a theory of entrepreneurial rents in endogenous growth mark sanders utrecht school of economics max...
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A Theory of Entrepreneurial Rents in Endogenous Growth
Mark SandersUtrecht School of Economics
Max Planck Institute of [email protected]
IECER7 March 2008Regensburg
MotivationSchumpeter and Endogenous Growth Theory
Innovation vs. InventionWho gets rents?Opportunities vs. Patents/Ideas
The ultimate source of growth
Growth and Ideas; the basic model structureConsumersProducers/IntermediatesInnovationGrowth
Back to “Reality”:Knowledge CreationKnowledge SpilloverIncentives and Rewards
Growth and IdeasBasic Structure: Consumers
1. Need to be willing to save2. Need to have latent demand for
innovations
Basic Structure: Producers1. Need to make profit2. Need to demand factors
Growth and IdeasBasic Structure: Inventors/Innovators
1. Make zero-profit (free entry)2. Need to demand R&D factors
dttiπeTVTVT
ttrnq ),()()( )(
Auction off ideas at willingness to pay:
),(
),(
&
&
DR
DR
Lqfq
Lnfn
Produce ideas according to:
Growth and IdeasBasic Structure:
1. Growth is positive for positive R&D2. Sub-optimal in case of spillovers
Intra-temporal knowledge spilloversInter-temporal knowledge spilloversPositive steady state growth requires:
latent demand for innovationimperfect competition appropriation of rents by inventors/innovatorsincreasing returns to scale in aggregate production
Optimal growth requires stimulation of R&D
Back to “Reality”:Knowledge Creation:
Is all knowledge creation invention?Is all invention also innovation?
Knowledge Spillovers:Are knowledge spillovers automatic?Are knowledge spillovers localized?Are knowledge spillovers costly?
Incentives and Rewards:What drives knowledge creation?What drives invention?What drives innovation?
A Model (Acs and Sanders 2008)
Producers of final good C
Consumers of final good C
Producers of n intermediate
goods
Capital Market
Labor Market
A Model (Acs and Sanders 2008)
tttt
tτ
tτρ
E
BCrBYts
τdCet
:..
)log(:max )(
ρrCC tt /
Consumers (standard)
A Model (Acs and Sanders 2008)
Final Goods Producers
w
Xβl jj
wXβ
L
)(
0
1),()()()(:..tn
i
βαj
βPj
αjj tixtLtAtXts
dttixtiχtLtLtwtXeVtn
ijRjPjj
rtj
tLtLtX RjPjj
0
)(
0)(),(),(
),(),()()()()(max
jn
i
βαβα
βαD
j Xβα
iχ
iχix )1(
)(
)()(
0
1
1
Xβα
iχ
iχix
n
i
βαβα
βαD )1(
)(
)()(
0
1
1
)()()()( 1 tLtntAtA Rjγγ
jj
A Model (Acs and Sanders 2008)
Final Goods Producers (R&D)
Rjγγ
jjj
j
jjt
Rjγγ
jj
n
i
βαj
βPj
αj
rtj
j
j
γγjj
rt
Rj
j
LnAAλ
H
tAtλ
LnAλγixLAeλA
H
nAλweL
H
1
0
11
1
0)()(lim
)1()(
0
Rjγγ
jj
n
ijRjPj
n
i
βαj
βPj
αj
rtj LnAλixiχLLwixLAeH
1
00
1 )()()(
nnγwwr
nAXαw
γγjj
j //
A Model (Acs and Sanders 2007)
Intermediate Goods Producers
)()()()(:max)(
irKixiχiπiχ
Xβα
iχ
iχix
iKix
n
i
βαβα
βαD )1(
)(
)()(
)()(
0
1
1
βαr
iχ
1
)(n
Xβαβαiπ
)1)(()(
A Model (Acs and Sanders 2007)
Intermediate Goods Producers (Entry)
dttntX
eβαβαdttiπeTVT
rt
T
rtE )(
)()1)((),()(
EALn
XnA
XXnnr
βαβαw
//
)1)((~
Entry-Arbitrage:
A Model (Acs and Sanders 2008)
Equilibrium in labor market:
]~,max[ www
]~,max[ www
www ~www ~
A Model (Acs and Sanders 2008)
Equilibrium
A/n
1
A/n*
AAnn //0
0// AAnn
ww~
A Model (Acs and Sanders 2008)
Equilibrium Steady State:
γ
nnγρnnρ
βαβαα
nA
11
//
)1)((
γ
E
R
nA
LL
1
βαβα
nn
ρrww
BB
CC
XX
KK 2
ERP LLLL *
A Model (Acs and Sanders 2008)
Features:Spillover R&D=>Entrepreneurs proportionalSpillover Entrepreneurs=>R&D less than proportionalGrowth Sub-OptimalBoth R&D and Entrepreneurs should be supportedR&D more than EntrepreneursRents reward commercialization (not knowledge creation)Opportunity is pure spillover from (process) R&DProcess R&D is self sustaining/financedCaptures spin-out/offCaptures entrepreneurshipCaptures up stream spillovers (how?)Captures downstream spillovers (how?)
A Model (Acs and Sanders 2008)
In the tradition of Joseph Schumpeter we:
…separate commercialization and invention,…allocate the monopoly rents to the entrepreneur,…assume opportunity to be a costless spillover/externality…but also endogenize knowledge creation.
Innovation and Entrepreneurship should… …and can be put at the heart of growth theory.