The Optimal Innovation Decision for an Innovative Supplier in a Supply Chain

Transcription

1 The Optimal Innovation Decision for an Innovative Supplier in a Supply Chain Jingqi Wang Kellogg School of Management Northwestern University Hyoduk Shin Rady School of Management University of California - San Diego February 013 Abstract We study a supply chain consisting of an upstream supplier who invests in innovation, which increases the value of products to end users, and downstream manufacturers who sell to end users. We analyze the supplier s optimal innovation decision and show that the supplier s optimal innovation level is higher with the wholesale price contract than with bilateral bargaining. Moreover, with the wholesale price contract, the downstream competition does not affect the supplier s optimal innovation decision. However, if the manufacturers and the supplier bargain, the supplier s optimal innovation level under the downstream competition can be either higher or lower than that under the downstream monopoly, depending on the cost structure. Furthermore, these results are robust under the presence of complementary components suppliers. We also demonstrate that the supplier is better off using the wholesale price contract than using bilateral bargaining. Interestingly, the manufacturers profits can also be higher with the wholesale price contract in some cases. In the bargaining case, surprisingly, we find that under certain conditions, the downstream competition hurts the supplier. Lastly, we show that a horizontal merger between two manufacturers may not always benefit them. Keywords: supply chain management; innovation decision; competition Northwestern University, Evanston, IL jingqi-wang@kellogg.northwestern.edu University of California - San Diego, La Jolla, CA hdshin@ucsd.edu

2 1 Introduction Technology innovation is a primary source for many firms to improve the value of their products to customers, and also to increase customers willingness to pay. In some industries, it is the supplier who drives the technology innovation of certain key components. Manufacturers buy from this innovative supplier, assemble the products and then sell to end users. From example, the tap changer is a key component in power transformer equipments. The speed and size of tap changers significantly affect the performance of transformers and thus also the end customers willingness to pay for transformers. A German company Maschinenfabrik Reinhausen is almost a monopolistic supplier of tap changers in the world. Reinhausen makes investment in technology innovation to improve tap changers, and then sell to downstream transformer manufacturers such as Siemens, ABB, Alstom, and General Electric(GE). These manufacturers then sell transformers to their customers, such as utility companies. In this paper, we first address the following questions: How should a supplier like Reinhausen make its innovation investment decision under different downstream industry structure in a supply chain with different contract forms? Moreover, as a monopolistic supplier of tap changers, how should Reinhausen leverage its strong market power to gain more profit? More specifically, which contract type is better? In addition, does the competition between downstream manufacturers help Reinhausen to maximize its profit? These questions are relevant since Reinhausen may be able to design the right contract with its supply chain partners in order to maximize its profit, and also to manipulate the downstream transformer manufacturing industry competition to some extent. For example, if the downstream competition is detrimental to Reinhausen, it may limit its supply to some manufacturers to push them to exit the market. Lastly, considering the possible actions that downstream manufacturers may take, we ask the following question: Do competing manufacturers benefit from a stronger bargaining power if they consolidate their orders and negotiate with the supplier as a single entity? These questions are of interest to firms in other industries as well. For example, in the computer industry, Intel focuses on innovating better CPUs and then sells them to downstream competing manufacturers, such as Dell and HP, who then sell to end consumers. In some other industries, it is the manufacturer that innovates and downstream retailers that compete on the consumer market. In the pharmaceutical industry, an upstream manufacturer, Pfizer, innovates new drugs and sells to end patients through retailers such as CVS and Walgreens; in the electric car industry, 1

3 Nissan develops Nissan Leaf and sells to consumers through competing dealers. In these cases, the upstream manufacturer focuses on innovations and outsources distribution to downstream retailers. To answer these research questions, we consider a supply chain with one upstream supplier who invests in innovation and downstream manufacturers selling products to end users. 1 model the end user market as a horizontally differentiated market, in order to capture the fact that the transportation cost is an important factor in the transformer industry. The supplier first makes an innovation investment, which increases the quality of the component and thus also the value of the product to end users. Then the supplier and manufacturers engage in supply chain contracting. We explore two widely-used contract forms: (i) the wholesale price contract; and (ii) firms engage in sequential bilateral bargainings, that is, each manufacturer collaborates with the supplier to maximize their joint profit, and then splits the profit with the supplier, taking each other s reservation profit into consideration. Lastly, downstream manufacturers set retail prices and compete against each other for orders from end users. We first examine the supplier s optimal innovation decision, and find that the supplier should make a higher innovation investment when she sets the wholesale price comparing to the bilateral bargaining case. Furthermore, the downstream competition does not affect her optimal innovation level when she sets the wholesale price. In contrast, with bilateral bargaining, the supplier needs to take the downstream competition into consideration, when making her optimal innovation decision. Specifically, comparing to the downstream monopoly, when the innovation cost is relatively low, the supplier should invest less under the downstream competition, whereas when the innovation cost is relatively high, she should increase her investment level under the downstream competition. We then consider how the supplier can leverage her strong market power. The supplier may be able to specify which contract to use. We show that if the supplier can successfully commit to a takeit-or-leave-it wholesale price contract, then she can gain more profit than bilateral bargaining. Even though the wholesale price contract suffers from the double marginalization problem, the benefit of extracting more supply chain profit dominates. We Furthermore, in certain cases, interestingly, the downstream manufacturers are also better off with this wholesale price contract, because the supplier invest more in innovation, which enables manufacturers to charge higher retail prices. However, manufacturers may also have some channel power and negotiating a coordinating contract 1 In the rest of the paper, we refer to the competing downstream firms as manufacturers and the upstream innovating firm as the supplier. However, our analysis also applies to the situation with an upstream manufacturer and downstream retailers. In addition, we designate the upstream supplier as female and the downstream manufacturer(s) as male.

4 can be prevalent. For example, even though GE, as a transformer manufacturer, has competitors, it may still have a significant channel power and be able to negotiate with Reinhausen, rather than acting as a price-taker. We find that, in such cases, surprisingly, if the innovation cost is low, then having a monopolistic manufacturer in the downstream is desired from the supplier s point of view, whereas if the innovation cost is relatively high, then the competition between manufacturers benefits the supplier. Moreover, from the manufacturers point of view, interestingly, we find that manufacturers do not always benefit from the stronger channel power gained from a horizontal merger or collaborative purchasing. The reason is that it may reduce the supplier s incentive to invest in innovation and thus decrease the total supply chain profit. Lastly, as extensions, we study the end users surplus and the social welfare, as well as the impact of the presence of complementary components suppliers. In power transformers, the insulation material is another component whose technology innovation is also important. Weidmann is the global leader in the electrical insulation for transformer manufacturers. We extend our model to incorporate complementarity and show that our insights on suppliers optimal innovation decisions are robust. Our paper makes three primary contributions to the literature: First, we analyze how the competition between downstream manufacturers and different supply chain contracts affect the supplier s optimal innovation decision, a subject which has not yet been fully explored in the supply chain management literature. Second, we study how a monopolistic supplier can use her strong channel power to gain more profit, by either specifying supply chain contracts or influencing the competition between downstream manufacturers. Lastly, we demonstrate that a horizontal merger or collaborative purchasing does not always benefit manufacturers, because it reduces the supplier s innovation incentive. The rest of the paper is organized as follows: Section reviews the related literature. Section 3 introduces the model. The supplier s optimal innovation decisions under different scenarios are presented in Section 4. We then discuss the supplier s and manufacturers profits in Section 5. Section 6 examines the user surplus and the social welfare, and extends the model to include complementarity. Section 7 offers concluding remarks. Proofs are relegated to Appendix B throughout. 3

5 Literature Review Our paper is related to the operations management literature on innovation and new product development. Krishnan and Ulrich (001) review this literature with a focus on product innovation within a single firm. Studying sequential innovation with product design and pricing, Krishnan and Ramachandran (01) identify design inconsistency and suggest a way to solve this inconsistency problem. Bhaskaran and Ramachandran (011) explore how to manage product development with dynamically-evolving technologies, and analyze the trade-offs between performance and introduction timing decisions under competitive environment. They show that firms can strategically invest and manage introduction timing in order to weaken the competition. Bhaskaran and Krishnan (009) examine various collaborative strategies, such as investment sharing and innovation sharing, for joint product development between two firms, and identify more attractive strategies under different environments. Studying the interactions and conflicts between Intel and Microsoft in pricing and the timing of new product releases, Casadesus-Masanell and Yoffie (007) show that both investment levels and profits are higher if Intel and Microsoft can cooperate. Turning their attention to a supply chain setting, Ulku et al. (005) study the timing of process adoption for new products. They show that outsourced manufacturing can hurt the original equipment manufacturer (OEM), and the OEM can share the risk and accelerate the process adoption through joint investment. Adelman et al. (011) consider innovation by downstream customers, and address the question of when and how an upstream firm can encourage its customers to improve their products and also increase its own profit. Erat et al. (01) study the question of what fraction of end-product functionalities an upstream supplier should put in a subsystem when selling to downstream end-product manufacturers. They show that providing more functions in the subsystem has both positive and negative effects on the supplier s profit. Analyzing an upstream technology provider s development and introduction decisions in a supply chain, Erat and Kavadias (006) find that the technology provider may want to induce partial technology adoption by downstream manufacturers. Our paper incorporates downstream firms price competition and differs from the papers above by focusing on the impact of downstream competition on an upstream firm s optimal innovation decision in a supply chain. In the economics literature, theoretical research on the relationship between competition and innovation can be traced back to Schumpeter (194), who posited a negative relationship between competition and innovation. Recent research has discovered that the relationship between compe- 4

6 tition and innovation is more complex than Schumpeter suggested. For example, in studying the effect of competition on product innovation under a Cournot model, Dubey and Wu (00) show that companies willingness to innovate is higher when competition is intermediate and lower when competition is either intense or weak. Vives (008) studies the impact of competition on process innovation and entry, and analyzes a wide variety of demand systems under both Bertrand and Cournot models. He concludes that a higher industry concentration induces more process innovation in general. Analyzing the impact of buyer power on a monopolist supplier s incentive to innovate, Battigalli et al. (007) find that downstream competition increases the supplier s incentive to innovate. Inderst and Wey (007) consider independent demands for manufacturers and a convex production cost for the supplier, and demonstrate that the presence of larger buyers induces the supplier to invest more than the socially optimal level in product innovation. Our paper complements this stream of research by studying the supplier s optimal innovation decision in a supply chain with different contracts. We further consider how the supplier can leverage its market power to gain more profit via different contracting mechanisms. On the empirical side, Cohen and Levin (1989) provide a survey of the empirical literature about the relationship between market structure and innovation. They find that the empirical research (through 1989) testing the impact of market structure on innovation is inconclusive. In a more recent study, using panel data on U.K. patents, Aghion et al. (005) propose an inverted-u relationship between competition and innovation, and develop a theoretical model that explains this inverted-u relationship. Our model is different from the papers in this stream of literature because we look at the impact of competition on innovation in a supply chain, specifically, the impact of the downstream competition on upstream innovation. Our paper is also related to the literature on supply chain contracts, as reviewed extensively in Cachon (003). Considering product quality decisions, Villas-Boas (1998) examines how selling through a retailer affects an upstream manufacturer s decision on the product line compared to direct selling, and shows that the manufacturer should increase the differences in quality of the products in the product line when it sells through a retailer. Liu and Cui (010) examine how a manufacturer designs the product line in centralized versus decentralized channels, and find that the product line decision can be socially optimal in a decentralized channel, whereas it is never socially optimal in a centralized channel. Similar to the last two papers, we also study product quality decisions in supply chains. However, the focus of this paper is the impact of competition on the supplier s product innovation decision, which has been underexplored in the supply chain 5

7 (a) Downstream monopoly (b) Downstream duopoly Supplier Supplier Monopolistic Manufacturer Manufacturing facility 1 Manufacturing facility Manufacturer 1 Manufacturer Figure 1: The baseline supply chain structure: downstream monopoly vs. downstream duopoly. management literature. In addition, we consider widely-used wholesale pricing contracts as well as bargaining among the firms within a supply chain. 3 Model We first study a baseline supply chain structure with one upstream supplier who invests in innovation and sells to manufacturer(s), as illustrated in Figure 1. In the power transformer equipment industry, Reinhausen is almost a monopolistic supplier of tap changers. In the downstream, the transformer manufacturing industry is highly concentrated in most countries. For example, in the United States, the top five manufacturers control around 80% of the transformer market; and Iran Transfo is almost a monopoly in Iran. We model the end user market as horizontally differentiated (i.e., Hotelling 199); specifically, users are uniformly distributed on a unit interval [0, 1] and there are two manufacturing facilities located at both ends, 0 and 1. Users have a per-unit traveling cost t. In practice, transformers are very heavy and the corresponding transportation costs are quite significant. Moreover, due to the technological complexity, manufacturers cannot always perform maintenance on-site and sometimes have to transport transformers back to their factories. As a result, the location of the manufacturer is a big consideration when users make their purchase decisions. A user s utility is the product quality less the traveling cost and the retail price. Specifically, if a user located at a [0, 1] buys a product with quality Q at price p from the manufacturing facility located at 0, her net utility is u = Q p at. A user needs at most one product and makes her purchase decision to maximize her utility. Furthermore, the manufacturer owns both facilities in the downstream monopoly case, whereas two competing manufacturers own one facility each in the 6

8 The supplier invests in innovation. The supplier and manufacturer(s) contract. Manufacturers set the retail priceandtherevenueis realized. s=1 s= s=3 Figure : The model timeline downstream duopoly case, as depicted in Figure 1. The timeline of our model is illustrated in Figure. There are three stages. At the initial stage, s = 1, the supplier makes an innovation decision, which determines the product quality Q, and incurs a corresponding innovation cost CQ /. The unit production cost for the supplier c S is increasing in this quality Q; that is, c S = c S + kq, where c S is normalized to be zero. At the second stage, s =, the supplier and manufacturers contract. We consider two different contract forms. (i) The supplier sets the wholesale price w and makes a take-it-or-leave-it offer to the manufacturers. (ii) The supplier and manufacturers bargain on how to split the gross profit, not including the innovation investment cost which is sunk at this point. We employ the sequential bilateral bargaining model in de Fontenay and Gans (007), which formally develops a framework for analyzing a bargaining game between agents in a network with externalities. The bargaining outcomes in de Fontenay and Gans (007) are bilaterally efficient, but may not be socially efficient due to externalities; specifically, in this bargaining case, each bilateral contract maximizes the bilateral surplus, taking other contracts as given. For example, a two-part tariff and any other sophisticated supply chain contracts with lump sum payments can achieve such a result. Finally, at the last stage, s = 3, the manufacturers set retail prices and the revenue is realized. The manufacturers also have a unit manufacturing cost (or unit selling cost for retailers) c M. 4 The Supplier s Optimal Innovation Decision In this section, we study the supplier s optimal innovation decision under different scenarios. We first consider a wholesale price contract which is simple and widely-used in practice (see., e.g., Cachon 004) and examine how the supplier should make her innovation decision with or without the downstream competition. We then analyze the case where manufacturers negotiate with the supplier to set bilateral efficient contracts and split the profit. Lastly, we compare the supplier s optimal innovation levels with different contracts. In addition, we also provide a centralized supply chain case in Section A of the Appendix. 7

9 4.1 The wholesale price contract We first look at the scenario in which the supplier sets the wholesale price to a monopolist manufacturer with two manufacturing facilities on both ends. To obtain the supplier s optimal innovation decision, we solve backwards. At stage 3, given the innovation level Q and the wholesale price w, if the manufacturer charges a retail price p > Q t/, the utility that the user in the middle obtains from purchasing the product is Q t/ p < 0, and thus the market is partially covered and the total demand is (Q p)/t. However, if the manufacturer charges a retail price p Q t/, all users have a nonnegative utility from purchasing the product, and thus the market is fully covered. Therefore, the manufacturer s pricing problem at stage 3 is to maximize his profit, which is as follows: p w c M, if p Q t Π M (p) = ; (Q p)(p w c M ) t, otherwise. (1) Optimizing (1) over p, we obtain the optimal retail price as p Q t (w, Q) =, if w Q c M t ; Q+w+c M, if w > Q c M t. () Under the optimal retail price (), the supplier s corresponding profit in terms of the wholesale price and the innovation level is π S (w, Q) = w kq CQ, if w Q c M t ; (Q w c M )(w kq) t CQ, if w > Q c M t. (3) The supplier then sets the wholesale price w and the innovation level Q to maximize her profit, which is given in (3). In the duopoly manufacturers setting, for the pricing game between the two manufacturers, given the quality Q and the wholesale price w, any symmetric equilibrium must fall into one of the following three cases: (i) the user market is fully covered and the user in the middle obtains strictly positive surplus; (ii) the user market is fully covered and the user in the middle gets zero surplus; (iii) the user market is partially covered. Suppose that the equilibrium falls into case (i), Note that the equilibrium outcome is equivalent to the one in which the monopolist manufacturer owns one store located in the middle. 8

10 given p = P, manufacturer 1 s profit can be written as: Π M1 (p 1 ) = ( ) 1 p 1 P t (p 1 w c M ), if p 1 < Q P t ; (Q p 1 )(p 1 w c M ) t, if p 1 Q P t. (4) Optimizing (4), we obtain the best response p 1 (P ). Similarly, we can also obtain the best response p (P ) for manufacturer given manufacturer 1 s price P. By intersecting those two best response functions, we find that p 1 = p = t+w +c M is an equilibrium. Since the user market is fully covered and the user in the middle has strictly positive surplus in this case, the condition w < Q c M 3t/ should be satisfied, under which the corresponding supplier s profit becomes w kq CQ /. We can also analyze cases (ii) and (iii) similarly, and obtain the equilibrium retail price as: w + c M + t, p 1 (w) = p (w) = Q t, if w < Q c M 3t ; if Q c M 3t w Q c M t ; Q+w+c M, if w > Q c M t ; (5) and the supplier s profit as a function of the wholesale price w and the innovation level Q is the same as (3). So after optimizing over the wholesale price w and the innovation level Q, the downstream monopoly and the downstream duopoly actually produce the same innovation level, as presented in the following proposition: Proposition 1 If the upstream supplier sets the wholesale price, then downstream competition has no impact on the supplier s optimal innovation level, which is as follows: If C (1 k) (c M +t), then Q = (1 k)/c; otherwise, Q = 0. And the supplier s optimal wholesale price and the manufacturers equilibrium retail price are as follows: If C (1 k) (c M +t), then p = (1 k)/c t/, and w = (1 k)/c t c M ; otherwise, p = w = 0. When the supplier sets the wholesale price, she can control the intensity of the downstream competition by setting the wholesale price appropriately. If the wholesale price is very high, the user market is partially covered in equilibrium, i.e., each manufacturer becomes a monopolist in his own local market and the downstream competition does not affect the supplier. In contrast, if the wholesale price is very low, the user market is fully covered in equilibrium and the manufacturers compete to attract more users. 9

11 When the upstream supplier sets the wholesale price, she sets it in such a way that the user market is fully covered in equilibrium. At the same time, the competing manufacturers set the retail price at the same level as the monopolist manufacturer so that each covers exactly one-half of the user market in equilibrium. At the optimal wholesale price, under the downstream competition, the retail prices are the same as those prices under the downstream monopoly. This wholesale price therefore attenuates the impact of downstream competition. As a result, the supplier s optimal innovation decision is not affected by the downstream competition. This result suggests that if Reinhausen is setting the wholesale prices of tap changers, then its optimal innovation decision is not affected by the competition between downstream transformer manufacturers, such as Siemens and ABB. Similarly, considering electric cars whose innovation is a critical factor for sales, if Nissan as a manufacturer sells its Nissan LEAF through competing retail dealers in one region and it sets the wholesale price, Proposition 1 implies that the downstream competition among the dealers will have no substantial impact on the innovation decision of Nissan. Moreover, if Pfizer sets the wholesale price for its drugs, its innovation investment decision does not depend on the competition between downstream retailers such as CVS and Walgreens. However, in practice, many more sophisticated contracts exist to improve supply chain efficiency. Moreover, big manufacturers such as GE may not always act as price-takers and may negotiate on contract terms with the supplier. Some of those sophisticated contracts, such as two-part tariff contracts, can be represented by a bargaining model. We hence analyze the supplier s optimal innovation decision using a bargaining model in a supply chain. 4. Bargaining In this section, we study the supplier s optimal innovation decision when firms within a supply chain bargain. For a bargaining model, we employ the framework in de Fontenay and Gans (007), which uses a sequential bilateral bargaining model with passive beliefs. The bargaining outcome is independent of the negotiation sequence. The model also captures bilateral efficiency between the bargaining firms, i.e., any bilateral bargaining contract maximizes the two parties total profit, taking other contracts as given. In our model, the supplier cannot directly control retail prices, and hence, the downstream competition may reduce the total supply chain profit; that is, the downstream competition imposes negative externalities by reducing the total supply chain profit, a feature that is also captured in de Fontenay and Gans (007), which analyzes a bargaining game between agents in a network with externalities. 10

12 The logic of the bargaining model is as follows. Consider a network of N players and m possible bilateral contracts, where m N(N 1)/. In any bilateral bargaining in the network, denote the two parties as party 1 and party, respectively. If the contract between them breaks down, party 1 gets reservation profit R 1 and party gets R. These reservation profits are calculated taking other contracts in the network as given. Then parties 1 and get equal value added, that is, π 1 R 1 = π R, where π i is party i s profit as a bargaining outcome. If the total profit is not sufficient to make this extra profit nonnegative, this bilateral contract breaks down and all parties bargain in the new network structure. Moreover, all these conditions must be satisfied for all bilateral contracts. We first analyze the downstream monopoly case. 3 In this case, given a fixed quality Q, the manufacturer captures one-half of the total gross profit under the bilateral bargaining model, since neither party gets any reservation profit if the relationship breaks down. Therefore, the retail price is set to maximize the total profit, which is: p c M kq, if p Q t Π SC (p) = ; (Q p)(p c M kq) t, otherwise. Optimizing (6) with respect to p, we obtain the optimal price as: p (Q) = Q t, if Q c M +t 1 k ; (6) Q(1+k)+c M, if Q < c M +t 1 k. (7) The supplier enjoys half of the total gross profit, and incurs the innovation cost. Her net profit is: π S (Q) = Q(1 k) c M +t 4 CQ, if Q c M +t 1 k ; (8) (Q(1 k) c M ) 4t CQ, if Q < c M +t 1 k. Optimizing (8) over Q provides the optimal innovation decision, which is presented in the following proposition: Proposition In the bargaining case, under the downstream monopoly, the supplier s optimal innovation level is: If C (1 k) (c M +t), then Q = (1 k)/(c); otherwise, Q = 0. Furthermore, the retail price in equilibrium is as follows: If C (1 k) (c M +t), p = (1 k)/(c) t/; otherwise, p = 0. To determine the bargaining outcome under the downstream duopoly, we first study what hap- 3 In the downstream monopoly case, the bargaining contract is equivalent to a Nash bargaining outcome. 11

13 pens when an initial bilateral bargaining between the supplier and a manufacturer breaks down. The manufacturer s reservation value after this breakdown of the bargaining is zero, that is, R M (Q) = 0, since he has no other option for procuring the components. In contrast, the supplier can still sell her components to the remaining manufacturer, which provides her with a positive reservation value. Note that this reservation value for the supplier is exactly the same as her profit under the downstream monopoly case in which the monopolist manufacturer now owns only one manufacturing facility (or, equivalently, the manufacturer owns two facilities with the doubled user s transportation cost t). 4 Consequently, in this case, the supplier s gross profit from selling to only one manufacturer, which equals the reservation value for the supplier in bargaining, becomes: R S (Q) = Q(1 k) c M +t, if Q c M +t 1 k ; (Q(1 k) c M ) 8t, if Q < c M +t 1 k. (9) After obtaining this reservation value for the supplier when the initial bilateral bargaining breaks down, we can then determine the overall bargaining outcomes based on this reservation value. If the supplier sells to both manufacturers, the pricing game in this scenario becomes a special case of (5) with w = kq. Hence, the total gross profit, not including the innovation cost, is: Π(Q) = t, Q(1 k) c M +t, if c M +t 1 k if Q c M +3t/ 1 k ; (Q(1 k) c M ) t, if Q < c M +t 1 k. Q < c M +3t/ 1 k ; (10) The negotiation model implies that if the supplier sells to both manufacturers, the distribution of the revenue must satisfy the following system of equations: Π S (Q) + Π M (Q) = Π(Q) ; Π S (Q) R S (Q) = Π M (Q) R M (Q), (11) where Π S (Q) and Π M (Q) are the gross profits, not including the innovation cost, for the supplier and the manufacturer, respectively. Solving (11) and considering the fact that the supplier will sell to both manufacturers if and only if her gross profit Π S (Q) is larger than her reservation value 4 Under the downstream monopoly, the reservation value after the breakdown of bilateral bargaining is zero for both the supplier and the manufacturer, as discussed previously. 1

14 R S (Q), we obtain { } Π(Q) + RS (Q) Π S (Q) = max, R S (Q), (1) 3 from which it follows that the supplier s profit (including her innovation cost) becomes: π S (Q) = Q(1 k) c M t CQ, if Q c M +3t 1 k ; Q(1 k) c M 3 CQ, if c M +t 1 k Q < c M +3t 1 k ; (Q(1 k) c M ) 1t (Q(1 k) c M ) 1t (Q(1 k) c M ) 4t + t 3 CQ, if c M +3t/ 1 k < Q < c M +t 1 k ; + Q(1 k) c M 3 t 6 CQ, if c M +t 1 k Q c M +3t/ 1 k ; CQ, if Q < c M +t 1 k. (13) Lastly, we use this bargaining outcome for the supplier s profit and analyze her optimal innovation level: by optimizing (13) over Q, we obtain the supplier s optimal investment decision and the equilibrium retail price as presented in the following proposition: 5 Proposition 3 In the bargaining case, with the downstream competition, there exists c M such that for all c M < c M, the supplier s optimal innovation level and the equilibrium retail price are as follows: (Q, p ) = (0, 0), if C > (1 k) ( (1 k)(cm t) (1 k) 6tC, (1 k)(c M t) (1 k) 6tC t ( ) cm +3t (1 k), c M +t(+k) (1 k) ( 1 k 3C, c M + t + (1 k)k 3C ( 1 k ), if, if ), if (c M +t) ; 7(1 k) 6(c M +3t) < C (1 k) (c M +t) ; C, 1 k C t), if C 5(1 k) (1 k) (c M +3t) < C 7(1 k) 6(c M +3t) ; 5(1 k) 1(c M +3t) < C (1 k) (c M +3t) ; 1(c M +3t). (14) If it is too costly to invest in innovation, i.e., if C > (1 k) (c M +t), the supplier does not do so, which results in Q = 0. In contrast, if C 5(1 k) 1(c M +3t), innovation is cheap and thus the supplier chooses a high innovation level. In this case, the downstream competition between manufacturers hurts the total supply chain profit so much that in equilibrium only one manufacturer remains in business; that is, the supplier wants to sell to only one manufacturer to prevent the loss of the total supply chain profit due to the downstream competition. This provides one explanation for 5 There are too many cases to consider if one examines all values of c M and t. So for illustration purposes, we present the results for the case in which c M is relatively small; in that case, the impact of the downstream competition on the supplier s optimal innovation level can go either way. 13

15 the phenomenon of an exclusive regional downstream retailer in some industries. In addition, such an exclusive dealing provision can also be initiated by the downstream firms during the bargaining process. If the cost of innovation is intermediate, i.e., in the middle three ranges of C ( 5(1 k) 1(c M +3t) < C (1 k) (c M +t) ), the supplier invests in innovation in such a way that the user market is fully covered in equilibrium. But her reservation value depends on whether the user market is fully covered when an initial bilateral bargaining breaks down, after which she bargains with only one remaining manufacturer. Specifically, if 7(1 k) 6(c M +3t) < C (1 k) (c M +t), the user market will be covered partially after the breakdown of an initial bilateral bargaining. Otherwise (i.e., when 5(1 k) 1(c M +3t) < C 7(1 k) 6(c M +3t) ), the user market will still be fully covered even after an initial bilateral bargaining breaks down and the supplier bargains with the remaining manufacturer. Additionally, if (1 k) (c M +3t) < C 7(1 k) 6(c M +3t), the user market is fully covered, but just barely, in the sense that the user in the middle (a = 1/) is indifferent between buying and not buying. On the other hand, if then all users have positive surplus by purchasing the product. 5(1 k) 1(c M +3t) < C (1 k) (c M +3t), Comparing the supplier s optimal innovation decision in Propositions and 3, we obtain the following results: Proposition 4 In the bargaining case, the supplier s optimal innovation decision depends on the downstream competition in the following way: There exists c M such that for all c M < c M, the following hold: (ii) If (iii) If (i) If C > (1 k) (c M +t), then no innovation occurs under both the downstream monopoly and the downstream duopoly. (1 k) c M +3t < C (1 k) (c M +t), then the supplier invests more under the downstream competition. 5(1 k) 1(c M +3t) < C (1 k) c M +3t, then the supplier invests less under the downstream competition. (iv) If C 5(1 k) 1(c M +3t), then the supplier should choose the same innovation level in both cases. First, if the innovation cost is very high (C > (1 k) (c M +t) ), the downstream competition has no impact on innovation because this high cost dissuades the supplier from investing in innovation regardless of the downstream competition. Second, if the innovation cost is very low (C 5(1 k) 1(c M +3t) ), as illustrated in Proposition 3, only one manufacturer remains in business even under the downstream competition; in other words, exclusive dealing occurs in this case. And the marginal benefit of innovating is the same under both cases, which implies that the supplier s optimal innovation 14

16 level is the same as well. Consequently, the downstream competition has no impact on the supplier s optimal innovation decision. Third, if the innovation cost is intermediate, i.e., if 5(1 k) 1(c M +3t) < C (1 k) (c M +t), the downstream competition has two opposite impacts on the supplier s incentive to innovate. First, the manufacturers competition decreases the total supply chain profit because the supplier cannot directly control retail prices. The downstream competition therefore hurts the supply chain, which in turn decreases the supplier s profit. A smaller profit for the supplier is also associated with a smaller marginal revenue from innovation investment, which then induces the supplier to invest less in innovation. On the other hand, the downstream competition strengthens the supplier s bargaining position. Note that without the competition between manufacturers, the supplier s reservation value is zero if her bilateral bargaining with the monopolistic manufacturer breaks down. With the downstream competition, however, her reservation value R S becomes positive because she can still bargain with the other manufacturer if the bilateral bargaining with the first breaks down. This improved bargaining position increases the supplier s share of the supply chain profit, which is also associated with the increased marginal revenue of her investment in innovation. As a result, the improved supplier s bargaining position due to the downstream competition provides her an incentive to invest more in innovation. When the innovation is relatively cheap ( 5(1 k) 1(c M +3t) < C (1 k) c M +3t ), the impact of this decrease in the supply chain profit dominates the impact of the supplier s improved bargaining position from the downstream competition. Consequently, it is optimal for the supplier to invest less in innovation. In contrast, if the innovation is relatively expensive ( (1 k) c M +3t < C (1 k) (c M +t) ), the impact of the improved supplier s bargaining position on innovation dominates. As a result, the supplier should invest more in innovation under the downstream competition. Proposition 4 implies that if bilateral bargaining is employed in certain the industries, it is important for a manager of an upstream supplier such as Reinhausen to understand the structure of the downstream industry, in order to make an optimal innovation decision. Depending on the innovation cost, the supplier s optimal innovation level under the downstream competition could be higher or lower than that under the downstream monopoly. Moreover, the supplier s optimal innovation level may also depend on the type of the supply chain contract used, as shown in the following proposition: Proposition 5 When the supplier sets the wholesale price, her optimal innovation level is never lower than that in the bilateral bargaining case and strictly higher if and only if C (1 k) (c M +t). 15

17 In the bargaining model, the supplier and the manufacturer(s) split the supply chain profit based on the bargaining outcome given the innovation level, whereas when the supplier sets the wholesale price, she extracts more supply chain profit from the manufacturers. This potentially increases the benefit of innovation for the supplier under a wholesale price contract, comparing to the bilateral bargaining case. On the other hand, if she sets the wholesale price, the total supply chain profit can suffer due to the double marginalization problem, which then reduces her profit; this in turn implies that the supplier should innovate less when she sets the wholesale price than when she bargains with the manufacturers. Comparing the optimal innovation levels in the bargaining model for the downstream monopoly and for the downstream duopoly with those when the supplier sets the wholesale price, we find that if the innovation cost is low (C (1 k) (c M +t) ), the supplier should invest more under a wholesale price contract than under bilateral bargaining. Proposition 5 suggests that managers of upstream suppliers should consider the type of the supply chain contract when making innovation decisions. For example, if the innovation cost is low and Reinhausen is using bilateral bargaining in its relationship with transformer manufacturers such as GE, then Reinhausen should invest less than the case in which it sets the wholesale price. 5 The Impact on Profits So far, we have analyzed the supplier s optimal innovation decision under different scenarios. What if the supplier has a strong channel power either to choose the type of the supply chain contract or to manipulate the downstream competition to some extent? How should a monopolistic supplier like Reinhausen get the most from its strong channel power? In this section, we first answer the question: which supply chain contract is more desired from the supplier s point of view? We then explore the conditions under which the downstream competition benefits or hurts the supplier. Lastly, we consider the possible strategies that manufacturers may take, and show that manufacturers may not always benefit from a stronger channel power gained from a horizonal merger or colluding. We start by comparing the suppler s profit with a wholesale price contract than that with bilateral bargaining. The result is shown as follows: Proposition 6 The supplier s profit is higher when the supplier sets the wholesale price than when the manufacturers bargain with the supplier, and strictly higher if C < (1 k) (c M +t). With the wholesale price contract, after the quality exceeds a certain level, the supplier is able to extract all the marginal benefit of further innovation and leave manufacturers with a constant 16

18 profit. In contrast, with bilateral bargaining, manufacturers take a significant portion of the total profit. As a result, the supplier gains more profit with the wholesale price contract. Proposition 6 implies that it is better for Reinhausen to employ a wholesale price contract than bargaining with transformer manufacturers such as GE. Then is it really practical for Reinhausen to push GE or Siemens to take its wholesale price? When the supplier sets the wholesale price, she sets it to extract as much profit as possible from the manufacturers. At first glance, it seems that manufacturers would always resist such a wholesale price contract. In certain cases, however, it might not be so hard for the supplier to implement a wholesale price contract, because, surprisingly, manufacturers are also better off with the wholesale price contract set by the supplier, as stated in the next proposition: Proposition 7 Under the downstream monopoly, the manufacturer s profit is strictly higher when the supplier sets the wholesale price than that when the manufacturer bargains with the supplier, if and only if (1 k) c M +3t < C < (1 k) (c M +t) is satisfied. Under the downstream competition, there exists c M, such that for all c M < c M, manufacturers profits are strictly higher when the supplier sets the wholesale price than those when the manufacturers bargain with the supplier, if and only if 5(1 k) 1(c M +3t) < C < (1 k) (c M +t) is satisfied. If the innovation investment level is fixed, the monopolist manufacturer prefers bargaining over the wholesale price contract offered by the supplier for the following two reasons: (i) bargaining increases the total supply chain profit since the bilateral bargaining maximizes the two parties total profits; and (ii) the manufacturer gains a larger share of the total supply chain profit than what he can get with the wholesale price contract. However, if we take the endogenous innovation investment into consideration, the monopolist manufacturer may prefer to let the supplier set the wholesale price, instead of bargaining. If the supplier sets the wholesale price, it encourages her to invest more in innovation than in the bargaining case, as shown in Proposition 5; her investment also increases the total supply chain profit, which then benefits the manufacturer as well. This benefit then outweighs the two previous disadvantages to the manufacturer. In that sense, the monopolist manufacturer sacrifices his share of the supply chain profits by letting the supplier set the wholesale price rather than bargaining, because he gains more from the supplier s higher innovation investment. In this sense, if the supplier sets the wholesale price rather than bargaining, this can be considered a win-win situation for both the supplier and the manufacturer. The above intuition remains valid even under the downstream competition. The benefit of 17

19 the increased innovation investment when the supplier sets the wholesale price is even larger under the downstream competition than under the downstream monopoly, in that the downstream competition enlarges the win-win region, in which both the supplier and the manufacturers prefer the wholesale price contract over bargaining; that is, (1 k) c M +3t < C < (1 k) (c M +t) in the downstream monopoly case. 5(1 k) 1(c M +3t) < C < (1 k) (c M +t) compared to However, in order to enjoy the benefit of the wholesale price contract, before the supplier innovates, manufacturers have to commit to taking whatever wholesale price the supplier sets afterwards. Such a commitment may not always be credible in practice and manufacturers may try to renegotiate the contracts with the supplier later. Moreover, there are still cases where manufacturers gain more profit with bargaining than the wholesale price contract. Then the natural question to follow is: in the bargaining case, how should the supplier leverage her strong market power to influence the competition between downstream manufacturers to gain more profit? The next proposition illustrates the conditions under which the downstream competition benefits the supplier in the bilateral bargaining case. Proposition 8 For the bargaining case, there exists c M such that for all c M < c M, the supplier s profit is higher under the downstream competition than that under the downstream monopoly, if and only if 1(1 k) 4c M +37t+ t(48c M +73t) < C < (1 k) (c M +t) is satisfied. The downstream competition strengthens the supplier s bargaining position by increasing her reservation profit, and at the same time may hurt the total supply chain profit. When the innovation cost is relatively high ( 1(1 k) 4c M +37t+ t(48c M +73t) < C < (1 k) (c M +t) ), the product quality is low and the market that each manufacturer can cover is relatively small, which then implies that their competition is mild. As a result, the negative impact of the downstream competition on the supply chain profit is small and the supplier gains more profit under the downstream competition, due to her stronger bargaining position. In contrast, when the innovation cost is low, the product quality is high and the competition between manufacturers becomes intense, which significantly reduces the supply chain profit. Therefore, the supplier is better off with one monopolistic manufacturer. Then from the manufacturers point of view, would two competing manufacturers benefit from the monopolistic position gained from a horizontal merger? Do they gain profit from combining their orders and negotiate with the supplier as a single entity? Intuitively, the competition often harms firms total profit in an industry; hence, one might expect that the downstream competition between manufacturers would decrease the manufacturers total profit. The next proposition demonstrates 18

20 that this intuition can be wrong, if we take the upstream firm s innovation into consideration: Proposition 9 In the bargaining case, there exists c M such that for all c M < c M, the total manufacturers profit is higher under the downstream competition than that under the downstream monopoly, if and only if 1(1 k) 4c M +35t < C < (1 k) (c M +t) is satisfied. Given a fixed innovation level, the total manufacturers profit for the bargaining case is lower under the downstream competition than that under the downstream monopoly, as expected. However, as illustrated in Proposition 4, in certain cases the downstream competition increases the innovation in a supply chain, whose positive impact can dominate the negative impact due to the competition; consequently, both the total manufacturers profit and the supplier s profit can be higher under the downstream competition than those under the downstream monopoly. et al. (01) show that pooling purchases may lead to lower profits because it reduces the demand variability and makes it easier for the supplier to extract profits. Proposition 9 provides another reason why pooling purchases can be detrimental to manufacturers in that it hurts the supplier s incentive to make the innovation investment. This result suggests that in making its acquisition decision of the Trasfor Group, a transformer manufacturer, managers of ABB, another transformer manufacturer, should also consider how this acquisition will affect Reinhausen s innovation decision on tap changers. We provide a summary of the optimal innovation levels and firms profits in Table 3. Note that the coordinated supply chain is the centralized case; the detailed proof for the expressions in that case is provided in Section A of the Appendix. Hu 19

21 Contract and Parameter range Innovation Total downstream profit The supplier s profit industry structure level The supplier sets C (1 k) (cm +t) the wholesale price. C > (1 k) (cm +t) Bargaining; C (1 k) (cm +t) downstream monopoly. C > (1 k) Bargaining; downstream duopoly. 1 k C 1 k C t (1 k) 4C c M +t 4 (cm +t) C > (1 k) (cm +t) 7(1 k) 6(cM +3t) < C (1 k) (1 k) (cm +t) (cm +3t) < C 7(1 k) 5(1 k) Coordinated C (1 k) cm +t 6(cM +3t) 1(cM +3t) < C (1 k) C 5(1 k) 1(cM +3t) (cm +3t) (1 k)(cm t) (1 k) 6tC cm +3t (1 k) supply chain. C > (1 k) 0 0 cm +t 1 k 3C 1 k C 1 k C t{6c(1 k) (cm +t) A} {6tC (1 k) ) } 3t 48 3C(cM +3t) (1 k) 9C (1 k) 4C c M +t (1 k) C c M +t (1 k) C (cm + t) (1 k) 8C c M +t 4 t(1 k) +C(c M 4c M t t ) 1tC (1 k) 5t 48 C(c M +3t) 8(1 k) (1 k) 18C c M 3 (1 k) 8C c M +t Table 1: Summary of equilibrium outcomes: Coordinated supply chain is the centralized case, and A = (1 k) + 3C (c M + 8c Mt+4t ). 0