R&D Flashcards
3 types of R&D
Basic (research with no specific application)
Applied (research with a particular application)
Experimental (applied research directed towards new/existing systems)
Key assumption for R&D
Pr(Innov=1) = Φ(F irmCharacteristics)
I.e
R&D as a % of GDP
Around 3%
Why is it risky
Doesn’t always lead to innovation
How to address
public and private funds towards r&d
why both pay? as innovation (progress) benefits both producers and consumers
Start with bertrand competition pg 10
Add small innovation in diagram pg 12
Add large innovation pg 13
Innovation reduces marginal costs, c0 to c1
small innovation results in moves from bertrand to monopoly. (only reduce c0 to c1 a little)
large innovation reduced c0 to c1 a lot, so results in a lower price
pg 14
Why engage in R&D
Monopoly profits
signal of high quality
2 factors important for innovation race
investment amount
nunber of rivals
Assumption for innovation race
Once a firm invests I in a lab, it has a probability α of discovering a technology that yields profit V , as long as it is the sole discoverer, or V2 if another firm discovers it too. It earns 0 if no discovery occurs.
Expected profits Eπ if only 1 firm (sole discoverer)
Prob of discovery α
Diagram for 1 firms decision to innovate pg 17
left side of line = no r&d as expected profits ngeative
right side of line = invest as expected profit positive
Now add a 2nd firm. what do we have (2)
Technological uncertainty
Market uncertainty as dont know whether you, or the other firm will innovate first.
Expected profit of each firm
Eπi(2)=α(1−α)V +α2V2 −I
invest if Eπi(2) > 0
This expression shows situation if both discover
α(1 − α)V + α² V2 − I = 0 (firms share)
rearrange to get α(2−α)V =I
diagram for 2 firms pg 20
Why are firms disincentivised by other firms engaging in R&D
As firms engagin in R&D provide negative externality to other firms
Society’s welfare is measured bywhat
industry expected profit
Society welfare function (for 1 firm)
b) function for 2 firms
c) when is it socially optimal to have 2 firms vs 1
Eπs(1)=Eπ(1)=αV −I.
(since based on industry profit)
b)
Eπs(2)=PEπi(2)=2α(1−α)V +α2V −2I.
c) if
Eπs(2) > Eπs(1)
i.e 2α(1−α)V +α2V −2I >αV −I
Add society welfare to the diagram pg 24
4 parts: we have the:
no R&D scenario
1 firm
2 firm but not socially desirable
2 firms and socially desirable
Intuition of these 4 regions
No R&D: as cost of R&D relatively high (compared to expected profits)
1 firm: externalities are high enough to prevent 2nd firm entering
2 firm but not socially desirable: market failure (since firms investing in r&d create neg externalities)
2 firms and socially desirable: cost is low enough to compensate the externaltiies
2 firms not socially desirable: Market failure
how can we express it
α(1−α) < IR&D < α(2−α)V/2
Policy makers can influence level of IR&D
What should they do then (2)
identify determinants of Ir&d
calculate socially optimal thresholds
(despite firms engaging in R&D creating negative externalities for other firms and thus disincentivises R&D….) (note: disincentivise firms or society?)
Why do we need more firms engaging in R&D
shortens time of discovery
Shorterns time of discovery algebra pg 27
1 δ δ2
= 1 − δ + 1 − δ + 1 − δ + …
final equation was
1 / 1-δ ²
if each period an event can occur with probability a
Probabilityof event occuring period 2
It won’t occur in period 1, so occurs in period 2
so Pr(t=2) = (1-a)a
If 2 rounds, what is probability of event occuring
could occur at period 1 (a) or 2 (1-a)a
expected prob = a + (1-a)a
= a+a-a²
=a(2-a)
Assuming 2 rounds, what is expected date of event happening?
ET(t=2) α×1 + (1−α)α×2
=3α−2α²
=α(3−2α)
What if 3 periods, what is the expected time of discovery
b) relationship found
Prob of discovery in P1 = a
prob of disc in p2 = 1-a)a
prob of disc in p3 = (1-a)(1-a)a i.e (1-a)²a
so expected time
ET = 1α + 2(1 − α)α + 3(1 − α)2α + ..
= 1/a
b) Shows relationship betwen time and probability of discovery! As prob of discovery (a) bigger, expected time falls!
Now consider time of discovery with 2 firms:
how do we start going about this
Find the probability that no firms discover in any period is (1-a)²
thus remaining probability is of at least 1 firm making discovery: 1 - (1-a)²
= a(2-a)
then we can make our ET expression
Expected time of discover (ET) expression for 2 firms
B) intuition
ET (2) = 1α(2 − α) + 2(1 − α)2α(2 − α) + 3(1 − α)4α(2 − α) + ..
= 1/a(2-a)
which is < 1/a
(ET for 2 firms is less than ET for 1 firm)
B) as firm number increases, ET falls
Should firms work together in R&D?
Proceed with
2 firms
2 stages
Assume market demand p = 100 - q
What are 2 stages
Stage 1: firms choose to cooperate or not in R&D expenditure
Stage 2: firms compete in quantities in the final good (cournot)
Model innovation:
assume r&d cost reducing
ci(xi,xj)≡50−xi−βxj
1>β>0 B is externalities
unit cost of production is decreasing but
R&D is costly TCi(xi) = x²i / 2
Start by solving stage 2 (cournot)
Find quantity price and profit functions
then use profit function for stage 1
Key findings after derivartions: does cooperation in R&D benefit?
yes. increases firms’ profits
what if R&D spillover effect is large (β>1/2)
then cooperative R&D level are higher than noncooperative ones
but if β<1/2 then better to privately invest in R&D
hence why people try to estimate β to find whether government should contribute or not
