http://www.rcsb.org aventis.com, ‐ http://www.sanofi sources:

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“Timing Vertical Relationships” / 2011 E. Billette de Villemeur, R. Ruble, B. Versaevel

Richard Ruble, EMLYON Business School & GATE Bruno Versaevel, EMLYON Business School & GATE

(2)

In a growing market with uncertain demand, where one or several firms need investing in a key input to start operations, we adapt the standard analysis of vertical relationships (“separation”) to investment decisions.

What if the intermediate market is not competitive ?

What is the impact of separation on the cost and timing of investments ? On firm values? With one or several downstream firms ?

Sensitivity to demand parameters (growth, volatility) ?

(3)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(4)

sources: http://www.sanofi‐aventis.com, http://www.rcsb.org

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source: www.tropika.net/svc/review/061001‐Dengue_Burden_of_disease

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lyophilizator supplier

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1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(8)

We formalize investment decisions in a key technology which is needed to serve a continuously changing and uncertain final demand.

We compare “integration” (1 firm) with “separation” (1 technology supplier + 1 downstream firm) and “preemption” (1 technology supplier + 2 downstream firms).

Approach

(i) Separation introduces distortions in the cost of technology, hence in the investment timing.

(ii) Vertical restraints, as adapted from the static framework, may eliminate the distortions.

(iii) Preemption and price discrimination restore private efficiency.

Main Results

(9)

Specifications (1/3)

Model specifications similar to models of real option games (Smit and Trigeorgis, PUP

2004; Mason and Weeds, IJIO 2009; Boyer, Lasserre and Moreaux, CIRANO WP 2010),

plus an upstream input supplier which prices with market power:

(10)

Model specifications similar to models of real option games (Smit and Trigeorgis, PUP 2004; Mason and Weeds, IJIO 2009; Boyer, Lasserre and Moreaux, CIRANO WP 2010), plus an upstream input supplier which prices with market power:

• continuous time

• a key input is needed (no resale value)

• changing demand with deterministic positive drift + stochastic term

• integration (benchmark): the firm produces the input

• separation: one upstream firm, one (or two) downstream firm(s)

• two-level strategic interaction:

◦ in investment timing (max. of net expected value) = “long run”

◦ in price or quantity (max. of gross instant. profits) = “short run”

Specifications (1/3)

(11)

Xt



^t ^X_t



P ,

 

0 D t’

t’’

Yt

t

output random

shock

growth rate

volatility

Specifications (2/3)

Wiener process

(12)

: current “market size”

: investment trigger

i = D for “downstream”

P for “preemption”

F for “follower”

L for “leader”

: “true” cost of investment

: price charged upstream to single buyer : price charged upstream to “follower”

: price charged upstream to “leader”

: instantaneous monopoly profits : instantaneous duopoly profits

Specifications (3/3)

(13)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(14)

Integration (benchmark)

(15)

Separation

(16)

>

(17)

>

(18)

> ¹

>

(19)

< ¹

(20)

Impact of a change in  (growth) and/or  (volatility)?

(21)

(22)

.

(23)

real option indirect effect

price

indirect effect

Comparative statics: growth

(24)

real option indirect effect

price

indirect effect

Comparative statics: volatility

(25)

(26)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(27)

p

U

y

_D

(p

_U

)

y

_i

separation ?

1

(28)

A .

W

p

U

y

_i

y

_D

* = 4

y

_D

(p

_U

)

W

W*

(U’s part.

constraint)

I P

_U

*

separation

without restraint

1

(29)

W

W*

(U’s part.

constraint)

W

V*

(D’s part.

constraint)

p

U

y

_D

* = 4 y

_D

(p

_U

)

y

_i

A .

I P

_U

*

1

(30)

Analogous to RPM upstream problem:

(31)

Analogous to RPM upstream problem:

(32)

B .

W

W*

W

V*

p

U

y

_D

* = 4 y* = 2

y

_D

(p

_U

)

y

_i

A .

I P

_U

*

1

(33)

W

W*

W

V*

.

*) ( y p

_U

*) ( y p

U

p

U

y

_D

* = 4 y* = 2

y

_D

(p

_U

)

y

_i

A .

B .

I

“RPM”

P

_U

*

1

(34)

Analogous to TPT upstream problem:

(35)

Analogous to TPT upstream problem:

(36)

“TPT”

W

W*

W

V*

p

U

y

_D

* = 4 y* = 2

y

_D

(p

_U

)

y

_i

.

C

A .

I

P

_U

*

(37)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(38)

same price as with separation with a single buyer, with delayed investment

=

>

(39)

L(y, y, y

_F

, p*

_UL

)

F(y, y

_F

, p*

_UF

)

~

y*

_F

y

_i

preemption value .

(40)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

y*

L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

maximum value

y*

_F

preemption value

.

(41)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

) .

y*

L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

.

maximum value

y*

_F

preemption value

.

(42)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

preemption value maximum value

y*

_F

y*

. .

.

(43)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

preemption value maximum value

y*

_F

y*

. .

.

(44)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

preemption value maximum value

y*

_F

y*

. .

.

(45)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

y*

_P

= y*

L(y, y

_L

, y*

_F

, p*

_UL

) L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

. preemption value maximum value

y*

_F

. .

(46)

L(y, y, y

_F

, I)

L(y, y, y

_F

, p*

_UL

)

L(y, y

_L

, y*

_F

, p*

_UL

) L(y, y

_L

, y*

_F

, I )

F(y, y

_F

, p*

_UF

)

~

y

_i

y*

_P

= y*

preemption value maximum value

y*

_F

.

. . .

(47)

< =

Downstream competition (with only two firms) restores private efficiency, in that the leader invests at the same time as in the benchmark integrated structure.

= <

(48)

Downstream competition (with only two firms) restores private efficiency, in that the leader invests at the same time as in the benchmark integrated structure.

The leader pays a lower price than with integration. The follower, which invests later, pays the same price as in the separated case with only one buyer.

= <

< =

(49)

(50)

(51)

(52)

(53)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

(54)

• learning effects may decrease the production cost for the second input supplied

• relax the assumption of a geometric Brownian motion (jumps)

• more market power for downstream firms

Next Now

• vertical contract with upstream supplier as a pre-commitment to value maximization

• less market power upstream results in privately sub-optimal investment sequence

(55)

http://www.rcsb.org aventis.com, ‐ http://www.sanofi sources:

In a growing market with uncertain demand, where one or several firms need investing in a key input to start operations, we adapt the standard analysis of vertical relationships (“separation”) to investment decisions.

What if the intermediate market is not competitive ?

What is the impact of separation on the cost and timing of investments ? On firm values? With one or several downstream firms ?

Sensitivity to demand parameters (growth, volatility) ?

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

We formalize investment decisions in a key technology which is needed to serve a continuously changing and uncertain final demand.

We compare “integration” (1 firm) with “separation” (1 technology supplier + 1 downstream firm) and “preemption” (1 technology supplier + 2 downstream firms).

Approach

(i) Separation introduces distortions in the cost of technology, hence in the investment timing.

(ii) Vertical restraints, as adapted from the static framework, may eliminate the distortions.

(iii) Preemption and price discrimination restore private efficiency.

Main Results

Specifications (1/3)

Model specifications similar to models of real option games (Smit and Trigeorgis, PUP

2004; Mason and Weeds, IJIO 2009; Boyer, Lasserre and Moreaux, CIRANO WP 2010),

plus an upstream input supplier which prices with market power:

Model specifications similar to models of real option games (Smit and Trigeorgis, PUP 2004; Mason and Weeds, IJIO 2009; Boyer, Lasserre and Moreaux, CIRANO WP 2010), plus an upstream input supplier which prices with market power:

• continuous time

• a key input is needed (no resale value)

• changing demand with deterministic positive drift + stochastic term

• integration (benchmark): the firm produces the input

• separation: one upstream firm, one (or two) downstream firm(s)

• two-level strategic interaction:

◦ in investment timing (max. of net expected value) = “long run”

◦ in price or quantity (max. of gross instant. profits) = “short run”

Specifications (1/3)





 

Specifications (2/3)

: current “market size”

: investment trigger

i = D for “downstream”

P for “preemption”

F for “follower”

L for “leader”

: “true” cost of investment

: price charged upstream to single buyer : price charged upstream to “follower”

: price charged upstream to “leader”

: instantaneous monopoly profits : instantaneous duopoly profits

Specifications (3/3)

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

Integration (benchmark)

Separation

>

>

> 1

>

< 1

< 1

Impact of a change in  (growth) and/or  (volatility)?

.

Comparative statics: growth

Comparative statics: volatility

1. Motivation 2. The Model

3. Integration/Separation 4. Vertical Restraints

5. Two Buyers

6. Final Remarks

p

y

(p

)

y

separation ?

1

A .

W

p

y

> ¹

< ¹

< ¹

W*

W*

V*

W*

V*

W*

V*

W*