R&D and competition
Motivation: to investigate the relation between
competition and R&D expenditures
Schumpeterian hypotheses
Incentives
A case: steam engines
Patent races
Common pool problem
Recent developments

Schumpeterian hypotheses:
Monopoly power and firm size are conducive
for R&D
– A monopolist is well-placed (distribution, reaction
to rivals)
– Internal finance of innovation (moral hazard)
– Advantage on labour market for engineers
– More internal spillovers in a large R&D team
– Technology push favours firms with large
resources for R&D
– Demand pull favours firms with a deep knowledge
of market and large scope

Incentives
Same context as in the patent length model: a
process innovation
Compare profits with and without innovation:
the difference is what a firm would maximally
pay to get the innovation (=maximum amount
of R&D it is willing to spend)

Incentives – mathematics
q A Bp,
Monopolist:
2
qp
2
A1 1 1 (A Bc)
p c, qp (A Bc), ,
2B 2 2 4 B B
c
1 1
B(c 2 c 2)
(c) (c) q(p (c)) dc A(c c)
2 4
c
Competitive firm:
c
minor
q(c) dc (A Bc) (c c).
c
c
q(c) dc.
Social planner:
c

Incentives: conclusion
The incentive for a monopolist is strictly
smaller than that for a competitive firm with a
minor innovation, which is again strictly
smaller than that for a social planner

Steam engines – An illustration
Engine builders in Cornwall in 1800 could charge 1/3rd of the
total fuel savings relative to a Newcomen engine
P C
× × HP × H ,
Fuel consumption: 240 2240
P=266 pence, HP=3250, H=4000 (Cornwall, 1800)
Newcomen engine: C=24.3
266 (24.3 − 61)
.
× × 3250 × 4000 ≈ 117068
Watt engine: C=6.1 240 2240
266 (24.3 − 33)
.
× × 3250 × 4000 ≈ 135078
Woolf engine: C=3.3 240 2240
266 (24.3 − 4.3)
× × 3250 × 4000 ≈ 128646
Trevithick engine: C=4.3 240 2240

Patent race Incumbent vs entrant
Efficiency effect
m d d
(c) (c, c) (c, c).
Incumbent:
m d
(c) (c, c)
(R1 R2 ) m(c)
V1 e e R1 R1 R2
0
m m d
(c) R1 R1 (c) / R2 (c,c) /
.
R1 R2
Entrant:
d
d R2 (c,c) / R2
(c,c)
(R1 R2 )
V2 e e R2 R2 .
R1 R2
0

Patent race Incumbent vs entrant
Nash equilibrium:
1
R1 [ m(c) m m d
V1 [ R1 R2 ] (c) R2 [ (c) (c,c)] / R1]
0
R1 2
( R1 R2 )
R2 1 [ d(c,c) R2 d
V2 R1 R2 (c, c) / R2]
0.
R2 2
( R1 R2 )
Drastic innovation: π d (c, c ) = π m (c), π d (c , c,) = 0
1 1
R1 R2 R2 R1
1 1 1
m m
(c) R1 (c) [R1 R2 ] R1 R2 .

Patent race Incumbent vs entrant

Symmetric patent race
R1 R1
(R1 (n 1)R )
V e e (R1 R1) d .
R1 (n 1) R
0
1
[(n 1) R ][ R1 1] R1 (1 ) 0.
1
[(n 1) R1 ][ R1 1] R1 (1 ) 0.

Symmetric patent race

Symmetric patent race
Monopolist (centralized):
Rm Rm
(nRm)
Vne e (Rm Rm) d n .
nRm
0
nRm (1 )
1
Rm 1 .
Decentralized:
R1 (1 )
1
R1 1 .
(n 1) R1

Patent race as a common pool problem
Number of fishermen Catch per fisherman Total catch Marginal increase in
total catch
0 - 0 -
1 100 100 100
2 90 180 80
3 80 240 60
4 70 280 40
5 60 300 20
6 50 300 0
7 40 280 -20

Recent developments
Patent races with memory (leads to a single
dominant firm)
Mixed strategies
repeated games: if leapfrogging is possible
this favours a large number of firms
undertaking R&D

recent developments
Invariance theorem
– if all players in a race are allowed to engage in
multiple projects without externalities between
them, it does not matter how many players there
are (and otherwise it does!)
Second-mover advantages (it may pay to
wait, see inventing around example)
Size of prize depends on R&D

R&D and competition
An alternative view: technology regimes in a
boundedly rational, evolutionary world
When uncertainty is strong, the rational
behaviour of patent race and patent
protection models is not very realistic
Nelson & Winter model

Technology regimes
Basic idea is that the nature of the knowledge
base has an impact on the way innovation
and technological change takes place, and
this influences market structure
Schumpeter Mark I vs Mark II
Different regimes within the same industry?
(Saxenian)
The Nelson & Winter model can generate
technology regimes

A (more) realistic Model: Nelson &
Winter
Firms differ, they are characterized by
– A labour coefficient (labour output ratio)
– A capital coefficient (capital output ratio)
– A capital stock
Firms sell a homogenous output, and hire
homogenous labour
Rationality is bounded: based on rules of
thumb and routines
Firms engage in search (R&D) to improve
their technology (input coefficients)

R&D in the Nelson & Winter model
R&D can be imitative (trying to imitate
technology of other firms) or innovative (trying
to find new techniques
R&D is local search, it starts from the
technology that the firm has now; this is in
line with the notion of a technological
paradigm
In one version of the model, R&D depends on
the nature of the knowledge base

The market structure model
Two technological regimes:
– Routinized
– Entrepreneurial
This is modeled after Schumpeter Mark I vs
Mark II

The routinized regime
Lower probability of innovation (for equal
levels of R&D spending)
Innovative step depends on external
(scientific) developments and the firm’s own
performance (innovation in the past breeds
more success): cumulativeness
As a result outsiders (potential entrants) have
a low probability of success (they have no
experience)

The entrepreneurial regime
A high probability for innovation
Outsiders (potential entrants) are as good in
innovation as incumbents

Simulation analysis
The usual way of analysis of a model is to
find the equilibrium
The evolutionary Nelson and Winter model
does not have a clear-cut equilibrium
Outcomes of the model depend on random
factors (e.g., innovative success)
The model can be analyzed by running it on a
computer

Guidance for simulation analysis
A single simulation run is not enough to show
a result
Monte Carlo experiment: run multiple times
with different parameter settings, and then
compare the outcomes by means of a
statistical analysis

Technology regimes – Nelson & Winter
http://www.tm.tue.nl/ecis/bart/nwreg.zip

Simulation results – Nelson & Winter

Simulation results – a systematic
comparison of the regimes

Technology regimes – Nelson & Winter
A conclusion: differences in knowledge base
cause differences in R&D spending and
market structure
Which regime generates which market
structure?
How can the changes between the regimes
be influenced?
– Explorations of parameter space