Modelling B2B E-Marketplaces: The Role of Intermediaries

Transcription

1 Modelling B2B E-Marketplaces: The Role of Intermediaries Markos Kourgiantakis, Emmanuel Petrakis Business Economics and New Technologies Laboratory (B.E.NE.TeC.), Department of Economics, University of Crete Rethymno, Greece Last revised: January 2007 Version 2.0 Abstract The bulk of the theoretical literature in e-commerce assumes that the owner of an e- marketplace extracts rents through the membership (entrance) fees from suppliers and buyers. We instead assume that the intermediary can also charge commission fees over the quantities that are sold through the platform. We investigate this more realistic business model from the intermediary s point of view, under different conditions in B2B two-sided markets. In an e-marketplace where all participants act strategically, our analysis suggests that, although the intermediary s optimal pricing policy can include membership fees and commissions, the intermediary prefers to operate a vertical e-marketplace under market conditions allowing him to impose high membership fees and low commissions for both sides of the market. Keywords: e-commerce, B2B, intermediary, two-sided markets, pricing behaviour, network effects JEL Classification: D40; L13, L86 The material is based upon work supported by the Ministry of Development, General Secretariat of Research and Technology under The Operational Programme "Competitiveness" (Grant No. 01ΕΔ332). A shorter version of this paper was presented in CRETE 2005 Conference (poster) and will be presented in IADIS E-commerce Conference

2 1. INTRODUCTION The revolution in Information and Communication Technology (ICT) changed the way people conduct business. Managers, market experts, and researchers are predicting the huge potential of the latest networking technologies in business. They forecast that the size of on-line trading revenues in the next few years will vary from a few hundred billion to a few trillion dollars for some economic sectors. Today, the e before words like commerce, business, marketing, etc., indicates a philosophy that must be followed by companies and organizations that want to keep their competitiveness and efficiency. The phenomenon of e-business is still quite new also to academics and researchers. It is clearly a fertile field for research. Economists, marketeers, operations researchers, computer scientists, engineers of every kind, and many other categories of scientists investigate the impact of ICT in business, develop improved information systems and techniques, and propose new business methodologies and frameworks. In other words, they are looking for the optimum in e-commerce. In this new economy two basic business models enabling transactions are met in the Internet, the new global market: the e-shops (e.g. Amazon.com) which usually refer to a business model dedicated to business-to-consumer (B2C) e-commerce, and the model of electronic marketplaces (e-marketplace or e-market). E- marketplaces are Internet platforms that concentrate many buyers and sellers who transact electronically. This kind of platforms are used for B2C transactions (e-malls), for consumer-to-consumer (C2C) transactions (e.g. ebay, flea.com), as well as for business-to-business (B2B) transactions (e.g. RetailExchange.com). Modern B2B e- marketplaces offer many advantages to participating firms, even buyers or suppliers, such as reduction in transaction and communication costs, variety of suppliers/ buyers, several transaction mechanisms (exchanges, catalogs, auctions, etc), services that lead to more efficient supply chain management, finance services, etc. It is generally argued that the success of B2B e-commerce 1 is due to significant 1 According to UNCTAD (2002) B2B e-commerce accounts for around 95 % of all e- commerce in most estimates. Several sources, such as the Gartner Group and Forrester Research, estimated an intense growth potential of the worldwide B2B volume from around $433 billion in 2000 to already more than $1 trillion in Around 37% of this total volume will be done via B2B marketplaces acting as intermediaries in two-sided buyer-seller markets. 2

3 advantages B2B e-marketplaces offer to participating firms relative to the traditional B2B markets. Business-to-business e-marketplaces are classified according to several criteria in e- commerce literature. Popovic (2002) classify B2B e-marketplaces according to their ownership structure and their industry focus. In terms of industry, a B2B e-market is characterized vertical when is organized in a specific industry or industry segment, and horizontal when it offers services across multiple industries. In terms of ownership structure, there is a classification independent (or third-party ) and dependent (or consortia ) B2B marketplaces. The third-party marketplaces are owned and managed by independent entities who are neither sellers nor buyers. In contrast, consortia e-marketplaces are built by a small number of industry agents (buyers or sellers), usually leaders that dominate their respective industries. Especially in the first wave of B2B e-commerce, the majority of e-marketplaces were created by independent firms like venture capitalists or technology firms. This trend still exists with the vast majority of them having a vertical industry focus and be owned by third-parties (Popovic, 2002). B2B marketplaces (especially vertical and third-party ones) appear thus as typical examples of two-sided markets. As intuitively defined by Jullien (2004), the concept of two-sided markets refers to situations where one or several competing platforms provide services that are used by two types of trading partners to interact and operate an exchange. More precisely, Evans (2003) defines two-sided markets by the combination of three main features: first, the presence of two distinct categories of agents (here buyers and sellers); second, the existence of positive indirect network effects (i.e., the benefits accruing to an agent of one category increase as the pool of members from the other category enlarges); third, the agents inability to internalize these indirect benefits efficiently and, thereby, the scope for intermediation. In other words, the owners of independent e-marketplaces are a new kind of intermediaries 2 in B2B two-sided markets. There role of the latter is significant in 2 In the economic literature, an intermediary, also called middleman or broker, is a firm between the suppliers (producers) and buyers, which sells products but does not create or consume them. For example, Spulber (1996) describes an intermediary as an economic agent that purchases from suppliers for resale to buyers or that helps buyers and sellers meet and transact. In contrast to traditional intermediaries, intermediaries acting in the Internet usually do not resale products but offer services facilitating interaction between buyers and 3

4 modern B2B transactions and run in contrast to the theory of disintermediation, which refers to the elimination of intermediaries that new technology believed to bring in the B2B landscape (Giaglis et. al., 2002; Sulzle, 2005). Bailey and Bakos (1997) categorize web intermediaries services in four basic categories: aggregation of buyers and sellers, trust enhancement among participants, market facilitation, and matching of buyers and sellers. Beyond matchmaking and market facilitation, the recent literature often refers to more sophisticate and advanced services for intermediaries, such as providing negotiation mechanisms, coordination services, etc (e.g. Kaplan and Sawhney, 2000; Wise and Morrison, 2000). Intermediaries in electronic platforms traditionally use membership fees (or entry fees) and usage fees (commissions or transaction fees) as sources of their revenues. As it is described in the next paragraph, the optimal pricing policy of the intermediary in an e-marketplace is still an open question in the broader e-commerce literature, mainly because it usually entails a multidimensional profit maximization problem. Before applying any pricing strategy, electronic middlemen should consider many, if not all, of the characteristics of the B2B market structure such as the size of the downstream and upstream (buyers and suppliers) markets and the strength of competition among firms. In turn, in such multi-agent systems, the pricing decisions of an intermediary affect the number of firms that participate to the electronic platform, as well as the firms strategic decisions, such as their level of produced quantities. This paper presents a theoretical model that analyzes B2B e-marketplaces in a traditional industrial organization setting. We investigate the two-sided aspects of such marketplaces and we focus on the role and the pricing behaviour of the intermediary under different conditions in B2B markets. In contrast to the bulk of the theoretical literature in e-commerce and two-sided markets that limit their analysis to the use only of membership fees and/ or fixed transaction fees (e.g. Julien, 2004; Katsamakas and Bakos, 2004), we include in our analysis membership and commission fees as basic pricing instruments for the intermediary. Commissions are a kind of transaction fees that are imposed by the intermediaries over the transacted quantity in the e-marketplace. This setting allows us to address the following questions: Which is the optimal pricing strategy for an intermediary charging both membership fees and commissions to participating firms? How does the existing sellers. A discussion for the role of intermediaries in e-commerce compared to the role of traditional intermediaries in B2B markets is given by Chirchu and Kauffman (2000). 4

5 structure of B2B market affect the intermediary s decisions and vice versa? Which will be the strategy of the intermediary in case that he has the market power to determine through its pricing policy, firms that will participate in the e-marketplace? In our model we consider a two- tier industry consisting of buyers and sellers, and an independent intermediary who owns a vertical e-marketplace. Initially, in our fourstage game the intermediary sets up the levels of membership fees and (per unit of exchanged quantity) commissions charged to buyers and suppliers. In the next stage, all firms enter in the e-market up to the point that their net profits are zero. In the third stage all the input suppliers compete in upstream market by setting their quantities simultaneously and independently, while in the forth stage the downstream firms (buyers) buy their inputs from suppliers and compete a la Cournot in the downstream market. Assuming that the e-market is the only platform for transactions between buyers and suppliers, we examine two cases with different strength in intermediary s monopoly power. In the first case the intermediary is unable to determine the number of buyers and suppliers participating in his market. Such a case corresponds to situations where the intermediary plans his policy without the power or the willingness to disturb the structure of the B2B market, or situations where a social planner prevents the intermediary to do so. The findings from the second case reveal which is the optimal pricing behaviour of a monopolistic middleman, who can also determine the number of participants in the e-market, through its pricing policy. The latter case could be the case of a monopolistic intermediary with strong market power in local or niche B2B markets 3. Concerning the strategic decisions of buyers and sellers participating in a vertical e- marketplace, we show the existence of strong direct and indirect network effects for both sides of the market. In addition, it is found that the production decisions of firms in B2B market is affected by the aggregate price level and not the price allocation of 3 A further reason for the investigation of the two cases in this paper is the complexity of e- marketplace systems due to several externalities they present. In essence, the first case in which the intermediary can not determine the number of firms participating in its e-market, offers an auxiliary analysis that contributes significantly on the analysis of the second case. 5

6 commission fees charged by the intermediary 4. That is, commissions act like a tax in transactions between the two sides of the market. We next show that intermediary can use both membership fees and commissions but there is a negative relation between these two pricing instruments. The larger the number of agents in one side (e.g. buyers side), the higher the optimal total commission and the lower the membership fee imposed to this side of the market. Under some market conditions, membership fees are negative, i.e. subsidies are needed for the participation of firms in the e-market, and the intermediary extracts profits exclusively from commissions. However, the intermediary prefers to operate his e-market in market conditions that allow him to impose high membership fess and low commissions to firms. In case of an intermediary that can define the number of firms in the e-market, the intermediary reaches the maximum profits by creating a B2B two-sided market with only one firm in the supply side. Interestingly, under this setting the aggregate level of commissions is negative, that is the intermediary, although a monopolist, offers subsidies per unit of quantity exchanged in the e- marketplace. In general, it seems that the owner of a vertical e-market prefers pricing strategies with high membership fees and low commissions and in order to achieve such strategies, he prefers to define or to operate in industries with a small number of agents at least in one market-side. The rest of the paper is organized as follows. The next section refers to the related literature concerning e-marketplace systems and indicates the contribution of our research within this literature. Section 3 presents the model, while Section 4 includes the analysis for the optimal pricing strategy of the intermediary both in the case where he has the power to determine the number of agents in both sides of the market and in the case where he is unable to do so. In Section 5, we carry out a welfare analysis and finally, Section 6 concludes. 4 If z b and z s represent commission fees for buyers and suppliers respectively, the aggregate level on commission fees (z b + z s ) and not the price allocation, i.e. the level for z b, z s separately, affects the production decisions of firms in the B2B e-market. 6

7 2. RELATIVE LITERATURE AND THE CONTRIBUTION OF THIS RESEARCH Electronic marketplaces are economic systems with strong network effects and our model is related to several strands of the literature that investigates strategic decisions of firms in network environments. There is an extensive literature that focuses on networks appear only direct network effects, that is on networks with a single type of participants whose benefits accruing to an additional agent (e.g. Katz and Shapiro 1985; Economides 1996). Examples of such networks are telecommunications networks and software application networks. Two-sided systems, or more generally multi-sided systems, are consider as more difficult systems to be analyzed by researchers, because of the large number of agents (buyers, sellers, intermediaries) that participate in them, their distinct nature, as well as the strong network effects among all those agents. Characteristic examples of two-sided markets are credit cards, advertising in media markets and e- marketplaces. As Katsamakas and Bakos (2004) say many aspects of these networks are not well understood, such as the determinants of participants benefits, the implications of actions by the intermediary, and how the value created by the network is allocated between the two sides and the intermediary. Rochet and Tirole (2004) propose a useful and general introduction for the two-sided market literature. One of the basic questions in two-sided markets is the pricing behaviour of intermediaries, a question that is mainly addressed in this paper. Contributions to this direction in case of internet intermediaries are provided by Rochet and Tirole (2003), Evans (2003), Caillaud and Jullien (2003), Yoo et. al. (2003), Armstrong (2004), Katsamakas and Bakos (2004), Julien (2004), Nocke et. al. (2004), Bhargava and Choudhary (2004), and Sulzle (2005) 5. These papers investigate how intermediaries pricing policy is affected by several two-sided market aspects, such as the ownership structure of e-market, the single or multi-homing of buyers and sellers in e- marketplaces, the strength of positive and negative network effects, the product differentiation in intermediary s services, etc. 5 A more extended presentation of this kind of research is given in Kourgiantakis and Mandalianos (2007). 7

8 The above mentioned literature follows a similar formulation for modeling utility functions of the agents under network-related benefits. Specifically, general valuation functions of type a + b. N are used, where a usually represents an ad hoc (exogenous) standalone benefit gained by the participation in e-market and bn represents a benefit due to the network (b is the strength of network effect and N the number of agents). In such settings the major pricing instrument for intermediaries is the membership fee p, which is represented in the utility function of buyers and sellers as a fixed cost (e.g. p + a + b N). In some cases (e.g. Julien 2004) a kind of a two-part additive valuation that includes also fixed transaction fees is adopted. Nevertheless, this type of formulation presents the benefits of participants in a B2B e- market in a very stochastic form, which from one hand facilitates the analysis of network effects but from the other hand does not allow a better analysis of the participants strategic decisions, such as their level of produced quantity. Contrary to this, the model developed in this paper follows a more traditional economic approach which incorporates the quantities of inputs-outputs that are exchanged through the e- marketplace. In this manner, important strategic decisions of participating firms can be determined endogenously, and the usage of alternative pricing tools other than membership fees (like commissions) by intermediaries can be investigated. The only work which is closely related to this paper is a similar but less general model analyzed by Belleflamme and Toulemonde (2004). In their research, Belleflamme and Toulemonde (2004) examine two-sided aspects of a B2B e- marketplace, endogenizing both buyers and suppliers payoffs but excluding commissions (usage fees) as a pricing tool for the intermediary. Moreover, they focus to the intermediary s optimal strategy on which side of the market should attract first. Nevertheless, their and our settings are the first theoretical models enforcing a more endogenous analysis in two-sided markets. Of particular relevance for this paper is also the more general literature on strategic effects of B2B e-commerce and e-marketplaces to firms, which however does not focus on the two-sided nature of e-marketplaces and/ or on the pricing policy of intermediaries. In contrast to our model, this recent literature usually does not focus on intermediaries in e-markets, neither it focuses on specific relationships or specific transaction mechanisms between buyers and sellers. For example, Milliou and Petrakis (2004), as well as Dai and Kauffman (2003), investigate buyer-firms incentives to join a public e-marketplace or to create their own private B2B electronic network for the transactions with their suppliers, while Chen et al. (2002) model 8

9 multi-unit Vickrey electronic auctions without the existence of an intermediary 6. This research contributes to the existing literature by proposing a new model formulation that includes an intermediary. 3. THE MODEL Consider a two-tier industry consisting of n b downstream firms final good producers and n s upstream firms input suppliers. The upstream, as well as the downstream firms are identical. The upstream firms (suppliers) produce a homogeneous input and the downstream firms (buyers) produce differentiated final goods, transforming one unit of input into one unit of final good. All transactions between the two sides of the market take place on an e-marketplace, which is owned by an independent intermediary. It is assumed that the intermediary offers the only platform in which buyers and sellers can make transactions. It is further assumed that the intermediary does not own or price any of the inputs exchanged in the e-market; he only provides services to facilitate buyers-suppliers interactions. The e-marketplace owner is a profit maximizer who disposes two price instruments: the membership fees charged to every participating firm in the e-marketplace and the commission fees charged for every unit exchanged in the e-marketplace. The utility of the representative consumer is given by the quasi-linear function: n b U Iq 1,q 2..., q nb M = aq i - 1 i n b j i=1 2 2 q i +g k i=1 i=1 n b k i y n b q i q j z - p i q i + m { i=1 where 0 γ 1 indicates the degree of product differentiation. The variable q i denotes the quantity produced by the downstream firm i, i,k=1,2,,n b, while m represents the representative consumer s expenses on the rest of the goods. The above utility function implies that each consumer spends only a small part of his income on the products of the specific industry. Hence, income effects on this industry can be ignored and a partial equilibrium analysis can be applied. 6 There are also many papers studying for the optimum in several less related to e- marketplace topics (like electronic supply chain coordination) using operations research, game theory, and mathematical programming techniques. An overview of such literature is given in Kourgiantakis et. al. (2006). 9

10 The solution of the utility maximization problem of the representative consumer leads to the inverse demand function faced by each downstream firm i, p i = a - q i γ Q -i, where Q -i = Σ q k denotes the aggregate output produced by its rivals. Downstream firms have a production cost t b for the transformation of one unit of input to one unit of output. Additionally, a typical downstream firm (buyer) faces two other kinds of variable cost, first, the input price w, charged by the upstream firms and second the commission z b, charged by the intermediary for every unit of input exchanged. Concerning fixed costs, buyers have to pay an entry fee p b, charged by the e-market owner and a connection cost f b. The connection cost can be considered as the investment in information technology and business process redesign in order buyers (downstream firms) to be able to transact electronically through the e- marketplace. As a consequence, the buyer s profit function is given by: Π i =-p b - f b + q i Ha - q i -gq -i - w - z b - t b L (1) All the upstream firms (suppliers) participating in the e-marketplace compete by adjusting their quantities simultaneously and independently (Cournot competition). Since there is one-to-one transformation of inputs to outputs, the total quantity of output (Q) is equal to the total quantity of input (X). Every supplier j (j = 1,2,3,,n s ) sells a quantity of input x j. It is assumed that a typical supplier faces two kinds of variable cost: the commission z s and the production cost t s for each unit of input sold. As in the buyers case, suppliers also face two fixed costs: the fixed entry fee p s and the connection cost f s for the participation in the e-market. In this way, the profits of each upstream firm j, j = 1,2,3,,n s, are given by: Π j =-p s - f s + x j H w - z s - t s L (2) Finally, the intermediary extracts revenues by both suppliers and buyers, using entry (membership) fees (p b, p s ) and commissions (z b, z s ) for the quantity of input exchanged in the e-marketplace. Assuming negligible set up and maintenance cost for the operation of the e-market, the profit function for the intermediary is: Π I = p b n b + p s n s + X H z b + z s L (3) 10

11 where X is the total quantity exchanged in e-marketplace and (z b + z s ) the sum of commissions charged to buyers and suppliers. We consider a general four-stage game. In particular, the sequence of events is as follows: Stage1: The Intermediary sets the commission fees (z b, z s ), as well as membership fees (p b, p s ) for buyers and suppliers and, if possible, chooses the optimal number of buyers and sellers participating in his e-marketplace. These prices are public information and all downstream and upstream firms have perfect information about intermediary s decisions. Stage 2: Firms enter in the e-market up to the point that their net profits are zero (free entrance condition or zero profit condition). Stage 3: All the input suppliers compete in upstream market by setting their quantities simultaneously and independently. Stage 4: All the downstream firms (buyers) buy their inputs from suppliers, transform them into final goods and compete in the downstream market by setting their quantities simultaneously and independently. 4. ANALYSIS 4.1. Strategic decisions for upstream and downstream firms In the last stage of the game a typical downstream firm (buyer), taking as given the aggregate output of its rivals Q -i, the input price it faces w, the transformation cost t b and the connection cost f b, chooses its quantity q i in order to maximize its profits given in eq.(2). The first-order condition (foc) for buyer s profit maximization yields: q i * = a - w - z b - t b 2 -g+gn b (4) 11

12 Due to symmetry, summing up the focs, the equilibrium aggregated output and each firm s profits are 7 : Q = n b H a - w - z b - t b L 2 +ghn b -1L (5) Π i * =-p b - f b + H a - w - z b -t b L 2 H2 +ghn b - 1LL 2 (6) From the above expressions, it is obvious that firm i s output (q i =Q/n b ) and profits are decreasing in the number of buyers in e-marketplace, the input price, the transformation cost and the commission fee that intermediary charges to buyers. Moreover, by inverting eq. (5), we obtain input price w, as a function of total output Q: w = an b - H 2 - gl Q- n b H t b +gq+ z b L n b (7) In the third stage, all the upstream firms (suppliers) participating in e-marketplace compete by adjusting their quantities simultaneously and independently (Cournot competition). Because of the one-to-one transformation of inputs to outputs, the total quantity of the outputs (Q) is equal to the total quantity of the input (X) and thus eq.(7) gives the inverse demand function faced by the suppliers. A typical supplier taking as given the aggregate input of its rivals X -j, the input price w, the production cost t s and the connection cost f s, chooses its quantity x j in order to maximize its profits given in eq.(3). The foc in eq.(3) shows that in a symmetric Cournot equilibrium, each supplier j produces a quantity: x j = n b H a - t b - t s - z b - z s L H 2 +gh n b -1LLH1 +n s L (8) where it is assumed that a is large enough such that a t b + t s + z b + z s. Hence, the total quantity of input, as well as the total quantity of output (i.e. the total quantity exchanged on the e-marketplace), is equal to: 7 We assume that a is large enough, such that a > w + z b + t b. 12

13 X Hn b,n s,z b,z s L = QHn b,n s,z b,z s L = n b n s H a - t b - t s - z b - z s L H 2 +ghn b - 1LLH1 +n s L (9) Eq.(9) reveals that the total quantity exchanged on the e-marketplace increases with the number of buyers and suppliers and decreases with the commission fees charged by the intermediary, the degree of product substitutability and the production costs for both buyers and suppliers. It is of course independent of the membership fees. Substituting eq.(9) into eq.(6) and eq.(5), and eq.(8) and eq.(6) into eq.(7), the firms profits in both sides of the market at the equilibrium are: For buyers: Π b i * =-p b - f b + n s 2 H a - t b - t s - z b - z s L 2 H1 + n s L 2 H2 +ghn b - 1LL 2 (10a) For suppliers Π s j * =-p s - f s + n b H a - t b - t s - z b - z s L 2 H1 + n s L 2 H2 +ghn b - 1LL (10b) The above expressions lead to the following lemmas: Lemma 1: Direct and indirect network effects 8 exist for both sides of the market participating in an e-marketplace Proof: Equations (10) documents the existence of indirect network effects, since downstream firm s profit (upstream firm s profits) increases in the number of upstream firms (downstream firms): Π b i * Hn b,n s L < Π b i * Hn b,n s + 1L In contrast, firm s profit (e.g. buyer s profit) decreases as the number of firms of the same type (buyers) increases: Π b i * Hn b,n s L > Π b i * Hn b + 1, n s L 8 With a more classic economic terminology, indirect network effects refer to vertical externalities, i.e. externalities between buyers and suppliers, while direct network effects refer to horizontal externalities, that is externalities among competing firms (either buyers or suppliers). 13

14 The latter reveals the existence of direct (or competition or negative) network effects. These results are compatible to the existing literature in e-marketplaces and in twosided markets presented in section 2 (e.g. Sulzle, 2005). Lemma 2: The price allocation in commission fees charged by the intermediary does not affect the structure of the market Proof: Equations (9) and (10) show that firms profits as well as the quantity in the e- marketplace depend on the aggregate level on commission fees (z b + z s ) and not on price allocation, i.e. the price level for z b, z s separately. According to Rochet and Tirole (2004) the finding in Lemma 2 does not define a twosided market because, based on their definition, in a two-sided market the quantity exchanged depends on aggregate price level and the price allocation. Our finding coincides with the corresponding one obtained by Belleflamme and Toulemonde (2004). As Belleflamme and Toulemonde (2004) claim the e-marketplace is onesided in terms of usage externalities or in other words usage fees are neutral in such a setting. The above equations also reveal the negative relation between the aggregative level of commission fees and firms profits. Moreover, from equations (9) - (10) we conclude that only the sum of marginal production costs (t b + t s ), and not the upstream and downstream marginal cost individually (t b or t s ), affects the buyers and suppliers profits in equilibrium. This fact in combination with the result of Lemma 2 allows us to simplify the rest of the analysis by defining z as the aggregate price level on commission fees (z = z b + z s ) and t as the sum of marginal production costs, for buyers and suppliers (t = t b + t s ) Strategic decisions for the intermediary In the second stage of the game, the downstream and upstream firms enter in the e- market up to the point that their net profits are zero (free entrance condition or zero profit condition). As a monopolist, offering the only transaction platform, the intermediary can extract all the surplus of participants in the e-marketplace. This implies that the fees, both membership fees and commissions, could be such that the 14

15 zero profit condition is satisfied 9. The latter can determine either the number of downstream/ upstream firms in equilibrium or, equivalently, the equilibrium value of the intermediary s strategic variable. Here, the second option is selected, i.e. the determination of maximum membership fees. Then, the level of aggregate commission fee is determined through intermediary s profit function either with a given number of buyers and suppliers (Case 1 with exogenous variables n b, n s ), or with the intermediary having the ability to define the number of agents in both sides of the market (Case 2 where the variables n b, n s determined endogeneously). For buyers, the zero profit condition (Π b i * = 0) leads to the following equation: p b Hn b,n s,zl =-f b + n s 2 H a - t - zl 2 H1 + n s L 2 H2 +ghn b - 1LL 2 (11) In the same way, the zero profit condition for suppliers (Π s j * = 0) leads to the following equation: p s Hn b,n s,zl =-f s + n b H a - t - zl 2 H1 + n s L 2 H2 +ghn b - 1LL (12) As it can be easily checked, the above equations lead to the following lemma. Lemma 3: a) The entrance fee that can be charged to one side of the market depends not only on the number of firms on this market-side, but also on the number of firms on the other side (due to network effects) b) There is a negative relation between the commission fee and the membership fee charged by the intermediary to the same market side. 9 The zero profit condition is used when monopoly power exists in vertical relationships with a monopolist intermediary. Since the intermediary is the only one offering the transaction platform for buyers and suppliers, it can extract their entire surplus, if it wishes so. Instead of zero profits, the intermediary could allow firms to have profits equal with a constant positive price k. The analysis in the latter case leads to same findings as in the zero profit condition setting. 15

16 Case 1: The intermediary can not determine the number of participants in the market The intermediary maximizes its profits by selecting the price level for the commission fees for buyers and suppliers participating in the e-marketplace, taking as given the number of participating firms. The Intermediary s profit function is given by the following equation: Π I = p b Hn b,n s,zl n b + p s Hn b,n s,zl n s + X Hn b,n s,zl z (13) This profit function consists of two parts; the first refers to the revenues that the intermediary gains from the participation of firms in the e-marketplace (participation revenues) and expressed by the sum p b (n b, n s, z) n b + p s (n b, n s, z) n s. The second part of eq.(13), i.e. X(n b, n s, z) z, indicates the revenues from the commission fees (quantity revenues). This is so because every unit of the total quantity exchanged in the e-marketplace is charged with z b and z s, i.e. it is overall charged with z, by the intermediary. Substituting equations (9), (11) and (12) into eq.(13) and applying first order conditions, the equilibrium aggregate price level for commission fees is given by: z * = H-2 +ghn b - 1LHn s - 1LL H a - tl 2 H 1 + ghn b - 1LL n s (14) In case that the number of participants in both sides of the market are given (i.e. n b, n s ) and given the above equilibrium price for z, from equations (9) and (11) - (13) the entry fees for suppliers and buyers, the intermediary s profits and total quantity exchanged in equilibrium are: p b * = -f b + 2 n s H a - t 2 L 4 H1 +ghn b - 1LL 2 (15) p s * =-f s + H2 +ghn b - 1LL n b H a - t L 2 4 H1 +ghn b - 1LL 2 n s 2 (16) Π I * n b H a - tl 2 = -H f b n b + f s n s L + 4 H 1 +ghn b - 1LL (17) 16

17 Q * = X * = n b H a - tl 2 H1 +ghn b - 1LL (18) The above allow us to establish the following propositions. Proposition 1: There exist a critical proportion of n b, as a function of n s given by: n b min = 2 g Hn s - 1L - 1 (19) such that the intermediary can impose positive aggregate price level of commission fees for buyers and suppliers participating in its e-marketplace. Proof: Eq. (14) is always positive for every number of suppliers and buyers that satisfies inequality n b > n min b, given any γ, 0 γ 1 and (a t) >0. Proposition 2: For every structure of a two-sided B2B market, such that the number of participants is at most: n b max = a - 2 è!!!!! f b H 1 -gl - t 2 è!!!!! f b g (20) "################################ max a + 2 è!!!!! f b - t "#################################################### a - 2 è!!!!! f b H 1 - gl - t n s = 2 è!!!!! g è!!!!! f s (21) the owner of the e-marketplace can follow a pricing policy that includes both membership fees and commissions. In a two-sided B2B markets with number of agents more than n max b and/or n max s, the intermediary must subsidize one or both sides of the market. Proof: From equations (15) and (16) and given that 0 γ 1 and a, f b, f s, t >0, the membership fee for buyers p b * is always positive when n b < n max b, while the membership fee for suppliers p s * is positive if 17

18 n s è!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 2 +gh n b - 1 L è!!!!!!! n b H a - tl 2 H 1 +gh n b -1LL è!!!!! f s Substituting n max b to the above inequality we have that for any n s < n max s the fee p s * is always positive. Moreover, it is easily proven that for any 0 γ 1, {a, f b, f s, t} >0, (a t) >0, and for every n b, n s N, the minimum number of buyers for z to be positive, is always smaller than n max b (n min b < n max b ). Hence, in general, given equations (20)-(21): * p b Hnb,n s, gl > 0 * p s Hnb,n s, gl > 0 z * Hn b,n s, gl > 0 Π I * Hn b,n s, gl > 0 n b < n b max, n s < n s max, γ (0, 1], a, f b, f s, t >0 In fact, the latter proposition is valid for any industry where the agents move to e- commerce transactions, face positive connection costs and need an intermediary to establish their transactions. This can be proved if we consider the case in which no membership fee is charged. Then, the maximum numbers of downstream and upstream firms in the market are given by n max b and n max s respectively. In other words, in any industry with n b < n max b and n s < n max s, the intermediary can always follow a pricing policy constituted by both membership fees and commissions 10. Proposition 2 is also supported by empirical evidence, since most of the B2B e- marketplaces have revenues both from membership and usage fees (commissions or transaction fees). However, one important finding arises from the combination of Proposition 2 with Lemma 3. The inverse relation between membership fees and commissions charged by the intermediary leads to the conclusion that, the intermediary faces a trade-off between these two pricing instruments, and he can not charge high prices in both of these instruments. The latter is, to some extent, in contrast to the common sense according to which a monopolist intermediary could 10 Of course, the setting in the present model, where the intermediary have monopoly power, enhances a finding like this. However, the empirical evidence shows that monopoly power exists in many B2B e-marketplaces in most industries. 18

19 set very high prices in membership and usage fees independently of the conditions in the market. Moreover, subsidy policies by intermediaries that are sometimes observed in the real world, can be also explained in our setup. Suppose that the intermediary creates an e-marketplace in a given B2B market and he is forced by a social planner or a policy maker to offer his services to all firms operating in the market (i.e. the number of buyer and sellers is given and cannot be changed). Proposition 2 indicates that the maximum number of agents (n max b, n max s ) that allow positive membership fees (i.e. no subsidies) is decreasing in some structural characteristics of the two-sided market, such as connection and production costs and the degree of product differentiation in the downstream market. High values of these parameters reduce n max b and n max s and subsequently can lead to negative prices for p b and p s, i.e. a kind of subsidy to one or both sides of the market. For example, the intermediary prefers to operate its electronic platform in e-commerce mature markets, where agents have already the know-how and the technology to support electronic B2B transactions (low connection costs). In an opposite case, e.g. in B2B markets with agents more than n max b and/or n s max and low e-readiness, the intermediary does not want to charge positive membership fees, but instead he prefers to subsidize one or both side(s) of the market. The level of subsidy in such cases is given by the absolute values of equations (15) and (16). The above analysis is summarized in the following proposition. Proposition 3: If the number of agents in a B2B market is large, the intermediary prefers to charge high commissions and very membership fees. In markets with n b >n max b and/or n s >n max s he prefers to subsidize the participation of some or all of the firms. Proof: According to Proposition 2, membership fees for buyers and sellers decrease max and become zero when n b =n b and n s =n max max s. For n b >n b and/or n s >n max s, membership fees are negative and their absolute value gives the level of subsidy in each side of the market. Ceteris paribus, the equilibrium level of commission z always increases with an increase in the number of participants in the market: 19

20 z *, z > 0 nb ns * The intermediary s profits when n b =n max max b and n s =n s is still positive although p b =p s =0 because Π Ι* (n max b, n max s )>0. When n b >n max b and n s >n max s, the profits of Intermediary decrease with the number of buyers and suppliers: Π I * Hn b max,ns max L > Π I * Hnb max + k1,n s max + k2 L where k 1, k 2 N. Note that, the intermediary will have zero profits when the proportion of buyers and sellers is: Π I * = 0 Ø n s = n b H a - tl 2 4 H 1 +ghn b - 1LL f s - f b f s Proposition 3 is very important since it describes the way the intermediary optimally uses his pricing instruments in B2B markets with different number of agents. When there is a large number of participants from both sides of the market, the intermediary follows a pricing strategy with negligible membership fees for all agents in the market in order to attract/ keep them in the e-marketplace. The large number of participants increases the quantity exchanged in the e-marketplace, and the intermediary obtains profits in this case by charging higher commissions for the increased quantity. The following proposition investigates the pricing behaviour of the intermediary as a function of product differentiation (γ). Proposition 4: A stronger competition among downstream firms (buyers), i.e. a higher γ, forces the intermediary to charge lower membership fees and higher commissions for both sides of the market; the profits of intermediary decrease with the intensity of competition in the downstream market (as γ increases). Proof: Ceteris paribus, it can be easily seen from Equations (15) to (18) that for γ 1 < γ 2 : 20

21 p b * Hnb,n s, g 1 L > p b * Hnb,n s, g 2 L p s * Hnb,n s, g 1 L > p s * Hnb,n s, g 2 L z * Hn b,n s, g 1 L < z * Hn b,n s, g 2 L Π I * Hn b,n s, g 1 L > Π I * Hn b,n s, g 2 L The intuition behind this result is as follows: as the degree of product substitutability (γ) in the downstream market increases, the competition among downstream firms become more intensive and firm s output quantities decrease. On the other side, the competition in the downstream market reduces also the quantity of input and the total quantity exchanged in the e-marketplace (see Q* in eq.(18)). Consequently, the profits of buyers and sellers decrease and the reaction of the intermediary has to set up lower membership fees (even subsidies when f b and f s are high enough) for both buyers and sellers, in order to keep a constant number of agents in the electronic platform. Proposition 4 also claims that in less differentiated downstream markets, the intermediary charges a larger commission fee in order to restrict the reduction of his profits. Nevertheless, the decrease of intermediary s profits is inevitable in those cases Case 2: The intermediary can determine the number of participants in the market When the intermediary has the ability to determine the number of upstream and downstream firms in the market, the first stage of the game is as follows: By substituting eq.(11)-(12) and eq.(9), the intermediary s profit function (eq.(13)) becomes: Π I = n i b j-f b + k 2 n s H a - t 2 L y 4 H1 +ghn b - 1LL 2 z +n i s j- f s + { k n b H a - t - zl 2 y n b n s H a - t - zl z H1 + n s L 2 z + H2 +ghn b - 1LL{ H 2 +ghn b - 1LLH1 +n s L Applying first order conditions, the aggregate price level for commission fees and the number of upstream and downstream firms in equilibrium are given by: 21

22 z * = - 2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g (22) n b * = è!!!!!!!!!!!!!! 1 - gh a - t L 2 è!!!!! g f b g g (23) n s * = 1 (24) Then, from equations (9) and (11) - (13) the entry fees for suppliers and buyers, the intermediary s profits and total quantity exchanged in equilibrium are: p b * = f b g 1 - g (25) p s * =-f s + H a - t L 2-4 f b + 2 "###### f b g H a - t L "########### 1 - g 4 g (26) Π I * =-f s + I a - 2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g -t M 2 4 g (27) Q * = X * = a - 2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g -t 2 g (28) The above equilibrium values imply two important findings that are summarized in the following proposition. Proposition 5a (Intermediary s first choice): A monopolistic intermediary determines a B2B two-sided market with only one firm in the supply side and offers subsidies per quantity exchanged in the e-marketplace. Proof: From Equations (22) and (24) it is easily seen that z* < 0 and n s * = 1. 22

23 Interestingly, the intermediary prefers a monopolistic structure for the upstream market. The intuition is as follows: Having the ability to extract the entire surplus from the participants in its e-market (zero profit condition), the intermediary prefers low competition in upstream market with just one supplier which creates large surplus. The potential negative impact of the existence of a monopolist supplier on the number of upstream agents on the other side of the market, that is a reduced number of downstream firms due to indirect network effects, seems to be negligible in this setting as the intermediary s platform is supposed to be the only transaction platform for the firms. In addition, the intermediary can also extract the entire surplus of downstream firms independently of their small or large number. Equation (23) shows that the optimal for the intermediary number of downstream firms depends negatively on the intensity of competition among them, on their connection and production costs (f b and t) and positively on the demand in final product market. The latter findings are in line with the analysis in paragraph for the effects of different market conditions in equilibrium prices. The second and even most surprising finding in Proposition 5a is the subsidization applied by the intermediary for the quantity exchanged in the e-marketplace. In contrast to membership fees, for which negative prices are used and interpreted as subsidies, the literature in e-commerce and two-sided markets usually does not refer to negative commissions and usage or transaction fees. Nevertheless, there is empirical evidence by two-side markets, such as credit cards, where these fees are used as a kind of subsidy. For example, in credit cards market, issuers often offer to users credit cards with zero usage (or transaction) fees and/ or with bonuses (discounts, money returns, etc) depending on the usage of credit cards. Moreover, the nature of B2B e-commerce allows an interpretation of negative commission as subsidy per quantity because there are many online services that can be offered for free and depend on the amount of exchanged quantity (e.g. logistics or finance services). The remaining question is why the intermediary, although being a monopolist in this setting, prefers to subsidize the quantity exchanged in his e-marketplace. The answer is given in the following proposition. Proposition 5b (Intermediary s second choice): In order to reach its maximum profits without subsidizing exchanged quantity in its e-market, a monopolist 23

24 intermediary determines a B2B two-side market with two firms in the supply side (n s *=2) and imposes an aggregate commission fee and a supplier s membership fee given by: z H2L * = H a - t L 4-2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g (29a) p s H2L * =-f s + H a - t L 2-4 f b + 2 "###### f b g H a - t L "########### 1 - g 16 g (30a) Proof: By substituting eq.(11) - (12) and eq.(9), the intermediary s profit function (eq.(13)) becomes: Π I = n i b j-f b + k 2 n s H a - t 2 L y 4 H1 +ghn b - 1LL 2 z +n i s j- f s + { k n b H a - t - zl 2 y n b n s H a - t - zl z H1 + n s L 2 z + H2 +ghn b - 1LL{ H 2 +ghn b - 1LLH1 +n s L Applying first order conditions, the aggregate price level for commission fees and the number of upstream firms in equilibrium are given by: z * = H n s - 1 LHa - t L - 2 è!!!!! f b 2n è!!!!!!!!!!!!!! s 1 - g (29b) n b * = è!!!!!!!!!!!!!! 1 - gh a - t L 2 è!!!!! g f b g g Then, the entry fees for suppliers and buyers, the intermediary s profits and total quantity exchanged in equilibrium are: p b * = f b g 1 - g (30a) p s * =-f s + H a - t L 2-4 f b + 2 "###### f b g H a - t L "########### 1 - g 4 g n s 2 (30b) Π I * =-n s f s + I a - 2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g -t M 2 4 g (31) 24

25 Q * = X * = a - 2 è!!!!! f b è!!!!!!!!!!!!!! 1 - g -t 2 g Eq. (31) shows that the intermediary s profits (Π I *) decrease as the number of upstream firms (n s ) increases: Π I * =-f s < 0 n s For n s *=1, the intermediary subsidizes the quantity exchanged in the e-marketplace and all variables have the values presented in equations (22)-(28). For n s *=2, equations (29b) and (30b) give the aggregate commission fee and the supplier s membership fee in equations (29) and (30) respectively. The aggregate level of z is always positive in Eq.(29). For n s *=2, eq.(31) gives: I * Π H2L =-2fs + I a - 2 è!!!!! f è!!!!!!!!!!!!!! b 1 - g -t M 2 4 g (32) The Proposition 5b shows that by selecting n s =2 the intermediary can charge positive commissions reaching however lower profits, as Π I * > Π I (2) *. Lower profits are caused because there is a negative relation between the commission and the membership fees charged by the intermediary (Lemma 3). This is proven by the comparison of the values of commissions and suppliers membership fees in intermediary s first and second choice strategy (z* < z (2) * and p s * > p s(2) * ). In other words, the answer to why the intermediary prefers to subsidize the quantity exchanged in its marketplace is that in this way it can charge higher membership fees. The latter also reveals that the impact on intermediary s profits from the participation revenues (stemming from membership fees) is greater compared with the impact from quantity revenues (stemming from commissions). Combined with the findings in section (Proposition 3), it seems that Participation revenues have a decreasing rate bigger than the increasing rate of quantity revenues as the number of participants in the e-marketplace increases. All the above can lead to a more general conclusion about the preferences and pricing policy of the intermediary. 25