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Modelling strategic information technology impact on inter-firm competition: pricing Nault, Barrie R. 1990

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MODELLING STRATEGIC INFORMATION TECHNOLOGY IMPACT ON INTER-FIRM COMPETITION: PRICING By BARRIE R. NAULT B. Comm. (Management Science), McGill University, 1983 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF D O C T O R OF P H I L O S O P H Y in T H E F A C U L T Y OF G R A D U A T E STUDIES C O M M E R C E A N D BUSINESS A D M I N I S T R A T I O N We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A August 1990 © BARRIE R. NAULT, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract This research studies normative pricing strategies for information technology (IT) used by suppliers to supplement an underlying primary good. Transactions with consumers and customer firms are considered. Characteristics of IT are divided into IT impacts on customers, and IT impacts on suppliers. IT impacts on customers include vertical differentiation or reduced turnover costs for the primary good, and positive IT adoption costs. IT impacts on suppliers include reduced production costs for the primary good, and the costs of IT. Optimal pricing for the IT and the primary good is modelled for monopoly, and Bertrand competition based on IT and the primary good is modelled for oligopoly. Two part tariffs are used for the IT and IT enhanced primary good. Results of pricing to consumers show that the fixed component of an optimal (or equilibrium) two part tariff can either be a net tax or a net subsidy, confirming the possibility of taxed or subsidized IT adoption. For the monopolist offering the IT and IT enhanced primary good only, the consumer's adoption/switching cost limits the possible subsidy. Consistent with previous economics research, in a duopoly where one supplier has IT, the IT supplier abandons the original primary good. Two suppliers with identical IT cannot attain a positive profit equilibrium. Analogous results obtain for a special case of pricing to customer firms. Empirical results support differential (premium) pricing for an IT enhanced primary good over an original good. n Acknowledgement It is my pleasure to acknowledge the valuable contributions made to this work by the members of my dissertation committee: Professors Albert S. Dexter (Research Supervi-sor), Ken Hendricks, Kenneth R. MacCrimmon, and Charles B. Weinberg. It has been my privilege to be associated with Professors MacCrimmon and Weinberg both in research activities and in graduate courses at the Faculty of Commerce and Business Administra-tion at the University of British Columbia. I also wish to recognize the strong councel on the mathematical aspects of this work by Professor Hendricks. Finally, I reserve a very special thanks to Professor Dexter (Al) who has performed an excellent job guiding me through the rigors of a dissertation. Most importantly, I have gained a great friend in the process. in Table of Contents Abstract ii Acknowledgement iii 1 Introduction 1 1.1 The Research Problem 1 1.2 Principle Thesis of This Research 3 1.3 Research Strategy 5 1.4 Need for Research 6 1.5 Limitations 8 1.6 Organization of The Thesis 10 2 MIS Literature Review 11 2.1 Introduction 11 2.2 Strategic IT and the Researcher/Practitioner 12 2.2.1 IT and Porter's Model 12 2.2.2 Models to Guide Discovery of IT Opportunities 12 2.3 In Depth Studies of Particular Strategic IT Applications 14 2.4 Research Denning Characteristics of IT 16 3 Characterizing Interorganizational IT 20 3.1 Introduction 20 3.2 Characterization of IT Enhanced Primary Goods 22 iv 3.3 IT Effects on the Primary Good for Customers 25 3.3.1 IT Effects on the Primary Good to Consumers 25 3.3.2 IT Effects on the Primary Good for Customer Firms 26 3.3.3 IT Switching Costs 27 3.4 IT Effects on Supplier Costs 30 3.4.1 IT Effect on Supplier's Primary Good Costs 30 3.5 Supplier's IT Cost Structure 30 3.6 Pricing Structure Assumptions 32 3.6.1 Justification for Integrated Pricing of the Primary Good and the IT 32 3.6.2 Justification of Two Part Tariffs With IT 32 4 Suppliers Offering IT to Consumers 35 4.1 Introduction 35 4.2 Model 4.1: Monopoly Supplier Offering the IT Enhanced Primary Good . 36 4.2.1 Demands 36 4.2.2 Supplier Profit Maximization 38 4.3 Model 4.2: Monopoly Supplier Offering the IT Enhanced Primary Good and the Original Primary Good 44 4.3.1 Demands 44 4.3.2 Supplier Profit Maximization 48 4.3.3 Discussion 52 4.4 Model 4.3: Oligopoly Suppliers Where One Supplier Has IT 54 4.4.1 Formulation 54 4.4.2 Stage 2 Subgame: S2.1 55 4.4.3 Stage 2 Subgame: S2.2 59 4.4.4 Stage 2 Subgame: S2.3 61 v 4.4.5 Stage 1 62 4.4.6 Discussion . . 64 4.5 Model 4.4: Two Suppliers Offering Undifferentiated IT Enhanced Primary Goods 67 4.5.1 Formulation 67 4.5.2 Dominating Price Pairs 68 4.5.3 Asymmetric Price Pairs 69 4.5.4 Equal Price Pairs 75 4.5.5 Discussion 77 4.6 Model 4.5: Two Suppliers Offering Differentiated IT Enhanced Primary Goods 78 4.6.1 Demands 78 4.6.2 Supplier Profit Maximization 82 4.6.3 Discussion 85 4.7 Analysis 87 4.8 Conclusions 89 4.9 Appendices to Chapter 4 90 4.9.1 Appendix 4.1 90 4.9.2 Appendix 4.2 94 4.9.3 Appendix 4.3 100 4.9.4 Appendix 4.4 104 4.9.5 Appendix 4.5 107 5 Suppliers Offering IT Directly to Customer Firms 111 5.1 Introduction I l l 5.2 Model 5.1: Monopoly Supplier Offering the IT Enhanced Primary Good . 113 vi 5.2.1 Factor Demands 113 5.2.2 Supplier Profit Maximization 116 5.3 Model 5.2: Monopoly Supplier Offering the IT enhanced Primary Good and the Original Primary Good 121 5.3.1 Factor Demands 121 5.3.2 Supplier Profit Maximization 126 5.4 Model 5.3: Oligopoly Suppliers Where One Supplier Has IT 130 5.4.1 Formulation 130 5.4.2 Stage 2 Subgame: S2.1 130 5.4.3 Stage 2 Subgame: S2.2 131 5.4.4 Stage 2 Subgame: S2.3 134 5.4.5 Stage 1 134 5.5 Model 5.4: Two Suppliers Offering Undifferentiated IT Enhanced Primary Goods 138 5.5.1 Formulation 138 5.5.2 Dominating Price Pairs 139 5.5.3 Asymmetric Price Pairs 139 5.5.4 Equal Price Pairs 145 5.6 Model 5.5: Two Suppliers Offering Differentiated IT Enhanced Primary Goods 147 5.6.1 Factor Demands 147 5.6.2 Supplier Profit Maximization 151 5.7 Analysis: Parallels Between Pricing Strategies for Suppliers to Consumers and Suppliers to Customer Firms 155 5.8 Conclusions 158 5.9 Appendices to Chapter 5 159 vii 5.9.1 Appendix 5.1 159 5.9.2 Appendix 5.2 165 5.9.3 Appendix 5.3 169 5.9.4 Appendix 5.4 172 5.9.5 Appendix 5.5 175 6 Empirical Examination 177 6.1 Introduction 177 6.2 The Research Site and the IT 178 6.3 Research Methodology 179 6.3.1 Studying the Assumptions of the Models 179 6.3.2 Testing the Pricing Results 181 6.4 Analysis and Results: Analysis of the Models' Assumptions 183 6.4.1 IT Decreases Customer Firm Costs 183 6.4.2 Customers Incur Internalization Switching Costs Adopting IT . . 184 6.4.3 IT Decreases Supplier Costs 185 6.4.4 Pacific Pride's IT Costs 186 6.4.5 Factor Input Price Flow Through to Downstream Output 187 6.4.6 Demand and Customer Firm Efficiency 188 6.4.7 Are Two Part tariffs Being Used? 188 6.5 Analysis and Results: Testing The Pricing Results 190 6.5.1 Policy Model 190 6.5.2 Prediction of Theoretical Models 192 6.5.3 Examining the Policy Model 193 6.5.4 Policy Model and Pricing Behaviour 195 6.6 Conclusions 199 V l l l 6.7 Appendices to Chapter 6 200 6.7.1 Appendix 6.1: Salem Fuel Prices 200 6.7.2 Appendix 6.2: Eugene Fuel Prices 202 7 Conclusions, Contributions, and Future Research 204 7.1 Introduction 204 7.2 Conclusions 205 7.2.1 Implications 206 7.3 Contributions 208 7.4 Future Research 210 Bibliography 212 ix Chapter 1 Introduction 1.1 The Research Problem Consider suppliers which use information technology (IT) interorganizationally to sup-port or enhance an underlying primary good in their main line of business. Once suppliers commit to deploy IT with this potential they must answer one major question in order to maximize profits: • What pricing policy should be employed for the IT and the IT enhanced primary good? The objective of this research is to provide normative pricing strategies for suppliers to fohow, and then to assess the assumptions and prescriptions from these strategies empirically. Pricing decisions are examined for suppliers that sell their primary good directly to customers. The IT is provided to these customers as a supplement to the underlying primary good. The term "customer" has two different meanings. At the retail level, the customer is a consumer who consumes the primary good and derives utility. To illustrate, banks (suppliers) offer automated teller machine (ATM) access (IT) to the public (consumers) as an enhancement to normal banking services (primary good). If not at the retail level, the customer is a firm which uses the primary good as a factor input to a production technology. Referring to a specific example, American Hospital 1 Chapter 1. Introduction 2 Supply Corp. (supplier) offers their ASAP order entry system (IT) to hospitals (customer firms) in support of hospital supply (primary good) transactions ([1]). Chapter 1. Introduction 3 1.2 Principle Thesis of This Research There are three predominant and related themes to this research: • Suppliers must consider joint pricing between the IT, the IT enhanced primary good, and the original primary good • IT provides a separate basis for pricing • IT changes the both the nature of the underlying primary good, and relationship between supplier and customer. From prior work, there has been an implicit belief that the pricing of the primary good is separable from the pricing of the IT. In other words, how an IT provider prices the technology should not be linked with the pricing structure of the primary good1. This belief is not shared here. For the IT supplier, having control over the IT and the IT enhanced primary good (as well as possibly the original primary good), profit maximization is only possible through a coordinated selection of prices. With the tangible connection between a supplier and customers through the IT, the IT itself becomes a basis for pricing. Typically the customer's decision to adopt a sup-plier's IT is a single decision, with each customer purchasing varying quantities of the IT enhanced primary good through the IT. IT adoption changes the characteristics of the underlying primary good for customers. Customer IT adoption also entails internal modifications to accommodate the IT. Thus, the dominant thrust of this work centers on • Joint pricing, and a two part tariff for the IT and IT enhanced primary good 1 Reich and Benbasat ([39]) in their study of customer oriented strategic systems (COSS) show a con-ceptual model with the COSS relationship and product relationship between a company and customers as separate relationships. Chapter 1. Introduction 4 • Differentiation of the primary good by the IT, and customer costs of IT adoption. Chapter 1. Introduction 5 1.3 Research Strategy The research strategy employed has three separate elements: • Determine a distinct characterization of IT • Analytically model supplier pricing strategies • Empirically examine the results from the two points above. The sequence embodied in the research strategy is critical. The characterization of IT is reflected in the analytical models, and assumptions and results from the models form the foundation of the empirical study. The methodology used to determine the characterization of IT concentrated first on a. literature review, directed towards articles published in the leading Management Information Systems (MIS) journals2, and an examination of recent theses in the area. From this work important attributes incorporating the effects of IT were then synthesized. The second step in the research strategy focused on modelling techniques from re-search in Industrial Organization. Characteristics of IT were incorporated in the math-ematical models, and five different static pricing models were studied for each of the parallel cases of consumers and customer firms. The five models reflected monopoly versus oligopoly, and different combinations of IT enhanced and original primary goods available to customers. Agreement to conduct an empirical study was obtained from Pacific Pride Systems, a commercial fueling system. The methodology employed consisted of structured interviews to assess the modelling assumptions, and statistical testing of pricing relationships. 2For example Management Science, MIS Quarterly, Communications of the ACM, Harvard Business Review. Chapter 1. Introduction 6 1.4 Need for Research As evidenced by the prior research (reviewed in a subsequent chapter), there has been significant interest in IT used inter organization ally in the MIS discipline. As with many topics, early work has focused on qualitative studies, with perhaps more of an eye towards the practitioner (for example, [6], [30], [35], [38]). When it comes to understanding actions firms should take with this type of IT only conjectures based on experiences or rough conceptual models have been provided. In fact, no established frameworks or models to direct research have been proposed, outside of vague references to transaction cost theory ([46], [47]). While there is current research being conducted, prior work using economic modelling methods to study interorganiza-tional IT has been limited (for example, [2]). Therefore, there clearly is a gap in prior research with respect to normative strategies firms should follow with IT. Referring to prior MIS work related to interorganizational IT, there have been calls for, and identification of, research opportunities and needs which are partially addressed by this research. In one of the early IT papers Barrett and Konsynski ([4]) identified several future research opportunities including understanding the economic impacts of interorganizational sharing systems (IS*) on the primary business activities of the firm. More recent work ([6]) has suggested pricing and cost decisions were crucial in exploiting IT. The empirical work by Reich and Benbasat ([39]) implied that pricing is a critical determinant of system adoption, and therefore success with IT. Finally, much of the MIS literature mentions switching costs as a way to tie consumers to a particular system. As recently as late 1986 Clemons and Kimbrough, discussing the lack of depth in understanding of the organizational use of competitive IT, state that Chapter 1. Introduction 7 "... Normative and predictive models, which would be valuable for assessing options and choosing preferred strategies, seem even more distant." ([7], p. 99) Jarvenpaa and Ives ([19]) note that as an area of academic research, the relationship between IT and corporate strategy has been soundly criticized, basically because of a lack of rigor. While their focus is on empirical work, the commentary on prior studies is also valid for theoretical work, perhaps even more so. In fact, a case could be made that the problem of insufficient rigor in the empirical work is a reflection of the absence of theoretical explanations, results which in other sciences are used as foundations for what should be measured empirically. MIS researchers have of course realized the relevance of the work in various areas of economics to the question of how organizations should treat IT. Several articles described in the following chapter allude to market structure, transaction cost theory, microeco-nomics, etc. However, for the most part these theories have been brought in as concepts only. There has been little formal use of the more quantitative theoretical techniques and analyses, methods which turn out to be fundamental in building theory, carrying research forward, and providing concrete knowledge. Chapter 1. Introduction 8 1.5 Limitations As in any research there are limitations of the work done here. There are three main limitations to this study. First is the use of two part tariffs as a pricing scheme for the IT and IT enhanced primary good. Other pricing schemes are possible; however the two part tariff fits the view of charging (or subsidizing) once for IT access in addition to charging per unit of the underlying primary good. Nonetheless, the use of a two part tariff is restrictive. Second, the analytical models focus on static pricing policies. Essentially this represents a balance between richness and complexity. While there is some loss of richness associated with dynamic phenomena which is not captured by static models, these aspects increase the complexity of the models to the extent that they can become intractable. Moreover, in our case the static models are sufficient to examine the possibility of taxing or subsidizing IT adoption. Third, no assumptions are made about customer firm downstream markets. Thus, the effects of downstream competition are not included as part of the models. Simplifying assumptions, which obviously detract from the scope of the analysis, are made. Again, this is a tradeoff between richness of the specification and mathematical tractability. Not surprisingly, the approach here conforms to the majority of work in Industrial Organization related to this thesis. In addition to the above limitations, it is also useful to outline at least some of what is not examined in this research. First, vertical market structure remains stable. In other words, no forward or backward integration is considered. The question of whether a market or a hierarchy is more efficient/effective is not addressed. Transactions occur via markets. Second, aspects of competition outside of pricing are held constant. Therefore, new entries, other substitutes, investment and learning, and marketing, are excluded. Third, no supply or production capacity constraints are considered for either the primary good or the IT. Demand for both the primary good and the IT connection can be filled Chapter 1. Introduction 9 immediately. Fourth, IT can only originate from suppliers. This eliminates the strategic interactions between customers and suppliers both offering IT to support primary good transactions. Fifth, as described in the individual models, a given customer can only purchase the primary good from one supplier, and can only purchase one type of primary good. Finally, only static pricing strategies are modelled. Chapter 1. Introduction 10 1.6 Organization of The Thesis The remaining chapters of the thesis are structured as follows. Chapter 2 scrutinizes the relevant MIS literature, paying particular attention to facets which are distinctive about IT. Chapter 3 argues for a general characterization of IT based on differentiation, switching costs, production costs, and IT costs. Chapter 4 begins the modelling exercise. Five pricing models for suppliers to con-sumers are presented in sequence: monopoly supplier with IT, monopoly supplier offering both the IT enhanced and original primary goods, oligopoly where one supplier has IT, duopoly where suppliers compete with identical IT, and duopoly where suppliers compete with different IT. This is followed by a brief analysis. Chapter 5, modelling suppliers to customer firms, is identically organized. Much of the mathematics in each of these chapters is relegated to appendices. Although cumbersome, all the arguments are given to make the functional dependencies in the mathematical derivations clear. Chapter 6 contains the empirical examination. The research site and research method-ology are outlined. This is succeeded by an analysis of the elements characterizing IT and assumptions from the analytical models. The pricing results are then tested. The thesis closes with Chapter 7. This chapter summarizes the conclusions from the previous chapters, reviews contributions from the thesis, and makes suggestions for future research. Chapter 2 MIS Literature Review 2.1 Introduction Rather than simply "cover the literature", this literature review has the objective of isolating what is important about information technology supporting an underlying pri-mary good. With an eye towards the next chapter, properties characterizing IT are of particular interest. Most of the research on using IT for gaining strategic advantage has focused on four areas: • discussions, based on industry examples, of Porter's ([36], [37]) model with respect to IT (for example [30], [6], [35], [38]) • conceptual models to guide the discovery of IT opportunities (for example [38], [18]) • in depth studies of particular strategic IT applications (for example [21], [8], [9]), e frameworks and conceptual models defining characteristics of IT (for example [4], [3], [27]. [39]) Previous work in each of these areas is discussed below; the first two are combined, the next two are covered in sequence. References to the economics and marketing literature associated with the analytical models appear in the particular chapter to which they apply. 11 Chapter 2. MIS Literature Review 12 2.2 Strategic IT and the Researcher/Practitioner 2.2.1 IT and Porter's Model The research from Industrial Organization most heavily referenced by MIS researchers and practitioners is the work by Michael Porter ([36], [37]). Porter believes strategies should be evaluated in the context of his five forces model: buyers, suppliers, substitutes, new entrants, and competitors. Several articles directed towards the practitioner have related strategic IT to Porter's model through example ([38], [30], [35], [6]). The examples highlighted in these papers has shown that IT can alter each of the five competitive forces, as well as vertical market structure. IT is shown modifying bargaining relationships between competitors, their channels, their suppliers, and their buyers, thereby changing vertical market structure. Cases of coordination, with or without dependence of one party on the other, and chang-ing economies of scale are provided as examples of strategic uses of IT which have affected the structure of competition through changes in firm concentration and barriers to entry. There is a consensus among this group that IT can transform the nature of the product or service, distinguishing the good from its competition. IT is also seen as potentially changing the economics of production both in terms of cost and flexibility. Due to increased competition, exploiting IT is viewed as critically depending on pricing and costing decisions. 2.2.2 Models to Guide Discovery of IT Opportunities There have been several conceptual models presented which have as their objective the uncovering of previously hidden opportunities to take advantage of IT capabilities. A thirteen stage "customer resource life cycle" was proposed by Ives and Learmonth in [18] as a systematic method to search for strategic IT opportunities. Interestingly, Chapter 2. MIS Literature Review 13 they see IT applications as strategic if IT modifies the primary product or if IT changes the way firms compete. The customer resource life cycle bears some resemblance to Porter's value chain, in that stages of the life cycle are similar to many of the value chain activities, subdivided to arrive at smaller activities. All four of [38], [30], [35], [6], alluded to above, suggest the use of Porter's five forces model to identify the range of strategic possibilities. Supporters of this model believe strategic IT openings can be found by systematically going through the value chain and by considering each of the five competitive forces. Chapter 2. MIS Literature Review 14 2.3 In Depth Studies of Particular Strategic IT Applications In an examination of the impact of ATMs, Kauffman ([21]) built a "business value link-age" to understand how direct outputs of ATMs are transformed into increased revenues and reduced costs. It was noted that if one considers this form of IT as enhancing the bank's service (i.e. product differentiation) then first mover advantages could improve market share. With ATMs banks were found to incur fixed initial capital costs for im-plementation and hardware, and fixed period costs for security and network connections. Variable costs included costs of cash at an A T M , as well as maintenance and stocking costs. Interestingly, costs per transaction were not considered. In terms of cost reduc-tion, models showed that ATMs were able to substitute (imperfectly) for teller labour. In outlining future research, Kauffman believed interesting extensions in A T M evalua-tions would be to model competition in a Nash equilibrium framework. He also observed that banks had moved towards pricing A T M services, which opens another avenue for research. One of the clearest examples of a strategic system is McKesson Drug Company's Economost order entry system which links McKesson to retail pharmacies ( [8]). Economost provides several benefits to its customers, two of which are lower transaction costs and reduced inventory holding costs. An interesting pricing policy has included larger dis-counts to customers ordering through Economost. In fact, customers see reduced costs from these discounts as the largest of the cost savings Economost provides. McKesson has at least one other major competitor offering a comparable system. Therefore, similar to ATMs, it is argued that systems linking drug wholesalers to retail drugstores have now become strategic necessities: it is difficult for wholesalers who do not have this capability to compete effectively. Chapter 2. MIS Literature Review 15 Using historical analyses of computer reservation systems (CRS) in airlines as a refer-ence, Copeland and McKenney ([9]) concluded much of the impetus behind this IT was the idea of providing differentiated service. As such, airlines with CRS realized product advantages over competitors. CRS also had the effect of transforming the travel agent function into an information provider. Moreover, since much of the CRS began as IT used internally to reduce costs, the ultimate advantage of CRS was defined not only in terms of differentiation but also through internal cost savings. Chapter 2. MIS Literature Review 16 2.4 Research Defining Characteristics of IT Definition of the key characteristics of IT has been remarkably consistent through the last several years, in spite of different researchers favouring a variety of conceptual models or frameworks attempting to organize these characteristics. Interorganizational sharing systems (IS*), studied by Barrett and Konsynski ([4]), suggested the following incentives for organizations to participate in IS*: cost reductions, productivity improvements, and product/market strategy1. Cost reductions focus on potential economies of scale provided by computing. Improvements in productivity accrue from cost avoidance (e.g. elimination of tasks, decreases in error rates), cost displacement (e.g. shared costs), and increased productivity via more effective resource allocation and more efficient resource utilization. Underlying these benefits are potential characteristics of using IT strategically in an interorganizational context: coordination, sharing of costs and development, and dependency of one party on another. It was suggested that both a competitive edge and market leadership/share could result from dependencies in the IS* relationship. They believed IS* could also be considered a movement towards a separate product/service, separate from the primary good. Pricing and costing decisions were considered crucial in exploiting IT, but no guidelines for these decisions were provided. Several studies have focused on the structure of vertical markets. IT has been seen as potentially changing the way firms organize the flow of goods and services through the value chain, and as a result disturbing vertical market structure (for example [38]). Other research ([28]) has viewed information processing capability as a key criterion in determining whether coordination should be accomplished through hierarchies or mar-kets, and which type of governance or market structure is most efficient. However, no analytical or normative models were proposed. 1 Of course, the first two of these are typically used to justify any information system. Chapter 2. MIS Literature Review 17 Having observed the increasing number of electronic interconnections between orga-nizations, Malone et al. ([27]) believed this was a result of IT reducing coordination costs, costs which are typified by asset specificity and complexity of product descriptions (amount of detail buyers need to know in order to make a selection). They felt these changes could be studied by examining three effects of the IT: electronic communication (higher volume, lower costs), electronic brokerage (electronic markets), and electronic in-tegration (tighter coupling of the processes that use information). Their thesis was that reduced asset specificity, and the ability to manage more complex product descriptions brought about through electronic interconnections, favour shifts away from hierarchies, towards markets, for coordination of economic activities. A framework of four areas of opportunity for using IT was outlined by Bakos and Treacy in [3]. The first area is internal uses of IT to improve organizational efficiency and functional effectiveness. The second area is similar to the first except involving more that one firm: a joint or cooperative information system (somewhat similar to IS*). The third area of opportunity is bundling IT with a product, for example using microprocessors in automobiles. Finally, there are uses of IT to create bargaining advantages vertically by creating idiosyncratic switching costs. Although useful for thinking about IT capabilities, there are problems with this framework. For example, the areas of opportunity are overlapping in a severe way: CRS in the airline industry could fit into all four areas. Two underlying factors are suggested in the paper as key to the areas of opportunity: comparative efficiency and bargaining power. In a multiple case study examining factors influencing the success of customer oriented strategic systems (COSS) Reich and Benbasat ([39]) observed that COSS price tended to distinguish between quickly and slowly adopted systems. The quickly adopted systems were offered at a nominal cost whereas the more slowly adopted systems had prices both customers and originators considered high. Even after several years COSS price continued Chapter 2. MIS Literature Review 18 to discriminate between those systems which were and were not successful. Because most of the systems studied were first movers in their respective areas there were no conclusions relating to IT introduction. Moreover, no systematic pricing strategies beyond offering IT at low cost were uncovered. IT is considered strategic by Clemons and Kimbrough if it significantly affects com-petitive position or industry structure ([7]). Strategic IT includes responses to other firm's IT. IT for competitive advantage is defined as IT which provides a higher than "normal" return on investment. With these definitions neither strategic nor competitive advantage obtained with IT require the firm be an innovator or first mover. Several studies (for example [45] and [2]) viewed sustainability of competitive advan-tage gained by IT as important. [7] states three necessary conditions: First, IT must reduce cost or add value. It is suggested that the most attractive way to reduce costs is to focus on transaction costs (broadly defined as per Williamson ([46], [47])). Second, there must be idiosyncratic switching costs placed on the customer. Hence, the initial IT developer can receive some lasting benefit. Finally, customer adoption time must be small relative to competitor imitation time. Thereafter the switching costs will help keep the customers attached to the IT they originally adopted. Supporting the idea of IT as a potential strategic necessity, Vitale suggested there may be dangerous unintended and unanticipated consequences of technical success with IT ([45]). Use of the IT may become required just to remain competitive, and further investment at little return may be needed. In some cases it is hypothesized that ultimately a good strategy may be to not introduce IT as in the absence of strong first mover advantages the IT may not produce positive payoffs. Bakos ([2]) argued that interorganizational systems (IOS) cost structure would include high initial development costs (fixed), smaller capacity and maintenance costs (mixed), and minimal marginal costs. This was contrasted with manual systems which incur Chapter 2. MIS Literature Review 19 higher, and sometimes substantial, marginal costs. Using a model based on information capacity it was shown that an IOS which increases volume in an information link can decrease inventory costs, for example allowing a change from an inter process inventory system to a just-in-time system. In some rare analytical modelling, the case was made that reduced search costs for buyers could result in lower prices and profits for sellers ([2]). Considering differences in location as horizontal product differentiation, monopoly rents were obtained with positive search costs; an electronic market (IOS) would reduce buyer search and drive prices towards competitive equilibrium. Examining buyers joining an IOS with positive linear network externalities, if buyers could be ordered according to their eagerness to join, it was also shown that there does exist a point at which no additional buyers join or terminate from the IOS. This result persists if there is initial uncertainty about the value of the IT (which can be resolved either by true revelation or observation of other suppliers' IT trials). Thus, adoption of an IOS by a subset of buyers can be stable, rather than stability requiring full diffusion. Chapter 3 Characterizing Interorganizational IT 3.1 Introduction The characterization of the effects of interorganizational IT on customers and suppliers is key because it is the element which links the theoretical models and analytical techniques used to the real MIS research problems. The characterization determines exactly how IT should enter into the theoretical models. Therefore, this is not only a step towards more fully identifying the research problem, but the synthesis produced by integrating prior work on the individual effects of IT is a significant part of the creative contribution of this thesis. In addition, it is important in allowing us to distinguish (to some degree) IT from other innovations. There are two approaches to trying to characterize IT. The first is to assume IT is unique in its effects on customers and suppliers, and look for special characteristics which make IT unique. Unfortunately, there is no a priori reason to believe that these IT effects are unique to IT, and hence a search for unique features may reveal nothing. The second is to try and identify features which characterize these IT effects, without requiring that they be unique to IT. This latter approach is followed here. The chapter starts with a general characterization of primary goods enhanced with IT. Subsequently, this characterization is used to incorporate the effects of the IT on the primary good as seen by customers and then by suppliers. A justification for integrated primary good and IT pricing is presented, suggesting a two part tariff as the appropriate 20 Chapter 3. Characterizing Interorganizational IT pricing mechanism. Chapter 3. Characterizing Interorganizational IT 22 3.2 Characterization of IT Enhanced Primary Goods Consider a good in a given commodity1 class as made up of a set of utility bearing (or profit providing) attributes, with each particular good having amounts or levels of each attribute ([40], [10]). This is the so-called hedonic hypothesis. In any product or service transaction there are additional attributes which characterize the transaction it-self. For example, transaction attributes could include coordination costs2 of contacting (e.g. search costs) and physically transferring ownership (e.g. lead time, cost of order-ing, delivery scheduling). These attributes could also encompass dimensions underlying Williamson's view of transactions ([46], [47]): uncertainty as to the number of possible contingencies and their probability of occurrence, the frequency of transaction recur-rence, and the degree to which asset specific investments play a role in the optimal cost structure. The result of combining these two sets of attributes is to provide a complete description of the primary good, including aspects of its transaction. Compare an original primary good and an IT enhanced primary good, supported by a particular IT. It is argued that, ignoring primary good price and other IT costs, the IT enhanced primary good is superior to the original primary good, in that at least one of the good's attributes (including the transaction's attributes) is enhanced, and no other relevant attributes are diminished3. The magnitude of the enhancement provided by the IT comes from a particular IT applied to the primary good. Any given information system or IT (even a manual system) has a set of properties which relate to how "well" it performs a particular application. Depending on how performance is measured, performance on a given application can be 1 Commodity here implies substitutable goods. 2 This is a different definition of coordination costs than that given by [27]. Their definition includes all costs not directly related to production such as pricing, design, and quantity. These are included in most other formulations of production costs, and would already be reflected in the good's attributes. 3In a lexicographic ordering a positive impact on a dominant attribute would be sufficient. Chapter 3. Characterizing Interorganizational IT 23 related to impacts on the primary good. Specifically, performance can be measured in terms of properties which affect attributes of the primary good. These properties can be partitioned into two sets. The first set relates to the scope of the system, or its functionality (i.e. the functions it performs). For example, an interorganizational system offered by a drugstore wholesaler which supports transactions between the wholesaler and independent retail drugstores could manage order processing and inventory control for the retailer. IT which manages order processing and inventory control has more functionality than one supporting order processing only. The second set is linked to performance on a particular set of requirements. Focusing on information economics, properties such as timeliness and accuracy (see [13] [29] [15] for example) can be used to compare information systems, although imperfectly. Other characteristics such as reliability, capacity, compatibility, and ease of use can also determine the performance of a given IT. Both sets of IT properties are only measurable for a particular application. Measuring the impact of an IT in a given application is not trivial. For a given application, a complete ordering over different ITs requires comparability between each pair of IT as well as transitivity, or alternatively a function which reduces the multidi-mensionality into a single value on which different IT can be compared4. Comparability and transitivity could be based on Pareto dominance over the property space or on a lexicographic structure. The difficulties underlying simply an ordering of IT, let alone interval measurement, are acknowledged. Nonetheless, the concept is somewhat similar to comparing informa-tion systems in information economics. Comparisons based on expected value or expected utility are similar to the case of a resulting single valued function discussed above in that the information system, which maps signals to states, is reduced to a single value ([13], 4The properties are assumed to be objectively measured. Otherwise any subjective ordering would be individual specific. Chapter 3. Characterizing Interorganizational IT 24 [29]). Expected utility comparisons require, among other things, a utility function which transforms consequences and costs, the consequence and cost functions themselves, and a decision function converting signals from the information system into actions, all in addition to the specification of the information system itself. An approach that does not rely on the reduction of multiple properties to a single value are direct comparisons of information systems based on signal generation (e.g. fineness, sufficiency, garbling). However, direct comparisons based on signal generation cannot always provide a com-plete ordering of information systems because in order for two information systems to be comparable certain conditions for each of fineness, sufficiency and garbling must be satisfied (see [16], [17]). Although not the topic of research here, the above discussion highlights the difficulty in actually measuring the effects of IT, particularly the relative effects of different IT. Chapter 3. Characterizing Interorganizational IT 25 3.3 IT Effects on the Primary Good for Customers There are two types of effects of IT on the primary good for customers: a direct effect from the attributes of the primary good, and an indirect effect through switching costs incurred by the IT. The direct IT effects on the primary good for customers can be subdivided into effects on the primary good for consumers (individuals) and effects on the primary good for customer firms. These are covered in sequence, followed by a discussion of switching costs. 3.3.1 IT Effects on the Primary Good to Consumers From the point of view of a consumer, any transaction of the primary good can be characterized by its utility bearing attributes. An application of IT yields a superior primary good in that at least one of the attributes of the good are positively affected. To illustrate, with increased processing power, memory, and telecommunications, IT can enhance attributes by providing greater service, likely predicated on timeliness, accuracy, and availability. For example, ATMs provide a degree of banking services at any time of day, in many more locations, and possibly more quickly. Ignoring the attributes related to primary good price and IT costs, an IT enhanced primary good can dominate the original primary good. Hence, to consumers an IT supplement to the primary good vertically differentiates the enhanced primary good from the original unenhanced primary good. Or put more simply, IT increases quality. Therefore, all consumers prefer the IT version over the original good, assuming equivalent prices and the cost of using and/or adopting the IT is low or zero5. 5Notice that the consumer who is willing to pay positive amounts to avoid information technology is being ignored. Even if a consumer did not want the IT enhancement to the primary good that individual could always choose not to use the enhanced features of the enhanced good. For example, one can always choose not to use an ATM; to change banks because the present bank has installed ATMs would not Chapter 3. Characterizing Interorganizational IT 26 The case for IT providing vertical differentiation has strong support in the MIS liter-ature. For example, referring to airline computer reservation systems (CRS), Copeland and McKenney [9] state: "... To the extent that a passenger inquiry could be processed more quickly and effectively, an airline realized a product advantage." (p. 366) To operationalize vertical differentiation, a good's attributes are typically combined (usually implicitly) into a scalar whose value is increasing in the underlying attributes6. In this case it means the reduced attribute space (reduced by the primary good price and IT costs) for the primary good is combined into a single valued function, which is increasing in each of the reduced attributes of the primary good. Therefore, this single valued function can be viewed as the primary good's quality index. For example, if the properties of banking services could be combined into a single valued function, then each of longer hours, more locations, and faster service would increase the value of this function. 3.3.2 IT Effects on the Primary Good for Customer Firms Barrett and Konsynski ([4]) suggested two areas where costs could be reduced by IT. First is cost reductions, mostly coming from economies of scale provided by computing. Essen-tially what this means is IT can allow the reaching of minimum efficient scale7 at lower levels of production8. Second is productivity improvements from cost avoidance (fewer be rational. In fact, because ATMs may reduce bank lineups there may even be advantages to those consumers at an ATM bank who do not use the ATMs. Of course, reductions in human teller staff may negate this advantage. GClearly, this assumes an objective and consistent way of measuring and combining the reduced set of attributes. 7Most economic theory suggests long run U-shaped average costs, sometimes "flat bottomed" average cost curves. Minimum efficient scale is the lowest level of output at which average cost is minimized. 8This can also be interpreted as a steeper learning curve. Chapter 3. Characterizing Interorganizational IT 27 errors, less manpower), cost displacement from shared development cost (economies of scope), and increased effectiveness in resource allocation and efficiency in resource utiliza-tion (superior coordination as per [27]). Moreover, several practitioner directed articles have described IT as changing the economies of production. For example, [38] suggest IT alters the relationships among scale, automation, and flexibility. [35] argues that IT may change the basic economies of production in some industries, and [6] see IOS improving efficiency and scale in production and distribution. Using duality theory (see [44]), the result of achieving production economies due to the IT enhanced primary good show up in either the production function or the cost function of the primary good. IT is viewed as causing downward shifts in the cost function of the primary good. Note that the effect of IT allowing for better decision making would be included in the downward shift of the cost function. Consider a customer firm with a given cost function. Taking the primary good as a factor input, the effect of IT on the cost function comes via increases in the attributes of the primary good, again excluding those attributes relating to the primary good price and IT costs. With a fixed level of output, and equal prices for factor inputs (including the primary good), IT results in production and transaction cost reductions, assuming negligible IT costs. Observe that this cost to customer firms is actually the cost of turning over the primary good, whether via a bundling operation of through a production process. In the hospital supply example, reduced costs of inventory and ordering brought about by IT are reflected in the incremental decrease in the overall costs of goods for the hospital, at equal hospital supply prices and quantities purchased. 3.3.3 IT Switching Costs There is an additional characteristic of IT: costs of switching IT. Switching costs are observed in many contexts such as changing banks and switching telephone companies Chapter 3. Characterizing Interorganizational IT 28 ([22], [23]). With IT, idiosyncratic switching costs serve as a barrier to customers initially adopting IT or switching from one IT to another IT. These switching costs can be divided into two parts: IT installation costs and internalization switching costs. The installation part of switching costs is the IT installation cost component of the IT cost structure, to be discussed in the next section. This component is the direct cost the IT supplier incurs as part of his own system when adding a new customer to the system, and does not include any costs from the IT customer's site. Hence, this component is independent of any previous IT used by the customer. Notice this IT installation cost is incurred in full any time a new customer joins a system. Internalization switching costs relate to costs incurred at the customer's site. For a customer firm this may entail training or equipment purchase, for a consumer this may involve learning how to operate an ATM or shop-at-home software. These costs can also include an IT customer's costs of changing internal business systems, broadly defined to include procedures, methods and policies, which are brought about by using adopting IT or switching to a different IT 9. Internal business systems are usually built around the transaction processing system which interfaces the organization and its boundary. Interorganizational IT is often exactly that type of system, for example an interorgani-zational order entry system which links a supplier to its customers. A change of IT, to IT from nothing, or a change away from IT altogether, may require substantial costs in modifications to internal business systems. This refers directly to asset specific invest-ments having an impact on switching costs. Whether tangible or intangible, some assets employed may be specific to a particular situation, and therefore force a set of collateral costs to adoption or switching of IT. Examples include skills using a particular IT sup-plier's software, changes in data formats which are input to internal systems, and even 9Costs of breaking contracts, whether explicit or implicit, may also be incurred by IT adoption or switching IT. Chapter 3. Characterizing Interorganizational IT 29 inventory numbering schemes. To some degree internalization switching costs involve replacing skills and methods which have been learned over time or are force of habit and cannot be changed or replaced immediately (e.g. the experience curve), analogous to Williamson's human asset specificity ([46], [47]). Two aspects influence the size of internalization switching costs: the present IT (which could be no IT) and the target IT. Typically, internalization switching costs are increasing with a more sophisticated or complex target IT, often because larger modifications to internal systems are required to accommodate a more extensive target IT. The effect of the present IT on these internalization costs is less clear. One argument would be that more advanced IT is more costly to dismantle, and therefore switching away from a more complex IT requires more alterations. Alternatively, a case could be made that more advanced IT makes for more simple integration of new IT, typically because of greater modularity10 1 1 . 10Obviously, there is the issue of compatibility between the new and old IT which could figure promi-nently in a given situation. 1 1 Related to the earlier discussion, the issue of the old IT being asset specific, or even the future costs of the new IT having high asset specificity, could also be important in a given situation. Chapter 3. Characterizing Interorganizational IT 30 3.4 IT Effects on Supplier Costs IT has two impacts on supplier's costs. The first is through the primary good itself, as the IT enhanced good can affect the production process. The second comes directly from the costs of IT. 3.4.1 IT Effect on Supplier's Primary Good Costs Consider now the effects of IT on a supplier's cost function for producing and transacting the primary good, ignoring the direct costs of the IT. Clearly, the economies of scale provided by computing, cost avoidance and displacement, and resource allocation and utilization benefits, from the IT enhanced primary good described previously in the effects of IT on customer firms can also apply to the supplier. Hence, these effects impact both sides of the IT transaction: IT suppliers and IT customers. Case evidence for reduced marginal costs to suppliers from implementing interorgani-zational IT is extensive. In the airline industry CRS started as internal booking systems with both higher productivity and cost reductions as objectives, although part of the move towards providing CRS to travel agents was marketing related ([9]). McKesson Drug's Economost system focuses on reducing the cost of the primary good transaction, as well as keeping drugstore retailers tied to McKesson ([8]). Finally, there is no question that one of the justifications for ATMs was the expected savings in teller labour ([21]). 3.5 Supplier's IT Cost Structure Referring to prior MIS research, ATMs were found to have fixed set up and period costs, and some variable costs related to use (although not allocated by transaction) ([21]). For IOS it was argued that there would be high initial (fixed) costs, smaller capacity and maintenance costs (mixed), and minimal marginal costs ([2]). Chapter 3. Characterizing Interorganizational IT 31 With a focus on IT supplier costs, the general form of an IT cost function begins with an initial one time fixed implementation cost of the IT, for example purchases of hardware and software as well as software development. A second component for fixed period costs is also required to cover normal maintenance and operations. For each new customer adopting IT an additional one time installation cost is incurred, typically the costs of setting up a new account. Finally, there is some small marginal cost of each originating transaction. The resulting functional form of the IT cost function can be additive in these components. Chapter 3. Characterizing Interorganizational IT 32 3.6 Pricing Structure Assumptions 3.6.1 Justification for Integrated Pricing of the Primary Good and the IT As discussed in Chapter 1, in previous MIS work there has been an implicit belief that the pricing of the primary good can be separated from the pricing of the IT. That is, the price of access to the technology should not be linked with the pricing structure of the primary good. Combined strategies for pricing are not explicitly considered in the MIS literature. In light of IT providing differentiation and incurring switching costs, this research makes the argument that there are important interdependencies in the pricing of the primary good and the IT used to support the primary good. Therefore, profit maximization may only be achieved via joint pricing strategies of IT and the primary good. In a simplified example, if one considers IT as increasing product quality, the enhanced (IT) primary good could attract those customers who value the quality increase more highly, leaving a different set of potential customers for the original primary good. The distribution of customers between the original and enhanced primary good would depend on the prices of both goods, not just one. 3.6.2 Justification of Two Part Tariffs With IT In absence of a basis for differential pricing over consumers, and in absence of any pure price discrimination mechanisms12, pricing structure is usually a linear tariff with a zero intercept. In the case of the original primary good (without IT), a linear tariff faced by an individual customer would simply be price times quantity. Typically in a relationship between suppliers and customers, interorganizational IT is installed as a system, and then the benefits of IT accrue to each unit of the primary good transacted via that 1 2For example, quantity discounts. Chapter 3. Characterizing Interorganizational IT 33 system. This provides an additional "degree of freedom" for pricing in that the supplier can charge both for a one time IT installation (or adoption) providing access, and on a per unit (of the primary good) basis. As a result, a two part tariff is the appropriate pricing mechanism. Two part tariffs are made up of a fixed portion (e.g. IT installation) and a linear portion (e.g. per unit). Using R as the fixed component, p as the variable component, and q as quantity purchased, R + pq represents the two part tariff. Of critical importance is that the fixed component of a two part tariff is not constrained to be positive. That is, the fixed component may be used as a subsidy rather than a tax 1 3. While it is true that a monopolist could use a two part tariff to extract higher profit in absence of any legitimate basis, the focus here is that IT provides the underlying justification for an access/adoption charge or rebate. Clearly, from the supplier's point of view a two part tariff dominates a linear tariff with a zero intercept, as the fixed component could always be set to zero. Hence, the two part tariff could always cover the case of a linear tariff. A way to interpret two part tariffs is as a price discrimination device. The ability to price discriminate over customers is directly related to the degree to which individual customers can be identified. In this formulation, for those customers who adopt IT the usage of IT is perfectly correlated with primary good purchases. Hence, level of IT usage cannot be separated from primary good purchases. If this were not the case it would be possible to price discriminate not only on the basis of IT adoption (e.g. with a two part tariff) but also on the basis of IT usage. Effectively the supplier could set a fee for adoption, a per unit fee for the primary good, and an additional charge for the level of IT usage. Interestingly, early information systems chargeback schemes relied heavily on the distinction between CPU time, input/output units, connect time, main memory usage, secondary storage usage, as well as time of day, to discriminate between mainframe 1 3 The variable component must be positive or else customers would demand infinite quantities. Chapter 3. Characterizing Interorganizational IT 34 computer users ([11]). Chapter 4 Suppliers Offering IT to Consumers 4.1 Introduction This chapter focuses on the prices suppliers select when offering IT enhancements of the primary good to consumers. The underlying themes are that joint pricing should be used for the primary goods and that two part tariffs should be used for pricing an IT enhanced primary good, with IT being the basis of the fixed component of the tariff. Five models are developed, each featuring a different scenario of IT and primary goods offered to the market. Organization of the chapter is as follows. The first model concentrates on a monopolist's two part tariff for the IT enhanced good, in absence of other primary goods. This is succeeded by an examination of the monopoly pricing problem where there is also an original primary good in addition to the IT enhanced primary good. Then oligopoly pricing problems are addressed. The case where only one supplier has IT is modelled, concentrating on a supplier duopoly. This is followed by an investigation of the case where two suppliers compete with identical IT using two part tariffs. Then pricing results for two suppliers with different ITs are presented. Finally, a brief overall analysis is given, along with conclusions. 35 Chapter 4. Supphers Offering IT to Consumers 36 4.2 Model 4.1: Monopoly Supplier Offering the IT Enhanced Primary Good Consider first the monopoly pricing problem where only one primary good is offered to the market, and this primary good is enhanced with IT. Prior work on monopoly two part tariffs has been extensive, starting with Oi, [32], and culminating with Schmalensee, [41]. Other references include [26], [25], and [12]. 4.2.1 Demands Consumers are assumed heterogeneous in their tastes for quality of the primary good. These differences in taste are represented by the taste parameter 9, 9 £ 1Z. 9 follows the density function f(9) > 0 over the closed interval [9min,9max]. This density has a cdf F(9), so F(9rnin) = 0 and F(9max) — 1. Hence, F(9) is the proportion of consumers with taste < 9. Preferences for the IT enhanced primary good follow U(q,9) where TT, f V(q,9) - R - pq - K if q > 1 I 0 otherwise, q — 0 q is the number of units purchased, V(q, 9) is a twice continuously differentiable function which is increasing and concave in q, and increasing in 9. Q ^ ' > 0, and V(0,9) = 0. The internalization switching cost is n > 0, and R + pq is the two part tariff. For those consumers who purchase, q must be greater or equal to unity as no restric-tions are placed on R. For example, R could be a subsidy in which case with no minimum purchase requirement all consumers would adopt the IT with some purchasing arbitrarily small e units. Trivially, p > 0 or consumers would purchase an infinite amount of the IT enhanced primary good. Observe the role of IT in this formulation of consumer preferences: IT provides a basis for the two part tariff (i.e. IT adoption or access), and IT adoption incurs some Chapter 4. SuppUers Offering IT to Consumers 37 positive internalization switching cost on the part of the consumer. The above specification assumes that preferences are additively separable in primary and numeraire goods1. That is, the preference structure for 6 is U(q,X,6) = U(q,6)+X subject to the budget constraint R + pq + X < I if q > 1, where X is the numeraire good and / is income. Define 5 = {t7|g = 0orc7>l}. Each consumer 8 chooses q to maximize utility, max£/(g, 9) qes For those consumers who choose q > 1 the first order (Kuhn- Tucker) conditions are dV(q,6) « -P< 0 , q>l dq [ - ^ - - P ] [ g - 1 ] = 0 . Given the properties of V(q,6), these conditions define a demand function which is non increasing in p and non decreasing in 6. Observe that both the fixed component of the two part tariff, R, and the internal-ization switching cost, K, have no impact on the quantity demanded, given consumers choose to purchase the IT enhanced primary good, as they do not appear in the first or-der conditions. Of course, the fixed component and internalization switching cost affects the choice of whether or not to purchase the IT enhanced primary good. •'Alternatively, it could be assumed that income changes related to purchasing the primary good are negligible (see [43] and/or [25]). Chapter 4. Supphers Offering IT to Consumers 38 Define 8 =inf{0 | q(p,9) > 1}. Alternatively, the condition U(q(p, 0), 9) = V(q(p, 6), B ) - R - pq(p, 9) - K = 0 implicitly defines 9(R,p). If 9(R,p) exists then it is unique because V(q, 9) is monotone in 9. As U(q(p,9),9) is non decreasing in 8, all 9 > 9(R,p) demand q(p,9) > 1. If 9(R,p) does not exist then either all consumers purchase, 9(R,p) = 9min, or no consumers purchase, 8(R,p) — 9max. The aggregate demand structure can be built up from individual consumer behaviour. Normalizing the total number of consumers to unity, the proportion of consumers who adopt IT is, N(R,p)= f f(9)d9 = l-F(9(R,p)) J6(R,p) and gruax Q(R,p)= I q(p,0)f(0)d8 J8(R,p) is aggregate demand for the IT enhanced primary good. 4.2.2 S u p p l i e r P r o f i t M a x i m i z a t i o n The supplier's cost function is of the form k F + kIN(R,p) + [c + kc}Q{R,p) where c is the constant marginal cost of producing the primary good (exclusive of IT costs), ,kF is the fixed implementation cost of the IT, k1 is the fixed cost of connecting Chapter 4. Supphers Offering IT to Consumers 39 and installing an additional consumer on the system, and kc is the constant marginal IT cost per primary good sold. For the monopolist selling the IT enhanced primary good exclusively, maximizing profits means selecting an optimal combination of R and p, max7T (R,p) = max[[# - k*]N(R,p) + \p - c - kc]Q(R,p) - kF}. R,P R,p The necessary first order conditions are ^ = m , ) + ^ [ « - * 1 + * ^ - c - * ° l = 0 Op Op Op Using the first order conditions, the following proposition establishes that a subsidy (negative R), along with the variable price for the minimum purchase, should be no larger than the consumer's internalization switching cost, K. The proof is constructed similarly to those developed in [25] and [41], showing the fixed charge could never be negative. The present formulation differs in that internalization switching costs borne by consumers from IT adoption are explicitly included. Proposition 4.1: R-\-p>—K. Proof: Suppose not one unit. Thus, This implies Then 6(R,p) = 6min. That is, all consumers will purchase at least dN(R,p) dQ(R,P) dR = a n d - ^ i ^ = ° -Chapter 4. Suppliers Offering IT to Consumers 40 This contradicts the initial hypothesis that all consumers purchase. • Proposition 4.1 effectively rules out an atom of consumers who, in order to receive a subsidy, purchase the minimum quantity, q = 1. Therefore, for all 8 > 8(R,p) the optimal demand, q(p, 8), is an interior solution (in the sense of d V ( q & e ) ' 9 ) = to consumer utility maximization. Then for 6 > 8(R,p), q(p,8) is decreasing in p and increasing in 8. For an interior profit maximizing solution to exist requires 8(R,p) < 8max so that N(R,p) < 1, and 8(R,p) > 8min s o A W P ) > 0 a n d ^ , ^ < 0 . The system resulting from profit maximization is solved in Appendix 4.1. The optimal prices (in marginal contribution form) are R h I _ N(R,P) q(p,8(R,P))[N(R,p)q(P)8(R,p))-Q(R,p)} n8(R,P))d-^ H l Z ^ n ^ 6 _ LC _ N(R,p)q(p,8(R,p)) - Q{RlP) J) C nJ — w h e r e 96'{R'p) - 1 / 9V(g(p,8(R,p)),e(R,P)) It is useful to separate supplier profits into variable profits made from purchases of the IT enhanced primary good, and profits made from the fixed IT connection or access component. The following proposition determines that positive variable profits are made with the optimal two part tariff. Chapter 4. Suppliers Offering IT to Consumers 41 Proposition 4.2 p — c — kc > 0. Proof: Consider N(R,p)q(p,8(R,p)) — Q(R,p). q(p,8) is increasing in 8 for 8 £ \8(R,p),8max}. Therefore, Q(R,P)= f q(P,8)f(6)d8 > f q(PJ(R,p))f(8)d8 J6(R,p) Je(RlP) = q(p,0(R,p)) I f(8)d8 = N(R,p)q(p,8(R,p)). Je(R.v) The strict inequality follows from the fact that the marginal consumer demands less than the average consumer who purchases. The proposition then follows from the fact that for 8 £ [8(R,p),8max], q(p,8) is decreasing in p (downward sloping demands). • The implication of the above is that for the monopolist selling solely the IT enhanced primary good, the per unit price of the primary good should always be larger than the marginal cost of both the good and the IT. Therefore, the IT monopolist always makes positive variable profits from the IT enhanced primary good. There are conjectures that it may be optimal to provide IT to customers free of charge, or even subsidize them to adopt. For the monopolist offering the IT enhanced good exclusively the sign of the fixed component cannot be determined. To see exactly what the fixed component is capturing, substitute the variable contribution into the equation of the fixed contribution, R - ^ = r ^ a L p ) ~ 9lP>HR,P))\P - c - n f(8(R,p))a-^ All the elements of the first term are positive. From Proposition 4.2, and because q(p,8(R,p)) > 0, the second term is also positive. Thus, the sign of R — k1 cannot be found. Chapter 4. Suppliers Offering IT to Consumers 42 The result is that the monopolist may make negative profits from the fixed compo-nent, and perhaps even pay a fixed subsidy to consumers adopting IT, although from Proposition 4.1 this subsidy should not exceed the incremental internalization switch-ing cost of installing the IT, K. Therefore, to some degree, this supports the conjecture that suppliers and consumers may share the switching costs resulting from IT adoption. Of course, any subsidy depends crucially on consumers' commitments to purchase their optimal quantities. In examining the optimal fixed component (rental) of a two part tariff, Littlechild ([26]) noted that "... it may well be profitable to "subsidize" subscribers into the system, by charging a rental less than marginal cost, because the profits which marginal subscribers generate on subsequent production outweigh the loss of rental rev-enue caused by the necessary reduction in rental." (p. 666) In his Proposition 8, Schmalensee ([41]) shows the marginal contribution from the fixed component of the two part tariff follows the sign of which can be derived directly from our solution to R — k1. As the sign of this equation is ambiguous he states "... If one thinks that the direct case, with q > q, is typical (our situation, where q is the average quantity purchased by those consumers who purchase) and that considerable buyer diversity is also the norm, this analysis suggests that pricing strategies that involve "giving away the razor and making money on the blades" are optimal more often than are policies in which most profits are earned on sales of the fixed input." (p. 457) Chapter 4. Suppliers Offering IT to Consumers 43 Following [41] and others, optimal prices can also be expressed in terms of the con-sumer surplus of the marginal consumer. Define CS(p,9) as the consumer surplus of the consumer represented by 9 when the fixed component of the two part tariff is zero (i.e. R = 0). Let q(p,9) be the quantity purchased by 9 > 9(R,p) when R = 0 (lower 9 consumers do not adopt IT and purchase). At the optimum, CS(p,9(R,P)) = R = V(q(p,9(R,p)),9(R,p)) - pq(p,9(R,p)) - K so that the fixed portion of the tariff is the consumer surplus of the marginal consumer, represented by 9(R,p). Note the impact of the internalization switching cost, K, reducing CS(p,9(R,p)) and therefore R. Recognize that all 9 > 9(R,p) have consumer surplus larger than R. Interestingly, if all consumers are identical then both individual demand and the consumer surplus is the same for all consumers. Then it can be shown that the primary good should be priced at marginal cost. The fixed component of the two part tariff is then unambiguously positive, and the IT charge is the vehicle with which to take the full consumer surplus for profit. Thus, marginal cost pricing maximizes consumer surplus, but the IT charge allows the supplier to take it away. Chapter 4. Supptiers Offering IT to Consumers 44 4.3 Model 4.2: Monopoly Supplier Offering the IT Enhanced Primary Good and the Original Primary Good Consider the monopoly pricing problem where two primary goods are offered to the market: the original primary good and the primary good enhanced with IT. In this model consumers are restricted to purchasing only one of the two types of primary goods. Thus, it is not possible for consumers to adopt IT and purchase the original primary good. 4.3.1 Demands Consumers are assumed heterogeneous in their tastes for quality of the primary good. These differences in taste are represented by the taste parameter 8, 8 £ 1Z. 9 follows the density function f(9) > 0 over the closed interval [6min, 9max). This density has a cdf F{9), so F(9Tnin) = 0 and F(8max) = 1. Preferences for the IT enhanced primary good follow U\(q\,9) where U1(q,,9)={ Vi(qi,6)-R-Piqi-K if<?!>l 0 otherwise, qx = 0. Preferences for the original primary good follow rr , m \ Voilo,9) -Poqo if qo > 0 Uo{qo,9) = < [ 0 otherwise, q0 = 0. Where q± is the number of units purchased of primary good i — 0, 1, Vi(qi,8) is a twice continuously differentiable function which is increasing and concave in q±, and increasing in 8. The cross partial derivative of Vi(qi,9), 9 ^ f j ^ , is positive, and Vi(0,9) = 0. The internalization switching cost is K > 0, and R + p-^qi is the two part tariff. The IT enhanced primary good is of higher quality; thus Vi(qi,0) > V0(q0,8) for a given 8 and q i = q0 > 1. Thus, in this formulation of consumer preferences IT is Chapter 4. Suppliers Offering IT to Consumers 45 characterized as the basis for the two part tariff, as incurring a positive internalization switching cost, and as providing a superior quality primary good. For those consumers who purchase, qx must be greater or equal to unity as no restric-tions are placed on R. For example, R could be a subsidy in which case with no minimum purchase requirement all consumers would adopt the IT with some purchasing arbitrarily small e units. Trivially, px > 0 or consumers would purchase an infinite amount of the IT enhanced primary good. Consumers are restricted to purchasing at most one type of primary good. The underlying preference structure of a given consumer is therefore subject to the appropriate budget constraint, either R-\-Piqi+X < I orpoqo-rX < I, where X is the numeraire good and / is income. Thus, it is assumed that preferences are Consider the consumer's optimal choice of quantity separately for each type of primary good. Examining first the IT enhanced primary good, each 9 chooses qi to maximize For those consumers who choose qi > 1 the first order (Kuhn-Tucker) conditions are U{qi,q0, X,6)= max{ (^c?!, 9), U0(qQ, 9)} + X additively separable in primary and numeraire goods2. utility, max[/i(i7i,0) 9 qi > 1 or qx = 0 91 dqi - Pl < 0, qi > 1 2Alternatively, it could be assumed that income changes related to purchasing either primary good are negligible (see [43] and/or [25]). Chapter 4. Supphers Offering IT to Consumers 46 With the properties of Vi(qi,6), these conditions define a demand function 9i(Pi>0) which is non increasing in pi and non decreasing in 6. The fixed component of the two part tariff, R, and the internalization switching cost, do not affect individual demand, as they drop out of the first order conditions. However, the fixed component and switching cost do effect whether a given 6 purchases the IT enhanced primary good. Turning the original primary good, each 6 maximizes utility by choosing q0, maxU0(q0,6) 3 q0 > 0 90 The first order (Kuhn-Tucker) conditions are 5 Po < 0, q0 > 0 oqo oqo Given the properties of V0(qo,8), a demand function is defined qo{Po,6) which is non increasing in p0 and non decreasing in 6. With these demands well defined each consumer chooses which primary good to pur-chase by m3,x{U1(q1(p1,e),6),Uo(qo{po,0),9)} where qi(pi,6) and qo(po,9) are optimal value functions. Chapter 4. SuppHers Offering IT to Consumers 47 Consider the consumer who is indifferent between the IT enhanced primary good and the original primary good. This consumer, 9(R,p\,po), is implicitly defined by U1(q1{Plte),6) = U0{q0(p0,§),§), or v1(qi(p1,e),§) - R - PMPIJ) - K = V0(q0(p0,e)J) -poqo(Po,0). Assume that at least one of the two primary goods is purchased. Thus, qi(Pi,9) is increasing in 9 and decreasing in P{. Hence, this ensures the market is covered by the IT enhanced and original primary goods. In addition, assume dVi{qi(Pi,e),0) avo(go(po,g),g) 30 89 This means that the utility function for the IT enhanced primary good has a higher slope with respect to 9 than the original primary good, at optimal demand levels. Thus, higher taste consumers receive larger increases in utility from purchasing the IT enhanced primary good. Notice that this is an application of the envelope theorem, as demands are optimal value functions. If 0(R,pi,po) exists then with the above properties it is unique. Hence, 9>9{R,Pi,Po) qi{Pi,9)> I, <? o(po,0) = O 9<9{R,Pl,Po) qo{po,6)>0, qi{Pl>9) = 0. Uniqueness and the separation of consumers follows from the monotonicity of the utility functions, interior solutions to utility maximizations, and the above assumption Chapter 4. Suppliers Offering IT to Consumers 48 o f mtflijpifilfl} > dv„[go(p0,e),e) I f § ( R i P u P o ) d o e s n o t e x i s t t h e n e i t n e r a l l consumers purchase the IT enhanced primary good, 6(R,Pi,po) — 8min, or all consumers purchase the original primary good, 8(R,Pi,Po) = QMAX. The aggregate demand structure can now be fully described. Normalizing the number of consumers to unity, the fraction of consumers who adopt the IT enhanced good is Qmax N(R,Pi,Po) = . f{e)d6 = 1 - F(6(R,Pl,p0)). J8(R,Pl,p0) Aggregate demand, or total quantity purchased, of the IT enhanced and original primary good are respectively Q1(R,Pl,Po)= I qi(Pl,6)f(6)d8 QO{R,PI,PO) = / , qo{po,e)f(d)de. 4.3.2 Supplier Profit Maximization The supplier's cost function is of the form kF + fc'TV^p^po) + [ci + kc}Qi(R,PL,PO) + c0Q0(R,PL,PO) where a is the constant marginal cost of producing primary good i = 0,1 (exclusive of IT costs for i = 1), kF is the fixed implementation cost of the IT, k1 is the fixed cost of connecting and installing an additional consumer on the IT system, and kc is the constant marginal IT cost per IT enhanced primary good sold. In this joint pricing problem the previous rule for the monopolist setting R equal to the consumer surplus for the IT enhanced primary good, as described in [41] and others (also in Model 4.1), no longer holds. To see this focus on 8(R,PL,PO) when R = 0. With Chapter 4. Suppliers Offering IT to Consumers 49 the preferences as defined, utility is in monetary units so that the consumer surplus of the marginal consumer is CS(pi,d(R,pi,p0)) = U1(q1(pi,e(R,p1,p0)),6(R,pl,p0)) = V1(q1{pi,9(R,p1,po)),8(R,pi,po)) - Piqi(pi,9(R,Pi,Po)) - «• If the fixed component is set to R = CS(Pl,e(R,Pl,Po)) = C/ 1(g 1(p 1,0(E,p 1,po)),^)Pi,Po)) so as to take the full consumer surplus on the IT enhanced good then 9(R,p1,p0) will prefer the original good with Uo(qo(po,8(R,Pi,Po)),6(R,Pi,Po)) > 0. Of course, the reason this rule no longer works is that the alternative to purchasing the IT enhanced good is no longer no purchase (which yields zero utility), but purchase of the original primary good (which yields strictly positive utility). Hence, R changes the identity of §(R,pup0). As a result, the monopolist's profit maximization problem must be set up as a maxi-mization over three price components: R, p 1 ; and p0. The profit maximization is then max T(R,p1,po) = max [N{R,Pl,p0)[R - k1} + Qi{R,pi,p0)\pi - ci - kc] R,Px ,po +Qo{R,Pi,Po)[po - c0] - kF). The necessary first order conditions are dn-(R,Pl,p0) 8R Chapter 4. Supphers Offering IT to Consumers 50 »r/ r> ^ dN(R,Pl,p0) u dQ1{R,p1,p0)[ C ] N{R,Pi,Po) + T j j ^ [R - k \ + — LPI - ca - k \ + ^ [ P o - c 0 ] = 0 dir(R,Pl,Po) _ dpi dpi dpi dQ0(R,Pi,Po)r , n + - x \P° - Co = 0 dpi dTv(R,pi,p0) _ dp0 dN(RPl,Po) _ k I + dQMpupp) _ ^ _ fcC dp0 Opo + n o ( # , P i , P o ) + ~ \Po - c 0j = 0 opo Assuming the necessary first and second order conditions hold, this system of three equations and three unknowns is solved in Appendix 4.2. The resulting optimal prices (in marginal contribution form) are R - k 1 = N{R,Pi,p0) qi{piJ(R,Pi,Po))[N(R,p1,p0)q1(p1,e(R,p1,p0)) - Qi(-R,pi,p0)] q0(p0J(R,puPo))\N(R,pupo)qo(p0,6(R,pup0)) + Qo{R,Pi,Po)} rB(R,pi,p0) dqu{pi),e) fla\JQ p i - C i - fe c _ N(R,pi>Po)qi(puHR>Pi>Po)) - QI(R,PI,PQ) 3qi{pi,8) Chapter 4. Supphers Offering IT to Consumers 51 _ N(R,pup0)q0(p0,§(R,p1,p0)) + Q0{R,pi,Po) r8(R,pi,po) dq0(p0,e) f(fl\JQ where ae~(R*l<P^ = j / r ^ f o i f r i W ) _ dvn(qo[pufi),8). It is of interest to divide profits from the IT enhanced primary good into variable profits from the per unit component of the two part tariff, and profits from the fixed component for access to the IT. The following propositions determine the signs of the variable profits from the IT enhanced primary good, and the profits from the original primary good. Proposition 4.3: Variable profits from the IT enhanced primary good are positive. Proof: Similar to the proof of Proposition 4.2., qi(pi,&) is increasing in 6. qi(p\,6) is decreasing in P i . Hence, px — cx — kc > 0. • Proposition 4.4: Profits from the original primary good are positive. Proof: N(R,p1,po)qQ(po,0(R,Pi,Pi)) + Qo(R,Pi,Po) > 0. q0(po,Q) decreasing in p0 implies / £ P l , P o ) dq^l^f(9)de < 0. Therefore, p0 - c0 > 0. • Observe the equation for marginal contribution per unit of the IT enhanced primary good is the same when the original primary good is also offered simultaneously, and when it is not offered at all (Model 4.1). However, even though the equations are the same they are not equivalent as 8(R,p) is unlikely to be equal to 6(R,Pi,p0). As in Model 4.1, the sign of the fixed component or the two part tariff, R, cannot be found. To see this substitute the variable contributions for both the IT enhanced and original primary goods into the equation for R — k1, Chapter 4. Supphers Offering IT to Consumers 52 R- k1 = N(R,Pl,p0) fMR,Pl,Po))°ii%i*Bi -qi(pi,9(R,Pi,Po))[pi - c i - kC] + qo{po,0{R,Pi,Po))\po ~ c 0 ] -As both of the variable contributions are positive, and demands from the marginal con-sumer, 6(R,pi,po)), are positive, the sign of the fixed component is ambiguous. There-fore, it can be optimal for the monopolist to either tax or subsidize IT adoption. 4.3.3 Discussion The additional profit taken from the consumer represented by 9(R,Pl,p0) for the IT through the fixed component has to be balanced off against the profit which would be gained per unit if consumer 0(R,p1,po) consumed the original primary good. The intuition is that the presence of the original primary good increases the optimal fixed charge, as the same additional rents could have been appropriated from the original good. The largest potential size of the subsidy cannot be found. Recalling the argument in Proposition 4.1, the reasoning was based on never providing positive utility through the IT subsidy in absence of more than a minimum level of demand. However, here there is potential positive utility which can be gained by some consumers purchasing the original primary good. Therefore, the effectiveness of a subsidy is not necessarily limited by the internalization switching cost, K. There is also no loss of generality restricting the analysis to where all consumers adopt one of the two primary goods as long as consumers who purchase remain separated by 8(R,p1,p0). Identical analytical results obtain for the two part tariff. The equation for the marginal contribution of the original primary good changes with non adopters as there Chapter 4. Supphers Offering IT to Consumers 53 is a lower bound on the consumers served by the original primary good which depends on original primary good price. If positive profits are not obtained from the original primary good the model reverts to the case of Model 4.1 where there is no original primary good. However, it is noted that the concavity of the supplier's profit function may be more difficult to maintain with non adopters, as non adopters effectively form a third market (no purchase as a third primary good). For more details see [5] and [31]. The pricing results from the two good case emphasize that joint pricing is critical to maximizing profits from using IT. Because 8 is a function of R, p1} and p0, each of the optimal prices are linked to the other two prices. This interdependence is directly evident through the last two terms of R — k1. Indeed, pricing between the IT enhanced good, original primary good, and IT adoption are not separable. Chapter 4. Supphers Offering IT to Consumers 54 4.4 Model 4.3: Oligopoly Suppliers Where One Supplier Has IT This section focuses on the first of the oligopoly models. Here both the IT enhanced and original primary goods can be offered in the market, but only one supplier has access to the IT. This model is similar to the general oligopoly problem studied by Judd, [20], except that particular elements relating to IT are explicitly included. As in the previous monopoly model, consumers are constrained to purchase one type of primary good only, thus a consumer cannot both adopt the IT and purchase the original primary good. 4.4.1 Formulation Concentrating on the duopoly case, there are two supphers, A and B, where supplier A has IT and can offer the IT enhanced primary good, and supplier B does not have IT. Supplier B is committed to offer the original primary good. The model is a two stage game where • Stage 1: Supplier A decides between three strategies: offering both the IT enhanced and original primary goods, offering the IT enhanced primary good only, or offering the original good only. • Stage 2: Supphers A and B compete in prices, with a two part tariff available for the IT enhanced primary good. The game is one of complete information. The solution concept employed is subgame perfect equilibrium ([24], and [42] as referenced in [43]). A subgame perfect equilibrium is a set of strategies for each supplier such that in any subgame the strategies form a Nash equilibrium. Therefore, each of the possible Stage 2 subgames must be characterized by a Nash equilibrium in prices. Chapter 4. Suppliers Offering IT to Consumers 55 The solution for the subgame perfect equilibrium is obtained by working backwards through the two stages of the game. Based on the supplier A's strategies in Stage 1, there are three possible subgames at Stage 2 where suppliers compete in prices: • S2.1: Supplier A offers both the IT enhanced and original primary goods, supplier B offers the original primary good. • S2.2: Supplier A offers the IT enhanced primary good only, supplier B offers the original primary good. • S2.3: Supplier A and B both offer the original primary good only. The equilibrium for each of these subgames are solved in turn. 4.4.2 Stage 2 Subgame: S2.1 Examine the case when supplier A offers both the IT enhanced and original primary goods, and supplier B offers the original primary good only. Here supplier A selects three prices: two components of the two part tariff, R and pi, and the per unit price of the original primary good, pp1 . The remaining supplier, B, chooses pf. Because consumers are assumed to choose the supplier with the lowest price for a given primary good, the effective p0 is Po = min{po , p * } . If PQ = p^ then demand for the original primary good is partitioned equally. Individual and aggregate demands are the same as those in Model 4.2; therefore their development is not repeated here. Chapter 4. Supphers Offering IT to Consumers 56 Focus first on supplier B setting pB. Supplier B faces contingent aggregate demands for the original primary good, with a given R, pi, for pB relative to p^ : Qo{R,Pi,p0) iiPo<Po Qo(R,Pi,Po)/2 if Po = Po = Po 0 ifp* >p0 4 For supplier B maximizing profits Tb (R,Pi,p0) means solving Qo(R^Pi^Po) = ' *B{R,Pi,Po) = < < K P o ) ~ Po = maxTTB(R,p1,p0) = max[[p£ - c0]QB(R,Pi,Po)]-Contingent on pfi, the possible outcomes to different choices of pB are [Po - co]Qo(R,Pi,Po) if Po < Po [po-c 0 ] 9 " ( f l ' P l ' P o ) i{pB=pt=p0 o xpfi>pi Thus, it is always optimal for suppher B to undercut p^ down to marginal cost. Therefore, suppher B's reaction function is P o - £ if>o> co c0 otherwise for e > 0. Now focus on supplier A. Supplier A faces aggregate demands in the original primary good opposite to suppher B, given R and P x , relative to pB: Qo{R,Pi,Po) ifPo<Po Qo(R,Pi,Po)/2 if Po4 = Po = Po 0 if Pb4 >Po Partition supplier A's profit function into profits from the IT enhanced primary good and the original primary good. Using Trf(R,Pl,pQ) to denote profits from primary good i, supplier A profit maximizing is Qt{R,Pi,p0) Chapter 4. SuppHers Offering IT to Consumers 57 max i-A(R,pi,p0) = max hf (R,pi,p0) + KA (R,Pl,p0)} R,PI,P„ R,PI,PO = max \irA(#,pi,p0) + [Po ~ co]<?o (#,Pi,Po)], R,PI,P$ with the effective po = min{po ,Po}- The three possible profit payoffs to supplier A selecting pA relative to p$ are *A(R,Pi,Po) = ' TTA(R,pi,Po) + \pA - c 0 } Q 0 ( R , p u P o ) i i p A < p$ KA(R,puPo) + [p0 - c 0 ] ^ * f ^ if p^ = p* = po 7r^( J R,p 1 ) p o ) + 0 i i p A > p t From these payoffs supplier A's reaction function for p A can de determined. It is clear that Po > PQ is dominated by both of the other alternatives when P Q > c0 for all two part tariff pairs, (R,Pi). Therefore, supplier A's reaction function for P Q is <t>(Po ) = Po Po ~ e o r Po i f Po > co c0 otherwise. for e > 0. Thus, <?KPo ) = <?KPo ) a t Po = Po = co characterizes the Nash equilibrium p 0, regardless of the two part tariff for the IT enhanced primary good. The solution for the equilibrium R and p 1 are obtained as best response functions to p 0 = c 0. Supplier A's cost function for the IT enhanced primary good is of the form fc'jV^Pi.o) + [ci + kc}Qi{R,Pi,c0) Chapter 4. Supphers Offering IT to Consumers 58 where ci is the constant marginal cost of producing the IT enhanced primary good (exclusive of IT costs), k1 is the fixed cost of connecting and installing an additional con-sumer on the IT system, and kc is the constant marginal IT cost per IT enhanced primary good sold. Inclusion of a positive fixed implementation cost of IT, kF, is postponed until later in this section. Suppher A's profits maximization from pricing the IT enhanced primary good is maxirA(R,p 1 ;c 0) = max[[.R - kI]N(R,p-[, c0) + [pi - ca - kc]Qi(R,p1,c0)]. R,pi R,pi The resulting necessary first order conditions are dirA(R,Pl,c0) dN(R,p1,c0) 7 , dQi(-R,Pi,c 0) r c , =N(R,Pl,c0) + - [R-k)-r m fo-d-k ] = 0 ^ ( f ' P l ' C 0 ) = ^ P l ' C 0 ) [R - *'] + Q^puco) + W M ^ f o - C l - * ' ] = 0, opi opi dpi which in the special case of Appendix 4.3 where p 0 = c 0 yield the following equilibrium two part tariff: R - k1 = N(R,Pl,c0) q1(p1,6(R,p1,co))[N(R,p1,co)q1(p1,9(R,p1,c0)) - Q^^p^cp)] A _ _ ,c N(R,p1,c0)q1(Pl,d(R,p1,c0)) - Qx(R,pi,c0) w n e r e 98(R,puco) = lndV1(qi(pu6),e) _ dV„(qo(c0,8),6)] dR ' L S0 QB J' Notice the reasoning behind marginal cost pricing in the original primary good is basically a form of the Bertrand paradox. Chapter 4. Supphers Offering IT to Consumers 59 4.4.3 Stage 2 Subgame: S2.2 Consider when supplier A offers the IT enhanced primary good only, and supplier B offers the original primary good only. Supplier A selects two prices: two components of the two part tariff, R and p\. The remaining supplier, B, chooses p0. Individual and aggregate demands are developed in a similar manner to those in Model 4.2 and are not restated. Supplier A's cost function is of the form fc7JV(fl,Pi,Po) + [ci + kc}Q1(R,PuPo) where C\ is the constant marginal cost of producing the IT enhanced primary good (exclusive of IT costs), k1 is the fixed cost of connecting and installing an additional con-sumer on the IT system, and kc is the constant marginal IT cost per IT enhanced primary good sold. Again, a positive fixed implementation cost of IT, kF, will be discussed later. Using constant marginal costs, Supplier B's costs are simply the costs of providing the original primary good, c0Q0(R,p1,p0). Supplier A maximizes profits by selecting R and pi, max.TrA(R,Pl,p0) = max[[R - kI]N(R,p1,pQ) + [pi - ca - kc]Q1(R,p1,Po)]. R,p i R,p i Notice this is not the same maximization as the monopolist supplier IT enhanced good only case in Model 4.1 because the original primary good is still available, hence N(R,pi,po) and Qi(R,Pi,Po) are different (as evidenced by the argument p 0). The necessary first order conditions for supplier A are dTvA(R,Pl,p0) dN(R,Pl,p0) u 0Qi(fl ,pi,p o) c  m =N(R,Pl,Po) + — [R-k] + m - f a - c - k ] = 0 *A{*Pl'Po) = 9 N { R ' P u ^ op i Op i oPl Chapter 4. Suppliers Offering IT to Consumers 60 Supplier B is the only supplier of the original primary good, and consequently B has a monopoly in that market. Hence, supplier B maximizes profits selecting p0, maxTrB(R,p1,p0) = max[[p0 - c0]Q0{R,pi,po)]. PO po Supplier B's necessary first order condition is dTrB(R,Pl,p0) dQ0{R,Pl,p0)f ~ = Qo{R,PuPo) + 5 \Po ~ c0j = 0 opo opo The Nash equilibrium solution comes from a joint solution of the system of three first order conditions, two for supplier A (i.e. R and Pi) and one for supplier B (i.e. p0). This solution represents the intersection of the three best response functions. The pricing equations are derived in Appendix 4.3. The equilibrium prices in marginal contribution form are R - k1 = N{R,Pl,Po) qi{pi,9(R,Pi,Po))[N(R,p1,po)q1(p1,§(R,PltPo)) - Qi(R,Pi,Po)} c _ N(R,Pi,Po)qi{piJ{R,P\,Po)) - QI(R,PI,PO) Pi-cx-k Po - c0 = Qo(R,pi,po) ^ . P O ) ; ^ where the derivatives of the marginal consumer are = \/ [ d V > ( « ' B V » M P O fi)fi) j and *£5g*2i = -a-^^qo(PoJ(R^,Po)). The ensuing proposition confirms that supplier B makes positive profits from the original primary good. Chapter 4. Supphers Offering IT to Consumers 61 Proposition 4.5: Supplier B makes positive profits from the original primary good. Proof: Qo(R,Pi,Po) > 0. With qo(po,0) decreasing in p0, Jemin opo In addition, de{R,Pl,p0) de(R,Pl,p0) -—Wo— = ak—totoo'WMM = - l / l -QQ QQ j9o(Po,e'(-K,Pi)Po)). From interior solutions to utility maximization go(Po> 8{R,Pi,Po)) > 0, and by assump-tion MMaffi•')•*) - ^»MPo,e),9) > 0 c l e a r l y ; f(e(R,puPo)) > 0. Therefore, P o - c0 > 0. • 4.4.4 Stage 2 Subgame: S2.3 Without the IT enhanced primary good, price competition between supphers A and B in the original primary good market is straightforward with a linear tariff as the only pricing vehicle. All of the demand will go to the suppher with the lowest p0. With two suppliers, A and B, at any price greater than marginal cost each suppher always has an incentive to undercut its competitor by a small amount and capture the full demand. With common constant marginal costs of the original primary good, c0, the result is a unique Nash equilibrium where both (all) suppliers price at marginal cost, Po = Po = co, and profits are zero, ^(co) = ^ (co) = 0. Chapter 4. Suppliers Offering IT to Consumers 62 4.4.5 Stage 1 At Stage 1 supplier A selects one of the three strategies: compete in the IT enhanced and original primary goods (S2.1), compete with the IT enhanced primary good only (S2.2), or compete head to head with the original primary good only (S2.3). In subgame S2.3 supplier A makes zero profits due to marginal cost pricing in the orig-inal primary good. Therefore, offering the original primary good is trivially dominated by either of the other two strategies in Stage 1. In subgame S2.1 supplier A also makes zero profits from the original primary good in equilibrium as p0 = c0. Thus, the comparison of subgames S2.1 and S2.2 focuses on the equilibrium profits from the IT enhanced primary good, the equilibrium irA(R,pi,po). The equilibrium two part tariff follows the same form in each of these subgames, except for the value of p0. The following proposition verifies that positive variable profits are made from the IT enhanced primary good in both subgame S2.1 and S2.2, regardless of Po-Proposition 4.6: Variable profits from the IT enhanced primary good are positive. Proof: Similar to the proof of Propositions 4.2 and 4.3, qi(pi,6) is increasing in 9. qi(Pi,8) is decreasing in px. Hence, p1 — ca — kc > 0. • As in both of Models 4.1 and 4.2 it is not possible to conclusively sign R — k1: R-Y= ,-, N(R,PI: PJL - *(PIAR,PUPO))\PI - C l - kc] f ^ R ^ p o ) ) 9 - ^ ^ As with the monopolist with two goods, this tax (subsidy) could be positive, negative, or zero. Now it is possible to assess the impact of p0 on supplier A's profits from the IT enhanced primary good. Writing out supplier A's profit function from the IT enhanced Chapter 4. Supphers Offering IT to Consumers 63 primary good, TvA{R,Pl,Po) = [R- k^NiR^po) + b i - c i - kc}Q1{R,Pl,Po). Taking the derivative of this profit function with respect to po produces dirf(R,Pl,p0) u dN(R,Pl,p0) c dQjXR^p^po) - = [R - k J — h [pa - cx - k j . Opo Opo Opo which, using the derivatives found in Appendix 4.2, equals r r> U-\t(a(T> ^96(R,Px,Po) -[R - k }f(6{R,px,po)) s  -\px - c x - kc]qx(pxJ(R,Px,Po))f(e\R,Px,Po))d6{R'Pl,PO) OPo where d8^R^'P0^ < 0. From Proposition 4.6 pi — cx — kc > 0. Thus, the second term is negative. However, with the sign of R — k1 ambiguous, the sign of d l T l ^ P l ' P "^ also appears to be ambiguous. Fortunately, intuition tell us otherwise. Reasoning from a different direction, it is clear that a less competitive original primary good (i.e. with a higher price, p0) cannot reduce profits from the IT enhanced primary good, unless the two goods are complements, which they are not. The following proposition confirms this intuition. Proposition 4.7: TrA(R,px,po) is increasing in p 0. Proof: The effects of p 0 on TA(R,px,po) only come through the number of consumers adopting IT which is defined by 0(i2,p 1 ;p o). If po increases then because  d6^ R^ ) 1J p^  < 0 the marginal consumer decreases, 6(R,px,po)- An offsetting increase in R can restore 6(R,px,Po) to its previous level as Chapter 4. Supphers Offering IT to Consumers 64 de(R,Pl,po) - d6(R,p1,p0) dfo = ^ P ^ P ^ 9R With 6(R,pi,p0) at its prior level N(R,Pi,Po) is unchanged, and because qi(Pi,6) is unaffected by changes in R or p0 then Qi(R,Pi,Po) is also unchanged. But R has been increased to compensate for a higher pQ. Therefore, the additional profit comes directly from the increase in R. • In subgame S2.1 the equilibrium p 0 is c0, in subgame S2.2 the equilibrium po > c 0. Therefore, supplier A makes greater profit from the S2.2 equilibrium, and subgame S2.1 is dominated by subgame S2.2. The resulting subgame perfect equilibrium of the game is that supplier A does not offer the original primary good but offers the IT enhanced primary good and uses R and pi in a two part tariff. Supplier B continues to offer (and has a monopoly over) the original primary good. 4.4.6 Discussion The interpretation is that if supplier A can commit not to go head to head with supplier B in the original primary good it would prefer not to do so as profits from the alternative IT enhanced primary good become depressed from the competition in the original good (see [20]). Hence, supplier A can make no profit from the original primary good with competition in that good. However, profits from the IT enhanced primary good are increasing in p 0; a higher p 0 pushes lower end consumers away from the original good and towards the IT enhanced good. Supplier A must withdraw from the original primary good in order to have p 0 > c0. From Proposition 4.5, supplier B makes positive profit when not facing direct compe-tition in the original good. Supplier A is thus providing supplier B with an opportunity Chapter 4. SuppHers Offering IT to Consumers 65 to make positive profits by introducing the IT enhanced primary good and withdrawing from the original primary good market. Supplier A may then have a claim (reasonable not legal) to some of supplier B's profits. Returning to the implementation costs of IT, kF, it was assumed in the analysis that these fixed costs were either sunk for supplier A or were zero. If incurring these fixed costs are part of supplier A's Stage 1 strategy of offering the IT enhanced primary good then for any strategy involving the IT enhanced primary good to be an equilibrium requires that profits from the IT enhanced primary good outweigh the fixed costs of IT implementation. It is possible that if supplier A cannot cover the fixed implementation costs of IT with profits from the two part tariff on the IT enhanced good, it may be that the combined profits of both suppliers A and B would more than cover these fixed IT costs. Then in principle both could benefit from the IT. However, as is generally the case with positive externalities, because property rights cannot be exercised over the externality's benefits (here the potential increased profits) neither party (suppliers A, B) may have an incentive to invest (introduce IT) and create the externality. As an area of future research, there may be contractual arrangements possible involving transfer payments between suppliers so that one supplier introduces IT and each supplier receives some of the benefits of IT introduction. If the assumption of a duopoly is abandoned, allowing multiple suppliers B who offer the original primary good, then marginal cost pricing will obtain in the original primary good (Bertrand paradox). Therefore, at Stage 1 supplier A will then be indifferent between offering and not offering the original primary good, profits would be identical in subgames S2.1 and S2.2, but supplier A would still offer the IT enhanced primary good as subgame S2.3 remains dominated. The equilibrium equations for the two components of the two part tariff remain the same. Therefore, in an oligopoly the supplier with IT Chapter 4. Suppliers Offering IT to Consumers 66 can still earn positive profits, although less than in a duopoly. As in the previous Model 4.2, there is no loss of generality from not considering consumers who are non adopters as long as consumers who purchase remain separated based on 8(R,p\,Po). Identical analytical results obtain for the two part tariff. The marginal contribution of the original primary good is modified as the lower bound on the consumers purchasing the original primary good depends on the original primary good price. However, positive profits are still obtained from being a monopoly in the original primary good. It continues to be the case than the concavity of the supplier's profit function may be more difficult to maintain with non adopters. The reader is again referred to [5] and [31]. Chapter 4. Supphers Offering IT to Consumers 67 4.5 Model 4.4: Two Suppliers Offering Undifferentiated IT Enhanced Pri-mary Goods This oligopoly model examines Bertrand competition with an undifferentiated IT en-hanced primary good in two part tariffs. Every consumer is limited to adopting and purchasing only one IT supplier's IT enhanced primary good. An example motivat-ing this competitive scenario is telephone services in the U.S.. There are at least three different telephone service providers (Bell, GTE, MCI), each using at least a two part tariff, with some offering to subsidize switching. Typically, telephone subscribers are only connected to one supplier3. 4.5.1 Formulation This section focuses on competition between multiple supphers offering identical IT and IT enhanced primary goods. Specifically, a duopoly case is examined where both sup-phers have already committed to providing the IT enhanced primary good (e.g. have already incurred the sunk cost, if any, of implementing the IT) and the two suppliers simultaneously select two part tariffs. Both supphers have equal marginal costs, c, IT related costs, k1 and kc, as well as their IT's incurring the same internalization switching costs, K. There is no original primary good available to consumers4. Consideration of any remaining positive fixed IT implementation cost, kF, as well as the presence of an original primary good, is postponed until the end of this section. The analysis concentrates on looking for a Nash equilibrium, particularly a pure strategy equilibrium. The potential for choosing two pricing parameters as opposed to one makes analysis of this direct competition more complex than previously with 3However, long distance services in the United States can provide access to other lines, therefore for long distance service a customer could subscribe to more than one supplier. Alternatively, all consumers have a sufficiently strong preference for the IT enhanced primary good. Chapter 4. Supphers Offering IT to Consumers 68 competition in the original primary good. Bertrand paradox type arguments driving prices to marginal cost are not conclusive here. Moreover, at the outset it is not clear that the symmetry of typical Bertrand results necessarily holds. Consider two supphers, A and B. Exploring the possible configurations of prices, there are three generic possibilities for equilibria: • Dominating Price Pairs: Rl > R3 and p 1 >p 3, with one of the inequalities strict. • Asymmetric Price Pairs: R1 > R3 and p l < p 3. • Equal Price Pairs: Rl = R3 and p1 = p 3. where i,j = {A, B}, i ^ j. The possibilities for equilibria from each of the above alternatives are considered in turn. 4.5.2 Dominating Price Pairs Investigating the pricing affects on aggregate demand it is clear that with R1 > R3' and p { > p 3 or Rl > R3' and p { > p 3' where i,j = {A, B}, i ^ j, all the demand will go to supplier j. If the result is that supplier j earns positive profits, Tr3(R,p) > 0, where R — (RA,RB) and p — (p A,p B), then supplier i has an incentive to reduce one or both of its pricing components to capture either a share of the positive profit, or the whole market, depending on the behaviour of its profit function. Considering supplier j with all the demand, the best response by Chapter 4. Supphers Offering IT to Consumers 69 supplier j at this point is to raise one of both of the pricing components by an arbitrarily small amount, while continuing to undercut supplier i. Therefore, as would be expected, a dominant price pair cannot support a Nash equi-librium since it is not a best response for at least one of the supphers. 4.5.3 Asymmetric Price Pairs The second possible equilibrium price configuration involves asymmetric price pairs, R{ > Rj and p{ < pj, where i,j = {A, B}, i ^ j. In this case it is not possible to determine whether an asymmetric price component equilibria exists from examining the relationships between the price components and profits alone. Specifically, verifying whether a particular price pair is a best response while maintaining the asymmetric price components precludes using constrained optimization techniques with Kuhn-Tucker conditions as the asymmetric price components assumption requires strict inequalities between prices. The key to any potential equilibrium for this configuration of prices are the strict inequalities in opposite directions for the two price components such that all consumers facing the two supplier's price pairs do not see one supplier's price pair as dominant. The following Lemma provides conditions under which an asymmetric price compo-nent equilibrium will not exist. Lemma 4.1 A Nash equilibrium in which R1 > RJ and pl < p3 for i, j = {A, B}, i ^ j, and where the market is covered by the undifferentiated IT enhanced goods, does not exist. Chapter 4. Suppliers Offering IT to Consumers 70 Proof: Assume there exists a Nash equilibrium where RA > RB and pA < pB (with no loss of generality), and where the market is covered by the undifferentiated IT enhanced goods. Focus first on consumer demands. Consumers are heterogeneous in their tastes for quality of the primary good. These differences in taste are represented by the taste parameter 8, 8 £ 1Z. 6 follows the density function f(0) > 0 over the closed interval [0mm,0ma*]- This density has a cdf F(8), so F(9rnin) = 0 and F(9max) = 1. Preferences for the IT enhanced primary good follow U(q%,9) where [ 0 otherwise, q' — 0. where i = {A, B} indexes supphers, ql is the number of units of IT enhanced primary good purchased from supplier i, V(q\9) is a twice continuously differentiate function which is increasing and concave in ql, and increasing in 8. ^QJFQ/^ is positive, and V(0,6) = 0. The internalization switching cost is K > 0, and Rl + plql is the two part tariff from supplier i. The IT aspects enter the formulation of consumer preferences through the internalization switching cost, and the two part tariff. Consumers are restricted to purchasing the IT enhanced primary good from one supplier. The underlying preference structure of a given consumer is assumed to be5 U(q\qi,X,8) = max{U(q\8),U(qi,8)} +X subject to either Rl + plql + X < I or Rj + pJq1 + X < I, where X is the numeraire good, / is income, and i,j = {A,B} where i ^ j. Thus, it is assumed that preferences are additively separable in primary and numeraire goods6. 5Discussion of the case which includes an original primary good is delayed until later in this section. Alternatively, it could be assumed that income changes related to purchasing either of the primary goods are negligible (see [43] and/or [25]). Chapter 4. Supphers Offering IT to Consumers 71 For each supplier's offering each consumer, 8, chooses ql to maximize utility, max U(q\6) 3 q{ > 1 or qi = 0, i = {A, B}. For those consumers who choose ql > 1 the first order (Kuhn-Tucker) conditions are [ i M - ^ - H - c , With the properties of V(ql,8), a demand function for each consumer is defined for each of the two suppliers i — {A, B}, which is non increasing in pl and non decreasing in 8. The demands from each supplier can be combined into a single demand function for each consumer, q(RpO)= \ q A { p A ' 6 ) ^ - ^ ( P V ) , * ) 9 ' P ' 1 qB(PB,0) if U(qB(PB,8),8)>U(qA(pA,8),8). where ql(pl,@) with i = {A,B} are optimal value functions. Consider the consumer who is indifferent between the IT enhanced primary good offered by suppher A and the IT enhanced primary good offered by suppher B, at R and p. This consumer, 8(R,p), is implicitly defined by U(qA(pA,6),8) = U(qB(pB,§),8) or Chapter 4. Supphers Offering IT to Consumers 72 v(qA(PAJ),e) - RA-pAqA(pA,e) - K = V(qB(pB,d),e)-RB-pBqB(pB,9)-« K It is assumed that interior solutions generate q(R,p,8). This guarantees one of the two IT enhanced primary goods is purchased, and thus the market is covered by the two This separation of consumers comes from the conditions imposed on the utility func-tions, and interior solutions to utility maximizations. Normalizing the number of consumers to unity the aggregate demand structure can now be fully described. The fraction of consumers who adopt the IT enhanced good from suppher A is IT enhanced primary goods. This also ensures ql(pl,0) is decreasing in pl, which implies qA{pA,0) > qB(pB,8) from the assumption of pA < pB. If 6(R,p) exists then with the above properties it is unique. Moreover, 6>6(R,p) qA(pA,e)>l, qB (PV) = O Aggregate demand from supplier A for the IT enhanced primary good is The fraction of consumers who adopt the IT enhanced good from supplier B is Chapter 4. Supphers Offering IT to Consumers 73 Aggregate demand from supplier B for the IT enhanced primary good is r8(R,p) QB(R,P)= / qB(pB,e)f(e)de. Each supplier's cost function is of the form kINI{R,p) + [c + k^Q^R,?) where i — {A, B}, c is the constant marginal cost of producing primary good (exclu-sive of IT costs), k1 is the fixed cost of connecting and installing an additional consumer on the IT system, and kc is the constant marginal IT cost per IT enhanced primary good sold. To solve for a Nash equilibrium to the simultaneous move pricing game requires a joint solution to the two supphers' profit maximization. Profit maximization for supplier i = {A,B}is max.irI(R,p) = max[iVi(JR,p)[JRi - k1} + Q^R,^ - c - kc}}. R' ,p' R' ,p* In the space where RA > RB and pA < pB the above profit functions are continu-ously differentiable. Therefore, leaving the details to Appendix 4.4, with necessary and sufficient conditions holding, the simultaneous solutions to the four first order conditions yields Nash equilibrium prices, observing that "*" denotes the computed Nash equilib-rium prices: i T - k1 = [_l]i WR";?) f(6(R*,p*))d-°%f^ q^r,e(R%p"))[N^R',p')qi(pi'',e(R',f')) - Ql(R*,f)} Chapter 4. Supphers Offering IT to Consumers 74 V — C — K — :  (J1 where j — 0 if i = A, j = 1 if i — B, and ffl~« dqA{PA\6) B rWP) dqB(pB%6) ' dvA md6> a = L . dvB m d e and where de\R\p) dv{qA{vA\e\e) _ dv(qB(PB~,e),e) dRA l [ de oe J' d9(R\p*) _ d§(R~,p-) dRB ~ OR* ' Focusing on the Nash equilibrium variable profits, the marginal contributions of the per unit price components can be signed. Consider first pA" — c — kc. Similar to Propo-sition 4.2, 4.3, and 4.6, NA(R*,p*)qA(pA*,6(R~,f)) - QA(R%p*) < 0 because qA(pA,8) is increasing in 6. In addition, 8 q ^A < 0, therefore, r 8-^f^mie < o. Je(R*,p*) opA Hence, pA" - c - kc > 0. Turning to pBx — c — kc, le. B&'P) dqB{pB*,6) dpB f{6)d6 < 0 Chapter 4. Supphers Offering IT to Consumers 75 because qB(pB,8) is also decreasing in own per unit price. Moreover, in contrast to above, NB(R*,p~)qB(pB~,6(R*,p<)) - QB(R~,p*) > 0 as qB(pB,0) is also increasing in 8. Thus, pB* — c — k c < 0. Therefore, variable profits are positive for supplier A and negative for suppher B. With equal costs this means pA* > pB*. But by assumption RA > RB and pA < pB. Thus a contradiction. This completes the proof of Lemma 4.1. • Interestingly, a model with two consumer types also has this existence problem. Therefore, an asymmetric price Nash equilibrium in two part tariffs does not exist when the market is covered by the two IT enhanced primary goods. 4.5.4 Equal Price Pairs The remaining possibility for a Nash equilibrium is a common setting of price components, RA = RB = R and pA = pB = p, where the suppliers share the market equally. Suppose irA(R,p) = irB(R,p) > 0. This cannot be an equilibrium as Tr Total(R,p) = TTA(R,P) + TrB(R,p), so both supphers have an incentive to make an e > 0 drop in either of their R or p and capture the whole market (dominating price pair). Therefore, any best response pair where RA = RB and pA = pB must be at zero profits, so an additional equilibrium condition must be irL(R,p) = 0. The question then is: does a Nash equilibrium exist with suppliers offering identical price pairs (R,p)l Given the above analysis both a net contribution of zero and equal price components are necessary conditions for equilibrium of this type. A characterization of the necessary Chapter 4. Suppliers Offering IT to Consumers 76 zero profit condition for equilibrium is: N(R,p) where Q(R,p) and N(R,p) represent aggregate demand and number of adopters re-spectively. The equal price pairs characterization defines a plane in 7c4 where the equi-libria may exist, the zero profit condition further constrains this plane to a curve in R X p space. Unfortunately it is not clear whether or not a Nash equilibrium exists, and if so if it is unique. Any Nash equilibrium price pair, (i?",p") would have to satisfy the following necessary and sufficient conditions: • (R',p') must satisfy R* -k1 = -\p~ - c - k N(R~,p~y RA* = RB~, pA" = VB~ and in addition positive profits cannot be made by either supplier unilaterally deviating from the price pair, (i?*,p'<). Notice that together these conditions cannot be expressed, or determined, using cal-culus as the profit functions are discontinuous moving from equal price pairs to unequal price pairs. If the move is to dominating price pairs then the equal sharing of the market changes to the dominant price pair supplier capturing the whole market; if the move is to asymmetric price pairs the market partition moves from equal sharing to a separating of consumers. Chapter 4. Supphers Offering IT to Consumers 77 4.5.5 Discussion In the case of asymmetric price pairs it was shown that a Nash equilibrium will not exist when the market is covered by the two IT enhanced primary goods. When the market is not covered by the two IT enhanced primary goods the non existence result does not necessarily hold. Recalling the proof of Lemma 4.1, when the market is not covered the sign of pB~ — c — kc is ambiguous. There are two conditions under which the market would not be covered by the two IT enhanced primary goods: there are non adopters or an original primary good is present and some consumers prefer to purchase the original primary good. Either of both of these conditions is sufficient to undermine the non-existence result. From the discussions in Models 4.2 and 4.3, it would also be more difficult to maintain concavity of the profit functions under either or both of these conditions. Notice that ruling out either of the conditions under which the market is not covered by the IT enhanced primary goods artificially constrains the two part tariffs supphers may charge, although these restrictions may have no impact in a given situation. Observe also that if an equilibrium does exist in asymmetric price pairs it could be at non-zero profits. The effect of a positive cost for IT implementation, kF, which is not sunk prior to price competition, would change the circumstances of the competitive game significantly. Although not pursued here, a likely formulation would involve at least one earlier stage of the game involving commitment by the suppliers to implement the IT. Chapter 4. Suppliers Offering IT to Consumers 78 4.6 Model 4.5: Two Suppliers Offering Differentiated IT Enhanced Primary Goods Now the focus turns to price competition between two supphers, each supplying different IT and IT enhanced primary goods. As ITs can be ranked in some circumstances 7 this suggests one supplier can have a superior IT than its competitor. A scenario which could lead to this situation would be a second mover with superior IT leapfrogging the supplier who first introduced IT. It is assumed that consumers are confined to purchasing one type of IT enhanced primary good, and that all consumers agree on the ranking of the two IT enhanced primary goods. 4.6.1 Demands Consumers are heterogeneous in their tastes for quality of the primary good. These differences in taste are represented by the taste parameter 6, 6 6 7Z. 6 follows the density function /(#) > 0 over the closed interval [9min,8max]- This density has cumulative density F(6), so F(8min) = 0 and F(8max) = 1. For a given IT, indexed by i = {1,2}, preferences for the IT enhanced primary good are defined as ui(qi,e) = { Vi{qi,6) - R t - Pim - « i if > i 0 otherwise, <fc = 0. qi is the number of units purchased of IT enhanced primary good i, Vi(qi,8) is a twice continuously differentiable function which is increasing and concave in and increasing in 6. The cross partial derivative of Vi(qi,6) is positive, and 1^ (0,0) = 0. The internalization switching cost is > 0, and Ri + p^ g, is the two part tariff. The IT enhanced primary good i = 2 is higher quality, thus V2(q2,0) > Vi(qi,6) for a given 8 and q2 — q\ > 1. Therefore, the IT is incorporated into this formulation of 7Refer to Chapter 3. Chapter 4. Supphers Offering IT to Consumers 79 preferences through quahty differentiation, a positive internahzation switching cost borne by the consumer from IT adoption, and as a basis for the two part tariff. Consumers who purchase either IT enhanced primary goods must have greater or equal to unity as no restrictions are placed on Ri. For example, if R( is a subsidy, with no minimum purchase requirement all consumers would adopt one of the ITs, with some consumers purchasing arbitrarily small e units. Consumers are restricted to purchasing at most one type of IT enhanced primary good. The underlying preference structure of a given 9 is assumed to be U(q2, qi,X,8) = m^x{U2(q2,9), U^q.,9)} + X subject to the appropriate budget constraint, Ri + piqi + X < I where X is the numeraire good, / is income, and i = {1,2}. Thus, it is assumed that preferences are additively separable in primary and numeraire goods8. Consider the consumer's optimal choice of quantity. For each IT enhanced primary good, each 9 chooses g; to maximize utility, max(7;(g;,#) 3 qi > 1 or qi = 0 For those consumers who choose qi > 1 the first order (Kuhn-Tucker) conditions are — 5 Pi < 0, qi > 1 Oqi and M(qi,6) I ^ ViMi - 1J = 0. Along with the properties of Vi(qi,8), these conditions define a demand function Alternatively, it could be assumed that income changes related to purchasing either of the IT en-hanced primary goods are negligible (see [43] and/or [25]). Chapter 4. Suppliers Offering IT to Consumers 80 This function is non increasing in pi and non decreasing in 6. Ri, the fixed component of the two part tariff, and K,-, the internahzation switching cost, do not impact this demand, as they drop out of the first order conditions. However, the fixed components of the two part tariffs and internahzation switching costs do impact which 6 purchases which IT enhanced primary good. With individual demands well defined each consumer chooses which IT enhanced primary good to purchase, if any, by max{U2(q2(p2, 6),6), U^q^B), 6)} where qi(pi,8) are optimal value functions, i = {1,2}. Define 6(R,p) implicitly to represent the consumer who is indifferent between pur-chasing the i = 2 IT enhanced primary good and the i — 1 IT enhanced primary good (re-calling i = 2 is the higher quality IT enhanced good), where (R,p) — ((R2,Ri),(p2,pi)). This condition is Vi(liiPiJ), 8) - R i - Piqi(piJ) ~ «i = ^2(92(7^2,0), 0)- R 2 - P2q2{p2,8) - «2 Assume that at least one of the two IT enhanced primary goods is purchased. There-fore, the market is covered by the two IT enhanced primary goods. Implications of the market not being covered by the two IT enhanced primary goods are discussed at the end of the section. In addition, assume dV2MP2,0),6) dv1(qi(Pl,e),e) 89 86 Chapter 4. Supphers Offering IT to Consumers 81 Therefore, higher taste consumers receive larger increases in utility from purchasing the superior IT enhanced primary good, similar to Model 4.2. If 8(R,p) exists then with the above properties it is unique. Hence, 6>8(R,p) q2(p2,6)>l, 9i(?i,0) = O 6 < 6{R,p) => <?!(/>!,0) > 1, q2(p2,6) = 0, Both uniqueness and consumer separation come from the monotonicity of Ui(qi,6), the relationship between the two Vi(qi,9) and their derivatives, and interior solutions to utility maximization. Suppose 8(R,p) does not exist. Then all consumers either purchase the i — 2 IT enhanced primary good, 9(R,p) — 6min, or all consumers purchase the i = 1 IT enhanced primary good, 6(R,p) = 9max. The resulting allocation of consumers and aggregate demand structure, normalizing the total number of consumers to unity, is QTTMLT. N2(R,P) = L . f(0)d9 = 1 - F(6(R,p)) Je(R,p) Q2{R,?)= . . q2(P2,e)f(e)de J8{R,p) Ni{R,p) = f{R'V) f(e)d9 = F(6(R,p)) Qi{R,?)= qi(Pl,6)f(6)d6 Chapter 4. Suppliers Offering IT to Consumers 82 4.6.2 Supplier Profit Maximization There are cost advantages gained in the delivery of the primary good from superior IT. For marginal costs, c2 < cx (ignoring IT costs). Each supplier's cost function is of the form kIiNi(R,p) + [ci + kf}Qi(R,p) where i — {1,2}, k\ is the fixed cost of connecting and installing an additional consumer on the IT system, and kf is the constant marginal IT cost per IT enhanced primary good sold. Each of the IT cost components is larger for the superior IT. kf,the fixed implementation cost of IT, can be considered sunk, and is reviewed at the end of the section. Let supplier A have the inferior IT (i = 1) and supplier B have the superior IT (z = 2). Accordingly, each supplier offers only one IT enhanced primary good. In this construction the two supphers together select levels of four pricing variables. The game is a simultaneous move game where supplier A chooses the fixed and variable components of the two part tariff for the primary good enhanced with IT i = 1: Ri and Pi; supplier B chooses similar components for the IT i = 2 enhanced primary good: R? and pi. With subscripts indicating the IT version, the profit maximization equation for each of the two supphers is: max7Ti(i2i,pj) = max[[Ri - kf]Ni(R,p) + [pi - a - kf]Q{(R,p)] Ri ,Pi Ri ,Pi The two optimizations each produce two equations and two unknowns in the necessary first order conditions, Chapter 4. Suppliers Offering IT to Consumers 83 —~dp-— = —dp- ~ QiiRiP) + ^ — L P i - ct - «; J = 0-The resulting system of equations is solved in Appendix 4 . 5 . Assuming the necessary first and sufficient second order conditions hold, a simultaneous solution to the four first order conditions represents the solution to the set of four best response functions: a Nash equilibrium. The equilibrium price components are R -k1 = \ i i ' K&P) _ qi(piJ(RJ))[Ni(R,p)gi(Pi,e(R,p)) - Qi(R,p)]  1 1 f(e(R,Pl)aW hc NjjR^MpiJjR,?)) - Qj(R,p) Pi — Ci — ^ = : where remax dq2(p2,8) , re(R>^ dqAv^e) <T2 = I , T 'f(e)de, a, = / )f(e)dd Je(R.v) dv> Je„;„ dv^ le(R,p) dp 2 ' Jemin dp i a n d w n e r e ™l*fl = lf[Wfr{p,fi{A*)Wa*)) - ^(9l(Pl,g-(fl,p)),e-(fi,p))3 > 0 ) a n d e8&£ = <0, where i = {1,2}. For both suppliers it is interesting to segregate profits from the IT enhanced primary goods into profits from the variable component of the two part tariff, and profits from the fixed component for IT access. The following propositions outline what can be deter-mined about the signs of profits from the variable per unit and fixed IT adoption/access components of the two part tariff. Proposition 4.8: Variable profits from the superior IT enhanced primary good, i = 2, are positive. Chapter 4. Supphers Offering IT to Consumers 84 Proof: Similar to Propositions 4.2, 4.3, 4.6, q2(p2,8) is increasing in 8, and decreasing in p2- Hence, the numerator is negative and the denominator is also negative. Therefore P2 - c2 - fc? > 0. D Proposition 4.9: Variable profits from the inferior IT enhanced primary good, i = 1, are negative. Proof: As qi{pi,&) is decreasing in pi the denominator is negative. In contrast to the preceding Proposition, with q\(pi,8) increasing in 8 the numerator is positive. Thus, P! - C i - fcf < 0 • Proposition 4.10: Profits from the fixed component of the two part tariff are positive for the inferior IT enhanced primary good, i = 1. Proof: With pt — cx — fcf < 0 (Proposition 4.9) and q1(p1,8(R,p)) > 0 the second term in Ri — k[ is negative. Ni(R,p) > 0 and f(8(R,p)) > 0. From the assumption of 88 88 aft is negative. Hence, the first term (including [— l]1) is positive. Thus, Rx — k[ > 0. • Similar to the results from Models 4.1, 4.2, and 4.3, the sign of the fixed component of the two part tariff for the superior IT, i = 2 cannot be determined; R> ~ k> = t ^ ' r t A i n ~ 92{P2,HR,P))\P2-C2- kc2}. f(8(R,p)f-^ Thus, profits from the fixed component of the superior IT enhanced primary good can again be positive or negative. Chapter 4. Suppliers Offering IT to Consumers 85 The intuition behind the somewhat startling result that negative variable profits are made from the inferior IT enhanced primary good is as follows. Higher taste consumers demand higher quantities, and therefore put more weight on a low variable price. With the inferior IT enhanced primary good capturing the lower taste consumers, a lower variable price is the better mechanism with which to capture more of the consumers in the market, even if this price falls below marginal cost. As a result, the fixed component is the charge by which positive profits are made from the inferior IT enhanced primary good. 4.6.3 Discussion The results relating to the signs of the profits from each of the two part tariff components for the inferior IT enhanced primary good are sensitive to the conditions corresponding to the market not being covered by the two IT enhanced primary goods: non adopters or an original primary good which is preferred by some consumers. If either or both of these conditions hold (i.e. the market is not covered) then the signs of each component of the two part tariff for the inferior IT are ambiguous. The results are also sensitive to the separation of consumers who purchase based on 9(R,p). Unlike Model 4.4, equilibrium existence is not disturbed by either of these conditions. As in earlier models, concavity of the profit functions is less likely if the market is not covered by two primary goods (again see [5] and [31]). There is some restrictiveness from assuming both supphers face positive demands in the IT enhanced primary goods. A different formulation might focus on one IT supplier forcing the other into a zero demand situation, thereby forcing the IT competitor out of the market. Referring to Chapter 3, asymmetric IT costs and internalization switching costs are expected as the two ITs are different. However, this does not impact the results. The Chapter 4. Suppliers Offering IT to Consumers 86 fixed IT implementation costs, kf, would not play an important role unless suppliers had a choice of which IT to implement at some point prior to the price competition. Of course, this would radically change the game played between the supphers. Chapter 4. Supphers Offering IT to Consumers 87 4.7 Analysis Consider the pricing results in the IT enhanced and original good case for monopoly and the one supplier with IT oligopoly. In both cases the net per unit charges were positive, and the fixed component of the two part tariff for IT could be either a net tax or a net subsidy. It is instructive to study the fixed components more closely. The equations for the net fixed components are (with per unit marginal contributions substituted in) Monopoly: R - k1 = N(R,Pl,p0) qi(piJ{R,Pi,Po))[Pi ~ c i - kc f{e(R,PuPo))d6{ReRUPtt) +%{PoJ(R,Pi,Po))[Po - c0]. Oligopoly: R-kI= ^ ' ^ L , i " 9X{PUHR,PUPO))\PI - * - kc]. Although 0{R,Pi,Po) is n ° t equal in each case (different prices result) they are de-fined equivalently. As such, the structure is the same. Recall that the net marginal contributions per unit are positive (Propositions 4.3, 4.6). Thus, it is clear how the fixed component is being used differently in the two cases. In the monopoly case the last term indicates the fixed component is being used to capture additional rents from all the IT adopters as though they were purchasing the original primary good at the level of 9(R,pi,p0) as well as purchasing the IT enhanced good. In the oligopoly case the tax (subsidy) is lower in principle as the last term from the monopolist's fixed component is missing, reflecting a concern only about purchases of the IT enhanced good from con-sumers who adopt IT. As opposed to the monopolist, the oligopolist does not use the fixed component to recapture some of the profits from lost purchases of the original good by IT adopters. The IT oligopolist accounts for competition from the original good by Chapter 4. Supphers Offering IT to Consumers 88 not forcing potential IT adopters back, through increases in R, to the original primary good. Chapter 4. Supphers Offering IT to Consumers 89 4.8 Conclusions T h e r e are four major conclusions from the research i n this chapter. F i r s t , it c a n be o p t i m a l to tax or subsidize I T a d o p t i o n separately f r o m the I T enhanced p r i m a r y good. Second, the interdependence of I T a d o p t i o n price, I T enhanced p r i m a r y good price, a n d original p r i m a r y good price is critical for o p t i m a l or e q u i l i b r i u m pricing; the pricing problems are not separable. B o t h these results a p p l y to a m o n o p o l i s t as well as an oligopolist w i t h I T . T h i r d , c o m p e t i t i o n from the original p r i m a r y good mitigates what supphers can charge for I T a d o p t i o n . F o u r t h , i n a d u o p o l y where one supplier has I T , b o t h supphers can make positive profits. T h e r e are two a d d i t i o n a l outcomes from the work i n this chapter. F i r s t , when two supphers offer identical I T enhanced p r i m a r y goods price equil ibria in two part tariffs m a y not exist. Second, when price c o m p e t i t i o n is i n two different I T s with two part tariffs the inferior I T m a y take positive profits f r o m I T a d o p t i o n while p r o v i d i n g a net subsidy o n the I T enhanced p r i m a r y good. Chapter 4. Supphers Offering IT to Consumers 90 4.9 Appendices to Chapter 4 4.9.1 Appendix 4.1 T h e first order conditions for a monopolist 's o p t i m a l two part tariff for an I T e n h a n c e d g o o d result i n the equation system T h i s system is i n the form of the m a t r i x equation Ax = d where x' = [[R — k1] \p — c - kc}], d' = [-N(R,p) - Q{R,p)}, a n d A is / 8N(R,p) 8Q(R,p) ^ _ j dR dR ~ I dN(R,p) 8Q(R,p) \ Bp Bp S o l v i n g for each of the components of A yields 9N(R,P) § n ^ ( f l , ? 0 9Q(R,p) , , ^d6(R>p) —OX— = -q{p,0{R,p))f{6(R,p)) Q R dN(R,p) = $ dJjR^ op op - W ~ = J m P ) ~ o ^ m d 6 - q { p ^ ^ S o l v i n g for the components of x using C r a m e r ' s rule requires the following determi-nants Chapter 4. Suppliers Offering IT to Consumers 91 |A| = dN{R,P)dQ(R,p) _ dN{R,P)dQ{R,p) dR dp dP dR Je(R,P) dp dR +q(pJ(R,p))f(HR,P))^^-{N(R,p)q(P,HR,p)) ~ Q(R,P)} | A 2 | = dN(R,p) 8N(R,p) d R ~ Q { R l P ) + ~ ^ p ~ N { R ' p ) = f(e(R,P))^§^-[Q(R,P) - N(R,p)q(pJ(R,p))} where Ai,i = 1,2 are the original A matrices with d substituted into the appropriate column, and q(p,6(R,p))a9<^p^ — di'^'p). This last result comes from using the imphcit function rule to solve for 8 t g ^ ' ^ , recognizing the first order conditions from an interior solution to consumer utihty maximization, d6{R,p) dV(q(pJ(R,P))J(R,p)) dR 1 dd Again using the implicit function rule, the derivative of 6(R,p) with respect to p is —d^-^q{p'e{R'p))~dR—-Chapter 4. Supphers Offering IT to Consumers 92 Using Cramer's rule the system is solved, R-k': |A| N(R,p) f(9{R,p))2igp q(p,e(R,p))[N(R,p)q(p,e(R,p)) - Q(R,p)] _ hc _ \M = N(R,P)q(PJ(R,p))-Q(R,P) To ensure optimality of these prices, concavity of the monopolist supplier's profit function with respect to both components of the two part tariff is assumed. An alternative way of establishing the derivatives of 6(R,p) uses the consumer surplus identity ([41]). Totally differentiating CS(pJ(R,p)) = R, where CS{pJ(R,p)) is the consumer surplus of the marginal consumer, produces flCSfefr*,,)) + BCS{p,HR,P))dH = i R dp do Changing R, holding p constant, and dividing through by dR provides d§(R,p) = dCS(p,B(R,p)) dR 1 86 Noting that consumer surplus is CS(Py8(R,p))= / q(P,6(R,p))dp, r + co it follows that 8CS(P,6(R,p)) . ^ = -q{p,0(R,p))-Chapter 4. Supphers Offering IT to Consumers 93 Now changing p holding R constant, dividing through by dp the above differential gives —dp—=*<p>e(R>p)y—w—• Hence, 9HR,P) , £ ( P ,MR,P) —Qp— = 9ip,HR,p))—QM--Chapter 4. Supphers Offering IT to Consumers 94 4.9.2 Appendix 4.2 T h e first order conditions for the monopolist offering b o t h the I T enhanced a n d original p r i m a r y goods can be rearranged into the following system of equations dN(R,Pl,Po) r dQ1(R,puPo): c dR + BR ^ - c > ~ * 1 dQ0(R,pupo) dR [po - c 0] = -N(R,p1,p0) dN(R,Pl,Po) u dQ1(R,p1,p0)! c [R- k J H ^ \px ~ c i - A; J dpi oPl 8Q0(R,Pi,Po), + ~ Wo ~ c 0 j = -Qi{R,Pi,Po) op i 9N(R,p1,p0)[ j , 0Qi(i2,Pi,Po) r ,ci — [K — k \-\ \pi - c i - k \ Opo dp0 dQ0{R,Pi,Po) dpc [Po - c 0] = -Qo{R,Pi,Po) T h i s system can be represented b y the m a t r i x equation Ax = d where now / R - k1 \ P i - c a - kc \ Po - c 0 / 1 -N(R,Pl,Po) X -Qi{R,Pi,Po) \ -Q0{R,pi,po) ) Chapter 4. Supphers Offering IT to Consumers A = V dR dR dR dN(R,PuPu) dQ0(R,pi,p0) dpi dpi dpi dN{R,PuPu) dQi(R,Pi,Pfl) dQ„(R,pi,p0) dpo dpo dpo As earlier, the elements of A can be found, and they are dN(R,Pl,Po) - dO(R,Pl,Po) ~ = -J\PK^PUPQ))-dR dR dQi[R,Pi,p0) f xf„ \\ff2(t> ^9e(RtPl,p0) - = -qi{pi,8{R,pi,po))f\0{R,pi,po))-8R dR dQ0(R,Pl,Po) , KIT, wrthiv ^9§(R,Pl,Po) - = qo{po,0{R,pi,po))f{0{R,Pi,Po))-dR dR dN(R,Pl,Po) - dO{R,Pl,p0) - = -j{0{R,Pi,Po))-dpi dp i 9QI{R,PI,PQ) _ dpi j ) f { e ) d e _qi'Pl,e(R,Pl,Po))f(e(R,Pl,PQ)) Je(R,Pup„) dPi dPi dQo{R,Pi,p0) , \\fla(T> \ \ d B ( f l>Pi>P°) « = qo{po,Q{R,pi,po))f{Q{R,PuPo)) dpi opi dN(R,Pl,Po) - de{R,Pl,po) w: = -J{y{R,Pi,Po))—-K-— dp0 dp0 g(gi(fi,Pi,p 0) _ dPo d0(R,pltpo) -qi{pi,6{R>PuPo))f(Q(R,pi,po))-dPc Chapter 4. Supphers Offering IT to Consumers 96 dQ0{R,pi,p0) __ dpo [e(R>Puro) dq0(Po,6) - ^de(R,Pl,po) / W~ f{8)d6 + qo{Po,6(R,Pi,Po))f{0{R,Pi,Po)) ~ Je„Lin upo "Po T h e solutions to the system can again be found using C r a m e r ' s rule. Solving for the determinant of A by expansion of the first c o l u m n yields dN(R,p1,p0) dQi(R,pup0) dQ0{R,pi,p0) _ dQi(R,pi,Po) dQ0(R,pi,p0) dR dpi dp0 dp0 dpi dN(R,Pl,p0),dQi(R,pi,p0) dQ0(R,pi,p0) _ dQi(R,pi,p0) dQ0(R,Pi,Po) dPl 1 dR dPo dPo dR J dN(R,pup0) dQ1{R,Pl,Po)dQ0(R,Pl)po) _ dQi(R,Pi,p0)dQ0{R,pup0) dPo [ dR dPl dpi dR J' M u l t i p l y i n g out the determinant using the partial derivatives defined above, a n d cancelling terms gives |A| = dR Je{R,Pl,p«) dpi Jemxn dp0 J8{R,Pl,Po) dpi dpo fe(R,puP*) dq0(p0,e) - ^dd(R,Pi,p0)^ - [ / — T r - f{6)d0}qi{pi,6{R,Pi,Po))f{6{R,pi,po)) ^ —J Jemi7l dp0 op i d6(R,pi,Po), -f(6(R,Pi,p0))- dpi e{R,Pl,Plt)dqo{p e ) d6(R,pi,Po)} f{d)de]qi(pi,e(R,p1,Po))f(e(R,p1,p0))-+[-f(e{R,Pl,Po)) d0{R,pi,Po), dPo Chapter 4. Supphers Offering IT to Consumers 97 [ / . ~ / ( T % O ( P O , 0 ( ^ , P I , P O ) ) / ( ^ ( ^ , P I , P O ) ) ^ J Je(R,pupu) op i OK Je(R,Pl,p0) dpi OK Jemin Op0 < 0. T o simplify later analytics the relationship between 8 § ^ ' P o ) , a n d ^ ^ g ^ need to be developed. U s i n g the definition of , p 0 ) , the i m p h c i t function rule yields the derivative w i t h respect to R d0(R,puPo) _ 1 ndVi{qi(pi,8{R,pi,Po)),8(R,pi,po)) _ dVo(q0(po,9(R,Pl,p0)),0(R,p1,po))  / [ 86 86 J' F r o m the a s s u m p t i o n o n the relative size of the derivatives of Vi(g;(pi, 0), 0) w i t h respect to 6, this derivative is positive. A g a i n using the i m p h c i t function rule with the equation defining 8(R,pi,p0), the derivative w i t h respect to pi is d§(R,pi,p0) 86(R,Pl,p0) 8Pi 8R T h r o u g h an almost identical analysis dO(R,p1,p0) d§(R,pi,p0) qi{pi,8(R,Pi,Po))-q0{po,6(R,PuPo))-8p0 8R R e t u r n i n g to the equation system, solving for the elements of x requires three more determinants: | A i | -N(R,Pl,Po)[ 8Qx(R,pi,p0) 8Q0{R,Pi,Po) 5Qi(i2,pi,p 0) dQ0(R,Pi,Po), dpi 8p0 dp0 dp i Chapter 4. Suppliers Offering IT to Consumers 98 r ^ /D s,rdQi{R,PuPo) 9Q0{R,Pi,Po) dQi(R)Plypo) 9Qo(iZ,pi,p0) 1 -[-Qi(i2,Pi,Po)][ ^ ^ ^ ^ J , r ^ tr> wdQi(R,Pi,Po)dQ0{R,Pi,Po) dQi{R,p1,po)dQo(R,p1,po) +[-QO(R,PI,PO)}[ M ^ ^ M ] IA i r M t u ,1[dN(R,p1,po)dQ0(R,p1,p0) aJV(iZ > p 1 ,p 0 )gQo(iZ,p 1 ,po) 1 | A 2 | = -[-N(R,PllPo)][ ^ W o — g — ^ ] ,, ~ ,„ ,vdN(R,pup0)dQo(R,PuPo) dN(R,Pup0) dQ0(R,PuPo), +[-Q1(R,Pl,Po))[ M ^ ^ M ] r rt (-D wdN{R,Pl,Po)dQo(R,Pi,Po) dN(R,PL,PO) dQ0(R,pup0)^ -[-QO(R,^PO)}[—^ ^ ^ M ] ,A | A T ( T } vdN{R,pl,p0)dQ1(R,pl,po) dN(R,Pl,Po) dQ1(R,Pl,p0)} A 3 = -N(R,Pi,Po) ~ A « fl dpi <9p0 ap0 opi wdN(R,Pl,p0) flC?i(-R,pi,po) dN(R,p1,pQ)dQl(R,p1,p0)1 -[-Qi{R,PuPo)][ ^ — ^ ^ m 1 , r nir> wdN{R,p1,p0)dQ1(R>Pl,Po) dN(R,Pl,p0)dQ1{R,pup0)1 +[-QO(R,PUPO)][ M — ^ ^ M ]• E m p l o y i n g the partial derivatives f o u n d earlier, a n d simplifying, the following obtains: Jemin opo Je{R,Pim) dpi \\M(R,Pi,Po) +f{0{R,Pi,Po)) 0£ 11 ?SsPLjf{9)d9]qi(plie{R,p1,po)) Jemin opo [N(R,Pi,Po)qi{piJ{R,PuPo)) - Qi{R,Pi,po)]] 9qi{pi,6) le(R,Pupn) dp, [N(R,p1,Po)qo{PoJ(R,Pi,Po)) + Qo{R,Pi,Po)}} + [ C' flgl^1,g)/(g)^]gb(Po,g(iZ>Pi,Po)) J6lR.vi.vo) OV-i Chapter 4. Supphers Offering IT to Consumers 99 ' _,^->^ / ( ,W ( 4 w , i^ ) )a?(w !) Jemin opo oR [N(R,p1,p0)q1(p1J(R,p1,p0)) - Qi{R,pi,p0)] | A 3 | = ^ ^ / ( , ^ ] / ( , - ( E p i ) P o ) ) M ( t o ) Je(R,Pl,Po) dpi OR [N(R,Pi,p0)qo{PoJ(R,Pi,Po)) + Qo(R,Pi,Po)]-Calling on Cramer's rule, the marginal contributions to profit of each of the pricing components is N(R,Pl,p0) f(§(R,PuPo))*&g*!l qi{pi,0{R,Pi,Po))[N(R,p1,po)q1(p1,6(R,p1,po)) - QjjRiPuPo)] qo{poJ(R,pi,p0))[N(R,p1,po)qo(pQ,e(R,p1,p0)) + Q0(R,Pl,pQ)} r.e(R,Pi,P(l) dq0(Po,6) £(Q\JQ _ C o = JA3! = N(R>Pi>Po)qo(Po>HR,PuPo)) + Qo(R,Pi,Po) |A| MR'PUPU) dqn(po,6) t(Q\£Q Concavity of the profit function is assumed to ensure the pricing components derived above are optimal. Chapter 4. Supphers Offering IT to Consumers 100 4.9.3 Appendix 4.3 The necessary first order conditions for suppher A's profit maximization can be rear-ranged as -[it — ft j H ^ [px - cx - k J = -JSI{R,pi,po) dR 8N(R,p1,p0).D , 9Qi(R,Pi,p0), , c i n in ^ „ \ [R - ft + [px - cx-k = -Qi[R,PitPo)-opx opx Rearranged, the necessary first order condition for suppher B maximizing profit is dQ0{R,Px,Po) { dp0 \jpo - c0] = -Q0{R,Pi,Po)-Putting these in the matrix equation Ax — d yields / R-k* \ Px- Cx~ kc \ Po - c0 / d = 1 -N(R,Pl,Po) X -Qi(RuPuPo) \ -Qo(R,Pi,Po) J \ Solving for the components of A, dN(R,px,Po) dR SJV(H l P l ,po) dR a<3i(fl,pi,pn) dR 0 dN(R,pi,PU) dpi dQi(Rj>i,p0) dpi 0 0 0 SQ 0 ( f i ,P i ,P i i ) Spo = -f(e(R,px,Po)) d§{R,Px,Po) dR Chapter 4. Supphers Offering IT to Consumers OX = -qi{pu0{R,Pi,Po))f{O{R,pi,po)) Q£ dN(R,Pl,p0) - ^d§(R,Pl,Po) — ^ — = -/m,pi,po))—^— 9QI(R,PI,PO) dpi rema* dqi{Pl,0) ....... , _ „ . , S / n _ _ „d0(RlPl,po) [/., -^f^f(0)d0}-qi(p1,6(R,p1,po))f(0(R,Pl,po))-Je(R,pUPo) oPl dp'i c?(go(iZ,yi,p0) _ [ / a f\B)de\ + <lo{Po,0{R,Pi,Po))f{0{R,Pi,Po)) - • Solving for the components of a; using Cramer's rule requires |A| = dQ0{R,Pl,p0) dN(R,Pup0)dQ1(R,p1,po) _ 8N(R,pup0)dQ^puPo) dPo [ dR dp! dpt dR 1 ,e(fi, P l l P„)0 g o^ . ^80{R,Pl,Po) • = / s /(# ^ + 9o{Po,0(R,PuPo))f{0{R,PuPo)) ~ Je,nin dp0 dp0 [-[JHR,pi,P„)—dpT~f{ 9 ) d 6 ] f { e(R>™°» ^ ] | A i | = dQo(R,Pl,p0) dQ^p^po) dQ^px^po) ^ [ _ t f ( i 2 > p i > p o ) _ _ + Ql(RtPliP0)- — ] Chapter 4. Suppliers Offering IT to Consumers 102 ,e(iWo) dq0(Po,6) - ^M(R,Pi,Po), = [[/ — 5 -f(0)d0} + qo{po,9(R,pupo))f(e(R,PuPo)) J J6{R,Pl,p„) Op i +qi(piJ(R,Pi,Po))f{0(R,Pi,Po))de^RQR1,P°^ [N(R,pupo)qi{pi,0{R,PuPo)) - Qi(i?,pi,p0)]] |A 2 c9Qo(iZ,pi,p0)r dN(R,Pl,Po)^ l r y dN(R,Pl,Po) ^ [ ^ Gi(*,Pi,Po) + W i N{R,Pl,p0)] = / ^ /(0)<*0 + qo{Po,8(R,PuPo))f{8{R,PuPo)) 5 J [ / (g( iZ,Pi > Po)) g g ( ^ 1 , P o ) [9i( iZ,Pi ,Po) - iV(/2,Pi,Po)gi(Pi,^.Pi.Po))]] | A 3 | = fdN(R,p1,p0)dQ1{R,puPo) dN(R,PuPo)dQ1(R,Pl,Po), •Qo(i2,Pi,Po)[- 8R dPl dPl dR dqi(pi,0) rfn^j^r/ntT, \\dHR> Pl > Po) i = -Qo(fl,Pl,Po)[-[/ . ^ X 1 ' J / (^)^]/(^,Pl ,P0))- or, , Je(R,puPo) dpi OK using the relationships between derivatives of ^ (ii^p^po) established in Appendix 4.2. Using Cramer's rule the system can be solved, R-k>JA |A| N(R,PuPo) f(HR,Pi,Po))aj1^ qi(PlJ(R,PiyPo))[N(R,PuPo)qi(Pl,6(R,pupo)) - Qi{R,Pi,p0)] J8{R,P\,po) dpi •> \ I Chapter 4. Supphers Offering IT to Consumers 103 Po — c 0 _ , c JA2I N(R,p1,po)q1(p1,6(R,p1,p0)) - Q1(R,p1,Po) = J A 3 J -QQ(R,PUPO)  Concavity of each supplier's profit function is assumed. Chapter 4. Suppliers Offering IT to Consumers 104 4.9.4 Appendix 4.4 Each supplier has two necessary first order conditions for profit maximization, = N'{R,P1 + ™2g2[*. - tf + ^ M> b < - c - * ° ] = 0 5 # 0# for t = {A, 5}. Rearranging the terms in the first order conditions and putting the four equations together in a system yields the matrix equation Ax — d where ( R A - y ^ pA - c - kc RB -k1 ^ pB - c- kc J 1 -NA(R,p) ^ -QA(R,f) -NB(R,p) \ -QB(R,P) j A = \ 8NA{R,p) dRA 9QA(R,P) dRA 0 0 9NA(R,p) dpA dQA(R,p) &pA 0 0 0 0 dND(R,p*) dRB 9QB(R,P) dRB 0 0 8NB (R,p) dpB 9Qd(R,P) a?* J A can be partitioned for easy inversion into 2 x 2 matrices in the northwest and southeast corners. Solving for supplier A's price pair {RA,pA} is virtually the same Chapter 4. Suppliers Offering IT to Consumers 105 problem as described in Appendix 4.1, except now 8 representing the limiting consumer is 8(R,p). From the imphcit function rule, and the definition of 8(R,p), de\R,p) 8RA dV(qA(PA,6(R,p)),9(R,p)) _ 8V{qB{pB,8{R,p))J{R,p))  / [ 86 88 V Moreover, again using the imphcit function rule, ]-qA(pA,8(R,p)). 88(R,p) _ 88(R,p) A . A 8pA 8RA Solving for supplier A's equilibrium prices results in RA-k' = NA(R,p) f(8(R,p))^^ dRA QA(PBJ(R,p)){NA(R,p)qA(pA,0(RJ)) - QA(R,P)} A , c = NA(R,p)qA(pA,8(R,p)) - QA(R,P) p c s^-^fm Finding supplier B's price components is slightly different because 8(R,p) delimits the upper rather than the lower end of the consumers supplier B serves. Focusing on the lower right 2 x 2 submatrix of A, the elements are: 8NB(R,p) _ ^d§(R,p) 8RB -fWR>p»-8RB-—^—=q (p ,6{R,p))f(6(R,P)) Q R B Chapter 4. Supphers Offering IT to Consumers 106 ONB(R,p) •• - ^d§(R,p) dpB - fMR>p))-opr-dQB(R,p) ^ dpB where d6(R,p) _ d6{R,p) dRB ~~ ~ dRA ' As above, using the implicit function rule and the condition that defines 9[R,p), ~^PB~ = ~dRB~q {P ' W p ) ) -Using matrix inversion the submatrix can be solved, and the resulting prices are RB - k1 = NB(R,p) f(e(R,p))a-^f qB(pBJ(R,mNB(R,p)qB(pB,6(R,p)) - QB(R,P)} JB „ ,c _ NB(R,p)qB(pB,6(R,p)) - QB(R,p) 8pL Again, each of the supplier's profit functions are assumed to be concave. Chapter 4. Supphers Offering IT to Consumers 107 4.9.5 Appendix 4.5 The necessary first derivative conditions for profit maximization with suppher A choosing Ri and px, and with suppher B selecting R2 and p2, produce a system of four equations with four unknowns, dN2(R,p)]T> j 7 l , 0Q2(R,p)^ _ u C 8R2 dN2(R,p) 9p2 d^jRJ) dRi [R2 - k[] + [R2 - kT2] + OR, \p2-c2-k^} = -N2(R,p) ii , dQ2(R,p) jC, n (B -«\ ^ \P2-c2-k2 } = -Q2{R,p) OP2 dp i dpi This system can be represented in Ax = d form, which results in 1 R2-k\ ^ P2 ~ c2 — k2 Rr - k[ \ p i - C i - fef J 1 -N2(R,p) X -Q2{R,P) -Ni(R,p) { -Qi(RJ) ) 0 0 8Ri dpi A = / 8N2(R,p) 8R2 8Q2(R,p) 8R2 0 8N2(R,p) 8p2 9Q2(R,P) 8p2 0 0 0 8Ni(R,p) 8Ri { 0 0 8Ni (R,p) dpi Chapter 4. Supphers Offering IT to Consumers 108 With the northwest and southeast 2 x 2 matrices on the major diagonal, the system can be solved by decomposition. Referring to the number of consumers and aggregate demand for the superior (i = 2) IT enhanced primary good, note that finding R2 and p2 is the same problem as solving for R and p in Appendix 4.1, except that here the lowest taste consumer who purchases positive quantities of the superior (i = 2) IT enhanced primary good is represented by 6(R,p). Thus, the marginal contributions to profit are R2-k[ = N2(R,P) f{e(RJ))^iM 8R2 q2(p2,e(R,p)){N2(R,p)q2(P2,HR,p)) ~ Q2(R,P)] _ ,c _ N2(R,P)g2(P2,HR,p)) - Q2{R,P) where 6(R,p) and the imphcit function rule produces d$(R,p) = dR2 i nW2(qafaj(R,fl)j(R,p)) _ dVfafaj&fflJiR,?)) / [ 86 88 J and -^—=q3{jfa,0(R,p))-M-. Solving for the marginal contribution of R\ and pi is similar to R2 and p2 above except that the marginal consumer is at the upper limit of the range of consumers who choose Chapter 4. Supphers Offering IT to Consumers 109 to purchase the inferior IT (T = 1) enhanced primary good. The necessary derivatives are where and — d R = qi(pu8(R,p))f{8{R,p)) dp, =mR>p))-dp7-dpi Jsmin Opj +qi(Plj(R,p))f(e\R,p))^^. dd(R,p) _ 89(R,p) dRi ~ 8R2 86(R,p) . ^8d(R,p) Solving using the inverse of the southeast 2 x 2 results in the following marginal contributions to profit: R-L-k[ = NI{R,P) f(HR,p)f-W qi(PlJ(R,P^(R,P)qM,e(R,P)) - Qi{R,p)] Chapter 4. Supphers Offering IT to Consumers i _ _ kc = ^i(f i ,p)gi(pi ,g(f i ,p)) - QI(R,P) As before, the suppliers' profit functions are assumed to be concave. Chapter 5 Suppliers Offering IT Directly to Customer Firms 5.1 Introduction IT and the relationship between supphers and customer or downstream firms is examined in this chapter. Here both the primary good and IT are used or "consumed" by the customer firm. The analytical framework used is heterogeneous customer firms who differ through their cost functions ([34], [41]). These customer firms use the primary good as a factor input to their production of some ultimate downstream output. This production could entail anything from a simple wholesaling or bundling operation to a production process where the factor input cannot be identified downstream. Continuing with the overall thesis of this dissertation, the IT provides supphers with a basis for two part tariffs. The principal theme of this chapter is that the case of suppliers to customer firms is very similar to the case of supphers to consumers examined in the previous chapter. In fact, telegraphing the main results of this chapter, there are conditions under which suppher pricing strategies to customer firms are the same as supplier pricing strategies to consumers. The objective of this chapter is to highlight the similarities and differences between the two cases, concentrating on the two part tariffs for IT. Five models, corresponding to the models in Chapter 4, are developed. The sequence of models matches that in Chapter 4: monopolist supplier offering solely the IT en-hanced primary good, monopolist supplier offering an IT enhanced and original primary 111 Chapter 5. Supphers Offering IT Directly to Customer Firms 112 good, oligopoly where only one suppher has IT, oligopoly where suppliers compete with undifferentiated IT enhanced primary goods in two part tariffs, and oligopoly where sup-phers compete with differentiated IT enhanced primary goods using two part tariffs. The chapter closes with a short analysis, followed by conclusions. Chapter 5. Supphers Offering IT Directly to Customer Firms 113 5.2 Model 5.1: Monopoly Supplier Offering the IT Enhanced Primary Good Corresponding to Model 4.1, this section examines the monopoly pricing problem where only the IT enhanced primary good is offered to customer firms. 5.2.1 Factor Demands Customer firms are assumed to differ in their costs of turning over the primary good. These differences in costs are represented by a cost parameter v, v £ 1Z. v follows the density function h(u) > 0 over the closed interval v £ \vmin, umax], and has a cumulative density H(u), where H(i/min) = 0 and H{vmax) = 1. Customer firm costs are assumed to be increasing in v. Thus, v can be considered an efficiency parameter. There are many customer firms, and therefore no customer firm individually has any effect on downstream price. Customer firm costs are a function of downstream output, factor input prices, and the cost parameter v. Observe that the factor input of interest here is the IT enhanced primary good. Customer firm cost functions are: where x is downstream output and p is the per unit factor input price of the IT enhanced primary good (i.e. variable component of the two part tariff). To avoid unnec-essary complication, prices of other factor inputs are omitted from the notation. C(x,p,v) is a twice continuously differentiable function, increasing in v and increasing and con-vex in x (increasing marginal costs). Marginal costs are positive, and increasing in u, 8 <dx3v'"^ ^ 0" Notice this is tantamount to saying the marginal cost curves of two differ-ent customer firms never cross. Without loss of generality, fixed costs of production are zero, C(0,p, v) = 0. Observe that the variable component of the two part tariff, p, can be Chapter 5. Supphers Offering IT Directly to Customer Firms 114 taken out of £(x,p, v>) as cost functions are linearly homogeneous in factor input prices ([44]). By Shephard's lemma ([44]), for a given level of output x, the cost minimizing factor demand is — f l £ — = ' ( W ) . For customer firms which produce, q must be at least unity as no prior restrictions are placed on the fixed component of the two part tariff. With R as a subsidy and no minimum purchase requirement all customer firms would adopt the IT with some purchasing arbitrarily small e units. Trivially, p > 0. No production is possible without the factor input, q = 0 =>• x = 0. The profit function of a customer firm using the IT enhanced primary good as a factor input is given by \ p(R,p)x-ax,P,v)-R-K i f ^ ^ = g ( a ; , p , I , ) > l I 0 otherwise, q — 0 where p(R,p) is the market price of the downstream output, R is the fixed component of the two part tariff, and K > 0 is the internalization switching cost. Notice that the price for downstream output may depend on the two part tariff. However, to the customer firm p, R, and p are parametric. The elements which characterize IT enter in the customer firm's decision making through the two part tariff for the IT enhanced factor input and the positive internaliza-tion switching cost incurred by IT adoption. Define S = {x | x = 0 or d^x^'v^ = l(x,p,v>) > 1}. Profit maximization for a given customer firm can be expressed as max w(x, u). Chapter 5. Supphers Offering IT Directly to Customer Firms 115 For those customer firms that choose to produce, the first order (Kuhn-Tucker) con-ditions are p{R,p)- dx < 0 dp > 1 [p(R,p)~ 9C{x,P,^)]M{x,p,iy) dx 11 dp 1] = 0. Using the properties of C(a:,p, v) these conditions provide a well defined optimal down-stream output function which is non decreasing in x, and non increasing in p. If the customer firm produces, then neither the fixed component of the two part tariff nor the internalization switching cost have any direct impact on factor demands, as they are absent from the first order conditions. However, they do affect the choice of whether or not to produce. v = sup{i/ | q(x(p(R,p),p,i/),p,v) > 1}. v can also be implicitly defined as 0(p(R,p), R,p) through the zero profit condition w(x(p(R,p),p,u),u) = 0, p{R,p)x(p(R,p),p,0) - ({x(p{R,p),p,u),p,i>) -R-K = 0. By the monotonicity of ((x,p, v), if i)(/9(i?,p), R,p) exists then it is unique. Thus, all v ^{p{RiP)-:R)P) produce and have factor demands q(x(p(R,p),p,u),p,v) > 1. x(p{R,p),P,v), and through Shephard's lemma a factor demand function obtains q(x(p(R,p),P,v),P,v), Define Chapter 5. Supphers Offering IT Directly to Customer Firms 116 Setting the number of customer firms to unity, the proportion of IT adopters and aggregate factor demands are as follows1: fi>{p{R,p),R,p) N(p(R,p),R,p) = / h{v)dv = H(v(p(R,p),R,p)), r0{p{R,p),R,p) Q(p(R,p),R,p) = / q(z(p(RiP),p,v),p,v)h(v)dv ' ' " r a i n 5.2.2 Supplier Profit Maximization The supplier's cost function is kF + k'Nipi^p), R,p) + [c + kc]Q(p(R,p), R,p) where c is the constant marginal cost for the IT enhanced primary good (exclusive of IT costs), and the IT costs include a fixed implementation cost, kF, an installation cost per IT adopter, k1, and the marginal cost per IT enhanced primary good, k°. Profit maximization for the IT monopolist using a two part tariff is maxTr{p(R,p),R,p) = max[[i? - fcJ]JV(p(i2Jp)> R,p) + [p - c - kc}Q{p(R,p), R,p) - kF}. /i,p H,p Corresponding to Model 4.1 and borrowing from [41], the necessary first order con-ditions are dTr(p(R,p),R,p) = dR N(P(R,p), R,P) + mp(R,P),R,P)[R _ k l ] + dQ(p(Rp),R,P)[p _ c _ k C ] = Q 1The limits of integration are reversed as compared to the prior chapter since v is a reverse ordering of 6. Chapter 5. Supphers Offering IT Directly to Customer Firms 117 dir(p(R,p),R,p) = dp dN(P(RP),R,P) _ + + i Q W B ^ p ) ^ ^ = ap ap noting the use of total derivatives. As in Model 4.1, the following proposition shows that a subsidy (along with the min-imum purchase) should be no greater than the customer firm's internalization switching cost. Proposition 5.1: R + P>—K. Proof: The proof is constructed in the same way as Proposition 4.1: Suppose not. Then u{p(R,p), R,p) = umax, and all customer firms purchase at least one unit of the factor input. Therefore, dN(P(R,p),R,p) = dQ(p(R,p),R,p) = dR a n dR This means dir(p(R,p),R,p) — = N{p{Ryp),R,p) = 0. This contradicts the initial hypothesis that all customer firms purchase. • The effect of Proposition 5.1 is to eliminate a group of inefficient customer firms pur-chasing the minimum quantity simply to receive the subsidy, and not producing. Thus, for v < i>(p(R,p), R,p) factor demands come from interior solutions for x(p(R,p),p,u). With an interior solution to profit maximization downstream output has several prop-erties as per [34]. Using the inverse function rule of differentiation and the first order condition for customer firm profit maximization, Chapter 5. Supphers Offering IT Directly to Customer Firms 118 dx(p(R,p),p,v) = 1.d2((x(p{R,p),p,u),p,v) > Q dp dx2 Setting this first order condition to zero, and using the implicit function rule, dx(p(R,p),p,v) = d2C{x{p(R,p),p,^)>P,u) d2t{x(p(R,p),p,i;),p,is) < Q du dxdv dx2 For the monopohst IT only suppher, an interior profit maximizing solution will exist only if u(p(R,p),R,p)£(vmin,umax) so that a positive number of customer firms produce, and DN(P(R'P)'R>P); *Q[P[R,P),R,P) 0. < Unfortunately, as detailed in Appendix 5.1, the signs of the marginal contributions for both components of the two part tariff are ambiguous. The ambiguity comes from the additional impact of factor input prices affecting downstream output prices. Therefore, it is not possible to establish if positive variable and/or fixed profits are made from the IT enhanced primary good. Following [41], consider when the downstream output price for customer firms is unaffected by factor input pricing. Then p is a parameter rather than a function. Focusing on the elements of A in Appendix 5.1, this means dp(R,P) _ dp(R,p) _ dR dp Employing the simplified derivatives in Appendix 5.1, the resulting two part tariff is almost exactly the same as the two part tariff found in Appendix 4.1, except for some minor changes in signs: Chapter 5. Supphers Offering IT Directly to Customer Firms 119 R- k1 = -N(p,R,p) h{u{p,R,p))^^ - [Q{X(P,P, £{p, R,p)),p, "(p, R,p))} [N(p,R,P)q(x(p,pii>(p,R,p))iP,i>(p,R,p)) - Q(p,R,p)] rO(p,R,P) aq(x(pw),P,i<)h,u}dv ''"min dp \ ' _ kc _ N(pyR1p)q(x(p,p,u(p,R,p)),p,v(p,R,p)) - Q(p,R,p) P 0 r"(p,R,p) 9q (x (p,p,l> ),p,u) ^  / w JlJmin dp \ ' where < 0, and p is no longer a function or R and p . Variable profits still cannot be signed without an additional condition. As discussed in the Analysis section towards the end of the chapter, the general relationship between factor demands and v is indefinite because there is an indirect effect of v on factor demands through the optimal output level and possibly an opposite direct effect from relative production efficiency. Under the assumption of 9 p ^ ' p ^ = 9p^p^ = 0, and with an additional condition on d-q{x[p,p^),p,v) ^ ^ e f 0 N _ 0 W j n g proposition estabhshes the sign of the variable contribution, similar to Proposition 4.1. Proposition 5.2: If M*(P**)W) < 0 t h e n v a r i a b l e profits are positive, if M*{PW)W) > 0 then variable profits are negative. Proof: q(x(p,p, v),p,v) is decreasing in p, so fi>{P,R,p) dq(x(p,p,u),p,u) f JVn dp h(v)dv < 0. 2 The reversing in ordering of v as compared to 6 is eliminated by a reversal in signs of the derivatives of the marginal customers firms/consumers. Chapter 5. Supphers Offering IT Directly to Customer Firms 120 If M<PW)W) < o t h e n t h e n u m e r a t o r is negative and p-c-kc > 0, if M*lf>w)w) > 0 then the numerator is positive and p — c — kc < 0. • Writing R — k1, substituting p — c — kc, R-k1 = -N{p,R,p) h{i,{p,RlV))*^ -[q(x(p>p,t(p,R,P)),P,HP>R>P))]\P ~ C -  K°}-Notice that if p — c — kc is negative then R — k1 is strictly positive as N(p, R,p) and h(i>(p, R,p)) are positive,  d°^g^' P^ < 0, and the profits are made through the fixed charge. Chapter 5. Supphers Offering IT Directly to Customer Firms 121 5.3 Model 5.2: Monopoly Supplier Offering the IT enhanced Primary Good and the Original Primary Good This section examines a monopolist suppher offering both the IT enhanced and original primary goods, similar to Model 4.2. Each customer firm only purchases one of the two primary goods; a customer firm cannot adopt IT and the purchase the original primary good. 5.3.1 Factor Demands Customer firms are assumed to differ in their costs of turning over the primary good. These differences in costs are represented by a cost parameter u, v 6 71. v follows the density h(v) > 0 over v 6 [vmin, umax], and has a cumulative density H(u), where H{vmin) = 0 and H(vmax) = 1. Customer firm costs are assumed to be increasing in v. There are many customer firms, and therefore no customer firm individually has any effect on downstream price. The factor inputs here are either the IT enhanced primary good or the original primary good. Customer firm cost functions are: IT enhanced primary good: Original primary good: £0(x,p0,v) where x is the undifferentiated downstream output and pi is the per unit price of the factor input, i — {0, 1}. To avoid unnecessary complication, prices of other factor inputs are omitted from the notation. d(x,pi,i/) is a twice continuously differentiable function, increasing in v and increasing and convex in x. Marginal costs are positive and increasing in v, d ^Sxdu'^ ^ -^ Without loss of generality, fixed costs of production are zero, &(0,pi, v) = 0. Chapter 5. Supphers Offering IT Directly to Customer Firms 122 IT makes it less costly to produce a given level of downstream output, at equal factor input prices (exclusive of IT costs). Therefore, (x(x,p,v) < Co(x,p,v). By Shephard's lemma, for a given level of output x, the cost minimizing factor demand is dCi(x,pi,u) . dpi where i = {0,1}. For customer firms which produce using the IT enhanced primary good, qx must be at least unity as no prior restrictions are placed on the fixed component of the two part tariff. Trivially, p; > 0. No production is possible without the factor input, = 0 => cc,- = 0. The profit function for the customer firm using the IT enhanced primary good as a factor input is given by [ p(R,Pi,po)x - Ci{x,puv) - R - K if 8 C l fcf ' ' / ) = qi{x,pi,v) > 1 m1(x,v) = < ^ [ 0 otherwise, qx = 0. The profit function for the customer firm using the original primary good as a factor input is f p(R,Pl,po)x-C0(x,p0^) if * o { ^ =qo(x,po,v)>0 [ 0 otherwise, qo = 0. Where p(R,p\,po) is the market price of the downstream output, R is the fixed component of the two part tariff, and K > 0 is the internalization switching cost. The characterization of IT enters the customer firm's profit function three ways: reduced costs of production at equal factor prices, a two part tariff for the IT enhanced factor input, and a positive internalization switching cost incurred by IT adoption. Chapter 5. Supphers Offering IT Directly to Customer Firms 123 Customer firms select the factor input which maximizes their profits. Profit maxi-mization for a given customer firm using the IT enhanced primary good can be expressed as max v&\(x, v) 3 > 1 or x — 0. dpi For those customer firms that choose to produce the first order (Kuhn-Tucker) con-ditions are ft, \ 9£1(x,p1,v) ^ n 9(1{x,p1,v) P(R,PI,PO) Q-X <o, > 1 [P{R,Pi,Po) J[ ^ 1J = 0. Using the properties of (\(x,pi,i/) these conditions define an optimal downstream output function x{p(R,Pi,Po),Pi,v), and through Shephard's lemma a factor demand function obtains, 1i(x(p{R,Pi,Po),Pi,v),Pi,v)-Directing our attention to the original primary good as a factor input, profit maxi-mization is maxZUQ(X, V\ 3 x > 0. X The first order (Kuhn-Tucker) conditions of those customer firms that choose to produce are ( D \ 9(o{x,p0,is) P\R,PuPo) < 0, x > 0 Chapter 5. Supphers Offering IT Directly to Customer Firms 124 \p{R,Pi,Po) ^ ]x = 0. With (0{x,Po,v) these conditions yield optimal downstream output *{p(R,Pi>Po),Po,u), which through Shephard's lemma gives a factor demand function qo{x(p(R,pi,Po),Po,v),po,v)-Factor demands are non decreasing in x, and non increasing in Pi, i = {0, 1}. With optimal output well defined under each factor input, the customer firm chooses which primary good to purchase: max{wi(x(p(R,p1,Po),p1,v),i>),zvo(x(p(R,pupo),po,v),i')}. Consider the customer firm which is indifferent between the two primary goods as factor inputs. This customer firm, v(p{R,Pi,Po), R,Pi>Po), is implicitly defined by the condition w1(x(p(Ripi,p0),Pl,v),i>) = w0(x(p(R,p1,p0),po,i>),i>) or p(R,p1,Po)x(p(R,p1,p0),p1,i>) - Ci{x(p(R,pup0),Pi,i>),pui>) -R-K = p(R,Pi,Po)x(p(R,PuPo),Po,r)) - (o{x(p(R,pl,p0),po,i>),pchv)-Chapter 5. Supphers Offering IT Directly to Customer Firms 125 Assume the market is covered, and thus factor demands are decreasing in P{. In addition, assume d(i(x(p(R,Pi,Po),Pi,v) d(o(x(p(R,p1,p0),p0,u) dv du Therefore, relative customer firm efficiency is more sensitive when using the IT en-hanced primary good as the factor input. This condition effectively allows for the sep-aration of customer firms. As discussed in Model 4.2, this condition makes use of the envelope theorem as optimal factor input quantities are assumed. Using the monotonicity of the cost functions in u, interior solutions to profit maxi-mization, and the assumed condition above, if u(p(R,pi,p0), R,pi,po) exists it is unique. Furthermore, v < i>(p(R,p1,p0),R1,Pl,po) => °i(x{p{R,Pi,Po),Pi,v),Pi,v) > 1, q0(x(p(R,Pi,Po),Po,v),Po,v) = 0 v > v{p(R)pl,p(i),R1,pl,p0) q0(x(p(R,p1,p0),p0,v),p0,v) > 0, q1(x(p(R,p1,p0),p1,u),p1,u) = 0. If £(p(.R,pi,po)) Ri,Pi,Po) does not exist.then either all customer firms produce with the IT enhanced primary good or they all produce with the original primary good. Normalizing the number of customer firms to one, the proportion of IT adopters and aggregate factor demands for each of the primary goods are3: rO{p(R,pi,pn),R,p1,p0) N{p(R,Pi,Po),R,PuPo) = / h(v)dv = H(i>(p(R,p1,p0),R,p1,Po)), 3The limits of integration are reversed as compared to the prior chapter since v is a reverse ordering of 6. Chapter 5. Supphers Offering IT Directly to Customer Firms 126 ri>(p(R,Pl,Po),R,Pi,Pt)) QI(P(R,PUPO),R,PUPO) = / qi(x{p{R,Pi,po),Pi,v),Pu")H")dv Qo(p(R,Pi,Po),R,Pi,Po) = I qo(x(p{Ripllpo)}poiv),p0,u)h{u)du. JV(P{R,PI,PO),R,PI,PO) 5.3.2 Supplier Profit Maximization The supplier's cost function is kF + k IN(p(R,p1,p0),R,p1,p0) + [ca + kc]Q1(p(R,p1,p0), R,pup0) +coQo(p(R,Pi,Po), R,Pi,Po) where c; is the constant marginal cost for the primary good (exclusive of IT costs for i = 1), and the IT costs include a fixed implementation cost, kF, an installation cost per IT adopter, k1, and the marginal cost per IT enhanced primary good, kc. The monopolist supplier's profit maximization problem is then set up as max n(p(R}Pl,p0),R,p1,po) = R,Pi .Po max [N(p(R,pup0),R,Pl,p0)[R- k1] +Qi{p{R,PuPo), R,Pi,Po)[pi - c i - kc] +Qo{p{R,pi,po),R,pi,po)[po - co ] - kF}. Consider when downstream output price is considered to be exogenous. That is, p is not a function of factor input prices. The first order conditions to the above optimization become Chapter 5. Supphers Offering IT Directly to Customer Firms 127 OR N{p, R,PI,PO) + [R - « J + [Pl - C i - fc J dQ0{p,R,pup0) + m \po-co} = 0 dir(p,R,p1}p0) _ dpi dN(p,R,pup0) ui-i.nf p \ , dQi{p,R,Pi,Po),_ „ u c } [R-k } + Q1(p,R,pi,po) + j. lPi - ci - fc j dpi opi dQ0(p,R,Pl,po) 1 H Q [Po - c0J = 0 op i dir(p,R,pi,p0) _ dPo dN(p,R,pi,po).R _ k I , + dQi{p,R,Py,p0)^^ _ ^ _ k C , dPo dp0 i i J ,nr D \ i °Qo(PiRiP^Po)i i n +Qo(p,/c,Pi,Po) + ^ |p0 - c0j = 0 op a which is similar to the equation system from Model 4.2. Assuming the necessary first and sufficient second order conditions hold, the system is solved in Appendix 5.2. The resulting contributions are R - k 1 = -N(p,R,pltp0) h(u(p,R,Pl,Po))d^f^ -[qi{x{p,PuO(p,R,Pup0)),pl,i>(p,R,p1,Po))} [N(p,R,p1,p0)q1(x(p,p1,v{ptR,p1,p0)),p1}u{p,R1p1,po)) - Qi(p,R,Pi,Po)] rO(p,R,pi,p„) gg i (x (p ,p i ,u ) , P i ,u ) f i^ .W y Jvinin dpi \ ' Chapter 5. Supphers Offering IT Directly to Customer Firms 128 -[qo(x{p,Po,HP>R>PuPo)),Po,i>{p,R,Pi,Po))] [N(p, R,pup0)q0(x(p,po, v(p, R,Pi,Po)),Po, v{p, R,Pi,Po)) + Qo(p, R,Pi,Po)] _c _kc _ ^{p,R,PuPo)qi{x(p,pi,i>(p1R,p1,p0)),p1,i>(p,R,pi}po)) - Qi(p,R,Pi,Po) P L C L ( • ' ' ( P A P I . P O ) 8qi (x(p,pi ,i/),pi ,V) fal^fo •'"min dpi \ / N(p,R,p1,Po)q0(x(p,po,i'(p,R,p1,po)),po,i>(p,R,PuPo)) + Qo(p, R,Pi,p'o) Po — c0 rv"lax dq0(x(p,po,v),p„,v), / w }(p,R,pi,po) dpu where dP(p,R,Pl,Po) dR dCi ( g ( P i P i ^ ( p . - R . P i 1P0 ) ) , P i . ^ ( p . - R . P i , P u ) ) _ 9Cn (g (p ,Po , i> (p,Jt ,P i ,Po ) ) ,Po , i> (p , f l ,P i ,Po ) ) ' S v S i ; Propositions similar to Proposition 4.3 and 4.4 are given below. The first proposition accounts for the direction of M ' ( , P ^ > ^ ) , Proposition 5.3: If ^ < P ^ > ^ ) < Q t h e n v a r i a b l e p r o n t s from the IT enhanced good are positive, if  dqii x{ p' pJj v)' Pl' v) > o then variable profits from the IT enhanced good are negative. Proof: qi(x,Pl,v) is decreasing in P l . If * M P * £ ' ) M ) < 0 then P l - C l - kc > 0, if dqi{x(P,pu»),puv) > Q t h e n pi_Ci_kc < Q D Proposition 5.4: Profits from the original good are positive. Chapter 5. Supphers Offering IT Directly to Customer Firms 129 Proof: q0(x,p0,v) is decreasing in p0. In addition, N{p,R,Pi,Po)qo(x(p,Po,v(p,R,Pi,Po)),Po,v(p,R,Pi,Po)) + Q0(p,R,PuPo) > 0. Thus, po — c0 > 0. • As before, substituting the variable contributions into the equation for the fixed con-tribution, it is not possible to determine the sign of the fixed component of the two part tariff unless - W ^ i ••')•»>'••'? > 0 , R-k' = h{u{p,R,Vl,p0))d^fp^ -qi(x(p,Pi,i>(p,R,p1,p0)),p1,£'(p,R,p1,p0))[p1 - C l - kc] +q0{x(p,pQ,C'(p,R,p1,po)),p0,0(p,R,p1,Po))[p0 - c0], observing  9 v { p > R ' ^ ' - P " ) < 0. Therefore, if variable profits from the two part tariff are negative then fixed profits must be positive. With no restrictions placed on the price of downstream output (i.e. p as a function of R, pi, and p0) solving for the three unknowns from the first order conditions becomes unmanageable. The discussion at the end of Model 4.2 concerning the intuition behind the two part tariff, non adopters, concavity of the profit functions, and joint pricing, also apphes to these results. Chapter 5. Supphers Offering IT Directly to Customer Firms 130 5.4 Model 5.3: Oligopoly Suppliers Where One Supplier Has IT This section addresses the situation where one suppher has the IT enhanced primary good to offer as a factor input, and other supphers do not. All supphers can offer the original primary good. Several of the more notable "IT for competitive advantage" cases faU into this structure, namely American Hospital Supply Corporation's ASAP system ([1]), and Pacific Pride's "card- lock" system ([33]). This model parallels Model 4.3, and to avoid repetition references to that section are used liberally. Again, customer firms can only purchase one type of primary good from one suppher. 5.4.1 Formulation As in Model 4.3, the focus is on the duopoly case where supplier A has the IT, suppher B does not. Suppher B is committed to offering the original primary good. The formulation is a two stage game where at the first stage suppher A decides which primary goods to offer and at the second stage supphers A and B compete in prices. The structure of the game and solution concept used is the same as in Model 4.3. Working backwards, each subgame of Stage 2 is examined followed by the game in Stage 1. 5.4.2 Stage 2 Subgame: S2.1 In this subgame suppher A offers both the IT enhanced and original primary goods and suppher B offers the original primary good. Suppher A selects the two parts of the two part tariff for the IT enhanced primary good (R and pi) as well as the per unit price of the original primary good (pA). Suppher B selects pB. Customer firms choose the lowest price for the original primary good, po = mm{pA,pB}. Chapter 5. Supphers Offering IT Directly to Customer Firms 131 If PQ = p B then factor demands for the original primary good are partitioned equally. Individual and aggregate factor demands are constructed identically to those in Model 5.2, and are not restated. In Model 4.3 the unique Nash equilibrium price for the original prima^ good was marginal cost, p A = p B — c0. The reasoning and intuition behind the equilibrium was based on the following argument. Because the effective p 0 = miii{p A,p B} and suppher B only has the original primary good available, at any p A > Co suppher B should undercut Po, down to marginal cost. Also because the effective p 0 = minjpojPo3}, it is always in suppher A's interest to at least meet p B with PQ . Thus, a form of the Bertrand paradox obtains. The analysis of the present supphers to customer firms is analogous to the analysis in Model 4.3. Therefore, the Nash equilibrium is p A = p B = c 0 5.4.3 Stage 2 Subgame: S2.2 In this subgame suppher A offers the IT enhanced primary good and chooses the two part tariff, R and P l , suppher B offers the original primary good and selects p 0. Individual and aggregate factor demands are constructed identically to those in Model 5.2. Suppher A's cost function is kIN(p(R,pup0),R,p1,po) + [a + kc}Q1(p(R,pi,p0),R,p1,p0). C j is the constant marginal cost of the IT enhanced primary good (exclusive of IT costs), k 1 is the IT installation cost per IT adopting customer firm, k c is the constant marginal cost per IT enhanced primary good sold. Suppher B's costs are simply the costs of the original primary good, Chapter 5. Supphers Offering IT Directly to Customer Firms c0Q0(p(R,PuPo),R,Pi,Po), where c0 is a constant. Profit maximization for suppher A is ma.yLnA(p(R,p1,p0), R,pi) = max[N(p(R,pi,p0), R,pi,p0)[R - k1] +Qi(p(R,Pi,Po),R,Pi,Po)\pi - c i - kc}} selecting the two part tariff for IT. The necessary first order conditions are dTrA(p(R,p1,p0)1R,p1,p0) _ dR AT/ / rt x p \ , dN{p(R,p1,Po),R,p1,po)iD j N{p{R,Pi,Po),R,Pi,Po) + l-R- fc j , dQ1(p(R,pl,p0),R,pi,p0)^^ _ C i _ fcC] = 0 dR dTTA(p(R,p1,p0),R,p1,p0) dN(p(R,PlP0),R,Pl,p0)[R _ k I ] + Q M R i P u P o l R y P l t P o ) dpi , dQi(p(R,pltp0),R,Pi,Po)r ,ci n [Pi-ci-k J = U. dpi Supplier B's profit maximization is m a x 7 r B ( / 9 ( i ? , p i , p o ) , P o ) = max.[Q0(p(R,p1,po),R,Pi,Po)\po ~ c 0 ] ] , po pn Chapter 5. Supphers Offering IT Directly to Customer Firms 133 and the necessary first order condition is d-KE\p{R,Pi,po), R,Pi,Po) _ dpo dQo(p(R,pupo),R,p1,p0) i , n , ^ p „ „ ^ _ n j \Po - c0\ + Qo(p(R,Pi,PohR,Pi,Po) - U. dpo For the case where p is exogenously determined (i.e. not a function of R, pt, and p0), the resulting system of three equations and three unknowns is solved in Appendix 5.3. Assuming the necessary and sufficient conditions hold, the equilibrium contributions to profit are R- k1 = -N(p,R,p1}p0) h(v(p,R,Pl,p0))a^f^ -[qi(*(p,Pi,HP>R>Pi>Po))>Pi>i'(p>R>Pi>Po))] [N(p,R,pi,po)qi(x(p,p1,u(p,R,p1,po)),pi,D{p,R,p1,p0)) - Qi{p,R,Pi,Po)] rv(p,R,Pl,p0) 8qi(x(PtPl ,v),pi <u)n<v\^v. •'"min dpi ^ ' 7 C Pl - C l - k = N(p,R,Pi,po)qi(x(p,p1,i>(p,fi,pi,p0)),pi,^(^,R,pup0)) - Qi(p,R,pitpo) ri>{p,R,pi,pu) dqi (a(p,pi ,v),pi ,v) M^fo •'"min dpi \ ' Po - c 0 = -Qo(p,R,pi,po)/ f % " dq0(x(p,p0,v),po,v) r~ 0 q ^ p ^ v ^ u h { u ) d v JO{p,R,pi,po) dp0 di>{p,R,pi,p0), -qo(x{p,Po,v(p, R,Pi,Po)),Po,i>(p, R,Pi,Po))h{i>(p, R,Pi,Po))-dpc Chapter 5. Supphers Offering IT Directly to Customer Firms 134 where and *qo{x(p,p0,v(p,R,pi,Po)),Po,Hp>R>Pi>Po))-Similar to Proposition 4.5, the following proposition shows that with downstream output price exogenous supplier B charges a positive marginal contribution on the original primary good. Proposition 5.5: Suppher B makes positive profits on the original primary good. Proof: Qo(p, R,PiiPo) > 0. q0(x(p,p0, v),p0, v) is decreasing in p0. By assumption Observe that even if downstream output price is endogenous, p(R,p1,p0), suppher B will never charge less than marginal cost for the original primary good, P o > c0, in any equilibrium. 5.4.4 Stage 2 Subgame: S2.3 To avoid repetition, as in Model 4.3, the Nash equilibrium result when both supphers compete head to head in the original primary good, without the IT enhanced good on the market, is marginal cost pricing. 5.4.5 Stage 1 At Stage 1 suppher A selects from the following strategies: compete with both the IT enhanced and original primary goods (S2.1), compete with the IT enhanced primary < 0. Therefore, p 0 - c 0 > 0. • Chapter 5. Supphers Offering IT Directly to Customer Firms 135 good only (S2.2), compete with the original primary good only (S2.3). As in Model 4.3, subgame S2.3 is dominated by either of the other two strategies as supplier A makes zero profits from S2.3. Therefore, the relevant comparison is between subgames S2.1 and S2.2. Suppher A also makes zero profits from the original primary good in subgame S2.1. Thus, suppher A's choice depends on profits from the IT enhanced primary good when p0 > c0 as compared to when p0 = c0. The equilibrium two part tariff is the same in both of these subgames, except for the value of p 0. When p does not depend on R, p l 5 and p 0, it is possible to sign the variable profits from the two part tariff, analogous to Proposition 4.6, contingent on the sign of The marginal contributions were given earlier in this section and in Appendix 5.3. Because the variable component of the two part tariff for the monopolist supplier in Model 5.2 is identical to the variable component here (except for the value of Po, this proposition is the same as Proposition 5.3: Proposition 5.6: If dqi(x(p<Pi1ju)<Pl'u) < o then variable profits from the IT enhanced good are positive, if ( j g l ( J ( p ' P ^ ' l / ) ' P l ' ' / ) > 0 then variable profits from the IT enhanced good are negative. Proof: qi(x,Pl,u) is decreasing in P l . If ^ N ^ ) ^ ) < 0 then P l - cx - kF > 0, if dtoMpw*)*^) > 0 t h e n p _ c _ kc < Q N In addition, fixed profits cannot be signed without d q iH p ' p^'")' P l ' 1 /) • R-k1 = •N(p,R,Pi,p0) h(u(p,R,PuPo))d^R^ -qi(x{p,Pui}(p,R,Pi,Po)),Pui>(p,R,p1,p0))[p1 - d - kc Chapter 5. Supphers Offering IT Directly to Customer Firms 136 Thus, fixed profits from the two part tariff cannot be negative if variable profits are negative. In the case where p is exogenous it is possible to ascertain the impact of p0 on suppher A's profits. Employing irA(p, R,Pi,Pi) to denote suppher A's profits from the IT enhanced primary good, the next proposition uses similar reasoning to Proposition 4.7. Proposition 5.7: irA(p, R,pi,po) is increasing in p0. Proof: The impact on irA(p, R,Pi,p0) of any changes in p0 come only through the marginal customer firm, 0(p, R,pi,p0). Given that du(piR,p1,p0) dv(p,R,pi,p0) d p o = qo{x{p,Po,v{p,R,Pi,Po)),Po,v{P,R,Pi,Po)), then for any increase in p0 an offsetting increase in R can restore R,pi,p0) to its initial level. With changes in R and p0 not affecting individual customer firm factor demands for the IT enhanced primary good, additional profit is captured through the increase in R. • The result is that when downstream output price is exogenous suppher A makes strictly greater profit in subgame S2.2. Therefore, the subgame perfect equilibrium of the game is that in Stage 1 suppher A chooses to offer only the IT enhanced primary good, and uses a two part tariff in Stage 2. Suppher B is thus allowed a monopoly in the original primary good. Unfortunately, with downstream output price depending on factor input prices it is not possible to sign either the fixed or variable contributions of the two part tariff. Moreover, when downstream prices are a function of factor input costs the reasoning in Proposition 5.7 does not necessarily hold. The difficulty can be illustrated by the follow-ing argument. Notice that now i>(p(Rip1,p0), R,plyp0). While an offsetting increase in Chapter 5. Supphers Offering IT Directly to Customer Firms 137 R may be able to offset the increase in po with respect to the marginal customer firm, there is another effect of changing R and po'. p(R,pi,po)- Unhke Proposition 5.7, these increases affect customer firm downstream output through p(R,pi,p0), and hence factor demands. Thus, if downstream output price is endogenous it is not clear what strategy suppher A should choose in Stage 1. The discussion at the end of Model 4.3 regarding the effects of a fixed IT implementation cost, an oligopoly rather than a duopoly, non adopters, and concavity of the profit functions, also applies to these results. Chapter 5. Supphers Offering IT Directly to Customer Firms 138 5.5 Model 5.4: Two Suppliers Offering Undifferentiated IT Enhanced Pri-mary Goods This section studies price competition between supphers using two part tariffs with iden-tical IT and IT enhanced primary goods. The analysis imitates the examination in Model 4.4. A given customer firm is restricted to adopting IT and purchasing the IT enhanced primary good from only one suppher. An example which follows this structure is the competition between McKesson Drug Company ([8]) and Bergen-Brunswig Corporation ([18], [8]). Both are drugstore wholesalers, and both have similar IT which is offered to individual retail drugstores. 5.5.1 Formulation Similar to Model 4.4, a supplier duopoly is studied where both supphers are committed to offering the IT enhanced primary good. The IT is undifferentiated, the IT costs and marginal primary good costs (exclusive of the IT costs) are equal for both supphers. As in Model 4.4, there is no original primary good available to consumers. The focus is on deriving Nash equilibria to the simultaneous pricing game in two part tariffs. With two suppliers there are three possible configurations of prices: • Dominating Price Pairs: Rl > Ri and pl > pi, with one of the inequalities strict. • Asymmetric Price Pairs: R1 > Ri and p% < pi. • Equal Price Pairs: R% = Ri and p1 = pi. where i, j = {A,B}, i ^ j. Potential equilibria from each of these configurations is investigated in sequence. Chapter 5. Supphers Offering IT Directly to Customer Firms 139 5.5.2 Dominating Price Pairs Avoiding repetition, it is clear that a dominating price pair cannot support an equilib-rium. At positive profits the dominated suppher has incentive to reduce at least one of the components of its two part tariff, at negative profits the dominating supplier prefers to raise its two part tariff. 5.5.3 Asymmetric Price Pairs As discussed in Model 4.4, it is not possible to establish whether an asymmetric price pair can support an equilibrium from studying the price components and profits alone. Consider first the more simple case where downstream output prices are exogenous. The succeeding Lemma, similar to Lemma 4.1, provides conditions under which a Nash equilibrium in asymmetric price pairs does not exist. Lemma 5.1; A Nash Equilibrium with Rl > Ri and pl < pi for i,j = {A, B}, i ^ j, where the market is covered by the undifferentiated IT enhanced primary goods, downstream output price is exogenous, and d q (x(p'^)'p 'v) < 0, i — {A, B}, does not exist. Proof: As in Lemma 4.1, assume there exists a Nash equilibrium where RA > RB and pA < pB (with no loss of generahty), where the market is covered by the undifferentiated IT enhanced primary goods, and where d q (!C(p'pj1')'p < 0, i = {A, B}. Derive first customer firm demands. Customer firms differ in their costs of turn-ing over the primary good with these differences represented by v, v £ 1Z. v follows the density h(u) > 0 over v £ [fTnin,umax}, and has a cumulative density H(v), where H(vmin) = 0 and H(ymax) = 1. Customer firm costs are assumed to be increasing in Chapter 5. Supphers Offering IT Directly to Customer Firms 140 v. There are many customer firms, and therefore no customer firm individually has any effect on downstream price. Customer firm cost functions are: where i — {A, B} indexes supphers, x is the undifferentiated downstream output, and pl is the per unit price of the factor input. To avoid unnecessary complication, prices of other factor inputs are omitted from the notation. £(x,pl,v) is a twice continuously differentiable function, increasing in v and increasing and convex in x. Marginal costs are positive and increasing in v, 9 ^*gP '"^  > 0. Fixed costs of production are zero, C(o,P>) = o. By Shephard's lemma, for a given x, the cost minimizing factor demand is For customer firms which produce purchasing from suppher i, ql > 1. No production is possible without the factor input, q = 0 => x = 0. The profit function for the customer firm using the IT enhanced primary good as a factor input is f , s - C ( * , p ' » - # - K i£°Ugrl=qi(Xtpitu)>l wl(x,u) = i . . [ 0 otherwise, q1 = 0, where p is the market price of the downstream output, Rl is the fixed component of the two part tariff, and K > 0 is the internahzation switching cost. Profit maximization for a given customer firm is i, \ = d({x,p\iy) maxro (x.v) 3 — > 1 or 1 = 0. J dp1 Chapter 5. Supphers Offering IT Directly to Customer Firms 141 F o r those customer firms that choose to p r o d u c e p u r c h a s i n g the I T enhanced p r i m a r y good from suppher i the first order ( K u h n - T u c k e r ) conditions are dC(x,pl,v) d({x,p\v) P a - °> a~i - 1 Ox Op1 r _ flC(»,P',»')irdCOc,P>) _ X l = o dx dp* U s i n g the properties of ((x,pl,u) these conditions define an o p t i m a l downstream o u t p u t function *(p,P\v), a n d t h r o u g h Shephard's l e m m a a factor d e m a n d function q1(x(p,p\u),pl,u). F a c t o r d e m a n d s are n o n decreasing i n x, a n d n o n increasing i n pi, i = {A,B}. T h e factor demands c a n be c o m b i n e d into one function: q(p,R,p,v) <lA(x{p,PA,v),PA,») if wA(x{p,pA,v),v)>mB(x(p,PB,u),v) qB(x{p,pB,v),pB,v) i f mB(x{p,pB,v),v)>mA(x(p,pB,u),v) where (R,p) = ((RA,RB),(pA,pB)). C o n s i d e r the customer firm which is indifferent between the two I T enhanced p r i -m a r y goods as factor inputs. T h i s customer firm, i)(p,R,p), is i m p l i c i t l y defined by the c o n d i t i o n mA(x(p,pA,i>),i>) Chapter 5. Supphers Offering IT Directly to Customer Firms 142 or px(p,pA,i>) - ({x{p,pA,i)),pA,i>) - RA - K = PX(P,PB,^) ~ C(x{p,PB,')),PB,')) - RB ~ «• Assume interior solutions for x(p,pl,u). This guarantees the market is covered, and that factor demands for suppher i are decreasing in pl. Using the monotonicity of the cost functions in u, and interior solutions to profit maximization, if i)(p,R,p) exists it is unique. Moreover, as pA < pB, v < i>(p,R,p) => qA(x(p,pA,v),pA,v)>l, qB(x(p,pB,v),pB,v) = 0 v > v(p,R,p) =4> qB(x(p,PB,v),pB,v)>l, /(*(p,pV),pV) = 0. Normahzing the number of customer firms to one, the proportion of IT adopters and aggregate factor demands for the IT enhanced primary good from each suppher is 4: N- [(p,R,p)= f h(v)<h, = HWPiR,p)) QA(p,R,p) = r(P'R'P)qA(x(p,pA,v),pA,v)h(v)dv \p,R,p)= _ h{v)dv = l-H{v{PlR,p)) Ji>{P,R,p) 4 Again, the limits of integration are reversed as compared to the prior chapter since v is a reverse ordering of 6. Chapter 5. Supphers Offering IT Directly to Customer Firms 143 Each supplier's cost function is Each supplier's profit maximization problem is then max 7r l(p, R,p) — Ri,pi m a x l N ' i p , - k1] + Q^R.p)]^ -c-kc}}. Where RA > RB and pA < pB these profit functions are continuously differentiable. Similar to Appendix 4.4, assuming necessary and sufficient conditions hold, Appendix 5.4 derives the Nash equilibrium prices, observing that here "*" denotes computed Nash equilibrium prices: i T - k1 = -[qi(x(p,pi',i>(p, R*,?*))^*, i>{P, R*>P*))] [N'ip, R'^WMPIP", HP, R^f)),r,Hp, R",P)) - Q{(p, Ni(P, R-rfWiziprf'^p, i i " , HP, R*,P*)) - Q'(P, R',f) where j> = 1 if i = A, j 0 if i — B, and Chapter 5. Supphers Offering IT Directly to Customer Firms 144 JO{P,R\F) dpB and where di>{P,R\p) = 8RA 1,M(X(P,PA*,HP,R\F)),PA\HP,R*,P')) dv dqx(p,pB%v(PJ~,f)),pB*,v(p,R~,p')) dv J' , dv(p,R\ir) _ du(p,R\f) ana a R B - - ^ Concentrate on the per unit contribution of the equilibrium two part tariff. Examining pA" - c - kc with ^ ( * ( P . P > ) . P > ) < o, i = {A, B}, analogous to Propositions 5.2, 5.3, and 5.6, NA(PJ\r)qA(x(p,pA%v(pJ',p')),pA\v(pJ'^))-QA(p,R\f)<0, and aA < 0. Therefore, pA' - c - kc > 0. Moving to pB* — c — kc, aB is also negative. Opposite to supplier A, NB(Pj^r)qB(x(p,pA%v(pj\f)),pB\v(pj'^))-QB(p,R\f)>o. Thus, PB~ - c - k c < 0. This implies pA' > pB*. But by assumption RA > RB and pA < pB. Hence, a contradiction. This completes the proof of Lemma 5.1. • . Notice that when dq (x(p>^)>p >v); { — {A,B}, is positive then Lemma 5.1 as proven does not hold. Moreover, if the sign of d q ^p'p^v)'p <v) i s unknown then Lemma 5.1 does Chapter 5. Supphers Offering IT Directly to Customer Firms 145 not necessarily hold. Therefore, an asymmetric price pair Nash equilibrium, even with downstream output price exogenous, has not been ruled out. When downstream output price is endogenous the situation is even more indetermi-nate. Recalling the derivation of the two part tariff in Appendix 5.1 (for Model 5.1), with downstream output prices a function of factor input prices, it was not possible to sign either component of the two part tariff. The development of suppher A's price pair in the above Lemma, for p endogenous, would be similar to Appendix 5.1 (Model 5.1), focusing on the upper left 2 x 2 submatrix of A in Appendix 5.4. Thus, it would not be possible to sign either component of either supplier's computed Nash equilibrium price pair in the endogenous downstream output price case. 5.5.4 Equal Price Pairs The last price configuration which may support a Nash equilibrium is each supplier offering the same two part tariff. Directly following the arguments in Model 4.4, any equilibrium of this type must also be at zero profits. A characterization of the necessary and sufficient conditions for a Nash equilibrium in equal price pairs is • (R*,p') must satisfy R* - k1 ~-\p'-c-kc} Q{P{Rrtp),R't?) N(p(R',p),R%?)' RA* = R B and positive profits cannot be made by either supplier unilaterally deviating from the price pair (R~,p*). Chapter 5. Supphers Offering IT Directly to Customer Firms 146 As before, these conditions cannot be expressed or determined using calculus as the profit functions are discontinuous moving away from equal price pairs. The result is that again it is not clear whether or not a Nash equilibrium in equal price pairs exists, regardless of whether downstream output price is endogenous or exogenous. The discussion at the end of Model 4.4 pertaining to non adopters and/or presence of the original primary good, concavity of the profit functions, and fixed IT implementation costs, also apphes here. Chapter 5. Supphers Offering IT Directly to Customer Firms 147 5.6 Model 5.5: Two Suppliers Offering Differentiated IT Enhanced Primary Attention is now directed towards competition with two part tariffs between two supph-ers offering vertically differentiated IT enhanced primary goods. Similar to Model 4.5, customer firms are restricted to adopting IT and purchasing only one of the IT enhanced primary goods. 5.6.1 Factor Demands Customer firms differ in their costs of turning over the primary good. These differences are represented by a cost efficiency parameter u, v £ 7c. v follows the density function h(i>) > 0 over v £ \vmin, umax], and has a cumulative density H(v), where H(vmin) = 0 and H(frnax) = 1. Customer firm costs are assumed to be increasing in v. There are many customer firms, and therefore no customer firm individually has any effect on downstream price. Customer firm cost functions are: where x is downstream output and pi is the per unit factor input price of the IT enhanced primary good, i = {1, 2}. To avoid unnecessary complication, prices of other factor inputs are omitted from the notation. d(x,Pi,u) is twice continuously differen-tiable, increasing in v and increasing and convex in x. Marginal costs are positive and increasing in u, 8 ^ Q ^ " 1 ^ > 0. Fixed costs of production are zero, £(0,pi, v) = 0. By Shephard's lemma, for a given level of output x, the cost minimizing factor demand is Goods d(i(x,pi,ts) dpi qi(x,pi,v). Chapter 5. Supphers Offering IT Directly to Customer Firms 148 For customer firms which produce using IT enhanced primary good i, qi must be at least unity as no prior restrictions are placed on the fixed component of the two part tariff. No production is possible without the factor input, q = 0 x — 0. The profit function of a customer firm using the IT enhanced primary good as a factor input is \ p(R,p)x - £i{x,pi,v) - Ri-m if d<-i^i>v) _ qi(x}pi,v) > 1 Wi(x,v)=< ™ [ 0 otherwise, qi = 0 where (R,p) = ((R2, Ri), (p2,Pi)), p(R,P) is the market price of the downstream output, Ri is the fixed component of the two part tariff, and Ki > 0 is the internalization switching cost, i = {1,2}. The IT enhanced primary good i = 2 is considered superior to the IT i = 1 enhanced primary good. Consequently it costs less to produce a given level of output using the superior IT enhanced primary good, £2(x,p, u) < (,i{x,p,v), at equal factor prices. Hence, the impacts of IT are incorporated through reduced costs of production with the superior IT enhanced primary good as factor input, the two part tariff for the IT enhanced factor input, and the positive internalization switching cost incurred by IT adoption. Profit maximization for a given customer firm using factor input i is / \ d(i(x,pi,u) max WAX,u) 3 > 1 or x = 0. dpi Customer firms choosing to produce with the IT enhanced primary good i have first order (Kuhn-Tucker) conditions: ,x -« 9Ci(x,Pi,u) n dCAx,Pi,u) p(R,p) - V ' ; < 0, V ' ' > 1 OX Opi W f i , f l - * ! ^ ] [ « « | ^ _ 1 ] = 0. Chapter 5. Supphers Offering IT Directly to Customer Firms 149 Using the properties of £,•(£,p ,^ i/) these conditions provide a well defined optimal downstream output function and by Shephard's lemma a factor demand function <li(x(p(R,p),Pi,v),Pi,v), which is non decreasing in x, and non increasing in p;. Notice the fixed component of the two part tariff and the internahzation switching cost only affect the choice of whether or not to produce. Each v has to select which IT enhanced good to purchase as factor input, if any, by ma,x{w2(x(p(R,p),p2, u), u), zu1(x(p{R,p),pl,u), u)} with outputs chosen optimally as above. Examine the customer firm which is indiffer-ent between the two IT enhanced factor inputs. Define u(p(R,p), R,p) imphcitly through the equal profit condition, or p(R,p)x(p(R,p),p2,u) - (2(x(p(R,p),p2,v)),p2,u) - R2- K2 = p{R,p)x(p(R,p),Pi,i>) - Ci(x{p(R,p),Pi,i>)),Pi,i>) - Ri - ica. Assume the market is covered and therefore factor demands for primary good i are increasing in p;. Moreover, assume d(2(x(p(R,p),p2,v)),p2,v) dCi{x{p{R,p))pl)v)))pi)v) dv du Thus, similar to Model 5.2, relative customer firm efficiency is more sensitive when using the superior IT enhanced primary good. Chapter 5. Supphers Offering IT Directly to Customer Firms 150 If v(p(R,p), R,p) exists then it is unique. In addition, u<u(p(R,f),R,p) ==» q2(x(p(R,p),p2,v),p2,v) > 1, q1(x(p(R,p),p1,u),Puu) = 0 v > J>{p(R,p),R,p) => qi(x(p(R,p)}pi,v),puv)>l, q2(x(p(R,p),p2,v),p2,v) = 0. Uniqueness and customer firm separation come from the monotonicity of the profit functions in v, interior solutions to profit maximization, and the relationship between derivatives of the cost functions with respect to v. Normalizing the number of customer firms to unity, the number of IT adopters and aggregate demand for each of the IT enhanced primary goods is N2(p(R,p),R,p) = / h{y)du = H(u(p(R,p),R,p)), "'"min /•"(p(i?,p),i?,p) Q2(p{R,p),R,p) = / q2(x(p(R,p),p2,v),p2,u)h(u)du ''"min ma* N1{p(R,p),R,p)= , , h(u)du = l-H{u{p{R,p),R,p)), Jv(p(R,p),R,p) f v m a x Q1(p(R,p),R,p)= , „ q1(x(p(R,p),Pl,u),Pl,iy)h(v)du Jv(p(R,p),R,p) Chapter 5. Supphers Offering IT Directly to Customer Firms 151 5.6.2 Supplier Profit Maximization Each suppher has a cost function kiNi(p(R,p),R,p) + [a + kf}Qi(p{R,p),R,p) where C j is the constant marginal cost of the IT enhanced primary good (exclusive of IT costs), and the IT costs include an installation cost, kf, and the marginal cost per IT enhanced primary good, kf. While c2 < cx, each of the IT cost components is larger for the superior IT. One suppher, say suppher A, has the inferior IT (z = 1), while the other suppher, say suppher B, offers the superior IT (i = 2). The two supphers simultaneously select two part tariffs for their IT enhanced primary goods. Profit maximization for each IT suppher using a two part tariff is max7ri(p(R,P),R,p) = max[[Ri - k!]Ni{p(R,p),R,p) + fa - a - kf]Qi(p(R,p), R,p)], for i = {1,2}. Investigate first the case where p is determined exogenously. This corresponds directly to Model 4.5. The necessary first order conditions are dni(p,R,p) = dRi N.MP) + ^ ^ [ * - H\ + - « - hf] = 0 diTi(p,R,p) _ dpi dPl [Ri - k(] + Qi(P,R,p) + ^RA^2ll[pi _ C i _ kc} = 0 OPi Chapter 5. Supphers Offering IT Directly to Customer Firms 152 The equilibrium solution to this system of four equations and four unknowns coincides with the results in Model 4.5. From Appendix 5.5 the equilibrium two part tariffs are: Ri-k1 = [-lYNi(p,R,p) -[9i(x(ptPi,i>{p,R,p^),Pi,i>(p,R,p))] [Ni(p,R,p)qi(x(p,pi,i>(p,R,p)),pi,i>(p,R,p)) - Qj(p,R,p)}  c N{(p,R,p)qi(x(p,Pi,v(p,R,p)),Pi,v(p,R,p))•- Qi(p,R,p) Pi — C — K = <*i where if i = 2 then j — 1 and if i = 1 then j — 0, and rp(P,R,p) dq2{x(p,p2,v),p2,v) o-2=l T. h{v)dv • ' " m i l . VPl Ju{pfi,p) dpi and where di>{p,R,p) dR2 [d(2(x{p,p2, v{p, R,p)),p2, i>(p, R,p)) d(i{x(p,pi,i>{p, R,p)),puv(p, R,p)) dv dv a l l J di>(p,R,p) _ 8t(p,R,p)  a l l u 3R2 ~ 3Ri ' Parallel to Model 4.5, the following propositions provide signs of the variable profits for each IT enhanced primary good, and the sign of the fixed profits from the inferior IT. In addition, noting that the variable contribution can be substituted into the equation for the fixed contribution, the sign of fixed profits from the superior IT can be conditionally determined. Chapter 5. Supphers Offering IT Directly to Customer Firms 153 Proposition 5.8: If < g then variable profits from the superior (i = 2) IT enhanced good are positive, if d 9 2 ( a ( p ' p ^ ) , P 2 ' ^ ) > 0 then variable profits from the superior (i — 2) IT enhanced good are negative. Proof: q2(x,p2,v) is decreasing in p2. If D M * ( ^ ) . P ^ ) < Q T H E N p 2 _ C2 _ kc > Qj if dQ2(X(PLP2,u)<P2tu) > Q P2_C2_KC < Q Q Proposition 5.9: If ^ '(PM)*^) < Q then variable profits from the inferior (i = 1) IT enhanced good are negative, if D Q ' ( A ( P ' P ^ ) ' P 1 ' ' / ) > 0 then variable profits from the inferior (z = 1) IT enhanced good are positive. Proof: qi(x,pi,v)is decreasing in P l . If M * ( P , P ^ ) , P I , " ) < 0 then P l - cx - fcf < 0, if dgi{x(P,Puv),Puv) > Q t h e n p i _ C l _ fec > o n Proposition 5.10: If ^ ' H ^ ) ^ ) < fj then fixed profits from the inferior (i — 1) IT enhanced good are positive. Proof: From Proposition 5.9, if d g l ( x ( p ' ^ ) ' p ' ^ ) < 0 then P i - C j - f e f < 0. By assumption d^afl?'^ > "^ AH other terms are positive. Therefore, — k[ > 0. • Proposition 5.11: If ^ ( x ( P , P 2 , ^ ) , P 2 , " ) > Q t h e n fixed p r o f i t s f r o m t h g s u p e r i o r ^ _ 2 ) IT enhanced good are positive. Proof: From Proposition 5.8, if - M * ( P , P ^ ) , P 2 , " ) > 0 then p 2 - c 2 - A f < 0. By assumption 9 I J ^ Q R ^ < 0. Al l other terms are positive. Therefore, R2 — k1 > 0. • Return now to the more general case when factor input prices affect downstream output price. Referring to Appendix 5.5, the solutions to the two part tariffs for the two IT enhanced primary goods come from solving each of the 2 x 2 matrices on the Chapter 5. Supphers Offering IT Directly to Customer Firms 154 major diagonal of A generated by the first order conditions, with p as a function of (R,p). Finding each of the two part tariffs involves derivations similar to Appendix 5.1, except that the derivatives of the marginal consumer and p itself are even more complex. Recalling that the components of the two part tariff from Appendix 5.1 could not be signed, it is not possible to sign the components of the two part tariffs when downstream output price is endogenous. The discussion at the end of Model 4.5 concerning non adopters and/or an origi-nal primary good, concavity of the profit functions, restrictiveness of strictly positive demands, and a fixed IT implementation cost, applies equally to this model. Chapter 5. Supphers Offering IT Directly to Customer Firms 155 5.7 Analysis: Parallels Between Pricing Strategies for Suppliers to Con-sumers and Suppliers to Customer Firms Model 5.1 through 5.5 have shown that under certain conditions the pricing problems and resulting strategies studied in the last chapter (supphers directly to consumers) are equivalent to the IT and IT enhanced primary good pricing problems and resulting strategies for supphers offering IT and IT enhanced primary goods as factor inputs to customer firms here. Assuming that the pricing components being selected by supphers are the same as in the preceding chapter, two conditions required for equivalency. The first condition for equivalency is that there is no feedback loop between factor input prices and the downstream output prices faced by customer firms5. Exphcitly, if the downstream output price for customer firms, p, is unaffected by the factor input pricing components then this pricing problem yields precisely the same results as in the previous chapter6. To see this, recognize that if downstream output price is exogenous then p is a fixed parameter in £(•), £(•)> (^-)> and £>(•) derived in this chapter's models. The second condition required for equivalence is that either case (1) dq{xip^)'F^ > 0 or case (2) M*{PW)W) < o h o l d s E x a c t equivalence obtains in case (2), the signs in Propositions 5.2, 5.3, 5.6, 5.8, and 5.9 are reversed with case (1). These conditions mean that factor input demands for each of the primary goods is either always increasing (case (1)) or always decreasing (case (2)) in the efficiency of the customer firm, represented by the cost parameter v. Thus, for producing customer firms, either less efficient customer firms always require larger inputs or more efficient customer firms need greater inputs, regardless of relative optimal output levels. 5Schmalensee, [41], outlines and uses this notion in his seminal article on monopolist two part pricing. 6 As footnoted earlier, the reversing in ordering of v as compared to 6 is eliminated by a reversal in signs of the derivatives of the marginal customers firms/consumers. Chapter 5. Supphers Offering IT Directly to Customer Firms 156 The question then is: how feasible are the conditions required for equivalency? First examine the exogeneity of p. There are two scenarios in which it can be reasonable to have customer firm output prices unaffected by factor input prices. First, this independence can occur if customer firm actions have no impact on price in their downstream output markets. Second, this independence can occur if the cost of the primary good factor input is such a negligible proportion of the total cost of providing the downstream output that neither downstream outputs nor the factor input mix is affected. Therefore, changes in the cost of the primary good factor input has a negligible effect on downstream output prices. Turning to the second condition, is it sensible that individual factor input demands of producing customer firms are rnonotonically increasing or decreasing in the cost param-eter vi By assumption, for a fixed level of output, higher v customer firms are no more efficient in their use of factor inputs than those represented by lower v. However, optimal output levels may vary among customer firms so that more efficient customer firms pro-duce higher levels of output at their optimum, and in spite of being more efficient require more of the primary good factor input. As a result the general relationship between factor input quantities and v is indeterminate, as can be determined using calculus: dq(x(p,p,v),p,v) = dq(x{p,p,v),p,v) dx(p,p,v) dq{x(p,p,v),p,v) dv dx dv dv The first term represents the indirect effect of v through the optimal output level, with the second term being the direct effect representing relative production efficiency. As factor inputs are increasing in outputs, d q ^ , v ) > 0. But from the properties of the profit function, d x ^ p ' v ) < 0 (as shown in Model 4.1), so the first term is negative. In many cases the relative superiority of one customer firm over another comes not from efficiencies in use of the primary good, but from efficiencies in other areas, for example plant operating costs. Hence, relative efficiencies between customer firms in their use of Chapter 5. Supphers Offering IT Directly to Customer Firms 157 factor inputs can also be zero, giving d q ^ , l > ) > fj. Chapter 5. Supphers Offering IT Directly to Customer Firms 158 5.8 Conclusions The most important conclusion from this chapter is that with no impact of factor input prices on downstream output prices, and with individual customer firm factor demands monotonic in their cost efficiency, the pricing results derived for supphers offering IT to consumers hold for supphers offering IT to customer firms. If the factor input prices do affect downstream output prices then, referring to the earlier results, the outcomes from this chapter are as follows. Interdependence of the two pricing components continues to be critical. In contrast to the previous results, for the one IT suppher duopoly it has not been shown to be optimal for the IT suppher to abandon the original primary good. For two supphers competing in two part tariffs with identical IT an asymmetric price pair equilibrium has not been ruled out, and existence of a symmetric price equilibrium has not been confirmed. Chapter 5. Supphers Offering IT Directly to Customer Firms 159 5.9 Appendices to Chapter 5 5.9.1 Appendix 5.1 The necessary first order conditions for an optimal two part tariff of an IT enhanced primary good can be rearranged as dN(P(RP),R,p)[R _ fc/] + dQipiRplR^)^ _ c _ k c ] = _ N { p { R i p ) t R t p ) dR dR dN(P(Rp),R,p) _ fc/ + dQ{p(R,p),R,p) _ c _ k c ] = - Q { p { R i P ) , R , p ) t dp dp w l fhich can be represented by Ay = d where y' = [[R — k1} [p — c — kc]], d' = [-N(p(R,p),R,p) - Q(p(R,p),R,p)] and A is A = Solving for the total derivatives in A gives / dN(p(R,p),R,p) dQ(p{R,p),R,p) \ dR dR . dN(p(R,p),R,p) dQ(p(R,p),R,p) . \ dp dp I dN(p(R,P),R,p) dR dO(p(R,p),R,P) h(0(p(R,p),R,p))-+h(i>(p(R,p),R,p)) dR du(p(R,p),R,p)dp{R,p) dp dR dQ(P(R,p),R,p) = dR q(x(p(R,p),p, t(p(R, P), R,p)),p, 0(p(R,pl R,p))h(u(p(R,p), R,p))Mp{R^R]> R ' p ) ^q(x(p(R,P),p,v(p(R,P),R,p)),p,0(p(R,p),R,P))h(u(P(R^ di>{p(R,p),R,p)dp{R,p)  [ dp dR J ri>{p(R,P),R,p) dq(x(p(R,p),p,v),p,v) dp{R,p) r(P(H,PhH,p) dq'x{p{R,p),p,v),p,v)^t  + [ L . dp ~ h { u ) d u ' dR Chapter 5. Supphers Offering IT Directly to Customer Firms 160 dN{p{R,p),R,p) dp du(p(R,p),R,p) h{v(p{R,p),R,p))-+h(i>(p{R1p)1R,p)) dp du(p(R,p),R,p)dp(R,p) dp dp dQ(p{R,p),R,p) = dp q(x(p(R,p),p,0(p(R,P),R,p)),p,u(p(R,p),R,p))h(u^ fo(P(RlP),R<P) dq(x(p{R,p),p,u),p,u)Lf + [/ « h{u)du\ •'•'min OP ^qixipiR^lp^ipiR^lR^^^p^ipiR^l^p^hiuipiR^yR^))] di>{p(R,p),R,p)dp(R,p)  [ dp dp 1 fu{p{R,P),R,P) dq(x(p(R,p),p,u),p,u)u/ ,dp(R,p) + [ L , ——dp h ^ ~ d p ~ -To determine the derivatives of u(p, R,p) define an imphcit function ijj(u,p,R,p) = px(p,p,u) - £{x(p,p,v),p,v) - R - K = 0, so that dip(v,p,R,p) djj(i>,p,R,p) -\ -\ M = - 1 , g-p = -q(x(p,p,u),p,u), dtp(u,p,R,p) di>(i>,p,R,p) d((x(p,p,i>),p,v) dp—=x{p>P>u)> du— = du ' where (interior) first order conditions for customer firm profit maximization cancels terms. Using the implicit function rule, du(p,R,p) d((x(p,p,u),p,i>) dR / [ du J Chapter 5. Supphers Offering IT Directly to Customer Firms 161 dv{p,R,p) dp l ( -\ «\n0t{x{p,P,v),P,v)^ ^ n -q(x(p,p,v),p,v)/[ < 0 dv dp = x ^ v ^ dv ] > °" Therefore, the derivatives are related by dv(p,R,p) dv(p,R,p) dp =*MP>P>»)>P>V) 9R 9v(p,R,p) dv{P,R,p) dp =~X^P^ DR • The derivatives of p(R,p) are also required. Following [41], implicitly define p(R,p) by rO(p,R,p) HP, R>P)= / x(p,p,v)h(v)dv - D(p) = 0 which, using D(p) as the demand function for downstream output, is the partial equilibrium condition of supply equal demand in the downstream output market. The foUowing derivatives obtain: 9<P(P,R,P) i -/ „ p ^dv{p>R,p) „ n — — = x{p,p,v{p,R,p))Hv{p,R,p))—ox— < o d(j>{p,R,p) = dp x{p,p,v{p, R,p))h(v{p, R,p)) + / h(v)dv < 0 op Jv„un dp Chapter 5. Suppliers Offering IT Directly to Customer Firms 162 d<p(p,R,p) = dp x{p-,P^{p,R,p))h{u{P,R,p))du^P,R,P^ dp + rWO*(pp,v) h{u)d„_d_m>0, Jvin.in dp dp where q(x,p, v) is a normal input. Using the imphcit function rule, dp(R,p) _ -x(p,p,u{p,R,p))h(i>{p,R,p))&l^ QR d<p{p,R,p) dp > 0 dp(R,p) = dp -x(Pip,u{p,R,P))h(Hp,R,p))§SL^£l - g f ' p ) M f ^ M ^ 8(j>(p,R,p) dp so that dP(R,p) = dp q(x(p,p,i)(p, R,p)),p, v(p, R>P))dp^P^ rC{P,RlP) dx{pw)h,sdv " d<t>(p,R,p) ' dp where d4>(p>fl>p) i s defined above. dp The effects of R and p on the marginal customer firm also come through p(R,p). Therefore, Chapter 5. Supphers Offering IT Directly to Customer Firms 163 du(p(R,p),R,p) _ dR dv{p,R,p) di>(p,R,p)dp{R,p) = dR dp dR dP(R,p) r i ^ ' p ) a-^Ku)du -dR x(p(R,p),p,i>(p(R,p),R,p))h(u(p(R,p),R,p)) and < 0 dt>(p(R,p),R,p) _ dp dC>(p,R,p) di>(p,R,p)dp(R,P) = dp dp dp d£>(p(R,p),R,p) -q(x(p,p,u(p,R,p)),p,i>(p,R,p)) 4 dR dP{R,p)&)d-^h{u)dv dR h{u(p,R,p)) The first term of ^P(RJP)<R<P) is positive, the second is negative. Therefore, it cannot be signed. Returning to the components of y, solving using Cramer's rule or through the inverse matrix requires the following determinant: |A| = dN(p(R,p), R,p) dQ(p(R,p), R,p) dN(p{R,p), R,p) dQ(p{R,p), R,p) dR dp dp dR fo(P(R,p),R,P) dq{x{p{R,p),p,v),p,v) = [ h[u)dv\ JVmin Op \h(u(p(R,p),R,p)) — +h(v(p(R,p),R,p))-dR ' v v r v dp dR i>{p(R,p),R,p) dq(x(p(R,p),p, v),p,i/). dp~ fu(P(n,P),n,P) 0q(x{p{K,p),p,v),p,v)uf + [ Q h{u)du J^tllin OO Chapter 5. Supphers Offering IT Directly to Customer Firms 164 [h{is{p{R,p),R,p)) — -Lht-f in \ j? ^d{)(p(R>P)>R>P)dP(R,P)i +h{iy{p{R,p),R,p)) — ]. Both terms involving derivatives of i>(p(R,p), R,p) in the square brackets cannot be signed, hence the sign of |A| is ambiguous. No useful cancellations obtain solving for R — k1 and p — c — kc. Therefore, the signs of the contributions for both components of the two part tariff, for the case where downstream output price is a function of factor input prices, are ambiguous. Concavity of the supplier's profit function is assumed. Chapter 5. Supphers Offering IT Directly to Customer Firms 165 5.9.2 Appendix 5.2 The first order conditions for the monopolist offering both the IT enhanced and original primary goods, when p is exogenous, can be rearranged into: dN(p,R,Pl,p0) j dQi(p,fl,Pi,Po) r , c i dR + QR I P i - c i - * 1 dQ0(p,R,p1>Po) + dR [ P o c0] = -N(p,R,p1,p0) dN(p,R,Pl,po), 7 . dQx{P)R,p1,p0) c [R -k] + \pi - ci - As <9pi dPl dQ0{p,R,Pi,po) + dp i [Po - c0] = -Qi(p,iZ,Pi,Po) dN(p,R,p1)p0) j dQ1{p,R,p1,p0){ c . - fc + • — 5 ^ i - ci - fc <9po "Po dQ0{p,R,Pi,po), i /o /- D ^ + ^ -[Po ~ c0J = -Qo{p,R,Pi,Po)-dp0 This system can be represented by the matrix equation Acc = d where now I R-k' \ Pi - ci - kc \ Po - c0 J d = 1 -N{p,R,pupQ) A -Qi(p,R,Pi,Po) V -Qo(p,R,puPo) Chapter 5. Supphers Offering IT Directly to Customer Firms 166 A = V dR dR dR dN{p,R,P1 .Po) dQi(p,R,pi dQo(p,R,Pi,po) dpi dpi dpi dN{p,R,pi .Po) dQi{P,R,pi .Po) dQ0(p,R,pi,pv) dpo dpo dpo As earlier, the elements of A can be found, and they are dN{p,R,pupo) T) ^9v{p,R,PuPo) — = h{v{P,R,Pi,Po))-dR dR 9Qi{p,R,Pi,Po) _ dR qi(*(p,Pi,HP>R>Pi>Po)),Pi,Hp>R>Pi>Po))h(v(p,R,Pi,Po)) di>(p,R,p1,p0) dR dQo(p,R,Pi,Po) _ dR -q0(x(p,p0, v{p, R,pi,p0)),p0, v{p, R,Pl,p0))h(i>(p, R,pup0)) dv{p,R,Pi,Po) dR dN(p,R,pup0) di>(p,R,pl,p0) — = HnP,R,Pi,Po))-dpi dpi dQi{p,R,pi,po) dpi <>(P,R,PI,P„) dqi(x(p,pi,v),Pi, v) t"\p, Jvmin dpi h(v)du +qi(x(p,pi,P(p,R,p1,p0)),pi,0(p,R,Pi,Po))h(j>(p,R,pi,p0)) dv{p,R,Pi,Po) dpi dQ0(p,R,puPo) _ dpi -q0(x(p,p0,i>(p,R,pi,p0)),p0,i>(p,R,pi,p0))h(i>(p,R,pi,p0)) dv(p,R,Pi,Po) dpi Chapter 5. Supphers Offering IT Directly to Customer Firms 167 dN(p,R,pup0) . . . . D dv(p,R,pup0) = h{u{p,R,pup0)) T, op0 OPo 9QI{P,R,PI,PO) _ dp0 qi{x(p>Pi,v(p,R,Pi,Po)),Pi,i>(p,R,Pi,Po))h{i>(p,R,Pi,po))dU^P dQo{p,R,p1,p0) _ dp0 JO(P,R,PIJ>O) dp0 -q0(x(p,Po,v(p,R,Pi,Po)),Po,v(p,R,Pi,Po))HHP,R>Pi,Po))9"^P Following the analysis in Appendix 4.2, with some minor changes in signs, the marginal contributions to profit of each of the pricing components is R-k1 = -N(p,R,p1,p0) h(v(p,R,Pl,p0))8^f^ -[qi(z(p,Pi,HP>R>Pi>Po))>PuHP>R>Pi>Po))] [N{p,R>Pupo)q1{x(p,p1,t>(p,R,pl,po)),p1,u{p,R,p1,p0)) - Qi(p,R,Pi,Po)] i-P(p,R,pi,pu) 8<?i(x(p,px,u),p uv)^/ J " r a i n dpi \ ' - [ g o ( » ( P i P o , v{p, R,PI,PO)),PO, v{p, R,PI,PO))] [N(p, R,Pi,Po)qo(x(p,po, u(p, R,PuPo)),Po, v{p, R,Pi,Po)) + Qo{p, R,Pi,Po)] rv,n-ar- dqn(x(p,pl),v),Pn,v) u (,.\j,t _c _kc _ N(p,R,pup0)q1{x(p,p1,i>(p,R,p1,po)),pl,v'{p,R,p1,po)) - Qi{p,R,Pi,Po) P l C l ~ rv{P,R,P\ ,P» ) 81l ( x ( P , P l ,V),P1 ,V) fofjy^dj; •>vllbin dpi \ ' Chapter 5. Supphers Offering IT Directly to Customer Firms 168 _ NJP, R,Pi,Po)q0(x(p,Po, i>{p, R,Pi,Po)),Po, "{p, R,Pi,Po)) + Qo{p, R,puPo) p o C o g;iP 1,o) 8 g o ( E (xr )' p o" )M^)^ where 90(p,R,Pi,Po) 8R - 1 9Ci(a(p,Pi fi(p,R,Pl ,P0 ) ) , P i fi{p,R,Pl , p o ) ) _ 3Cn(a(p,po ,£ (p , .R ,p i ,po ) ) , p 0 , i ^ ( p , f l , p i , p p ) ) ' Concavity of the supplier's profit function is assumed to ensure the pricing components derived above are optimal. Chapter 5. Supphers Offering IT Directly to Customer Firms 169 5.9.3 Appendix 5.3 With downstream output price exogenous, the two first order conditions for suppher A's two part tariff and the first order condition for suppher B choosing p0 can be rearranged as aN(p,R,ri,PJ)[R _ k I ] + a Q ^ , R , P l , P 0 ) ^ _ c ] _ k C ] = _ Q l ( , > B i P l j P o ) dpi dpi dQo(p,R,pi,p0) dp0 [Po - c0] = -Qo(p,R,Pi,Po)-In matrix equation form, Ax = d, ( R - y \ Pi- a - kc \ Po c0 / d = ( -N(p,R,pi,Po) X -Qi{p,R,Pi,Po) \ -Qo(p,R,pi,po) j ( dN(p,R,Pl,py) aQ1(p,R,p1j>„) dR dR 8N(P,R,Pl,pu) 9<?i(p,flj>i ,Po) dpi dpi 0 0 dQlt(p,R,pi,Po) c5po Chapter 5. Supphers Offering IT Directly to Customer Firms 170 The derivatives in A are identical to those in Appendix 5.2 and are not redone here. Following the analysis in Appendix 4.3, with some minor changes in signs reflected in Appendix 5.2, the equilibrium marginal contributions to profit are R- k1 = -N(p,R,pup0) h(u(p,R,puPo))^pf^ -[<li(x(p,Pi,i>(p, R,Pi,Po)),Pi,t(p, R,Pi,Po))} [N(p,R,p1,p0)q1(x(p,p1,i>(p,R,p1,po)),p1,i>(p,R,pl,po)) - Qi(p,R,pi,p0)] rv(p,R,P1,p0) dqi(a(p,pi ,"),pi i ^ u ^ y ^ •>Vmin dpi \ ' 1 C Pi - C l - k = N(p,R,p1,p0)q1(x(p,pl,i>(p,R,p1,po)),p1,u(p,R,p1,po)) - <?i(p,iZ,Pi,po) r £ ( p , R , p i , P o ) 5 g i ( z ( p , P i ,v),pi ,u) ^/^ • ' " m i l l 9 p i V ' Po - c 0 = -Qo(p,#,Pi,Po)/ r / " " 1 ^ gg0(a;(p,po,t/),po,i/) [/ h[y)dv Jv(P,R,Pl,po) OPO -q0{x{p,p0,i>{p,R,Pi,po)),Po,v{p,R,Pi,Po))h(i>(p,R,p1,po))dl' P , R ' P l , P o ] "Po where du(p,R,pup0) dR - 1 dCi(g(p,Pi,v{p,R,Pi,P»))>Pi,i>(p,R,pi ,po)) _ gCu(a(p,po,£(p,R,pi,Po)),p(),i;(p,fl,pi,po)) and Chapter 5. Supphers Offering IT Directly to Customer Firms 171 dv(p,R,pi,p0) dJ>(p,R,pltp0) \\ -t j> w 0^ = qo{x(p,po,v{p1Ryp1,po)),po,u(p,R,p1,p0)). Concavity of each supplier's profit function is assumed. Chapter 5. Supphers Offering IT Directly to Customer Firms 172 5.9.4 Appendix 5.4 Similar to Appendix 4.4, with p exogenous, each suppher has two necessary first order conditions for profit maximization, 9^{p,R,p) 8R{ Ni(p,RtP) + dR1 dRi dpi dp1 for i = {A, B}. Rearranging terms and putting the four equations together in a system yields Ax* = d where / RA - k1 ^ p A - c - k c RB — k1 \pB - c - kc j x — 1 -NA(p,R,p) ^ -QA(p,R,p) -NB(p,R,p) \ -QB(P,R,p) ] A = ( 8NA(p,R,p) 8QA(P,R,P) 8RA 8RA dNA(P,R,p) dQA(p,R,p) 8pA dpA 0 0 0 0 0 8NB(p,R,p) 8QB(p,R,p) 8RB 8RB 8NB(P,R,p) 8QB(p,R>p) 8pB &pD Chapter 5. Supphers Offering IT Directly to Customer Firms 173 A can be partitioned into two 2 x 2 matrices on the major diagonal. Solving for suppher A's price pair (RA,pA) is the same problem as in Appendix 5.3, except the marginal customer firm is i>(p,R,p). Using the implicit function rule, and the definition of u(p, R,p), du(p,R,p) = 8RA vM(x{p,PA,Hp,R,P)),PA,v(p,R,P)) _ 9C(x(p,pB,0{p,R,p)),pB,i>(p,R,p))] Moreover, again using the imphcit function rule, du{p,R,p) du(p,R,p) A A _. A —dp^— = —d~RA—Q (X(P>P 'HP,R,P)),P ,HP,R>P))-Solving for suppher A's equilibrium prices results in RA-kI = -NA(p,R,p) hiuip,^))8^} -[qA(*(p,pA, HP, R,P)),PA,HP, R,P))) [NA(p,R,p)qA(x(p,pA,u(p,R,p)),pA,u(p,R,p))-QA ri>(p,fi.tp) 8qA(x{p,pA ,v),pA ,w) . _ NA(n , p - c-k A l C NA(p,R,p)qA(x(p,pA,u(p,R,p)),pA,u(p,R,p))~QA(p,R,p) ru(p,R,p) dqA (x(p,pA ,w),pA ,v)y\£ For supplier B's price components u(p,R,p) delimits the upper rather than the lower end of the customer firms suppher B serves. Focusing on the lower right 2 x 2 submatrix of A, the elements are: dNB(P>R,p) du{pXp) dRB = ~hMP>R>r)) dRB Chapter 5. Supphers Offering IT Directly to Customer Firms 174 8QB(p,R,p) B B ••( B "w B 5 -\\uc-( p ~\\dHp>R>Pl —o^B— = _ 9 (xyp>p MP>R>P))>P ,np,R>p))hnp,R,p))—QftB— 8NB(p,R,p) ~ ^8i>(p,R,p) ^ = -h(u(p,R,p)) ^ dp1 8QB(p,R,p) dpB JO(p,R,p) dpB -qB(x(p,pB ,i>(p,R,p)),pB tO{pXvl)h{^pXvl)^^-where dO{p,R,p) = dv(p,R,p) 8RB 8RA ' As above, dv{p,R,p) di>(p,R,p) B B •• ( p -\\ B ••( n —dp = — 8 R B q ^ P , P >u(p>R>p»>p >U(P>R>P)) Using matrix inversion the submatrix can be solved, and the resulting prices are RB - k1 = NB(P,R,p) h{v{p,R,p))^^ - k B (x(p, pB, i>(P> R,p)),pB,i)(p,R} p))] [NB(pJj)qB(x(p,pB,i)(p,R,p)),pB,i>(p,R,p))-QB(P,R,p)} B_ kc = NB(p,R,p)qB(x(p,pB,u(p,R,p)),pB,i){p,R,p))-QB(p,R,p) Each supplier's profit function is assumed to be concave. Chapter 5. Supphers Offering IT Directly to Customer Firms 175 5.9.5 Appendix 5.5 Similar to Appendices 4.5 and 5.4, where p is exogenous, each suppher has two necessary first order conditions for profit maximization, 8N>(pJ,r)[R2 _ k l ] + dQ,(p,R,p)fo _C2_ t c j 0p2 op2 dpi dpi -N2{p,R,p) -Q2{p,R>P) -Ni(p,R,p) -Qi(p,R,p). Rearranging terms and putting the four equations together in a system yields Ai* = d where 1 R 2 - y x X = d = p2 - c2 - kc Ri - k1 \ Pi - ci - kc J ( -N2(p,R,p)^ -Q2(p,R,p) -Ni(p,R,p) \ -Qi(p,R,p) ) A / 8N2(p,R,p) 8R2 8Q2(p,R,p) 8R2 0 0 8N2(p,R,f) dp2 8Q2(p,^,p) 9p2 0 0 0 0 9N1(p,R,p) aRi 8Q1(p,R,p) 8Ri I 0 0 9 A T i ( p , f i , p ) 9 p i S Q , ( p , f l ^ ) 9 p i Chapter 5. Supphers Offering IT Directly to Customer Firms 176 Partitioning A into two 2 x 2 matrices on the major diagonal and solving for each supplier's two part tariff is the same as in Appendix 5.4, except the marginal customer firm is u(p,R,p), and each suppher offers a different IT enhanced primary good: suppher A has the inferior IT (i = 1) and suppher B has the superior IT (i = 2). Omitting the details of the derivation, the equihbrium two part tariffs are: Ri - k1 = l-lYNi(p,R,p) h(u(p,R,p))^} [Ni(p,R,p)qi(x(p,pi,v(p,R,p)),Pi,v(p,R,p)) - Qi(p,R,p)] p A - c - k c = Ni(P,R,p)qi(x(p,pi,i>(p,R,p)),pi,i>(p,R,p)) - Qi(p,R,p) where if i — 2 then j = 1 and if i = 1 then j = 0, and MP,R,P) dq2{x{p,p2,v)1p2,v) and where dv{p,R,p) dR2 d({x(p,P2,'>{p,R,p)),P2,i>{p,R,p] du ')) dC{x(p,p1,i>(p,R,p)),p1,i>(P,R,p)) du and Chapter 6 Empirical Examination 6.1 Introduction The empirical examination focuses on an example from the suppher to customer firm case, modelled in the previous chapter. The objective is to study both the analytical models' assumptions and test the pricing results. The undercurrent of this chapter is that this is a case where IT creates a differentiated primary good, and this differentiation provides some positive value to the customer. Thus, the IT enhanced primary good suppher should extract rents from customers based on the additional value the IT offers. The chapter is organized in the following sequence. First, a description of the sup-plier used in the study is provided, followed by an outline of the research methodology. Then the results from each of the two components of the empirical research strategy are presented. Finally, to compete the chapter, implications of the results are discussed. 177 Chapter 6. Empirical Examination 178 6.2 The Research Site and the IT The research site used was Pacific Pride Systems in Salem, Oregon ([33]). Pacific Pride is a commercial vehicle fueling system. The fueling system is comprised of a network of fuel stations covering most of the west coast of the United States, particularly the Pacific northwest. Customers are typically firms or organizations which maintain a fleet of vehicles. Customer firm sizes range from trucking companies moving freight along the interstate highways (large) to a local florist operating one or two delivery vans (small). The commercial fueling stations are unattended (i.e. no fuel station attendant), and operate similarly to an ATM: a driver enters the vehicle into the fuel station and inserts a plastic punched card into a card reader, inputs an identification number and optionally the vehicle oedometer reading, and is subsequently allowed access to the fuel pumps. The system then collects data on the amount of fuel purchased and time/location stamps the fuel transaction1. These stations are referred to as "cardlock" stations At the end of a billing period the customer firms receive an itemized ("country club") bill, which includes the card number, the personal identification number of the card user, the amount of fuel purchased, the time and location of the purchase, and optionally the oedometer reading at the time of the fuel purchase, for each transaction. This informa-tion allows customer firms to control their fuel costs by monitoring the fuel transaction. Moreover, the fueling decision is taken out of the hands of the vehicle driver: the driver must purchase fuel at a station on the Pacific Pride network. 1More information on the technical aspects of the system can be found in [33], or can be obtained from the author. Chapter 6. Empirical Examination 179 6.3 Research Methodology The research methodology is made up of two parts: a quahtative component and a quan-titative component. As the models were formulated and completed prior to the empirical work, the quahtative study focuses on the assumptions associated with the characteriza-tion of IT and other additional assumptions required in the analytical modelling process. The quantitative examination concentrates on testing the relationship between prices of fuel at retail fuehng outlets and prices of fuel at Pacific Pride's cardlock stations. Thus, the research strategy is able to study both the assumptions behind the models as well as to test some of the models' pricing results. 6.3.1 Studying the Assumptions of the Models With respect to the suppher to customer firm case, recall from Chapter 3 there were four aspects to the characterization of IT: • customer firms obtain decreased production/turnover costs (exclusive of primary good and IT pricing) from adopting IT and using the IT enhanced primary good • customer firms incur some positive internalization switching cost from the adoption of IT • supphers obtain decreased marginal costs in providing the IT enhanced primary good (exclusive of IT costs) • suppliers have an IT cost structure which can be described by a fixed implementa-tion/operation cost, an additional one time installation cost for each new customer on the system, and a marginal cost per transaction There are three additional assumptions which were found to be important: Chapter 6. Empirical Examination 180 • whether suppher pricing on the primary good impacts the price of the downstream output • whether individual customer firm factor demands are monotonic in customer firm efficiency • whether two part tariffs are being used From the analysis in Chapter 5, the first of the additional assumptions is important because it determines if the more powerful results from the suppher to customer firm case apply. That is, this assumption is one of the two conditions for equivalency of the models in Chapters 4 and 5. The second is a technical assumption, the other condition required for equivalency between pricing strategies for suppliers to consumers and supphers to customer firms. The third is a pricing pohcy assumption, a feature the conceptual and theoretical module of this research suggests is normatively important. Note that the case of the fixed component of the two part tariff being zero is included in the earlier analytical models. The data collection strategy used was a structured interview with two of the execu-tives from Pacific Pride. The structure was derived straight from the assumptions listed above. Therefore, a directed interview was possible, ensuring that each assumption was covered in the discussions. The interview was audio taped, with the permission of the participants. This allowed the researcher to have transcripts of the interview from which in depth data could be gathered. Items pertaining to each assumption were taken from the transcripts by the researcher and independently by another investigator. The two sets of items were then compared and areas where there was no overlap were resolved by reexamining the transcripts of the interview. Chapter 6. Empirical Examination 181 It is understood that a more ambitious methodology would include not only direct contact with the supplier, Pacific Pride, but also with commercial fuehng customers. However, see [33] for some confirming anecdotal evidence directly from customers. 6.3.2 Testing the Pricing Results The pricing models point towards two general relationships which can be examined em-pirically: (1) the relationship between the per unit price of the original primary good and the per unit price of the IT enhanced primary good; (2) the relationship between the two components of the two part tariff. To study either or both of these relationships required the following data for a common period: • a time series of original primary good prices • a time series of IT enhanced primary good per unit prices • a time series of fixed taxes or subsidies to new adopters, if any Pacific Pride was able to provide the first two components of the data set, as they maintain both retail fuel outlets and cardlock outlets. Bi-weekly data was available for the period beginning January 1987 to June 1988, or 36 observations. Per gallon fuel prices were gathered for regular and unleaded gasohne, at both retail and cardlock outlets associated with Pacific Pride as well as the acknowledged retail price leader in the area (Arco, Atlantic Richfield Co.). The retail data was collected for two cities in Oregon, Salem and Eugene. These were considered in the same cardlock pricing region, thus the same cardlock fuel price series apphed to both cities. The retail outlets data were taken from competitive pricing surveys conducted in each city, at least 3-4 times per month. Cardlock outlet prices were taken from computer reports produced at Pacific Pride, detailing cardlock prices for each region in the network. Chapter 6. Empirical Examination 182 As will be discussed later, Pacific Pride does not use an explicit two part tariff for its cardlock network. Moreover, costs of getting a customer on the system were not available in time series form. Therefore, a time series of fixed taxes or subsidies, exphcit or implicit, was unavailable. As a result it was not possible to examine the relationship between the two components of the two part tariff, (2) above. Observations of the cardlock fuel prices and retail fuel prices were not perfectly matched; the date of the city fuel price surveys and the date on the computer generated cardlock fuel prices did not always match exactly. However, the computer generated cardlock fuel price observations included each and every price change made to any of the regional cardlock prices, thus the cardlock prices in the intervening periods were known. For retail fuel outlets it was assumed that prices were stable through the periods of time between retail fuel price surveys. Although it is possible that more than one price change was made at the retail fueling outlets between two price surveys this was unhkely as overall fuel prices turned out to be surprisingly stable. Again, a more ambitious empirical study would favour tracking a wider set of fuel prices, more outlets in a given geographical area and/or data spanning a larger region. Chapter 6. Empirical Examination 183 6.4 Analysis and Results: Analysis of the Models' Assumptions The four assumptions associated with the characterization of IT are covered first, followed by the policy and technical assumptions. 6.4.1 IT Decreases Customer Firm Costs The first element in the characterization of IT is that IT can decrease the customer firm's costs of producing or turning over the downstream good, exclusive of the primary good's (factor input) cost. In the Pacific Pride case this assumption translates into a cost reduction for commercial fuel customers due to using Pacific Pride's cardlock system, exclusive of the price per gallon paid for fuel. Pacific Pride described the cost advantages they provide to customer firms as hnked to the "three Cs": convenience, control, and credit, which are discussed in turn. In terms of convenience Pacific Pride's customers have access to a network of fueling stations (multiple outlets), 24 hours a day, 7 days a week, and drivers are not required to carry cash or credit cards. Typically, it takes the drivers less time to refuel as lineups at retail stations are avoided (i.e. the general pubhc does not have access to the cardlock stations). Customers receive only one itemized bill (bi-weekly) for fuel purchases throughout the network which saves on transaction and monitoring costs. In addition, more timely information can be made available should customers require it. As a substitute, some of the larger customers have the option of maintaining their own fuel depots. However, the underground storage tanks needed for this type of operation require constant monitoring for leaks and are subject to extensive government regulation, both of which incur significant overhead. Furthermore, there is still the potential problem of requiring multiple fueling locations. Control plays a large part in customer cost savings. The ability to avoid giving drivers Chapter 6. Empirical Examination 184 cash, or credit cards for fuel saves the very real possibihty that drivers and/or fuel station attendants will divert some of the funds that are recorded as being fuel purchases for personal use2. Essentially the cardlock system removes the fuehng decision from the customer firm's drivers, thereby removing some of the potential moral hazard. Moreover, the activity control from the itemized billing gives a time and location stamp for each transaction, providing further ability to track and monitor drivers. This full reporting feature is used by some customers to schedule maintenance on their vehicle fleet. The problem of pilferage from a customer's proprietary underground storage tanks is also eliminated by adopting the cardlock system. Credit is the last area where customers can reduce costs. As compared to cash or elec-tronic funds transfers the bi-weekly billing extends some credit to customers. General use (e.g. Visa) or fuel specific (e.g. Shell) credit cards also have this feature, although there can be additional charges for use of these cards. As one would expect, it was confirmed that larger customers obtain greater benefits, in both absolute value and proportionally, than smaller customers. There seems to be ample evidence that the above cost reductions are recognized and accounted for by customers: Pacific Pride's customer base is large and growing. 6.4.2 Customers Incur Internalization Switching Costs Adopting IT The second characterization of IT is that IT adoption, or changing from one IT to another, entails some internal switching cost on the part of the customer; its drivers, dispatchers, and accounting department. Pacific Pride beheves the customer's switching costs to be low, but not necessarily zero. There is a small cost to training drivers to use the cardlock equipment. This was considered a larger problem if the driver has limited hteracy skills. There is an additional cost of issuing and distributing cards to the drivers, which is 2Both [33] and the author's personal experience strongly support this possibility. Chapter 6. Empirical Examination 185 usually borne by the customer's dispatcher. Thus, the dispatcher becomes an important component to ensure smooth transition to the cardlock system. The customer must also sell the concept to drivers. Common objections from drivers are that they benefit from truckstops that have food and shower facilities. These voiced objections may suggest underlying extra costs from driver resistance: drivers dishke the rigid controls, and miss the social aspects of regular truck stops. One of the key education/training costs is that it takes drivers three to six months to locate all the cardlock fuehng stations on a particular route. Moreover, as new stations are added to the system it takes drivers time to find these new locations. Finally, there is some immediate internal costs of adjusting to new reports, billings, etc., although transaction costs would fall after these adjustments. 6.4.3 IT Decreases Supplier Costs The third characterization of IT assumption is that IT decreases the supphers' costs of producing and/or delivering the primary good, exclusive of IT costs. Cost per billing at Pacific Pride have been reduced due to the IT. All of the transactions are on one system, thus all transactions relating to each customer can be put on one bill automatically. Typically the cost per billing is $5, with bi-weekly billing making this total $10/month. Pacific Pride sees a customer's fuel purchases of 200 gallons/month as sufficient to offset this cost, hence providing rationale for their 200 gaUons/month minimum fuel purchase. Obviously, part of this billing cost is a per transaction IT cost which must be compared with the costs of producing the same kind of billing manually. Overhead costs associated with the network has a slightly different structure than the overhead associated with retail fuehng. Overhead in the network includes costs for data communications between the nodes and the central system, and some systems maintenance, all of which are classified as IT costs. In contrast, the main cost in retail Chapter 6. Empirical Examination 186 fueling is the direct labour component. The cardlock system has an advantage in that its overhead costs are mostly fixed which provides it with economies of scale, in contrast to retail fuehng where direct labour is a mixed cost. 6.4.4 Pacific Pride's IT Costs From Chapter 3, IT costs were hypothesized as being made up of three separable com-ponents: an initial fixed implementation and operating cost, an installation cost for each new customer on the system, and a marginal cost per transaction. Although the Pacific Pride executives provided little information about the costs of implementing the central component of the system, they indicated the costs of equipment at each additional node (station) in the cardlock network were priced between $30,000 and $65,000. Fixed oper-ating costs were alluded to in the preceding section: there are data communication costs between each node and the central Pacific Pride system which are incurred at standard intervals, and costs for check ups and maintenance both at each node site and at the central system. The costs of putting a new customer on the system were quoted as being between $200 and $500 per customer. However, these costs include non IT costs such as credit investigations, card costs, and salesperson compensation for acquiring the new account. Of the $200 to $500 cost quoted above, the Pacific Pride executives were able to allocate about $100 as "hard dollar costs" of getting a new account set up on the system. In determining IT cost per transaction what comprises a transaction must be defined: a billing or a fuel stop. As covered in the prior section, there is a small cost per customer for each bi-weekly billing, much of which must be classified as an IT cost per billing transaction. Additional IT costs per fuel stop are negligible as transactions are gathered at each station on the network, then each station is polled at the end of the day and the transactions are batched to Pacific Pride's central computer. The actual number Chapter 6. Empirical Examination 187 of transactions batched from a given node has httle impact on the data communication costs, of which the initial connection charge is the largest component. 6.4.5 Factor Input Price Flow Through to Downstream Output Several of the results obtained in the suppher to consumer models (Chapter 4) require additional assumptions or conditions in order to hold in the suppher to customer firm models (Chapter 5). The first condition is that price changes in the factor input (the primary good) do not impact the price of the downstream good. In the Pacific Pride case this means that the price of fuel has no impact on the prices charged by their commercial customers for whatever good is being moved downstream. Pacific Pride indicated that in the short or medium term they never see their fuel prices translated into their customers' prices. A convincing case example was provided: In the Spring of 1989 a large tanker, the Exxon Valdez, ran aground off the coast of Alaska spiUing large quantities of oil. For a short time tanker traffic was interrupted. Because the Pacific northwest receives oil from Alaska, supply was temporarily constrained. As a result the price per gallon of fuel jumped by $.20, or roughly 20 percent, for several months. During this period Pacific Pride saw no changes in prices charged by their commercial customers for downstream goods, for example freight hauhng rates. Thus, their commercial customers were not passing the fuel price increases along. Pacific Pride's executives thought that in the long term the increased fuel costs would be passed through, but that in general the price on the end product reacted much more slowly. The hypothesis that fuel is a negligible proportion of the customer firm's costs does not apply. Fuel component estimates of total customer costs range between 10-20 percent. Hence, fuel is important, particularly for a small margin operation (e.g. groceries). Notice, however, if the change in fuel costs are small, for example 5 percent, the impact on customer firm costs is also small, here between 1/2 to 1 percent. Chapter 6. Empirical Examination 188 6.4.6 Demand and Customer Firm Efficiency For the analogous results from the consumer models in Chapter 4 to hold in the customer firm case, Chapter 5, a second condition is needed: individual customer firm factor demands must be monotonic in customer firm efficiency for a given primary good. In this context, more efficient customer firms must consistently have either greater fuel demands or smaller fuel demands. It was clear to Pacific Pride's executives that there are efficiency differences between customers, and generally the larger customers (in size of operation and demand for fuel) are more efficient. One group of customers, the interstate trucking industry, was described as an "ugly" industry where customers (Pacific Pride's) come and go all the time. Common sense suggested that those customers who had been around longer and that were larger must be more efficient in order to survive. In addition, the executives noted that the larger customers make greater use and receive more value from the information provided by the cardlock system. The rigorous competition customers face also has implications for the assumption discussed in the previous section. For example, stiff competition in hauling rates, both from other trucking companies and from substitutes (rail, air freight), could be the reason why there is httle impact of road fuel price increases, at least in the short term. 6.4.7 Are Two Part tariffs Being Used? To date Pacific Pride has not used an exphcit two part tariff. There has been a $25-$50 deposit requested from customers, which can be waived if the customer objects. However, a subsidy has been considered as an option. The executives indicated they would use a subsidy if they were convinced it would be successful. The upper limit of their estimated cost of getting a customer on the system is $500, mostly made up of salesperson effort, incentives, and general telemarketing schemes. If Pacific Pride was Chapter 6. Empirical Examination 189 able to get customers on the system and buying fuel they would pay up to this upper limit as a subsidy, although the need for a minimum volume requirement for subsidized customers was recognized. Interestingly, one of Pacific Pride's old competitors, Gas Card, used to have a set up fee and a fee of $5 per card per month. Gas Card has since filed for bankruptcy protection under Chapter 11 (unrelated to their multipart tariff), and has been reorganized. Other smaller commercial fuel operators have also been charging nominal fees per card. Implicitly a form of a subsidy is already being used. Customers get help from Pacific Pride in the form of explanations and meetings with the customer's staff to ease the transition to the cardlock system, as well as keeping the customers up to date with the network. This raises the possibility of (1) resources in the form of effort substituting for an explicit subsidy, and (2) this effort being directed towards overcoming the customer's internalization switching costs. These ideas will be further discussed in the following chapter. Pacific Pride recognizes they are providing implicit subsidies in this manner. When presented with the idea of an explicit fixed tax it was suggested that a more palatable alternative to new customers would be to charge a little more per gallon fuel for the first X gallons of fuel, a block pricing scheme ([25]). Chapter 6. Empirical Examination > 190 6.5 Analysis and Results: Testing The Pricing Results 6.5.1 Policy Model Pacific Pride has a general model for setting fuel prices at the cardlock facilities which is driven by retail competition. A simple diagram of the model is as follows: Retail Price Leader = > Retail Price => Cardlock Price with arrows indicating direction of the causal effects. In the Pacific northwest the retail price leader is Arco. Retail prices at other fuel stations are tied closely to local competition. These prices react quickly to changes in prices at the price leader 3, typically the "other station at the corner". Pacific Pride's cardlock pricing policy is to react to changes in the retail price, charg-ing a premium per gallon which is competitive with credit card pricing 4 . The stated differential is $.08 per gallon. Converted into the notation used in the Chapter 5 models, this suggests an increase in p0 triggers an equivalent increase in P i , maintaining an $.08 per gallon differential. Even with this pohcy the correlation between cardlock prices and retail prices of fuel is not expected to be perfect. In order to preserve some stability over the cardlock network fuel price the cardlock prices may not be changed each time a retail price fluctuation occurs. The pohcy of a premium at the cardlock station over the retail price has not always been the case. Prior to 1983 the price at the cardlock was lower than retail. The reasoning was that the cardlock was self serve, and often had no canopy to protect against the weather, and thus provided less than a full service station. Of course, between 1979 and 3This structure has been modelled as tacit collusion, see [14]. 4In much of the U.S. fuel stations have one price for cash purchases of fuel and another price for credit card purchases. Chapter 6. Empirical Examination 191 1983 there were also the usual initial implementation difficulties setting up the cardlock system and operating it reliably. However, in 1983 one of Pacific Pride's executives visited a similar facility in San Diego which was charging a premium per gallon. The explanation given to justify the premium was that at the very least the commercial fuel suppher was carrying credit and higher exposure, as well as providing superior control and convenience. When informed that Pacific Pride was selling fuel through the cardlock at a discount the San Diego commercial fueler executive stated clearly: "...you are leaving money on the table". The Pacific Pride executive then returned to Salem and immediately ordered an increase in the price per gallon at the cardlock such that the cardlock price would be at a premium. A loss of customers was forecasted by some of the Pacific Pride team, and one salesman even went so far as to resign. The resulting effect on the customer base was minor, perhaps even beneficial: several smaller volume customers were lost, those that had a card available but did not use the network or only used the network occasionally. For the true commercial customer there was little change. Hence, the net result was that undesirable customers (i.e. low volume) left the system. This last result can be explained in terms of the models in Chapter 5 when downstream output price is exogenous: pi is increased, thereby driving some customer firms away from the IT enhanced primary good by decreasing v representing the marginal customer firm. However, if dq^x{p'p^)'Pl'w) < Q (customer firm demands for fuel are increasing in customer firm efficiency) this means that the lowest volume customers are lost. If fixed profits are negative, R — k1 < 0, Pacific Pride may in fact have made money by dropping low volume customers. Competition with the credit card price appears to be based on the fact that credit cards are the closest substitute, although still imperfect as only the credit risk exposure is similar. Chapter 6. Empirical Examination 192 6.5.2 Prediction of Theoretical Models To determine which result from the previous chapter apphes to Pacific Pride's case de-pends on (1) the nature of the primary goods available, and (2) the nature of competition. Beginning with the second point, direct competition to Pacific Pride's cardlock net-work can best be described as early and fragmented. Pacific Pride identified three other commercial networks covering parts of the west coast: CFN, NCN, and Gas Card. NCN uses the same equipment as Pacific Pride but primarily targets interstate truckers. Most of their stations are diesel only and they compete on the basis of price. NCN typically uses Chevron distributors. In contrast, 40-45 percent of Pacific Pride fuel volume is gaso-line (not diesel). CFN, also hnked to Chevron stations, has been a late starter. FinaUy, Gas Card was reorganized after filing for bankruptcy and is now hnked to Arco. Gas Card's problem is that it has many nodes but few customers. Pacific Pride feels that any competitor hnked to a major oil company is at a disadvantage since the majors are slow to move, and most of the major's sites are independently owned. Moreover, these competitors spend less on advertising and customer recruitment than Pacific Pride. Another layer of competition consists of small local operators covering a city or county. These small local networks are effective in capturing local business, but are at an obvious disadvantage for any customer whose operations more than span the network's scope. It is not clear than any of Pacific Pride's competitors, local or national, offer equivalent or better control aspects which is the major IT advantage in this case. As a result Pacific Pride could be considered a monopoly in its cardlock system offering, at least with respect to its targeted customer base. Notice the monopoly could be characterized both by what the system offers, and by the geographical region and locations spanned (e.g a series of local monopolies). There is, however, plenty of competition for retail fuel sales. These facts indicate that the appropriate model to consult is an oligopoly where one Chapter 6. Empirical Examination 193 supplier has IT, Model 5.3 from Chapter 5. Thus, one supplier offers the IT enhanced primary good (fuel via the cardlock system), and aU supphers offer the original primary good (retail fuel). Using the persuasive Exxon Valdez example, factor input price changes have little or no impact on downstream prices (e.g. p is not a function of Ri, pi, po)- As described above, the size of customer fuel requirements are increasing in customer firm efficiency (e.g. ^ H ^ ) . P ^ ) < 0 ) . Translating the pohcy model described above into the theoretical models developed in the preceding Chapter suggests that changes in the per unit prices of the original primary good, p0, positively affect the per unit component of the two part tariff for the IT enhanced primary good, P l . Unfortunately, the comparative static of p, with respect to changes in p0 (i.e. d~ )^ is ambiguous. That is, for fuel as the primary good, the model does not indicate what impact changes in retail fuel prices should have on fuel prices at the cardlock stations. Moreover, with the general specification, the model does not indicate whether or not a premium should be charged on the variable component of the two part tariff, as compared to the original good price, precisely because the fixed component may be used for that purpose. Thus, the analytical model does not directly show whether or not a premium should be charged per gallon at the cardlock. 6.5.3 Examining the Policy Model Determination of Retail Prices Nonetheless, using the pohcy model it is possible to study the relationships governing the price of the original primary good, and its impact on the price of the IT enhanced primary good. Examining the first link in the policy model, Retail Price Leader Retail Price Chapter 6. Empirical Examination 194 correlations between per gallon prices at the acknowledged price leader, Arco, and per gallon prices Pacific Pride retail outlets are as follows: Correlations: Salem PP Retail Regular PP Retail NoLead Arco Regular .97 Arco NoLead .98 Correlations: Eugene PP Retail Regular PP Retail NoLead Arco Regular .91 Arco NoLead .90 using a sample size of 36 (biweekly data, January 1987 to June 1988 inclusive). Obvi-ously, the correlations are significant at a < .0001. Therefore, it appears the relationship between prices set by the retail price leader and Pacific Pride's retail sites is positive, with the causal direction implied by the policy model. Determination of Cardlock Prices Addressing the second link in the policy chain, Retail Price Cardlock Price the correlations between per gallon prices at Pacific Pride's retail outlets and Pacific Pride's cardlock stations were obtained using data from the same period. They are: Correlations: Salem PP Cardlock Regular PP Cardlock NoLead PP Retail Regular .97 PP Retail NoLead .96 Chapter 6. Empirical Examination 195 Correlations: Eugene PP Cardlock Regular PP Cardlock NoLead PP Retail Regular .89 PP Retail NoLead .90 Again, the correlations are significant at a = .0001. Graphs of the series in each city, for regular and nolead fuel, are given in Appendices 6.1 and 6.2. These results point to a strong positive relationship between retail fuel prices and the cardlock fuel prices, as before with the policy model determining the direction of the causality. 6.5.4 Policy Model and Pricing Behaviour From the above results, in the framework of Pacific Pride's policy model, it is clear that retail fuel prices drive the prices charged at the cardlock sites. The actual pricing rule employed was declared by Pacific Pride's executives as a fixed premium per gallon of fuel at the cardlock site over the retail per gallon price. Thus, the premium is a fixed markup on the appropriate retail price. Letting xt represent the retail price per gallon and yt represent the cardlock price per gallon, a restatement of this pricing rule is yt - xt + A where A is a constant, here hypothesized to be $.08 per gallon. To measure this pricing rule the expression can be written as yt - xt = A + et where et captures the deviations from the pricing rule. An unbiased estimator of yt — xt is A = S" = 1 (yt~^Xt)? assuming E(et) = 0 where E is the expectation operator. Thus, A is the estimate of the mean difference between the observed retail and cardlock Chapter 6. Empirical Examination 196 per gallon fuel prices. An unbiased estimate of Var(yt — xt) is Var(et) = S"_1 ^ yt~^~^^ . With a sample size of n — 36, the Central Limit Theorem gives a sampling distribution for A which is approximately normal with mean A and variance Var{K) = ^ r l f i i . The means and standard deviations of the estimates are provided below5. Differences Between Cardlock and Retail Prices Retail Mean, A Std Dev, Std(A) Salem PP Regular .06972 .00220 Salem PP NoLead .08028 .00294 Eugene PP Regular .04583 .00344 Eugene PP NoLead .04361 .00317 Salem Arco Regular .09778 .00304 Salem Arco NoLead .10833 .00346 Eugene Arco Regular .09694 .00342 Eugene Arco NoLead .08556 .00330 Two different sets of hypotheses can be checked. The first is whether or not cardlock fuel is priced at a premium over retail. Setting up the hypothesis, Ho: A < 0 Ha: A > 0 where the null hypothesis is that there is no fuel price premium at the cardlock outlets. For each of the eight cases above it is easily verified that the null hypothesis is rejected 5Note: cardlock regular was matched with retail regular, cardlock nolead was matched with retail nolead. Chapter 6. Empirical Examination 197 at a < .0001. Consequently, it seems clear that a premium per gallon is being charged at the cardlock stations. The question then becomes: which retail price is the basis for the fixed premium? The pohcy model would suggest the Pacific Pride retail price is the appropriate choice. Also note that Pacific Pride management stated that they wished to keep an $.08 premium per gallon over retail. Constructing the hypothesis test, Ho: A = .08 Ha: A ^ .08 Now, this hypothesis is not rejected only for the Salem NoLead case. The hypothesis is rejected for the three other cases at all reasonable levels of a. Hence, Pacific Pride does not appear to be using the same fixed markup, in all cases. As an aside, the hypotheses of an $.08 markup on the retail price leader's retail prices are also rejected for any reasonable a (except for the Eugene Arco NoLead case where the critical value of a was p = .092). There are several alternative explanations why the stated pricing pohcy was not borne out by the results. Recalling that Pacific Pride retail prices are driven by local competition, both Salem and Eugene are in the same cardlock price region so the cardlock prices are the equal in both cities. However, all Pacific Pride retail sites do not necessarily follow the same pohcy in reacting to local retail competition, so the Salem and Eugene sites may react differently. Moreover, the retail price leader can set different prices in each city, based on the characteristics of the immediate vicinity. Of course, another alternative is that Pacific Pride is simply not following their stated pricing pohcy. As a result it is clear that an $.08 markup pohcy is not being consistently followed based on any of the series available6. GOther statistical tests examined the markup as a percent of retail. These tests did not yield further results. Of course, other schemes could be tested as well, however this work concentrated only on explicitly stated pricing policies. Chapter 6. Empirical Examination 198 Nonetheless, it is apparent that a per gallon premium over retail is being charged at the cardlock stations. This supports the notion that the primary good with IT is viewed as providing cost savings to customer firms (here those with vehicle fleets), with the value of the cost savings being at least the per gallon premium price of fuel paid at the cardlock stations versus the normal retail outlet. If the market is in equilibrium, this implies that the market price of the IT enhancement is between 4.8 percent and 12.3 percent of a customer firm's retail fuehng cost7. Restating, the customer firms place sufficient value on the additional features that IT provides so that the IT suppher can price the underlying good between 4.8 and 12.3 percent higher. 7These figures were obtained by dividing the per gallon premium by the appropriate retail per gallon price, taking the upper and lower limits of the numbers generated. Chapter 6. Empirical Examination 199 6.6 Conclusions Each of the assumptions characterizing IT appear to be supported in the Pacific Pride case. The convenience, control, and credit provided by the cardlock system decreases customer firm costs. There are small, but positive, internalization switching costs for customers adopting the cardlock system. Pacific Pride's non IT costs are decreased for the primary good, partially because some of the IT costs act as a substitute for non IT costs. Finally, the IT cost function for the cardlock system can be described as a fixed implementation and operating cost, a fixed installation cost per new customer, and a marginal cost per transaction. In the short and medium term the impact of factor input price changes do not flow through to downstream prices, as is illustrated by the Exxon Valdez example. Typically, larger customer firms are more efficient and make greater use of the IT enhanced primary good. Unfortunately, Pacific Pride has not explicitly used two part tariffs for the IT and cardlock fuel prices, although subsidies to entice customers to adopt the system have been considered. Therefore, this aspect could not be tested. The empirical test confirms that a price premium is being charged for the IT enhanced primary good, fuel via the cardlock system. However, results do not confirm the structure of the premium follows the stated Pacific Pride policy of an $.08 mark up over the retail per gallon price. While there is no specific evidence that the present price premium reflects a price equilibrium, the markup due to IT in this case is consistent and ranges from 4.8 to 12.3 percent of the underlying original primary good price. Chapter 6. Empirical Examination 6.7 Appendices to Chapter 6 6.7.1 Appendix 6.1: Salem Fuel Prices Fuel Prices: Salem Cardlock v= Pacific Pride: Regular Fuel I I I I I I I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I J F M A M J J A S O N D J F M A M J January 1987 ta June 19SS. Biweekly 0 Cardlock +• Retail Fuel Prices: Salem Cardack v= Pacific Pride: NaLeod Fuel 1.02 -i J F M A M J J A S O N D J F M A M J January 19S7 ta June 19ES, Biweekly • Cardtack +• Retal Chapter 6. Empirical Examination 201 o f o. Fuel Prices: Salem Ccxdlock v s A rm: Regular F u d i i i i i r~r J F M A I I I I M J January 1967 t a June 1988. Biweekly Candlack + Retail g Fuel Prices: Salem Cardack vs Araa: NaLaad Fuel D O [ ) I I 1 I 1 I I I I I F M A M J I I I I I I I I I I I I I J A S Q N D J T 1 I I I 1 1 I V r M A M J January 1937 ta June 19SS, Biweekly D Card tack +- Retail Chapter 6. Empirical Examination 202 6.7.2 Appendix 6.2: Eugene Fuel Prices Fuel Prices: Eugene Cardlock v= Paci f ic P r i d e Regular Fuel Q S -0.78 -0.76 - -0 7 4 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I J F M A M J J A S O N D J F M A M J January 1987 t a June 1983. Biweekly • Cardlock +• Retdl Fuel Prices: Eugene Cardoek v= Paci f ic Pride: NaLcad Fuel "I I I I I I I 1 I I T T I I I I I I 1 I I I I I I I I I I I I I 1 I T J F M A M J J A S O N D J F M A M J January 1987 ta June 1983. Biweekly • C a r d b c k +• Retell Chapter 6. Empirical Examination 203 Fuel Prices: Eugene Cardlock vs Arm: Regular Fuel a. D D I ] I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I M A M J J A S Q N D J F M A M J January 1987 ta June 1983. Biweekly D Cardlock + Retail 0 ! a. Fuel Prices: Eugene Cardack vs Area: NaLead Fuel o-e-I I I 13 D • I ] if I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I J F H A M J J A S Q N D J F M A M J January 1987 ta June 1983, Biweekly D Ccrdlock +• Retail Chapter 7 Conclusions, Contributions, and Future Research 7.1 Introduction This final chapter concentrates on reviewing the conclusions from the previous chapters, summarizing the contributions made by this work, and discussing directions for future research. The conclusions begin with a synopsis of the research results, addressing each element of the research strategy. These results are then hnked back to the principle thesis of this research. Managerial imphcations of the results are then discussed. The contributions of the dissertation are briefly outlined, in the context of Management Information Systems research. Recommendations for future research start with questions coming directly from the analytical modelling and empirical study done here, targeting additional work within the current framework. Further research, branching out from the present static pricing structure, is also proposed. 204 Chapter 7. Conclusions, Contributions, and Future Research 205 7.2 Conclusions The results from this research are: • For customers IT has two effects: vertical differentiation (consumers) or reduced costs (customer firms) of the primary good, and a positive internahzation switching cost from IT adoption • For supphers IT has two effects: reduced costs of producing the primary good, and IT costs which include a fixed implementation cost, an installation cost per IT adopter, and a marginal cost per IT enhanced primary good • IT adoption may be taxed or subsidized through the fixed component of the two part tariff • The internahzation switching cost from IT adoption forms the upper bound on the size of an adoption subsidy • Pricing for IT and primary goods is interdependent • In an oligopoly, a single suppher with IT can make positive profits from the IT; in a duopoly it is in the IT supplier's interest to leave the original primary good to the suppher without IT • Competition between suppliers with identical IT does not yield positive profits • Competition between suppliers with vertically differentiated IT has the suppher with the inferior IT making positive profits with the fixed component of the two part tariff Chapter 7. Conclusions, Contributions, and Future Research 206 • Two conditions are needed for equivalence of supplier pricing strategies to con-sumers and customer firms: downstream output price must be exogenous, and customer firm factor demands must be monotonic in cost efficiency1 • Empirical evidence for the customer firm case was found to support the hypothe-sized effects of IT (first two points above) • Empirical testing indicates that differential (premium) pricing can be supported for an IT enhanced primary good over an original primary good The main themes of the research have been borne out by the results. Recall these interrelated themes centered on joint pricing, two part tariffs, differentiation, and positive IT adoption costs. The importance of joint pricing and the two part tariff for IT is best illustrated by the results of the monopolist offering both primary goods (Models 4.2 and 5.2), where the equation for the fixed component of the optimal two part tariff clearly has an element relating to the variable component of the two part tariff, and an element relating to the price of the original primary good. The hnk between pricing and IT adoption costs is most clearly seen in Propositions 4.1 and 5.1, where the fixed component of the two part tariff (a subsidy) is bounded from below by the internahzation switching cost. An unambiguous example of IT providing vertical differentiation of the primary good is the significant premium Pacific Pride charges per gallon of fuel purchased at their cardlock outlets over retail outlets, in absence of a two part tariff. 7.2.1 Implications Prior work on two part tariffs focused on monopoly, without customer adoption/switching costs. As a result, a subsidy could not be optimal. In our case the customer switching 1 Noting that the direction of the monotonicity is important to sign the pricing results. Chapter 7. Conclusions, Contributions, and Future Research 207 cost provides rationale for a subsidy, in a sense removing barriers to IT adoption. The argument that providing an implicit subsidy in the form of aid to ensure a smooth transition to the IT is particularly significant in this context. Examining the specification of customer utility or profit functions, the tradeoffs between the fixed component of the two part tariff and the internalization switching cost are immediate: they are perfect substitutes. Indeed, a supplier's choice of customer IT support level is actually part of selecting a two part tariff, and should be recognized as part of the pricing decision. Our results do not determine the relative per unit pricing of the IT enhanced and original primary goods, other than the optimal or equilibrium prices are likely not equal. In the empirical study a premium for the IT enhanced good, fuel via cardlock versus retail fuel, was found. However, as reported in the literature review, McKesson Drug Co. gave discounts on merchandise purchased through Economost ( [8]). Observe however, that it was argued the former case was a monopoly in the IT enhanced primary good, whereas the suppher in the latter faces direct IT competition2. 2The author also notes that as of January 1st, 1990, service charges for bill payments through the Bank of Montreal are now lower at the ATM than at the human teller. Chapter 7. Conclusions, Contributions, and Future Research 208 7.3 Contributions Referring to Chapter 1, researchers in the discipline stated that academic research on IT and corporate strategy had been soundly criticized due to a lack of rigor. Other researchers identified yet unfulfilled research opportunities which included the economic impact of IT on the firm's business activities, and the study of pricing and effects of switching costs. Given the state of the art it was suggested that there is a gap in prior research on normative strategies firms should use with IT. This research has taken a step towards satisfying the calls for rigorous analysis, ad-dressing economic impacts of IT through the study of normative pricing strategies, the examination of which included customer switching costs. In short, it has moved the discipline from frameworks towards theory. Methodologically, quantitative modelling techniques from the theory of Industrial Or-ganization have been used to rigorously formulate the pricing problems and derive norma-tive pricing strategies. The models were constructed to explicitly capture the distinctive characteristics of IT, which themselves were obtained from a thorough investigation of the relevant literature. Subsequently, an empirical study was conducted which allowed both for a qualitative assessment of the models' assumptions, and statistical tests of the pricing results. The main thesis of the research, joint pricing, two part tariffs for IT, and effects of IT on the primary good, has not previously been recognized, formulated, or studied. Regarding the research results, the characterization of IT arrived at here is new, although other models and frameworks have previously included most of its aspects. One contribution of the thesis is a parsimonious description of the effects of IT. To the MIS discipline the normative pricing strategies for the various market configurations, derived in rigorous form from economic principles, is original work. Key contributions Chapter 7. Conclusions, Contributions, and Future Research 209 from the economic modelling are the insights into the hnk between the fixed component of the two part tariff and internahzation switching costs, the possibility of subsidized adoption, and actual pricing strategies in the form of signing the components of the two part tariffs in some situations. Empirical examination of the specific model assumptions and conditions has provided positive feedback on the validity of economic modelling. The statistical tests of pricing results has confirmed the possibility of a differential (premium) price for the IT enhanced primary good. Chapter 7. Conclusions, Contributions, and Future Research 210 7.4 Future Research The first topic for further research is additional development of the relationship between the two parts of the two part tariff. Sketching one possible methodology, numerical analysis could be used, which would involve selecting a functional form for utility or cost functions, and performing a sensitivity analysis over a range of parameter values. Included in the parameter set could be a value or function representing the internahzation switching cost. Thus, the tradeoffs between the fixed component of the two part tariff and the internahzation switching cost could be explicitly examined. An immediate area for future research is the equilibrium existence problem where two suppliers compete with identical IT and IT enhanced primary goods using two part tariffs. This appears to be a technical economics problem, and as such may be difficult to resolve. As another extension, focusing on the models in Chapter 5, specification of the downstream market may allow for development of pricing results at the IT suppher level when downstream output price is endogenous. Turning to empirical work, there is a need to study IT customers directly in order to examine the IT impacts on customers in greater depth. In particular, extra effort should be made in measuring both the benefits gained from using the IT enhanced primary good, and the costs of IT adoption or switching. Stepping slightly further away from the present work, there is a need for analyzing pricing strategies used in the case where there is an intermediary involved with the IT between the supplier and customer. The particular reference is to airhne CRS ([9] and many others), where the travel agent performs an intermediary function. What makes the CRS case both interesting and more complex is that the IT is adopted and used by the travel agent rather than the customer, while the customer still derives benefits from the IT. Moreover, there are transfer payments both among supphers, and between travel Chapter 7. Conclusions, Contributions, and Future Research 211 agents and suppliers, as well as normal charges to customers. One limitation of the present work is that it concentrated on static pricing strategies. Future research should introduce dynamic aspects to the analysis. One possible avenue would be to examine timing of IT introduction, possibly taking advantage of the pricing outcomes here. Another alternative would be to concentrate on diffusion of IT through the customer population using a dynamic setting of one or both parts of the two part tariff, thus making the pricing itself the dynamic element. Bibliography [1] "American Hospital Supply Corp. (A) The ASAP System," 9-186-005, HBS Case Services, Harvard Business School, Boston, MA, 1985. [2] Bakos, J.Y., "Interorganizational Information Systems: Strategic Implications for Competition and Cooperation." Unpublished Ph.D. Thesis, Sloan School of Man-agement, Massachusetts Institute of Technology, 1988. [3] Bakos, J.Y., and M.E. Treacy, "Information Technology and Corporate Strategy: A Research Perspective," MIS Quarterly, June 1986, pp. 107-119. [4] Barrett, S and B. Konsynski, "Inter- Organization Information Sharing Systems." MIS Quarterly, Special Issue 1982, pp. 93-105. [5] Caphn, A. and B. Nalebuff, "After Hotelhng: Existence of Equilibrium for an Imperfectly Competitive Market," Princeton University Working Paper, January 1989. [6] Cash, J.I., and B.R. Konsynski, "IS Redraws Competitive Boundaries." Harvard Business Review, March-April 1985, pp. 134-142. [7] Clemons, E.K., and S.O. Kimbrough, "Information Systems, Telecommunications, and Their Effects on Industrial Organization." Proceedings of the Seventh Inter-national Conference on Information Systems, 1986, pp. 99-108. [8] Clemons, E.K., and M. Row, "McKesson Drug Company: A Case Study of Economost - A Strategic Information System," Journal of Management Informa-tion Systems, Vol. 5, No. 1, Summer 1988, pp. 36-50. [9] Copeland, D.G., and J.L. 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