垂直結合廠商防止連續結合的先占策略 - 政大學術集成

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(1)國立政治大學國際經營與貿易學系研究所碩士學位論文. 垂直結合廠商防止連續結合的先占策略 Preempting Successive Mergers 治 by a Vertically Merged Firm. 立. 政. 大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. 指導教授：溫偉任博士研究生：張馨云撰. 中華民國 107 年 7 月. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(2) Contents 1 Introduction ................................................................................................................. 3 2 The Model ................................................................................................................... 5 3 The Successive Model ................................................................................................ 6 3.1 A Vertically Merged Firm, a Non-Merged Upstream Firm and Two Non-Merged Downstream Firms ..................................................................................................... 7 3.2 A Vertically Merged Firm, a Horizontally Merged Firm and a Non-Merged Upstream Firm ........................................................................................................... 9 3.3 A Vertically Merged Firm Preempts the Horizontal Merger by Merging with the Downstream Firm .................................................................................................... 14 3.4 A Vertically Merged Firm Preempts the Vertical Merger by Merging with the Downstream Firm .................................................................................................... 19. 立. 政治大. ‧ 國. 學. 4 Conclusion ................................................................................................................ 22 References .................................................................................................................... 24. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(3) Abstract We investigate strategies that an incumbent vertically merged firm will implement to achieve maximal profit. When a horizontal merger occurs, it will decrease the profit of a vertically merged firm. Thus, the vertically merged firm will preempt the horizontal merger by merging with one of the downstream firms. However, this leaves open possibility for remaining firms to merge vertically. We then further analyze how a vertically merged firm preempts subsequent vertical mergers. We find that, among various preempting strategies, it is most profitable for the firm to merge with all of the downstream firms. Keywords: preempting successive mergers, vertically merged firm. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(4) 3. 1. Introduction Many real world mergers involve rival bids from both horizontally and vertically re-. lated firms. For example, in 2009, Oracle outbid IBM by 10 cents per share for the acquisition of Sun Microsystems Inc. This is considered a case of vertical merger because, unlike IBM and Sun, Oracle and Sun have little business overlap and their products complement each other (Clark and Worthen, 2009). In 2015, Ambit Microsystems Inc. vertically integrated with the Asia Pacific Telecom Co., Ltd., the top five telecom company in Taiwan, to acquire the 4G market (Hung and Gold, 2014). In 2017, the embattled Japanese conglomerate Toshiba sought a sale of the memory chip unit. 政治大 Toshiba Corporation finally立 completed the sale of its memory business, Toshiba Mem-. to make up for a multi-billion-dollar write-down in its nuclear operations. Recently,. ‧ 國. 學. ory Corporation, to a consortium led by Bain Capital Private Equity, SK Hynix and Apple Inc (Narioka, 2018). This deal is viewed as a horizontal merger because the main product of Toshiba is NAND flash which complements with DRAM that SK Hynix and. ‧. other corporation produce. In this paper, we set up a game-theoretical model to ana-. io. y. sit. downstream firm.. Nat. lyze the di↵erent incentives of a horizontally and a vertically related firm to acquire a. al. er. Among various reasons for mergers, one of them is to preempt rivals from merging.. n. v i n C h eliminating double izontal mergers because the gain from e n g c h i U marginalization outweighs the Colangelo’s (1995) seminal work demonstrates that vertical mergers often preempt hor-. gain from horizontal market power. In a follow-up study, Gelves and Heywood (2016) argue that with sufficient downstream cost asymmetry, a horizontal merger may preempt a vertical one if the horizontal merger results in a cost reduction for an inefficient firm. In this paper, we consider all possible mergers and investigate how an incumbent firm can do to preempt mergers. Several preempting strategies presented in this paper have not been addressed in previous studies. For example, the control of the intermediate good may be one way to preempt mergers. Besides, both of the aforementioned papers assume that there are two upstream and two downstream firms, while we make a more complex assumption. That is, we assume there are two upstream firms and three downstream firms and among these five firms, one upstream and one downstream firm are. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(5) 4 vertically merged. Furthermore, Colangelo (1995) only considers mergers when downstream goods are substitutes, while we extend the analysis to cases in which downstream goods can be either substitutes or complements. Ordover, Saloner and Salop (1990) set up a model to investigate the incentives of an integrated firm and the remaining unintegrated input suppliers to exclude rivals and the possible counterstrategies of competitors. Yao and Zhou (2015) show that a market structure is stable only when no firm merges or all firms merge, so mergers always occur in waves. Following the approaches taken by these papers, we use a three-stage game to incorporate all the features of interest.. 治政 acquire Qualcomm Inc. According to The Wall Street大 Journal, it is said that Intel’s 立 a combined Broadcom and Qualcomm would hold. In worried about the market power In March 2018, Singapore-based Broadcom Ltd decided to bid 117 billion dollars to. ‧ 國. 學. response, it could make an o↵er to buy Broadcom if it looks like Broadcom will succeed in its hostile bid for Qualcomm (Greenwald, 2018). However, in the end, President. ‧. Trump signed an order to halt the deal on concerns that a takeover of Qualcomm by the Singapore-based company would erode the United States’ lead in mobile technology and. y. Nat. sit. give China the upper hand (Meyersohn and Horowitz, 2018). In a successive model, we. al. er. io. analyze how an incumbent firm, a vertically merged firm, preempts mergers. First, it. n. preempts the horizontal merger by merging with one of the downstream firms. Second,. Ch. i n U. v. it preempts another vertical merger by merging with all of downstream firms.. engchi. In this paper, we will specifically look into how a vertically merged firm can preempt a horizontal merger and another vertical merger. We find that to preempt a horizontal merger, it costs less to merge with one of the downstream firms than to merge with an upstream firm. Furthermore, we find that to preempt another vertical merger, the vertically merged firm merges with all of downstream firms. The remainder of this paper is organized as follows. Section 2 formulates the model and derives the equilibrium outcomes. Section 3 presents when does a vertical (horizontal) merger preempt a horizontal (vertical) merger and formulates the successive model to look into how the vertically merged firm preempts mergers. This section is also applied to analyze the Broadcom and Qualcomm case. The final section concludes. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(6) 5 the paper.. 2. The Model Consider two upstream firms B1 , B2 produce a homogeneous input and sell to three. downstream firms D1 , D2 , D3 . One unit of input is transferred into one unit of output and the downstream firms each produces a di↵erentiated good. Assume that firms in both the upstream and the downstream market compete a la Cournot. Following H¨ ackner (2000, 2003), the final consumers’ preference takes the following form: ! 3 3 X X 1 X 2 qi qi + 2 qi qj + I. U (q, I) = 2. 政治大. i=1. i=1. 立. (1). i6=j. U (q) =. 3 X. qi. 2. i=1. 3 X. qi. i=1. !2. 3 X. 1. 學. ‧ 國. Rearrange the utility function, we get:. 2. qi2 .. (2). i=1. 2 (0, 1], the two final goods are substitutes; for. 2 [ 1, 0), the two. y. markets. For. Nat. 2 [ 1, 1] measures substitutability among the final goods in the downstream. sit. parameter. ‧. That is, the utility is quadratic in the consumption of three downstream goods. The. io. al. n. budget constraint:. er. final goods are complements. The consumers maximize utility subject to the following. i n C X h X XU p q +e In  gc ⇡h +i ⇧ , 3. 3. i i. where. P3. i=1 ⇡i. and. P3. j=1 ⇧j. 3. i. i=1. i=1. v. (3). j. j=1. denote the aggregate downstream and upstream profits,. respectively. With the first-order condition determining the optimal consumption of good i being @U =1 @qi. qi. (qj + qk ). pi = 0, i 6= j 6= k,. (4). Hence, firm i’s inverse demand is given by pi = 1. qi. (qj + qk ), i 6= j 6= k,. (5). Assume that the upstream firms produce the input at zero cost. To procure the input from the upstream market, independent downstream firms or horizontally merged firms. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(7) 6 pay the per unit market input price w, which they take as given. The vertically merged firm can acquire the input from its upstream division at zero cost. The total downstream production constitutes the derived demand for input. w is determined by equating the input demand and the input supply. We use backward induction to solve for the subgame perfect Nash equilibrium.. 3. The Successive Model In March 2018, two computer chip leaders brought about a number of concerns on. the development of the next generation of mobile networks. Broadcom Ltd. planned to. 政治大 could be the largest-ever technology 立 deal. Intel, the leading semiconductor company,. bid for its rival Qualcomm Inc. to about 117 billion dollars, in an attempt to force what. ‧ 國. 學. mulled a bid for Broadcom, according to a report from The Wall Street Journal (March 11, 2018). The newspaper said that Intel worried about the power a combined Broadcom and Qualcomm would hold. In response, it could make an o↵er to buy Broadcom.. ‧. Although the merger did not take place in the end, we adopt this case to our model.. sit. y. Nat. As mentioned before, we consider the case that there are two upstream firms B1 and B2 producing a homogeneous input and selling it to three downstream firms D1 , D2 and. io. n. al. er. D3 . B1 + D1 have formed a vertically merged firm such as Intel and will trade in the. i n U. v. upstream market. D2 and D3 are assumed to be Broadcom Ltd. and Qualcomm Inc.,. Ch. engchi. respectively, since they are in charge of manufacturing and selling chips. In the following model, we will prove that if the horizontal merger D2 + D3 decreases the profit of the vertically merged firm B1 + D1 , B1 + D1 would take actions to preempt the horizontal merger D2 + D3 . In order to incorporate all the features of interest, we analyze a three-stage game. In the first stage, the bidding stage, a horizontally and a vertically related firm have di↵erent incentives to acquire a downstream firm. As long as the horizontal merger occurs and it decreases the profit of the incumbent vertically merged firm, we enter the second stage. The vertical merged firm will preempt the horizontal merger by merging with one of the downstream firms. In the last stage, to compete with the incumbent vertically merged firm, another vertical merger will occur. However, the profit of the. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(8) 7 incumbent vertically merged firm will decrease, thus, it will preempt another vertical merger by merging with all of downstream firms.. 3.1. A Vertically Merged Firm, a Non-Merged Upstream Firm and Two Non-Merged Downstream Firms. 政治大. 立. ‧ 國. 學. As mentioned before, let s > 0 be the input that the vertically merged firm B1 + D1 sells in the upstream market. On the other hand, firm B1 + D1 buys the input in the. ‧. upstream market if s < 0. Besides, s can be equally divided into two parts, s2 and s3 .. sit. y. Nat. Furthermore, b is the input that the independent upstream firm B2 sells or buys in the upstream market. Similarly, b can be equally divided into two parts, b2 and b3 . The. io. n. al. er. downstream firms’ objective functions are therefore given as follows:. Ch. max ⇡B1 +D1 = p1 q1 + w(s2 q1. engchi. i + sn). U. v. (6). 3. max ⇡D2 = (p2. w)q2 .. (7). max ⇡D3 = (p3. w)q3 .. (8). q2 q3. Downstream profit maximization yields the following equilibrium quantities as functions of w: q1⇤ (w) =. 2 w 2( 2. +2 ⇤ 2w + , q2 (w) = 2) 2( 2. 2 2w + , q ⇤ (w) = 2) 3 2( 2. 2 . 2). (9). Combining equation (9) and the upstream market-clearing condition, s2 + b2 + s3 + b3 = q2⇤ (w) + q3⇤ (w).. (10). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(9) 8 We derive the inverse demand for the intermediate good as follows: w=. 2)(s2 + b2 + s3 + b3 2. (. 1 + s 2 + b 2 + s 3 + b3 ). .. (11). In the upstream market, given the equilibrium downstream production quantities, firm B1 + D1 chooses s, firm B2 chooses b to maximize their profits. Upstream profit maximization yields: si =. 2 2+ 4 3+ 2 2. bi =. 2 9 2. ( + 1)4. 2. 6. , 8i 2 {2, 3},. 2 , 8i 2 {2, 3}. 3 +6. (12). 政治大 + D立 and the independent downstream firm D. Accordingly, the equilibrium input price, downstream prices and downstream product 1. io. q11U 2D =. n. al. qi1U 2D =. y. er. Nat. 2D = p1U i. 2) 2)(2 2 + , 2 2(4 3 6) 2 2 5 +6 , 2(4 2 3 6) 4 2 3 3 2+2 , 8i 2 {2, 3}, 2 2(4 3 6) 2 2 5 +6 , 2(4 2 3 6) 3 4 , 8i 2 {2, 3}. 2 4 3 6 (. ‧. 2D p1U = 1. and D3 are as. sit. w1U 2D =. 2. 學. follows:. ‧ 國. quantities for firm B1. Ch. engchi. i n U. v. (13). The profits of the firm B1 + D1 , D2 and D3 are now: 1)(2 2 (5 + 2)(2 2 3 4(4 2 3 6)2 ( + 1) (3 4)2 = , 8i 2 {2, 3}. (4 2 3 6)2. 1U 2D ⇡B = 1 +D1 1U 2D ⇡D i. 2). , (14). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(10) 9. 3.2. A Vertically Merged Firm, a Horizontally Merged Firm and a Non-Merged Upstream Firm. 政治大. Now, we examine the influence on the vertically merged firm B1 +D1 when downstream. 立. horizontal merger D2 + D3 occurs. In other words, when Broadcom Ltd. merges with. ‧ 國. 學. Qualcomm Inc., are Intel’s profit being a↵ected?. The downstream firms’ objective functions are given as follows:. Nat. w)q2 + (p3. w)q3 .. (16). sit. q2 ,q3. y. q1. max ⇡D2 +D3 = (p2. (15). ‧. max ⇡B1 +D1 = p1 q1 + w(s2 + s3 ).. io. er. s is the input that the vertically merged firm B1 + D1 sells or buys. Besides, s = s2 + s3 and s2 = s3 . Downstream profit maximization yields the following equilibrium quantities. al. n. as functions of w: 1+w 2 2. q1⇤ (w) =. 2. Ch. , q2⇤ (w) =. i n U. v. e 2n+g +c 2w h i, q (w) =. 2(. 2. 2. 2). ⇤ 3. 2+ 2(. 2. + 2w . 2 2). (17). Combining equation (17) and the upstream market-clearing condition, s2 + b2 + s3 + b3 = q2⇤ (w) + q3⇤ (w).. (18). Similarly, the input that the firm B2 sells or buys is b. Besides, b = s2 + b3 and b2 = b3 . We derive the inverse demand for the intermediate good as follows: 1 w = s2 2. 2. s2. 1 s2 + b2 2. 2. b2. 1 b2 + s 3 2. 2. s3. 1 s3 + b3 2. 2. b3. b3 +1. 1 . (19) 2. In the upstream market, given the equilibrium downstream production quantities, firm B1 + D1 chooses s, firm B2 chooses b to maximize their profits. Upstream profit maxi-. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(11) 10 mization yields: 3. si =. 4. 2. 3 3. 7. 2(. 2. +2 , 8i 2 {2, 3}, + 12 + 6 4 2+4 +4 , 8i 2 {2, 3}. 2)(2 2 3 3) 2. 3. bi =. 2. 2. (20). Accordingly, the equilibrium input price, downstream price and production for the vertically merged firm and the horizontally merged firm are: w1U = p1U 1 = p1U i =. 立. qi1U =. 3. 2. 2 , 2(2 3 3) 2 +3 , 2(2 2 3 3) 3 2 2 , 8i 2 {2, 3}, 2 2(2 3 3) 2 +3 , 2 2(2 3 3) 3 4 , 8i 2 {2, 3}. 2 2(2 3 3) 2. 政治大. 學. ‧ 國. q11U =. 3. (21). 1)(5 2. 4. io. 4(2 3 ( + 1)(3 4)2 1U ⇡D = , 2 +D3 2(2 2 3 3)2 + 2)( 3 ( 3 3 2 1U = ⇡B 2 2(2 2 3 3)2 (. 4. n. al. 23 3 + 19 2 + 20 + 2) , 3)2 ( 2 2 2). y. 2. sit. (. Ch. 2. 2. er. Nat. 1U ⇡B = 1 +D1. ‧. The profits of the firm B1 + D1 , firm D2 + D3 and the firm B2 are:. v. + 4 + 4) . 2 2). engchi. i n U. (22). Given a vertically merged firm B1 + D1 , and then adopting from Colangelo (1995), an v upstream firm B2 knows that it will bid a maximum of ⇡B 2 +D2 h firm D3 will bid a maximum of ⇡D 2 +D3. h and a downstream ⇡B 2. v . Hence, D will win the bid game and a ⇡D 3 3. h horizontal merger will take place if and only if ⇡D 2 +D3. v > ⇡v ⇡D B2 +D2 3. h . ⇡B 2. Lemma 1 Given the vertically merged firm B1 + D1 , the downstream horizontal merger D2 +D3 will occur when. 0.517 <. < 1. That is, the downstream firm D3 ’s incentive to. 1U merge with D2 is stronger than the upstream firm B2 ’s incentive. Specifically, ⇡D 2 +D3 1D > ⇡ 1D ⇡D B2 +D2 3. 1U , where ⇡ 1U ⇡B D2 +D3 is the profit of the horizontal merged firm when 2. there are one horizontally merged firm, one vertically merged firm and one independent 1D is the profit of the independent downstream firm upstream firm in the market, ⇡D 3. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(12) 11 when there are two vertically merged firms and one independent downstream firm in the 1D is the profit of the vertically merged firm when there are two vertically market, ⇡B 2 +D2 1U is the profit of the merged firms and one independent downstream firm in the market, ⇡B 2. independent upstream firm when there are one vertically merged firm, one horizontally merged firm and one independent upstream firm in the market. Proof. After considering the case that the horizontal merger D2 + D3 occurs, we move on to the case that the vertical merger B2 +D2 occurs. The downstream firms’ objective functions are given as follows:. 政治大. max ⇡B1 +D1 = p1 q1 + ws. q1. 立max ⇡. B2 +D2. = p2 q2 + wb.. max ⇡D3 = (p3 q3. (24). 學. ‧ 國. q2. (23). w)q3 .. (25). Downstream profit maximization yields the following equilibrium quantities as functions. +2 w + 2w + 2 , q ⇤ (w) = . 2) 3 2( 2 2). y. w +2 , q ⇤ (w) = 2) 2 2( 2. io. sit. w 2( 2. Nat. q1⇤ (w) =. ‧. of w:. (26). n. al. er. Combining equation (26) and the upstream market-clearing condition,. Ch. s + b = q3⇤ (w).. engchi. i n U. v. (27). We derive the inverse demand for the intermediate good as follows: w=. (. 2)(2b + 2s 1 + 2s + 2b) . +2. (28). In the upstream market, given the equilibrium downstream production quantities, firm B1 + D1 chooses s , firm B2 + D2 chooses b to maximize their profits. Upstream profit maximization yields: 2. +2 4 2 2(3 + 5 12 2+2 4 b= 2(3 3 + 5 2 12 s=. 3. 12) 12). , .. (29). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(13) 12 Accordingly, the equilibrium input price, downstream price and production for the vertically merged firm and the horizontally merged firm are: w1D = p1D = i p1D 3 = qi1D = q31D =. 3 2 2)( 2) , 3 2 3 +5 12 12 (2 + 3)( 2) , 8i 2 {1, 2}, 3 2 3 +5 12 12 3 6 2+2 +8 , 3 3 + 5 2 12 12 (2 + 3)( 2) , 8i 2 {1, 2}, 3 2 3 +5 12 12 2+2 4 , 3 3 + 5 2 12 12 (. 3. 政治大. 立. (30). 1D 1D ⇡B = ⇡B = 1 +D1 2 +D2. 2)( 4 9 3 20 2 + 38 + 44) , 2(3 3 + 5 2 12 12)2. 4)2 ( 2+2 . (3 3 + 5 2 12 12)2. ‧. 1D = ⇡D 3. (. 學. ‧ 國. The profits of the firm B1 + D1 , firm B2 + D2 and firm D3 are:. (31). + 127 8 953 7 985 6 2(2 2 3 3)2 (3 3 + 5 2 12 12)2 +3972 5 + 2318 4 5928 3 3336 2 + 3168 + 2016 2(2 2 3 3)2 (3 3 + 5 2 12 12)2 81. al. 9. n. 1D ⇡D = 3. sit. io. 1U ⇡D 2 +D3. er. D2 is:. y. Nat. Then, the maximal bid from an downstream firm D3 to merge with a downstream firm. Ch. engchi. i n U. v. (32). And the maximal bid from an upstream firm B2 to merge with a downstream firm D2 is: 1D ⇡B 2 +D2. 1U ⇡B = 2. 9 12 + 52 11 221 10 575 9 + 1311 8 + 2235 7 2(3 3 + 5 2 12 12)2 (2 2 3 3)2 ( 2 2 2) 6 5 4 3 2 2081 4878 264 + 5328 + 2412 2160 1296 (33) 3 2 2 2 2 2 2(3 + 5 12 12) (2 3 3) ( 2 2). Compare the bidding function above, we get: 1U ⇡D 2 +D3. 1D > ⇡ 1D ⇡D B2 +D2 3. 1U , 0.517 < ⇡B 2. < 1.. Therefore, we know that given a vertically merged firm B1 +D1 , a downstream horizontal. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(14) 13 merger D2 + D3 will occur when. 0.517 <. < 1. Since if there are two vertical merger. B1 + D1 and B2 + D2 occurs, an independent downstream firm D3 will have no choice but buy the input at much higher cost. Theorem 1 When. 0.517 <. < 0, the downstream horizontal merger D2 + D3 will. decrease the profit of the vertically merged firm B1 +D1 . On the other hand, when. > 0,. the downstream horizontal merger D2 +D3 will increase the profit of the vertically merged firm B1 + D1 . Proof. 1U ⇡B = 1 +D1. 2. 治 1)(5 23 + 19 + 20 政大 4(2 3 3) ( 2 2) 4. 立 (5 + 2)(2 4(4. 1U 1U 2D ⇡B < ⇡B , if 1 +D1 1 +D1. 3. 2. 2. 2. 2. 3 3. + 2). 2. 1)(2 2 6)2 ( + 1). 0.517 <. < 0,. 2). ,. ,. (34). ‧. 1U 1U 2D > ⇡B , if > 0. ⇡B 1 +D1 1 +D1. 2. 學. ‧ 國. 1U 2D = ⇡B 1 +D1. (. When final goods are complements, the derived demand is elastic. Therefore, the ver-. y. Nat. sit. tically merged firm B1 + D1 has an incentive to sell the intermediate good to lower. al. er. io. the input price. However, the percentage decline in the input price is greater than the. v i n merged firm will decrease when C0.517 < < 0. On the other hand, when final goods hengchi U are substitutes, the derived demand is inelastic. The vertically merged firm B + D n. percentage increase in quantities. This is the reason why the profit of the vertically. 1. 1. has an incentive to buy the intermediate good to raise the input price and its profit will increase.. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(15) 14. 3.3. A Vertically Merged Firm Preempts the Horizontal Merger by Merging with the Downstream Firm. 治政 We know that the profit of the vertically merged firm大 B + D will decrease because 立merger when 0.517 < < 0, thus, it will take actions to of the downstream horizontal 1. 1. ‧ 國. 學. preempt the horizontal merger. There are two ways to achieve the goal. One is merging with either a downstream firm D2 or D3 . The other is merging with the independent. ‧. upstream firm B2 and setting the input price which leaves two downstream firms D2 and D3 no incentives to merge.. y. Nat. sit. We first consider the case that the vertically merged firm B1 + D1 preempts the. er. io. horizontal merger D2 + D3 by merging with the downstream firm D2 . The downstream. al. firms’ objective functions are given as follows:. n. v i n max ⇡ C h e n=gp cq h+ pi qU+ ws. q1 ,q2. 2 2. (35). w)q3 .. (36). 1 1. B1 +D1 +D2. max ⇡D3 = (p3 q3. Downstream profit maximization yields the following equilibrium quantities as functions of w: q1⇤ (w) =. w 2( 2. +2 , q ⇤ (w) = 2 2) 2. w 2( 2. +2 w +w , q3⇤ (w) = 2 2 2) 2. 1 . 2. (37). Combining equation (35) and the upstream market-clearing condition, s + b = q3⇤ (w).. (38). We derive the inverse demand for the intermediate good as follows: w=. 2s. 2s + s. 2. 2b +1. 2b + b. 2. +1. .. (39). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(16) 15 In the upstream market, given the equilibrium downstream production quantities, firm B1 + D1 + D2 chooses s and firm B2 chooses b to maximize their profits. Upstream profit maximization yields: 3. s=. 2. 4. 7. 2. 2. 3 3. b=. 2(. 2. +1 , + 12 + 6 4 2 2 2)(2 3. 2. 2. 3). .. (40). Accordingly, the equilibrium input price, downstream prices and downstream production quantities for the merged firm and independent firm are: 3. 4 2 , 2( + 1)(2 2 3 3) 6 3 2 4 , 8i 2 {1, 2}, = 2 4(2 3 3) 3+ 2 5 4 = , 2 2( + 1)(2 3 3) 6 3 2 4 , 8i 2 {1, 2}, = 4( + 1)(2 2 3 3) 2 . = 2 2(2 3 3). wP = pPi. 立. 學. qiP q3P. io. + 48 2 + 108 + 40) , 3 3)2 ( 2 2 2) 2)2 ( 3 4 , = 4( + 1)(2 2 3 3)2 ( 2 2 2) ( 2)2 = . 4(2 2 3 3)2. al. n. ⇡ B2. ⇡D3. 4. y. 2)(13 5 24 8( + 1)(2 2. (. 58. 3. sit. ⇡B1 +D1 +D2 =. (41). er. Nat. The profits of the firm B1 + D1 + D2 , firm B2 and firm D3 are:. ‧. ‧ 國. pP3. 政治大. Ch. engchi. i n U. v. (42). Theorem 2 Between two ways to preempt the downstream horizontal merger D2 + D3 , it is more profitable for the vertically merged firm B1 + D1 to merge with a downstream firm D2 or D3 than merge with an independent upstream firm B2 . Proof. 1U = ⇡B 1 +D1. (. ⇡B1 +D1 +D2. 2. 23 3 + 19 2 + 20 + 2) , 4(2 2 3 3)2 ( 2 2 2) ( 2)(13 5 24 4 58 3 + 48 2 + 108 + 40) = , 8( + 1)(2 2 3 3)2 ( 2 2 2) 1)(5. 4. 1U ⇡B1 +D1 +D2 > ⇡B , 0.517 < 1 +D1. < 0. (43). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(17) 16 We compare the profit of the vertically merged firm when it preempts the horizontal merger to that in the case that it does not preempt. We find that it is more profitable to preempt the horizontal merger. After considering the case that the vertically merged firm B1 + D1 preempts the horizontal merger D2 + D3 by merging a downstream firm D2 or D3 , we move on to the case that it preempts the horizontal merger D2 + D3 by merging with an independent upstream firm B2 and then setting an input price which makes two downstream firms D2 and D3 have no incentive to merge with each other. The downstream firms’ objective functions are given as follows:. 政治大. max ⇡B1 +D1 +B2 = p1 q1 + w(s2 + s3 ). q1. 立 max ⇡. w)q2 .. max ⇡D3 = (p3. w)q3 .. ‧ 國. D2. q3. (45). 學. = (p2. q2. (44). (46). ‧. As mentioned before, the input that the vertically merged firm B1 + D1 + B2 sells or buys is s. Besides, s = s2 + s3 and s2 = s3 . Downstream profit maximization yields the. y. sit. +2 2w + 2 2w + , q ⇤ (w) = , q ⇤ (w) = 2) 2 2( 2)( + 1) 3 2( 2. n. al. er. 2w 2( 2. io. q1⇤ (w) =. Nat. following equilibrium quantities as functions of w:. i n U. 2 . 2). (47). v. Combining equation (45) and the upstream market-clearing condition,. Ch. engchi. s2 + s3 = q2⇤ (w) + q3⇤ (w).. (48). We derive the inverse demand for the intermediate good as follows: w=. (s2 + s2 + s3 + s3 2. 1)(. 2). .. (49). In the upstream market, given the equilibrium downstream production quantities, firm B1 + D1 chooses s and let two downstream firms’ profits equal to. ( +1)(3 2(2 2 3. 4)2 3)2. which is. the profit that they merge horizontally, we get: si =. p. + 1(3 2(2 2 3. 4) , 8i 2 {2, 3}. 3). (50). DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(18) 17 The profit of the vertically merged firm B1 + D1 + B2 is: ⇡B1 +D1 +B2. p p 24 + 1 4 59 4 + 92 + 1 3 42 3 = 4(2 2 3 3)2 p p p 2 2 80 + 1 + 121 36 + 1 + 18 + 48 +1 2 2 4(2 3 3) 27. 5. 55. (51). Then, we compare two ways that the vertically merged firm B1 + D1 can apply to preempt the horizontal merger D2 + D3 , we get: ⇡B1 +D1 +D2 > ⇡B1 +D1 +B2 , 0.517 <. < 0.. (52). Although there are two ways for the vertically merged firm B1 + D1 to preempt the. 政治大 or D . It costs a lot to merge with an upstream firm B with a downstream firm D立. horizontal merger D2 +D3 , in fact, it will only preempt the horizontal merger by merging 2. 3. 2. ‧ 國. 學. since an independent upstream firm B2 has more market power than a downstream firm D2 or D3 . Thus, we complete the proof.. ‧. Lemma 2 We consider the case which is di↵erent from the previous discussion. That is, there are not only two firms, B2 and D3 , participate in the bidding game, but the. y. Nat. sit. vertically merged firm B1 + D1 also takes part in. In other words, there are three firms. al. er. io. intend to merge with D2 . However, although this bidding game is not the same as before,. v i n D o↵ers the highest price when 0.517 < < 0.853. the vertically merged firm B + C hengchi U Compared to the Theorem 2 that the vertically merged firm B + D merges with D n. we obtain the similar outcome. When there are three firms competing to merge with D2 , 1. 1. 1. when. 0.517 <. 1. 2. < 0, the vertically merged firm B1 + D1 now are more likely to merged. with D2 . However, the di↵erence in the upper bound will not bring the serious problem to our later discussion and we can obtain the same conclusion. Proof. The vertically merged firm B1 + D1 , the independent upstream firm B2 and the independent downstream firm D3 intend to merge with D2 . We first consider the maximal bid from a vertically merged firm B1 + D1 to merge with. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(19) 18 a downstream firm D2 : 1D ⇡B 1 +D1. ⇡B1 +D1 +D2. 1U ⇡B 1 +D1. 10 12 + 17 11 206 10 400 9 + 1666 8 + 30467 5896 6 8( + 1)(2 2 3 3)2 ( 2 2 2)( + 2)2 ( 3 + 2 2 4 4) 5 4 3 2 9276 + 7208 + 12800 432 5632 1792 . 2 2 2 2 3 2 8( + 1)(2 3 3) ( 2 2)( + 2) ( + 2 4 4) =. (53). The maximal bid from an upstream firm B2 to merge with a downstream firm D2 is: 1D ⇡B 2 +D2. 1U ⇡B 2. ⇡B 2. 2 12 9 11 46 10 + 176 9 + 310 8 1054 7 970 6 4( + 1)(2 2 3 3)2 ( 2 2 2)( + 2)2 ( 3 + 2 2 4 4) 5 4 3 2 +1868 + 1700 704 752 + 64 + 96 . 2 2 2 4( + 1)(2 3 3) ( 2 2)( + 2)2 ( 3 + 2 2 4 4). 政治大. =. 立. (54). ‧ 國. 學. The maximal bid from a downstream firm D3 to merge with a downstream firm D2 is:. + 25. 8. 7. 224. 60. 4(2. 2. 6. + 944 5 3 3)2 (. 3. 644 +2. 4. 656 3 + 608 4 4)2. 2. io. al. n 1D ⇡B 1 +D1. 1U ⇡D 2 +D3. 1U 1U > ⇡D ⇡B 1 +D1 2 +D3. ⇡D3. 1D > ⇡B 2 +D2. B2. ⇡D 3. Ch. e n g c⇡h i. 1D ⇡D > ⇡B1 +D1 +D2 3 1D > ⇡B 2 +D2. + 128. 128. (55). er. Comparing the bidding function above, we get: ⇡B1 +D1 +D2. 2. y. 9. sit. 18. 1D ⇡D 3. Nat. =. ⇡D 3. ‧. 1U ⇡D 2 +D3. ⇡B 2. i n U 1D ⇡D 3. v. 1U ⇡B , 0.517 < 2. 1D ⇡B 1 +D1. < 0.853,. (56). 1U ⇡B 1 +D1. 1U ⇡B , 0.853 < 2. < 1.. (57). Therefore, we know that the vertically merged firm B1 + D1 o↵ers the highest price to obtain the higher profit by merging with the downstream firm D2 when. 0.517 <. <. 0.853. It is because as long as the vertically merged firm B1 + D1 merges with D2 , its output increases. However, when the final goods becomes more substitute, the incentive for the independent downstream firm D3 to merge with D2 gets stronger. Since if the vertically merged firm B1 + D1 merges with D2 , the input price will be higher and the profit of the independent downstream firm D3 will decrease.. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(20) 19. 3.4. A Vertically Merged Firm Preempts the Vertical Merger by Merging with the Downstream Firm. Lemma 3 The independent upstream firm B2 will merge with the independent downstream firm D3 to compete with the vertically merged firm B1 + D1 + D2 . Both upstream and downstream divisions’ profits of the merged firm B2 + D3 will be higher than they stay independent. Proof. The downstream firms’ objective functions are given as follows:. 政治大. max ⇡B1 +D1 +D2 = p1 q1 + p2 q2 . q1 ,q2. max ⇡B2 +D3 = p3 q3 .. (59). q3. 學. ‧ 國. 立. (58). Downstream profit maximization yields the following equilibrium quantities: 2. 2(. 2. 2. 2). , q2⇤ (w) =. 2 2(. 2. 2. 2). , q3⇤ (w) =. 2(. n. a⇡l. B2 +D3. Ch. engchi U. 1 2. .. (60). y. 2). sit. io. ( + 1)( 2)2 , 2( 2 2 2)2 1 = . 2 2( 2 2)2. ⇡B1 +D1 +D2 =. er. Nat. The profits of the firm B1 + D1 + D2 and the firm B2 + D3 are:. 2. ‧. q1⇤ =. v ni. (61). Then, we compare the sum of independent upstream firm B2 ’s profit and independent downstream firm D3 ’s profit to the vertically merged firm’s profit B2 + D3 , we find that vertical merger B2 + D3 will take place. ⇡B2 +D3 > ⇡B2 + ⇡D3 , 0.517 <. < 0.. (62). In other words, double vertical mergers B1 + D1 + D2 and B2 + D3 will occur. However, if the double vertical merger occurs, the profit of the vertically merged firm B1 +D1 +D2 will decrease. As a result, the vertically merged firm B1 + D1 + D2 will preempt the vertical merger B2 + D3 . There are two ways to achieve the goal. One is merging with D3 , the other is buying the intermediate good strategically.. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(21) 20 Theorem 3 Between two ways to preempt another vertical merger B2 + D3 , it is more profitable for the vertically merged firm B1 + D1 + D2 to merge with the downstream firm D3 than buy the intermediate good strategically.. 立. 政治大. Proof. First, we consider the case that the vertically merged firm B1 + D1 + D2 merges. ‧. ‧ 國. follows:. 學. with a downstream firm D3 . The downstream firm’s objective function is given as. max ⇡B1 +D1 +D2 +D3 = p1 q1 + p2 q2 + p3 q3 .. q1 ,q2 ,q3. (63). sit. y. Nat. In this case, the independent upstream firm B2 no longer exits in the market. The vertically merged firm B1 + D1 + D2 + D3 becomes the monopoly.. io. n. al. er. Downstream profit maximization yields the following equilibrium quantities:. Ch. i n U. 1 , 8i 2 {1, 2, 3}. qi = 2(2 + 1). engchi. v. (64). The profit of the firm B1 + D1 + D2 + D3 is ⇡B1 +D1 +D2 +D3 =. 3 . 4(2 + 1). (65). Therefore, we know the gain when the vertically merged firm B1 + D1 + D2 merges with D3 . That is, the profit of the vertically merged firm B1 + D1 + D2 + D3 minus the opportunity cost: ⇡B1 +D1 +D2 +D3. ⇡D3 =. 12. 4. 4(2. 38. 3. 2. 3. 2. 2. + 50 + 23 . 3)2 (2 + 1). (66). Then, we consider the case that the vertically merged firm B1 + D1 + D2 buys the. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(22) 21 intermediate good strategically to preempt the vertical merger B2 + D3 . Substituting equation (28) into equation (26) and (25), we get the following equilibrium quantities, the non-merged upstream and downstream firm’s profit as functions of s3 +b3 : 1 ⇤ 1 ⇤ s3 + b3 s3 + b3 , q2 (s3 + b3 ) = , q3 (s3 + b3 ) = s3 + b3 , 2( + 1) 2( + 1) 2s3 + s3 2 + 1)2 2s3 + s3 2 1)2 ( 2s3 ( 2s3 ⇤ ⇤ , ⇡ (s + b ) = (s + b ) = . ⇡B 3 3 3 3 D 2 3 4( + 1)( 2 2 2) 4( 2 2 2)2. q1⇤ (s3 + b3 ) =. (67) As the leader, the vertically merged firm B1 +D1 +D2 will take into account the follower’s strategy, that is, the non-merged upstream firm’s strategy. Therefore, we can use the. 政治大 that it sells or buys (b ) as the function of the input that the vertically merged firm 立 first-order condition of the non-merged upstream firm’s profit function to get the input 3. s3. b⇤3 =. 2. 2s3. 2(. 2. 2. 學. ‧ 國. B1 + D1 + D2 sells or buys (s3 ).. 2s3 + 1 . 2). (68). ‧. To preempt the vertical merger, the vertically merged firm B1 +D1 +D2 has to make the. y. Nat. sum of non-merged upstream and downstream firms’ profits at least equal to. (. 2. 1 2. 2)2. io. sit. which is the profit of the merged vertical firm B2 + D3 in the case that double vertical. (. 2. 1 2. al. n. profits equal to. 2)2. , we get:. s⇤3 = Since s1 < 0 when. er. merger occurs. Substituting equation (68) into equation (67) and let the sum of two. Ch (. 4. e n g+c +h1i 2. 5. 3. +. 2. i n U. + 12 + 6). .. v. (69). 2 ( 0.517, 0), we can infer that the vertically merged firm B1 +. D1 + D2 buys the input in the upstream market to raise the input price. As long as the non-merged upstream firm B2 earns the same profit as the case that double vertical merger occurs, it has no incentive to merge vertically. Therefore, the vertically merged firm B1 +D1 +D2 preempts the vertical merger B2 +D3 . Finally, to ensure the vertically merged firm B1 + D1 + D2 will do so, we have to check if its profit in the case that it. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(23) 22 preempts the vertical merger is more than the case that it does not preempt. 2)(13 5 24 4 58 3 + 48 2 + 108 + 40) , 8( + 1)( 2 2 2)(2 2 3 3)2 ( + 1)( 2)2 2V = , ⇡B 1 +D1 +D2 2( 2 2 + 2 )2. ⇤ ⇡B = 1 +D1 +D2. (. ⇤ 2V ⇡B > ⇡B , 0.517 < 1 +D1 +D2 1 +D1 +D2. Therefore, we know that when. 0.517 <. < 1.. < 0, a vertically merged firm B1 + D1 + D2 2+. buys the intermediate good strategically by the amount of the input price raises to. 2. 2 3. 3. (70). 4. 5. +1. 3 + 2 +12. +6. so that. which preempts the vertical merger B2 + D3 .. 政治大. Finally, we compare equation (66) to the equation (70) to determine which way leads to the higher profit:. 立. ⇡B1 +D1 +D2 +D3. < 0.. (71). ‧ 國. 學. ⇤ ⇡D3 > ⇡B , 0.5 < 1 +D1 +D2. To conclude, between two ways to preempt another vertical merger B2 + D3 , it costs. ‧. less for the vertically merged firm B1 + D1 + D2 to merge with a downstream firm D3 than buy the intermediate good strategically since it gains more to be a monopoly.. sit. al. er. io. Conclusion. y. Nat. 4. n. v i n C profit. First, we analyze will implement to achieve maximal h e n g c h i U when the horizontal merger. In this paper, we attempt to investigate the strategies that the vertically merged firm. D2 + D3 will occur. Then, we show that a horizontal merger between D2 + D3 will decrease the profit of the vertically merged firm B1 + D1 . Thus, it will take actions to preempt the horizontal merger D2 + D3 . We further analyze how the vertically merged firm B1 +D1 preempts subsequent mergers. That is, it will merge with all of downstream firms and become a monopoly. The theoretical model provides hints about the forces at work in the real world merger events. For example, our model shows in the Broadcom and Qualcomm case, how the vertically merged firm, Intel, will preempt the horizontal merger between Broadcom and Qualcomm. Our model predicts that Intel will merge with one of the independent downstream firms to maintain its profit. Besides, as Intel merging with one of the. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(24) 23 independent downstream firms, the independent upstream firm will also merge with the other independent downstream firm to compete with the Intel. As a result, Intel will merge all of the downstream firms to preempt successive mergers. This paper investigates sequential merger decisions which is the expansion of the previous literature. However, the model is more complicated than the model in Colangelo (1995) and Gelves and Heywood (2016). Besides, several preempting strategies presented in this paper are not considered before. For example, the control of the intermediate good may be one way to preempt mergers. Furthermore, we even consider all decisions that firms will make in response to the action of the incumbent vertically merged firm.. 治政 profitable strategies for an incumbent firm to preempt its 大rivals. 立. All in all, we carefully look into every possibility of mergers and identify the most. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

(25) 24. References [1] Clark, D. and Worthen, B., 2009. “Oracle Snatches Sun, Foiling IBM,” The Wall Street Journal, Eastern edition, New York, N.Y., 21 April, 2009: A.1. [2] Colangelo, G., 1995. “Vertical vs. Horizontal Integration: Pre-emptive Merging,” The Journal of Industrial Economics, 43(3), 323-337. [3] Greenwald, T., 2018. “Why Intel Is So Wary of a Broadcom-Qualcomm Merger,” The Wall Street Journal, (March 11), https://www.wsj.com/articles/why-intel-isso-wary-of-a-broadcom-qualcomm-merger-1520800808 [4] H¨ ackner, J., 2000. “A Note on Price and Quantity Competition in Di↵erentiated Oligopolies ,” Journal of Economic Theory, 93, 233-239. [5] H¨ ackner, J., 2003. “Vertical Integration and Competition Policy,” Journal of Regulatory Economics, 24(2), 213-222.. 政治大. [6] Hung, F. and Gold, M., 2014. “Foxconn to buy 390 million dollars stake in Taiwan telecom operator in 4G push,” Yahoo Finance, (May 27), https://finance.yahoo.com/news/foxconn-buy-390-million-stake-071639997.html. 立. of14),. ‧. ‧ 國. 學. [7] Meyersohn, N. and Horowitz, J., 2018. “Broadcom ficially ends bid for Qualcomm,” CNNMoney, (March https://money.cnn.com/2018/03/14/news/companies/broadcom-qualcommdeal-trump/index.html. sit. y. Nat. [8] Narioka, K., 2018. “China Approves Toshiba’s 18 Billion Dollars Sale of Its Memory-Chip Unit,” The Wall Street Journal, (May 17), https://www.wsj.com/articles/china-approves-toshibas-18-billion-sale-of-memorychip-unit-1526552434. n. al. er. io. [9] Ordover, J. A., Saloner, G. and Salop, S. C., 1990, “Equilibrium Vertical Foreclosure,” The American Economic Review, 80(1), p.127-142.. i n U. v. [10] Yao, Z. and Zhou, W., 2015, “Vertical or Horizontal: Endogenous Merger Waves in Vertically Related Industries,” The B.E. Journal of Economics Analysis and Policy, 15(3), p.1237-1262.. Ch. engchi. DOI:10.6814/THE.NCCU.IB.036.2018.F06.

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