Industry Cohesion & Knowledge Sharing:
Network based Absorptive Capacity
David Dreyfus
1/27/2005 David Dreyfus 1

Industry Cohesion & Knowledge Sharing:
Network based Absorptive Capacity
What is the impact of search cost on R&D allocation decisions?
How does industry size and cohesion affect search cost and the optimal allocation of
R&D investments?
1/27/2005 David Dreyfus 2

Search and own R&D are complementary
The impact of a growing number of firms is dependent on the existing number and network cohesion
Network cohesion determines the quality and quantity of search
1/27/2005 David Dreyfus 3

Costless information (Arrow 1962)
Absorptive capacity (Cohen and Levinthal,
1999, 2000)
Joint knowledge production (Saxenian
1991)
Sticky Knowledge (Sakakibara 2002;
Alcacer et al. 2002; von Hippel 1994, 1988;
Mansfield 1988; Allen 1977)
1/27/2005 David Dreyfus 4

Firm boundaries and knowledge sharing
(Brynjolfsson 1994; Williamson 1975).
Innovation by borrowing (von Hippel 1988;
March et al. 1958)
Appropriation mechanism to control spillover varies by industry (Levin et al.
1987).
Formal and informal search
1/27/2005 David Dreyfus 5

1/27/2005 David Dreyfus 6

Social ties among firms shape economic action
Uzzi (1996)
Firms make strategic decisions in determining who they partnered with Baum et al. (2003)
Bounded Rationality (Simon 1945) leads to assertion that the size and shape of the firm’s network is a critical component of its knowledge investment decisions.
1/27/2005 David Dreyfus 7

Consider the actions of a single firm
Profits depend on knowledge
Allocating R&D in order to develop, learn and search
Subject to a constraint.
„ Explicit budget
„ Implicit marginal return on investment > 0
Find the optimal investment decision in terms of exogenous parameters (Lagrangian optimization)
1/27/2005 David Dreyfus 8

„ Profit maximizing firm.
„ Profits depend on knowledge
Π = t
„
∞
Constrained investment allocation
=
0
π
( t ) u ( t )
π
(t) =
π
(Z t
, K t
, L t
) z
=
M
+ γ
(
θ
J
j
j ⋅
Q j
+
T )
C
r
M
s
1/27/2005 David Dreyfus
∂
Z
∂ t
= z
9

„ Absorptive Capacity increases with M, decreases with Delta
„ Search Effectiveness increases with investment and cohesiveness, decreases with industry size
=
( 1
− e
−
M /
δ
)
( 1
e
− α
/( 1
+
J
2
( 1
− φ
))
)
Lim
J
→ ∞
J ( 1
− e
−
1 / J
)
=
1 Lim
→ ∞
J
J ( 1
− e
−
1 / J
2
)
=
0
1/27/2005 David Dreyfus 10

: α jjjj jjjj k jjjj jjjj jjjj jjjj jjjj jjjj s jjjj jjjj
− 1 +
−
M
δ jjjj i jjjj
−
1
+
α
−
1
+
J2
H −
1
+φ L
δ
JQ
θ−τ zzzz zzzz r
+
α
− 1 + J2
H − 1 +φ L k
1 −
−
M
δ
1 − J 2
H − 1 + φ L
{
J Q θ zzzz zzzz
{ zzzz zzzz zzzz zzzz zzzz zzzz
0,
H
C − M r − s α L jjjj jjjj
− 1 +
− M
δ jjjj i jjjj
− 1 +
α
−
1
+
J2
H −
1
+φ L
δ
JQ θ−τ zzzz zzzz
0
> r
1/27/2005 David Dreyfus 11

1/27/2005
2.5
2
1.5
1
0.5
0
0 2 4 6
Number of firms
8 10
David Dreyfus 12

γ =
M
⋅
( 1
− δ
),
∂ γ
∂
M
>
0 ,
∂ γ
∂ δ
<
0 , 0
≤
M
≤
1
χ = α
/( 1
+
J
2
( 1
− φ
)),
∂ χ
∂ α
>
0 ,
∂ χ
∂ φ
>
0 ,
∂ χ
∂
J
<
0 , 0
≤ α ≤
1
1/27/2005 David Dreyfus 13

M → 0, λ → 0 ,
M
M
→
→
α →
λ →
C r
, λ →
1 + τ − δ τ r
, α → 0 ,
C J Q − 1 + δ θ − s − 1 + − 1 + δ τ − 1 + J
2
2 J Q r − 1 + δ θ
C J Q − 1 + δ θ + s − 1 + − 1 + δ τ − 1 + J
2
2 J Q s − 1 + δ θ
C J Q − 1 + δ θ − s − 1 + − 1 + δ τ − 1 + J
2
2 r s − 1 + J 2 − 1 + φ
− 1 + φ
− 1 + φ
− 1 + φ
,
,
1/27/2005 David Dreyfus 14

∂
2
α z == −
∂
α
,M z ==
−
1 + J2
H
1 −φ L
−
H
M
δ
α k
1 −
− M
δ
{
1 + J 2
H
1 − φ LL 2
−
1 + J2
α
H
1 −φ L
J Q θ
J Q θ
δ 1 + J
−
α
1 + J2
H
1 −φ L
2 1 − φ
1 −
−
M
δ
< 0
> 0
J Q θ
∂
α z ==
1 + J 2 1 − φ
> 0
1/27/2005 David Dreyfus 15

Own R&D improves search
Cohesion increases search, infer it changes type of search
Information economics predicts more search
1/27/2005 David Dreyfus 16

Open Source focuses on the Search component
R&D investment as cost of entry (Pay to
Play)
Joint Ventures as Loss Leaders
1/27/2005 David Dreyfus 17

1/27/2005 David Dreyfus 18