Backward integration, forward integration, and vertical foreclosure. Yossi Spiegel, Tel Aviv University

Transcription

1 Backward integration, forward integration, and vertical foreclosure Yossi Spiegel, Tel Aviv University

2 Background Foreclosure is prob. the main competitive concern about vertical integration Three strands in the literature: Raising rivals cost - OSS (990, Salinger (988 Overcoming opportunism Hart and Tirole (990 Supply assurance Bolton and Whinston (99, 993 My paper departs from the literature by looking at partial vertical mergers It builds on Bolton and Whinston Foreclosure is a by product of investments rather than a deliberate refusal to sell

3 The model

4 The model U sells an input to D and D that use it to produce a final product (no supply shortage U w w D D p p Final consumers 4

5 Competition in the final market A unit mass of identical final consumers, each is interested in buying at most one unit Utility of buying from D i is V i - p i (V i is observed Utility of not buying is 0 Ex ante: V i V V H L with prob. with prob.- i i D i can increase i by investing k i /, k > V H -V L 5

6 Timing D and D choose and Bargaining with U over w and w V and V are determined D and D set p and p As in Bolton and Whinston (RES, 99 and Rey and Tirole (Handbook of IO, 007, the bargaining is as follows: D i gives U a TIOLI offer with prob. ½ U gives D i a TIOLI offer with prob. ½ 6

7 The non-integration benchmark

8 The nonintegrated euilibrium NE profits: V V H V V L V V H 0, 0, 0 V V L 0, 0, 0 is the premium for being the sole provider of high uality 8

9 The bargaining over the w and w and the downstream profits D i makes a TIOLI offer to U: w i c U makes a TIOLI offer to D i : w i i (- j Expected wholesale price w * i i ( j + c The profit of D i π i i ( j w i * ki i ( j c ki 9

10 The nonintegrated euilibrium /k ( k 45 0 Prob. of foreclosure: k φj* i *( j * + k ( /( +k NE ( k /( +k /k 0

11 Full vertical integration between U and D

12 Vertical integration bargaining over w When D makes a TIOLI to the integrated firm, VI, it offers ( V c ( VH + L + w c VI's profit under foreclosure When VI makes a TIOLI to D, it offers w ( 443 's profit when buying the input The expected input price: w D VI VL + ( VI's profit when selling to D + w VI > w * since U internalizes the negative externality that D imposes on D s profit c

13 Investments under vertical integration The profit of VI: π VI k VI ( + w ( c U's profit D 's profit The profit of D : π VI ( w ( k ( c V L k VI and D choose and simultaneously 3

14 The euilibrium under vertical integration internal solution ( k 45 0 D becomes more aggressive since it internalizes the positive externality on U s profit D becomes softer (w due to integration /k ( k NE NE with vertical integration /k /k / 4

15 The euilibrium under vertical integration boundary solution /k ( k 45 0 We get boundary sol n when /k > ½ or > k/ (large premium to being the sole provider of high uality ( k NE NE with vertical integration /k / /k 5

16 The welfare effects of vertical integration More foreclosure: D internalizes the positive externality on U, so Investments are strategic substitutes so w (U internalizes the negative externality on D s profits so Consumer surplus in the final market: V V H V V L V V H V H V H V L V V L V H V L V L Expected surplus: S (, V + ( V V + H L L 6

17 The welfare effects of vertical integration Comparing S(, with and w/o integration: 0.36 /k VI benefits consumers VI harms consumers Intuition: Expected consumer surplus depends on * * VI with /k, while VI is an inverse U-shaped function of /k VI VI is an inverse U-shaped function of /k VI harms consumers when /k is sufficiently large (when /k >, VI 0 7

18 Partial backward integration: D buys a stake α < in U

19 W under backward integration D makes a TIOLI it offers: ( V w + α( w c ( w + ( w + w c VH + L α D 's profit under foreclosure VI makes a TIOLI to D, it offers w The expected input price: w ( D 's profit if U sells to D D 's share in U's profit w BI when α : D must compensate D for the negative externality on D 's downstream profit D gets only α of U's profits, so w BI must be high enough so αw BI will cover the entire externality ( 443 D 's profit when buying the input ( + αc + α BI V, L + 9

20 The downstream profits under partial backward integration D s profit: ( c, U's profit D 's profit w BI (, is increasing with, so D has a stronger incentive to invest (+ D imposes a bigger externality on D when is higher (- lowers D s WTP for the input k BI π ( w + αw + w ( D s profit: π BI ( w (, BI and D choose and simultaneously k 0

21 The euilibrium under partial backward integration +α ( α + k 45 0 D internalizes a smaller fraction of the negative externality of on U's profit from selling to D ( k ( α α + α /k k NE NE with VI D pays more for the input NE with BI α + α /k /

22 The effect of partial backward integration A decrease in α (D s controlling stake in U is smaller leads to (BI invests more (D invests less φ BI BI (D is more likely to be foreclosed in the final market S (consumers are worse off Conclusion: Partial backward integration (α< is worse than full integration Intuition: S since has a bigger effect on the prob. that consumers enjoy a high uality at a low price than

23 The incentive to backward integrate Suppose that: U is controlled by a single shareholder, whose euity stakes is γ D offers a price T to the controlling shareholder of U for an euity stake α γ Then: Backward integration is always profitable If γ > /(k- ( BI > 0 when D buys all of γ, then D may prefer to acuire α < γ provided that k is sufficiently small If γ /(k- ( BI 0 when D buys all of γ, then D may prefer to acuire the smallest α that ensures control over U 3

24 Passive backward integration When D gets a passive stake in U, w and w are set as in the nonintegration case When D invests it Internalizes the positive externality on U Internalizes the negative externality on D s WTP Which effect is stronger depends on whether is above or below / 4

25 Passive Backward Integration ( α + α + k 45 0 (+α/(+α / /k NE NE with passive backward integration ( k /k (+α /k 5

26 Investments under passive and controlling ownership BI BIpass * * α BIpass BI α 6

27 Consumer surplus Passive ownership may be better or worse then controlling ownership: /k S BI < S BIpass S BI > S BIpass α 7

28 Conclusion Partial backward integration is worse than full integration Passive ownership may be better or worse for consumers than controlling ownership Partial forward integration is better than full integration 8

29 Partial forward integration: U buys a stake α < in D

30 W under forward integration Bargaining over w : When D makes a TIOLI it offers w c 3 U's profit under foreclosure w + w c 443 U's profit when it sell to D ( V + ( V w + α H L U's share in D 's profit under foreclosure ( ( w α When VI makes a TIOLI to D, it offers w + U's share in D 's profit when U sells to D ( 443 D 's profit when buying the input 30

31 W under forward integration The expected input price: w ( ( α FI (, + VL + α c w FI with α and is eual to w VI when α When U owns only part of D, it reuires only partial compensation for the negative externality of D on D s downstream profit 3

32 The downstream profits under partial backward integration U s profit: D s profit: FI π w + w π (, c + α ( U's profit FI ( w (, k c 's profit FI and D choose and simultaneously D k 3

33 The euilibrium under partial forward integration α + α ( α + α k 45 0 Boundary sol n when /k > /(+α NE with FI ( α + /k k NE NE with VI /k / +α 33

34 The effect of partial forward integration A decrease in α (U s controlling stake in D is smaller leads to (FI invests less for all α > /4 (D invests more φ BI BI (D is less likely to be foreclosed in the final market S for all α > / (consumers are better off Conclusion: Partial forward integration (α< is better than full integration Intuition: Under partial FI, U internalizes only a fraction of the externality of D on D 's profits, so w w Investments are strategic substitutes so U captures the full profit from selling the input to D, but captures only a fraction of D 's profits U wishes to restrict in order to keep w high has a bigger effect on φ than so less foreclosure S relative to full VI 34