Design of IP
• Two questions:
(1) How large should the rewards to innovation be?
(2) How should the reward be structured?
• How large?
– When ideas are scarce (no patent race)
– When ideas are common knowledge (patent race)
• Structure: Mainly about length and breadth of the
right.
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Size of the reward (e.g., patent life)
• Two arguments.
a) Nordhaus (scarce ideas) and b) race (# of firms)
• Nordhaus: Implicitly focuses on single inventors
with scarce ideas. Tradeoff is between “too few
innovations” and “too much deadweight loss.” The
number of innovations can always be increased by
increasing the patent value, but it increases
deadweight loss on every inframarginal innovation.
• Race: Arises where ideas are not scarce. The
problem is to avoid over-entry or under-rewards
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Optimal reward when Ideas are Scarce
A higher reward (patent life T) increases deadweight loss.
(This diagram is illustrative; know the idea, not the diagram.)
cost, c
space of ideas
(v,c)
vT’
 (vb,, cb )
vT
 (va,, ca )
value, v
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Optimal reward when ideas are common
knowledge
• A high reward may lead to a profit-dissipating race.
Racing can be inefficient.
– Duplication of effort.
– Pursuit of wrong ideas.
• Is a race beneficial for society?
– May duplicate costs (bad)
– May increase the probability of success or the time of
discovery (good).
• We cannot know whether a patent race is good or bad
without knowing how innovation works. We need the
right model of the creative environment.
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
“Duplication” is not well defined.
Races
• A simple patent race:
Suppose the social value of discovery is S.
Suppose each firm has an independent probability p of failure.
Let P(n) be the probability that at least one of n firms succeeds.
P(1) = (1-p) , P(2) = (1-p2) , P(3) = (1-p3) , P(n) = (1-pn) (increasing)
The expected social value of the investment (ignoring costs)
with one firm:
S P(1) =S(1-p).
with two firms:
S P(2) =S(1-p2).
with three firms:
S P(3) =S(1-p3)
with n firms:
S P(n) =S(1-pn)
The marginal social value contributed by
the first firm:
S(1-p).
the second firm:
S(p-p2).
the third firm:
S(p2 -p3)
the nth firm:
S(pn-1 -pn) (becomes close to zero)
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Races continued
• Now take account of costs.
Suppose that the winner of the patent race gets the entire
social value, S.
• Should the private reward be less than S? (Yes, why?)
S P(n)
cn
free entry outcome if winner
receives the whole social value
optimal
n*
ne
number of firms
n
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Races continued
• Modify diagram to account for the fact that the
winner receives less than the whole social value.
• Reduces number of entrants, possibly to the
efficient number.
Tandon 1983
cn
S x P(n)
 x P(n)
free entry outcome if winner
receives  instead of S
n*
ne
number of firms
n
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
What have we learned here?
There are two reasons that the reward should be less
than the social value of the innovation:
• If the reward is given as a patent, the patent
involves deadweight loss. We should be willing to
forego some high-cost innovations in order to
reduce DWL on innovations we will get in any
case.
• Cost duplication. Giving the entire social value
will lead to a profit-dissipating race, which also
dissipates social value by wasting resources.
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Size versus Structure of the reward
• So far we have mainly been discussing the optimal size
of the reward, however it is given. But the reward can
also be structured in different ways.
• Two important policy levers for intellectual property:
Length T
Breadth:
– Oncomouse. What about an oncowalrus?
– Amazon’s one-click patent.
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Breadth: Three Definitions
• Breadth excludes horizontal substitutes
– Define breadth on the product side
• Breadth defines cost of entry
– Define breadth on the technology side
• Breadth excludes vertical substitutes
– Defined for sequential innovation (later lecture)
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Breadth & Horizontal Competition
A higher price increases demand of substitute goods.
x1 ( p1 , pˆ2 )
x2 ( p2 , pˆ1 )
p̂1
p̂2
̂1
~
p1
~

1
x1 ( p1 , ~
p2 )
̂2
x2 ( p2 , ~
p1 )
~
p2 = mc
substitute good, x2
proprietary good, x1
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
Breadth & Cost of Entry, K
price p
The number of entrants, n(K), depends on the cost of entry, K.
If K decreases, the number of entrants n(K) increases.
If K decreases, the price p(K) decreases.
If K is 0 (free entry), “infinitely” many firms enter.
The price becomes competitive, p=MC=0.
Demand x(p)
Monopoly
price
P(n(K))
Price falls with the
number of entrants, n
Pc=MC=0
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
We can use this apparatus to ask whether
patents should be narrow or broad.
• The “breadth” is represented by K. High K means that
entrants must “invent around” the patent.
• Keeping the patent life, T, fixed, what happens to the
inventor’s incentives if the patent is narrower (K is
smaller)?
• To phrase the question sensibly -- how should patents be
structured – something should be kept fixed.
• Holding total profit fixed, should patents be long and
narrow? Short and broad?
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0
The ratio test: Should breadth cause price to
be lower, and the IP right to last longer?
• The consumer cost of raising money through
monopoly pricing is deadweight loss.
• Goal: Maximize ratio of profit to deadweight loss.
p
p
p*
p*
~
p
~
p
x(p*)
~
x(p)
x(p*)
~
x(p)
© Suzanne Scotchmer 2007 Contents May Be Used Pursuant to Creative
Commons Attribution-NoDerivs-NonCommercial Common Deed 1.0