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One Lab, Two Firms, Many Possibilities
E. Billette de Villemeur, & B. Versaevel1
2017
1 Billette de Villemeur: Universite de Lille & LEM CNRS; Versaevel: emlyon business
school & GATE CNRSEBdV & BV One Lab, Two Firms, Many Possibilities 2017 1 / 1
“After chemotherapy failed to cure Emily Whiteheads severe form of
leukaemia, Oxford BioMedica’s new treatment has given her five
cancer-free years. (...) In two weeks, America’s Food and Drug
Administration will put the treatment devised by Oxford BioMedica, in
league with Swiss pharmaceutical giant Novartis, before a panel of
independent experts. If they like the findings from the human trials, it
could pave the way for a full approval in October. A European Medicines
Agency filing could follow later this year.”
(Sabah Meddings, July 2 2017, The Sunday Times, UK)
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 2 / 1
Research questions
Research questions:
1) does more R&D outsourcing imply less internal activity?
2) how are R&D benefits distributed among contracting parties?
3) do firms pay more for equity than for contracted-out R&D?
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 3 / 1
Results Preview
In a model where two firms can choose to outsource R&D to an external
unit, and/or engage in internal R&D, before competing in a final market:
- internal/external operations neither substitutes nor complements;
- an aggregate measure of technological externalities drives the
distribution of industry profits;
- likely abandonment of projects with economic and medical value as
a likely consequence of outsourcing;
- founders of a research biotech (more than of a clinical services unit)
reappropriate industry profits by selling out the equity.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 4 / 1
Results Preview
In a model where two firms can choose to outsource R&D to an external
unit, and/or engage in internal R&D, before competing in a final market:
- internal/external operations neither substitutes nor complements;
- an aggregate measure of technological externalities drives the
distribution of industry profits;
- likely abandonment of projects with economic and medical value as
a likely consequence of outsourcing;
- founders of a research biotech (more than of a clinical services unit)
reappropriate industry profits by selling out the equity.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 4 / 1
Results Preview
In a model where two firms can choose to outsource R&D to an external
unit, and/or engage in internal R&D, before competing in a final market:
- internal/external operations neither substitutes nor complements;
- an aggregate measure of technological externalities drives the
distribution of industry profits;
- likely abandonment of projects with economic and medical value as
a likely consequence of outsourcing;
- founders of a research biotech (more than of a clinical services unit)
reappropriate industry profits by selling out the equity.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 4 / 1
Results Preview
In a model where two firms can choose to outsource R&D to an external
unit, and/or engage in internal R&D, before competing in a final market:
- internal/external operations neither substitutes nor complements;
- an aggregate measure of technological externalities drives the
distribution of industry profits;
- likely abandonment of projects with economic and medical value as
a likely consequence of outsourcing;
- founders of a research biotech (more than of a clinical services unit)
reappropriate industry profits by selling out the equity.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 4 / 1
Stylized facts
1) 16.6% annual growth rate of R&D outsourcing worldwide, expenses
from US$ 14 bn in 2003 to 47 bn in 2011 (Morton and Kyle, 2012).
2) from mid 70s onward “[v]irtually every new entrant ... formed at least
one, and usually several, contractual relationships with established
pharmaceutical (and sometimes chemical) companies” (Pisano, 2006).
3) “... a number of cases of the opposite philosophy, adding in-house
research where it previously didn’t exist, is also occasionally in evidence”
(Rydzewski, 2008).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 5 / 1
Stylized facts
4) contract usually designed by the demand side (pharma firms can “go for
it alone”; financial constraints faced by specialized units; high entry rate
on supply side; see Arora et al., 2004; Golec and Vernon, 2009).
5) complex clauses connect payments received by external unit from a
client firm and the R&D supplied to a competitor (“right of first refusal”,
“right to match offer”, see Folta, 1998; Hagedoorn and Hesen, 2007).
6) “Uncertainty related to the success/failure of R&D activities is the
major concern for R&D managers in the biopharmaceutical industry”
(Pennings and Sereno, 2011).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 6 / 1
Related literature (theory)
Aghion and Tirole (1994): exclusive division of R (upstream) and D
(downstream), relative efficiency of efforts drives separation/integration,
no downstream competition.
Anton and Yao (1994): no endogenous R&D effort, two client firms with
sequential bargaining, secret reselling, focus on profit distribution.
Bhattacharya and Guriev (2006, 2013): endogenous D effort chosen by
two client firms, secret reselling, information leaks, focus on contractual
form (“open form & exclusivity” vs. “closed form & reselling risk”).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 7 / 1
Related literature (theory)
Lai, Riezman, and Wang (2009): R&D unified, either upstream (with
leakage), or downstream in single firm (higher cost), focus on decision to
delegate or not.
Vencatachellum and Versaevel (2009): R&D unified, either upstream (with
(dis)economies of scope), or in two competing firms, with spillovers, focus
on choice to either delegate, cooperate, or compete, and welfare analysis.
Allain, Henry, and Kyle (2015): R part not considered, D may shift from
upstream to downstream client, focus on effect of downstream
competition.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 8 / 1
Related literature (empirical evidence)
Hagedoorn et al. (2012): above (below) a threshold of internal R&D, the
marginal returns to internal R&D is higher (lower) when R&D is sourced
externally, implying complements (substitutes).
Ceccagnoli et al. (2014): external and internal R&D neither complements
nor substitutes (complementarity increases with prior licensing experience).
Higgins et al. (2006): firms with greater R&D intensity are more likely to
engage in R&D outsourcing acquisitions.
Danzon et al. (2007): financially strong firms less likely to be part of
acquisition, and a merger has little effect on R&D expenses.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 9 / 1
The model
One external for-profit lab (0):
x.= (x1, x2) external R&D
Two firms (i , j = 1, 2):
y.= (y1, y2) internal R&D
z.= (z1, z2) commercial strategies
Firms compete (i) on the demand side of the intermediate R&D market,
(ii) in internal R&D levels, (iii) on the final product market.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 10 / 1
The model
Cooperation and Competition in R&D Contracts
Etienne Billette de Villemeur & Bruno Versaevel
2x1x
)(1 xt )(2 xt
xlab. 0
1z 2z
1y 2yfirm 1 firm 2
Figure 1: One lab (common agent) and two firms (principals)
which compete in external and internal R&D
and in the final product market
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 11 / 1
The model
The lab’s net profit:
v0(x).= t1(x) + t2(x)− f0(x)
Firm i ’s net profit:
vi (x, y, z).= gi (xi + yi , xj , yj , z)− fi (yi )− ti (x)
f0: lab’s R&D cost of x
fi : firm i ’s R&D cost function of yi
gi : firm i ’s gross profit function of x, y, z
ti : firm i ’s transfer payment function of x
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 12 / 1
The model
Timing:
(i) The firms choose non-cooperatively ti (x) ≥ 0,
(ii) The lab contracts with both firms, only one, or none,
by choosing x to max v0(x) (i.e., given ti the lab contracts with firm j
only if
v0(x) ≥ sup{
0, maxx{ti (x)− f0 (x)}
}for some x ≥ (0, 0), i = 1, 2, j 6= i).
(iii) The firms choose non-cooperatively yi ≥ 0,
(iv) The firms choose non-cooperatively zi ≥ 0.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 13 / 1
The model
Notation:
gi (xi + yi , xj , yj ).= gi (xi + yi , xj , yj , z
∗(x, y))
gi (x).= gi (xi + y ∗i (x), xj , y
∗j (x))− fi (y
∗i (x))
By assumption:
Given gi , for any (x, y) there exists a unique z∗(x, y),
Given gi , for any x there exists a unique y∗(x).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 14 / 1
The model
Technological assumptions:
∂gi∂xi≥∥∥∥∥∂gi
∂xj
∥∥∥∥ (1)
= ≤
∂gi∂yi≥∥∥∥∥∂gi
∂yj
∥∥∥∥ (2)
and ∥∥∥∥ ∂2gi∂yi∂xi
∥∥∥∥ ≥ ∥∥∥∥ ∂2gi∂yi∂xj
∥∥∥∥ (3)
= ≤∥∥∥∥∂2gi∂y2i
∥∥∥∥ ≥ ∥∥∥∥ ∂2gi∂yi∂yj
∥∥∥∥ (4)
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 15 / 1
External and internal R&D: complements or substitutes?
Proposition 1
The equilibrium level of a firm’s internal R&D activity y ∗i is decreasing in
the contracted external lab’s activity xi if and only if the gross profit
functions gi have decreasing returns in (xi , yi ):
dy ∗idxiQ 0⇔ ∂2gi
∂s2iQ 0,
where si.= xi + yi , and i = 1, 2.a
aMore specifically,dy ∗idxi
= 0 if and only if either (i) ∂2gi∂s2i
= 0, or (ii)
∂2gi∂x2
i= ∂2gi
∂xi ∂yj< 0,
∂2gj∂x2
j=
∂2gj∂xj ∂xj
< 0, and∂2fj∂y2
j= 0, where i , j = 1, 2, j 6= i .
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 16 / 1
External and internal R&D: complements or substitutes?
1) internal and external operations are neither substitutes
nor complements in general ,
2) second-order condition bears only on each firm i ’s own argument si
not on xj or yj , i , j = 1, 2, i 6= j ,
3) unlike models of horizontal agreements where inter-firm spillovers drive
strategic complementarity/substitutability of R&D choices.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 17 / 1
Distribution of R&D benefits
Value function:
v (S).= max
x
(∑i∈S
gi (x)− f0(x)
)where S ∈ {∅, {1}, {2}, {1, 2}}, v(∅) = v0 = 0 (normalization).
Aggregate measure of the two categories of externalities:
ε.= v ({1, 2})− v ({1})− v ({2})
ε =
≥ 0 positive externalities dominate
< 0 negative externalities dominate
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 18 / 1
Distribution of R&D benefits
� Non-increasing returns to R&D: Assume that ∂2gi∂s2i≤ 0.
Non-negative R&D externalities. Suppose that indirect and direct R&D
externalities are non-negative:
∂2f0∂xi∂xj
≤ 0 (5)
∂gi∂xj≥ 0
∂gi∂yj≥ 0 (6)
Characteristic of early-stage discovery with empirical evidence of
economies of scope and significant knowledge spillovers (Henderson and
Cockburn RAND 1996; Cockburn and Henderson JHE 2001)EBdV & BV One Lab, Two Firms, Many Possibilities 2017 19 / 1
Distribution of R&D benefits
Proposition 2
Conditions (??-??) imply that ε ≥ 0. In all TSPNE there exists a
continuum of firm payoffs (v ∗1 , v ∗2 ) ≥ (v1, v2) that verify
v ∗1 + v ∗2 = Λ, (7)
and the lab exactly breaks even, that is
v ∗0 = 0. (8)
There is delinkage of incentives to invest in external unit from the value
generated to exclusive benefit of downstream sponsors. Efficient projects
at the industry level are vulnerable to upstream unfavorable events.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 20 / 1
Example 1 (adapted from Symeonidis, IJIO 2003):
pi (qi , qj ) =(
1− 2qiu2i− qj
uiuj
), i , j = 1, 2, j 6= i , where ui is firm i ’s
product quality, which depends on R&D: ui = (si )14 + β (sj )
14 , β ∈ [0, 1] is
a spillover parameter, si.= xi + yi and sj
.= xj + yj . Set β = 1
2 , production
costs to zero, and solve for Cournot-Nash quantities q∗1(x , y) and q∗2(x , y).
Inserting the latter expressions in gi (si , xj , yj ,q) = pi (qi , qj ) qi leads to
gi (si , xj , yj ). We obtain ∂2gi∂s2i
< 0 (decreasing returns) for all si > 0, so
that from Proposition 1 we havedy ∗idxi
< 0 (R&D outsourcing reduces
internal activity). Any additive cost function for the lab, e.g.
f0 (x) = x1 + x2, satisfies (??). Moreover ∂gi∂xj
> 0 and ∂gi∂yj
> 0 (positive
direct externalities) for all xi , xj > 0, so that (??) is satisfied.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 21 / 1
Distribution of R&D benefits
Negative R&D externalities. Suppose that indirect and direct R&D
externalities are negative:∂2f0
∂xi∂xj> 0, (9)
∂gi∂xj≤ 0,
∂gi∂yj≤ 0. (10)
Characteristic of late-stage clinical trials with empirical evidence of
diseconomies of scope and non-existent spillovers (Danzon et al., JHE
2005; Macher and Boerner, SMJ 2006).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 22 / 1
Distribution of R&D benefits
Proposition 3
Conditions (??-??) imply that ε < 0. In all TSPNE there is a unique pair
of firm payoffs (v ∗1 , v ∗2 ) that verify
v ∗i = v({i})− |ε| ≥ v i , (11)
i , j = 1, 2, j 6= i , and the lab appropriates a share of industry profits
v ∗0 = |ε| > 0. (12)
The external unit can appropriates all profits in a buyers market where
client firms are principals and are no less informed than the external unit.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 23 / 1
Example 2 (adapted from Laussel and Le Breton, JET 2001):
x, y ∈ {0, 1}2 and the lab’s R&D costs are
f0(x) =
1 if x1 + x2 = 1
0 if x1 = x2 = 0
f0(x) = +∞ otherwise, satisfying condition (??). Each firm’s R&D cost is
fi (yi ) = γyi , with γ ≥ 1, and production cost is ci (xi + yi ), with
ci (0) = cH and 0 ≤ ci (1) = ci (2) = cL < cH . Total demand is
q = sup{0, a− p}, with p ≥ 0 and a > cH . Given (x, y), defining
π.= (cH − cL) (a− cH), and solving for Bertrand-Nash equilibrium prices
leads to gi (xi + yi , xj , yj ) = π > 0 if xi + yi ≥ 1 and xj + yj = 0, and
gi (xi + yi , xj , yj ) = 0 otherwise, so the condition in (??) is also satisfied.
Equilibrium payoffs are v ∗0 = π − 1, v ∗i = v ∗j = v = 0.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 24 / 1
Distribution of R&D benefits
� Non-decreasing returns to R&D. Assume that ∂2gi∂s2i≥ 0.
Simple sufficient conditions for Propositions 2 and 3 to remain valid:
Proposition 4
Suppose that returns to R&D are non-decreasing. Then Propositions 2
and 3 still hold if∂2gj
∂xj∂xi≥ 0, i , j = 1, 2, j 6= i . Otherwise a sufficient
condition isdy ∗jdxi
> −1.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 25 / 1
Example 4 (d’Aspremont and Jacquemin, AER 1988, & Vonortas IJIO
1994): f0(x) = (x1 + x2)2 − δ2x1x2, with δ ≥ 0, fi (yi ) = κ + y2i , with
κ > 0. Production cost is ci (x) = (c − si − βsj ), with c > 0, with
spillover parameter β ∈ [0, 1], and where si = xi + yi . Inverse demand is
p(q) = a− qi − qj , so q∗i (x, y) = [(a− c) + si (2− β) + sj (2β− 1)] /3.
Then ∂2gi/∂s2i = 2 (2− β)2 /9 > 0 (increasing returns to R&D), and:
(i) Proposition 2 applies if β ≥ 1/2 and δ ≥ 1,
(ii) Proposition 3 applies if β < 1/2 and δ < 1.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 26 / 1
Incentives to integrate
Cooperation and Competition in R&D Contracts
Etienne Billette de Villemeur & Bruno Versaevel
xlab. 0
1z 2z
firm 1 firm 2
1y 2y
2x1x
)()( 21 xx tt
Figure 2: Inter-firm cooperation: joint R&D procurement
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 27 / 1
Incentives to integrate
Cooperation and Competition in R&D Contracts
Etienne Billette de Villemeur & Bruno Versaevel
lab. 0
firm 1 firm 2
Figure 3: firm 1 and the lab integrate vertically
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 28 / 1
Incentives to integrate
Cooperation and Competition in R&D Contracts
Etienne Billette de Villemeur & Bruno Versaevel
lab. 0
firm 1 firm 2
Figure 4: firm 2 and the lab integrate vertically
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 29 / 1
Incentives to integrate
� Non-negative R&D externalities (ε ≥ 0)
From Proposition 2: v ∗0 = 0, and v ∗1 + v ∗2 = Λ (where v ∗i ≥ v i ).
The payoff distribution (v ∗1 , v ∗2 ) reflects circumstances outside of the
model specifications captured by bargaining powers (φ1, φ2):
v ∗k = vk + φk (Λ− v) ,
k = 1, 2, where (v1, v2) is the disagreement point, with v.= v1 + v2 and
φ1 + φ2 = 1. Then
φk =v ∗k − vkΛ− v
.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 30 / 1
Incentives to integrate
Suppose v ({i}) > v i . In case of vertical integration {0, i}:
v{0,i}0+i = v ({i}) + φi
(Λ− v ({i})− v j
)> v ∗i , (13)
v{0,i}j = v j + φj
(Λ− v ({i})− v j
)< v ∗j . (14)
From (??-??) willingness to pay for the lab simplifies to:
v{0,i}0+i − v
{0,j}i = φj (v ({i})− v i ) + φi
(v ({j})− v j
)> 0,
for a strictly higher payoff to the external unit than with outsourcing:
v{0,1}0 = v
{0,2}0 =
v ({1})− v1Λ− v
(v ∗2 − v2)
+v ({2})− v2
Λ− v(v ∗1 − v1) > v ∗0 = 0.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 31 / 1
Incentives to integrate
� Negative R&D externalities (ε < 0)
From Proposition 3: v ∗0 = |ε| > 0, and v ∗i = v({i})− |ε| ≥ v i .
In a horizontal arrangement for firms to behave as a unique principal:
v{1,2}0 = 0, v
{1,2}1 + v
{1,2}2 = Λ,
and the two firms’ payoffs(v{1,2}1 , v
{1,2}2
)verify:
v{1,2}k = v ∗k + ωk (Λ− v ∗1 − v ∗2 ) ,
so bargaining powers are:
ωk =v{1,2}k − v ∗k
Λ− v ∗1 − v ∗2.
...EBdV & BV One Lab, Two Firms, Many Possibilities 2017 32 / 1
Incentives to integrate
The two firms’ joint profit is maximized in the horizontal arrangement but
each firm has an incentive to depart unilaterally from 1, 2 by acquiring the
external unit. The bidding process results in:
v{0,1}0 = v
{0,2}0 =
v ({1})− v1|ε|
(v{1,2}2 − v ∗2
)+
v ({2})− v2|ε|
(v{1,2}1 − v ∗1
)≥ v ∗0 = |ε| .
With negative externalities the value extracted by the owners of the
external unit in the equity market is only weakly superior to the positive
outsourcing equilibrium payoff.
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 33 / 1
Incentives to integrate
Corollary 3
From the viewpoint of the labs owners, incentives to participate in the
equity market are weaker in the case of late-stage development (clinical
trials) activities characterized by negative externalities, as compared with
earlier-stage research (discovery).
Exit payoff results in a long-term financial incentive that motivates the
foundation of a new research biotech (more than a development services
provider).
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 34 / 1
Appendix (1/2)
Definitions:
(1) for any t.= (t1, t2) the lab’s profit-maximizing R&D set is
X (t).= arg maxx v0(x(t))
(2) for any x ∈ X (ti , tj ) and x′ ∈ X (t ′i , tj ), firm i ’s transfer function ti is a
best response to the other firm’s tj if gi (x)− ti (x) ≥ gi (x′)− t ′i (x′), all t ′i
(3) the transfer function ti is truthful relative to x if
ti (x).= sup{0, gi (x)− (gi (x)− ti (x))}
EBdV & BV One Lab, Two Firms, Many Possibilities 2017 35 / 1
Appendix (2/2)
Equilibrium concept:
(t, x, y, z) is a Truthful Subgame-Perfect Nash Equilibrium (TSPNE) if:
(i) z = z∗(x, y)
(ii) y = y∗(x)
(iii) x ∈ X (t)
(iv) ti is a best response to tj
(v) ti is truthful relative to x
ti (x) = sup{0, gi (x)− v ∗i }, where v ∗i.= gi (x)− ti (x) is firm i ’s net
equilibrium payoffEBdV & BV One Lab, Two Firms, Many Possibilities 2017 36 / 1