backward integration, forward integration, and vertical ... · backward integration, forward...

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 (1990), Salinger (1988)

� Overcoming opportunism – Hart and Tirole (1990)

� Supply assurance – Bolton and Whinston (1991, 1993)

� 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

The model


4

The model

� U sells an input to D1 and D2 that use it to produce a final product (no supply shortage)

U

D1 D2

Final consumers

w1 w2

p1 p2


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 Di is Vi - pi (Vi is observed)

� Utility of not buying is 0

� Ex ante:

� Di can increase qi by investing kqi2/2, k > ∆ ≡

VH-VL

=i

i

q-1 prob.with

q prob. with

L

H

iV

VV


6

Timing

� As in Bolton and Whinston (RES, 1991) and Rey and Tirole (Handbook of IO, 2007), the bargaining is as follows:

� Di gives U a TIOLI offer with prob. ½

� U gives Di a TIOLI offer with prob. ½

D1 and D2 choose q1 and q2

Bargaining with U over w1 and w2

V1 and V2 are determined

D1 and D2 set p1 and p2

The non-integration benchmark


8

The nonintegrated equilibrium

� NE profits:

� ∆ is the “premium” for being the sole provider of high quality

V2 = VH V2 = VL

V1 = VH 0, 0 ∆, 0

V1 = VL 0, ∆ 0, 0


9

The bargaining over the w1 and w2

and the downstream profits

� Di makes a TIOLI offer to U: wi = c

� U makes a TIOLI offer to Di: wi = qi(1-qj)∆

� Expected wholesale price

� The profit of Di

( )2

1*

cqqw

ji

i

+∆−=

( ) ( )22

1

2*1

22

ijiiijii

kqcqqkqwqq −

−∆−=−−∆−=π


10

( )k

qq

2

1 21

∆−=

NE

q1

q2

∆/2k

1

1

450

( )k

qq

2

1 12

∆−=

∆/2k∆/(∆+2k)

∆/(∆+2k)

The nonintegrated equilibrium

Prob. of foreclosure:

( )( )22

2*1**

k

kqq jij

+∆

∆=−=φ

Full vertical integration between U and D1


12

Vertical integration – bargaining over w2

� When D2 makes a TIOLI to the integrated firm, VI, it offers

� When VI makes a TIOLI to D2, it offers

� The expected input price:

� w2VI > w2* since U internalizes the negative externality

that D2 imposes on D1’s profit

( ) ( )444 3444 21444 3444 21

2D tosellingn profit whe sVI'

221

eforeclosurunder profit sVI'

11 211 cwqqcVqVq LH −+∆−=−−+

( )43421

input thebuyingn profit whe s'D

122

2

1 ∆−= qqw

( )2

222

cqVqw LVI +∆+

=


13

Investments under vertical integration

� The profit of VI:

� The profit of D2:

� VI and D2 choose q1 and q2 simultaneously

( ) ( ) ( )22

21

21

2

212

2

222122

kqVcqqkqqwqq LVI −

−−∆−=−−∆−=π

( ) ( )4434421

44 344 21 profit sU'

22

profit s'D

2

221 2

21

1

cqwkq

qqVI

VI −+−∆−=π


14

NE

q1

q2

∆/2k

1

1

450

∆/2k

( )k

qq

∆−= 2

1

1

( )k

qq

2

21 12

∆−=

∆/k 1/2

NE with vertical

integration

The equilibrium under vertical integration – internal solution

D1 becomes more aggressive since itinternalizes the positive externality on U’s profit

D2 becomes softer (w2↑ due to integration)


15

NE

q1

q2

1

1

450

1/2

NE with vertical

integration

∆/2k

∆/2k

( )k

qq

∆−= 2

1

1

( )k

qq

2

21 12

∆−=

∆/k

The equilibrium under vertical integration – boundary solution

We get boundary sol’n when ∆/k > ½ or ∆ > k/2 (large premium to being the sole provider of high quality)


16

The welfare effects of vertical integration

� More foreclosure:� D1 internalizes the positive externality on U, so q1↑� Investments are strategic substitutes so q1↑ ⇒ q2↓� w2↑ (U internalizes the negative externality on D1’s profits) so

q2↓

� Consumer surplus in the final market:

� Expected surplus:

V2 = VH V2 = VL

V1 = VH VH VH–∆ = VL

V1 = VL VH–∆ = VL VL

( ) ( ) ∆+=−+= 21212121 1, qqVVqqVqqqqS LLH


17

The welfare effects of vertical integration

� Comparing S(q1,q2) with and w/o integration:

� Intuition:� Expected consumer surplus depends on q1*q2*

� q1VI↑ with ∆/k, while q2

VI is an inverse U-shaped function of ∆/k ⇒ q1

VIq2VI is an inverse U-shaped function of ∆/k

� VI harms consumers when ∆/k is sufficiently large (when ∆/k > 2, q2

VI = 0)

VI benefits consumers VI harms consumers

0.326 ∆/k

Partial backward integration: D1 buys a stake α < 1 in U


19

W2 under backward integration� D2 makes a TIOLI it offers:

� VI makes a TIOLI to D2, it offers


� w2BI ↑ when α↓:

� D2 must compensate D1 for the negative externality on D1's downstream profit

� D1 gets only α of U's profits, so w2BI must be high enough so αw2

BI will cover the entire externality

( ) ( ) ( ) ( )44 344 2144 344 21444 3444 21profit sin U' share s'D

21

D tosells Uifprofit s'D

1211

eforeclosurunder profit s'D

111

1211

211 cwwwqqcwwVqVq LH −++−∆−=−+−−+ αα

( )43421


122

2

1 ∆−= qqw

( ) ( )αα

22

1, 2112

212LBI Vcqqqq

qqw++∆

+∆−

=


20

The downstream profits under partial backward integration

� D1’s profit:

� w2BI(q1,q2) is increasing with q1, so D1 has a stronger

incentive to invest� (+) D2 imposes a bigger externality on D1 when q1 is higher� (-) q1 lowers D2’s WTP for the input

� D2’s profit:

� BI and D2 choose q1 and q2 simultaneously

( ) ( )( )444 3444 21

444 3444 21 profit sU'

2121

profit s'D

2

11211 ,

21

1

cqqwwkq

wqqBI −++−−∆−= απ

( ) ( )2

,1

2

2212122

kqqqwqq

BI −−∆−=π


21

NE

q1

q2

∆/2k

1

450

( )k

qq

∆

+−=

ααα

2

1 12

∆/k 1/2

NE with VI

( )k

qq∆

+−= 21

2

11

αα+12

αα+1

NE with BI

The equilibrium under partial backward integration

( )k

qq

∆−= 2

1

1

D1 internalizes a smallerfraction of the negative externality of q1 on U's profit from selling to D2

D2 pays more for the input


22

The effect of partial backward integration

� A decrease in α (D1’s controlling stake in U is smaller) leads to� q1 ↑ (BI invests more)� q2 ↓ (D2 invests less) � φ ≡ q1

BI q2BI ↑ (D2 is more likely to be foreclosed in the final

market)� S↓ (consumers are worse off)

� Conclusion: Partial backward integration (α<1) is worse than full integration� Intuition: S↓ since q2↓ has a bigger effect on the prob. that

consumers enjoy a high quality at a low price than q1↑


23

The incentive to backward integrate

� Suppose that:� U is controlled by a single shareholder, whose equity

stakes is γ� D1 offers a price T to the controlling shareholder of U

for an equity stake α ≤ γ

� Then:� Backward integration is always profitable

� If γ > ∆/(k-∆) (q2BI > 0 when D1 buys all of γ), then D1

may prefer to acquire α < γ provided that k is sufficiently small

� If γ ≤ ∆/(k-∆) (q2BI = 0 when D1 buys all of γ), then D1

may prefer to acquire the smallest α that ensures control over U


24

Passive backward integration

� When D1 gets a passive stake in U, w1

and w2 are set as in the nonintegrationcase

� When D1 invests it� Internalizes the positive externality on U

� Internalizes the negative externality on D2’s WTP

� Which effect is stronger depends on whether q1 is above or below 1/2


25

( )k

qq

∆

+−+=

2

211 21

αα

NE

q1

q2

∆/2k

1

1

450

( )k

qq

2

1 12

∆−=

∆/2k

Passive Backward Integration

(1+α)∆/2k

NE with passive

backward

integration

(1+α)/(1+2α)

1/2


26

Investments under passive and controlling ownership

q1 q2

α α

q1* q2

*

q1BI

q2BI

q2BIpass

q1BIpass


27

Consumer surplus

� Passive ownership may be better or worse then controlling ownership:

α

∆/k

SBI > SBIpass

SBI < SBIpass


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

Partial forward integration:U buys a stake α < 1 in D1


30

W2 under forward integration

� Bargaining over w2:� When D2 makes a TIOLI it offers

� When VI makes a TIOLI to D2, it offers

( )( )

( )( )444 3444 2143421

4444 34444 21321

212

1

D tosells n Uprofit whe s'Din share sU'

121

D tosellit n profit whe sU'

21

eforeclosurunder profit s'Din share sU'

111

eforeclosurunder profit sU'

1

12

1

wqqcww

wVqVqcw LH

−∆−+−+=

−−++−

α

α

( )43421


122

2

1 ∆−= qqw


31

W2 under forward integration


� w2FI↑ with α and is equal to w2

VI when α = 1� When U owns only part of D1, it requires

only partial compensation for the negative externality of D2 on D1’s downstream profit

( ) ( )( )2

11, 12

212

cVqqqqw LFI ++∆−−

=αα


32

The downstream profits under partial backward integration

� U’s profit:

� D2’s profit:

� FI and D2 choose q1 and q2 simultaneously

( ) ( )4444 34444 21

444 3444 21

profit s'D

2

121

profit sU'

21211

1

212,

−−∆−+−+=kq

cqqcqqwwFI απ

( ) ( )2

,1

2

2212122

kqqqwqq

FI −−∆−=π


33

NE

q1

q2

∆/2k

1

450

( )k

qq

∆

+−=

2

11 12

α

∆/k 1/2

NE with VI

( )k

qq∆

+−= 21

2

11

αα

αα

+12

α+11

NE with FI

The equilibrium under partial forward integration

Boundary sol’n when∆/k > 1/(1+α)


34

The effect of partial forward integration

� A decrease in α (U’s controlling stake in D1 is smaller) leads to� q1 ↓ (FI invests less)� q2 ↑ for all α > 1/4 (D2 invests more) � φ ≡ q1

BI q2BI ↓ (D2 is less likely to be foreclosed in the final market)

� S↑ for all α > 1/2 (consumers are better off)

� Conclusion: Partial forward integration (α<1) is better than full integration

� Intuition: � Under partial FI, U internalizes only a fraction of the externality of D2 on

D1's profits, so w2↓� w2↓ ⇒ q2↑� Investments are strategic substitutes so q1↓� U captures the full profit from selling the input to D2, but captures only a

fraction of D1's profits ⇒ U wishes to restrict q1 in order to keep w2 high� q1↓ has a bigger effect on φ than q2 ↑ so less foreclosure ⇒ S↑ relative to

full VI

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