ2 Nλ μ2 Nλ μ2 Nλ μ1 Nλ (A4) F7 = α v( λ) + (1 α) v( λ) μ2 Nλ μ2 Nλ (A5) Option 8: Inequality (24) is the incentive compatibility of the low-type user, whereby his payoff from using the high-channel α fraction of the time (with liqui pricing) an using the low-channel the rest of the time (with its associate fixe cost) is higher than using the on-eman channel at all times. Inequality (25) is another incentive compatibility constraint of the low-type so that he prefers his current setup as compare to using the high-channel all the time with the fixe price of F 8. Inequality (26) is the incentive compatibility constraint of the low-type so that he prefers his current setup as compare to using the low-channel at all times for the fixe fee of F 9. Similarly, inequalities (28) an (29) are the incentive compatibility constraints of the high-type user, so that he prefers using the high-channel for a fixe fee rather than paying per-unit charges, an further, he prefers using the high-channel at all times than the low-channel at all times, respectively. Inequality (27) is the participation constraint of the low-type user, an (30) is the participation constraint of the high-type user. 33

34 Multiplying both sies of (28) by α, an both sies of (29) by (1 α), an aing them up, gives us the following inequality v( λ ) F8 μ N λ 1 α v( λ ) p λ + (1 α) v( λ ) (1 α) F 4 9 μ1 Nλ μ2 Nλ (A6) Since 0< α < 1, (1 α)f9 < F9, an therefore we can rewrite inequality (A6) as v( λ ) μ N λ 1 F 8 > α v( λ ) p λ + (1 α) v( λ ) F 4 9 μ1 Nλ μ2 Nλ (A6a) We then compare the left sie of inequality (27) with the right sie of inequality (A6a), an the latter is greater than the former if the following inequality (after simplification) hols true: (1 α) { v( λ) v( λ)} μ2 Nλ μ2 Nλ + α > 0 μ 1 N λ μ 1 N λ (A7) Since v( λ ) > v( λ ), >, N > N an Nλ > Nλ, it is easy to verify that the above inequality hols. This means that the left han sie of the inequality (A6) is strictly 34

35 greater than the left sie of the inequality (27). But the left sie of inequality (27) is the participation constraint of the low-type user, which is a non-negative quantity. Since the left sie of inequality (A6) is the rent of the high-type of user, it means that this value is strictly positive, an therefore inequality (30) the participation constraint of the hightype is not bining. Thus, the only participation constraint that the provier shoul consier is that of the low-type, an the provier will increase the fixe cost F 9 an the per-unit charges p 4, so that it is just worthwhile for the low-type to participate. In other wors, inequality (27) is bining (ensuring zero surplus for the low-type customer). The high-type user will extract a strictly positive surplus, an the provier will o such that it is just sufficient for the high-type to not choose a contract that either encourages him to choose the low-channel for a fixe fee or the high-channel using per-unit charges. In other wors, inequalities (28) an (29) will be bining. Thus, we get three equations, to solve for the three unknowns ( F8, F9, p 4). Solving, we get p λ = F (A8) 4 8 F 8 F9 = μ2 Nλ μ1 Nλ (A9) 1 F9 = α v( λ) + (1 α) v( λ) 1+ α μ2 Nλ μ2 Nλ (A10) 35

36 N λ Π 1 =Π 3,Π 2,Π Figure 1: Relative magnitues of the profits uner the various scenarios in Moel 1 N λ by changing the ratios an an = 5 N λ 36

37 N λ Π 1 =Π 3,Π 2,Π Figure 2: Relative magnitues of the profits uner the various scenarios in Moel 1 N λ by changing the ratios an an = 10 N λ 37

38 N λ Π 5 =Π 7,Π 6,Π Figure 3: Relative magnitues of the profits uner the various scenarios in Moel 2 N λ by changing the ratios an an = 5 N λ 38

39 N λ Π 5 =Π 7,Π 6,Π Figure 4: Relative magnitues of the profits uner the various scenarios in Moel 2 N λ by changing the ratios an an = 10 N λ 39