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Patents and Patent Policy
Chapter 23: Patents and Patent Policy
1
Introduction
Information is a public good
• Non-rivalry in consumption
– If Eli Lilly tells Merck how to make Prozac the information does not
leave Lilly
– Marginal cost of sharing info, e.g., the Prozac formula, is zero
– Allocationally efficient price = marginal cost = 0
• Non-excludability of people who don’t pay for information
– Easy to copy or reverse engineer products
– Trade secrets are hard to keep
– Effective price is zero
• If price of information is zero, no incentive to produce
information or develop new products—no dynamic efficiency
• Patent Policy must balance the demands of allocational and
dynamic efficiency
Chapter 23: Patents and Patent Policy
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Optimal Patent Length
• Patents may be used to protect innovators and make the
economy more dynamically efficient
– Temporarily create monopoly power (bad)
– Encourage creation of new products (good)
• Two central questions of patent policy
– How long should patent last
– How wide a range of substitutes should patent span?
• Optimal Patent Length
– No simple answer such as 14, 17 or 21 years
– Nordhaus (1969) classic model illustrates key factors in
determining optimal patent length
Chapter 23: Patents and Patent Policy
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Optimal Patent Length 2
• Competitive industry with constant cost c
– Firm can conduct R&D of intensity x at cost r(x) that rises with x
– Successful R&D lowers cost to c – x
$/unit = p
c
A
B
c-x
Demand
Q0C
Q TC
Chapter 23: Patents and Patent Policy
Quantit
y
4
Optimal Patent Length 3
• Assume that patent lasts for T years.
– During life of patent, innovator earns monopoly profit
area A
– When patent expires in T years, consumers gain surplus
A plus area B (formerly static deadweight loss)
• Trick is to choose length T that gives A to
producers for a long enough time to encourage
high R&D intensity x and therefore cost savings c
– x, incentives to producers but that does not
delay the realization of B for too long a time
Chapter 23: Patents and Patent Policy
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Optimal Patent Length 4
• Incentive to producers
–
–
–
–
–
Size of A research intensity x
Present value of A for T year is V(x,T)
Cost of research activity is r(x)
Net gain of R&D if patent lasts T years is: V(x,T) – r(x)
Firms will choose x that maximizes this gain x*(T)
Chapter 23: Patents and Patent Policy
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Optimal Patent Length 5
• Patent Office understands that for any value of T,
firms will optimally choose x(T) research intensity
– When patent expires in T years, areas A and B are
realized as consumer surplus forever. The present value
of this surplus that starts in T years is CS(x,T).
– Patent policy goal is to maximize net total surplus
recognizing that its choice of T determines the amount
of R&D intensity x*(T). That is, patent policy aims to
maximize:
– V[x*(T) ,T] – r[x(T)] + CS[x*(T)]
– This is a single equation in T and so standard
maximization techniques apply
Chapter 23: Patents and Patent Policy
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Optimal Patent Length 6
• Insights of the Nordhaus model
1. Optimal patent length is positive but finite
– If T = 0, firms will not do any R&D
– As T gets larger
 Firms do more R&D
 but effect diminishes because the cost of more
research intensity r(x) rises & because extra profit in
last years of a patent is discounted severely
 As T gets larger, society has to wait longer to gain
the welfare triangle B. At some point, this cost of
dominates the increment to x. T is finite.
Chapter 23: Patents and Patent Policy
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Optimal Patent Length 7
• Insights of the Nordhaus model (cont.)
2. Optimal patent length is shorter the more elastic
is demand
– The more elastic demand the greater the static welfare loss B
3. Optimal patent length is shorter the lower the
cost of R&D, r(x)
– Profit increases linearly with the size of the cost reduction
but the welfare loss increases quadratically.
– As the equilibrium cost reduction rises, so does the loss from
keeping T larger
Chapter 23: Patents and Patent Policy
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Patent Length and Breadth
• Optimal patent length may depend on how broad
patent protection is
– If patents are broad, length should probably be limited
because have broad and long patents would confer too much
monopoly power
– How should policy balance length against breadth of
patents?
• General Goal: Since the monopoly power of patent
will cause welfare loss, choose the design that
minimizes the welfare loss per dollar of monopoly
profit subject to achieving the profit needed to insure
the right innovative effort
Chapter 23: Patents and Patent Policy
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Patent Length and Breadth 2
• Gilbert and Shapiro (1990): Optimal to have very
long but narrow patents. Why?
– View time as a very long sequence of short-lived
intervals
– Wish to avoid “jumps” in price—want the marginal
value of good to move smoothly so that marginal utility
from consumption moves smoothly
– When patent expires, price falls to cost which would be
a large “jump”
– Implication: let patents live long but restrict their
breadth so just enough profit is made to do innovation
Chapter 23: Patents and Patent Policy
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Patent Length and Breadth 3
• Klemperer (1990) argues for broad but short-lived
patents
– Think of products on the Hotelling line—Breadth is
fraction of line covered by patent
– All ten consumers located at same point as patented
product and value it at $10—marginal cost = 0
– If no substitute is available price is $10, no consumer
surplus but full surplus of $100 goes to the patented
monopolist
– What if imperfect substitute is available at cost 0?
Chapter 23: Patents and Patent Policy
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Patent Length and Breadth 4
– Although customers all located at same spot, assume some
could travel to “distant” substitute location for $1, some
for $2, etc.
– At price of $10, patent-holder would lose all customers to
competitively-priced substitutes
– But this would entail $45 of transport costs so total surplus
would fall to $55
– Extending patent breadth so that no consumer finds it
worthwhile to switch to substitute thus increases the
surplus
– This avoids the waste of real resources to produce and
travel to less desired good
• Gallini (1992) expands this idea. Broad but short-lived
patents discourage duplicative efforts of inventing
around the patent because it will expire soon anyway
Chapter 23: Patents and Patent Policy
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Patent Length and Breadth 5
• Denicolo (1996) argues that optimal patent length
and breadth depends on market conditions—
– Long, narrow patents are appropriate for competitive
industries
– Short, broad patents are appropriate for oligopolistic
and monopolistic industries
– However, it is hard to implement a policy that doesn’t
treat all firms the same.
Chapter 23: Patents and Patent Policy
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Patent Races
• Technological break-throughs have a winner-take-all
feature—whoever discovers Prozac or invents the
Blackberry first wins the patent and associated monopoly
power whether they were first by a year or first by a week
• This winner-take-all feature makes R&D efforts a bit like a
race—all that matters is finishing first
• What are the implications of patent races?
Chapter 23: Patents and Patent Policy
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Patent Races 2
• Example:
–
–
–
–
Assume two firms, BMI and ECN
Developing a new product with Demand: P = 100 – 2Q.
Product will be produced at constant marginal cost c = 50
Development requires a lab and probability of successful
development is 0.8
– Cost of lab is K
• Qualitatively, there are three possible outcomes:
– Neither firm invests in a lab
– One firm invests in a lab and the other doesn’t
– Both firms invest in a lab
Chapter 23: Patents and Patent Policy
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Patent Races 3
• If no firm invests, each gets 0
• Suppose only one firm invests in a lab:
– if successful, it will be a monopolist and earn an
operating profit of $312.50
– Since the probability of success is 0.8, the expected
profit conditional upon spending K on the lab is
0.8*$312.50 – K = $250 – K
– This expected outcome is illustrated by the two offdiagonal elements in the payoff matrix below
Chapter 23: Patents and Patent Policy
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Patent Races 4
• Suppose both firms invest in a lab. From BMI’s perspective
there are three possible outcomes
– It is not successful and so earns 0 operating profit; Prob = 0.2
– It is successful and ECN is not. In this case, it will be a
monopolist and earn an operating profit of $312.50;
Prob = 0.8*0.2 = 0.16  Expected operating profit is $50.
– Both BMI and ECN are successful. In this case they each
earn duopoly operating profits of $138.89. Prob = 0.8*0.8 =
0.64. So the expected operating profit is $88.89.
– Taking all three outcomes together, the expected profit net of
lab costs when both invest in a lab is $138.89 – K
– See the lower right diagonal of the payoff matrix below
Chapter 23: Patents and Patent Policy
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If $0.138.89  K < $250, then the
Nash Equilibrium is for one firm to
If K  $250, then no firm will
5 in a lab. If both invested, at
invest
invest in a lab. Even a Patent Races
least one would want to change its
monopolist cannot expect to cover
The Pay-Off Matrix
decision. The issue here is which firm
lab costs this high.
will do the investment .
BMI
If K < $138.89, the Nash
Equilibrium is for both
firms to invest in No
a labR&D Lab
No R&D Lab
R&D Lab
(0, 0)
(0,$250 – K)
($250 – K, 0)
($138.89-K,
$138.89-K)
ECN
R&D Lab
Chapter 23: Patents and Patent Policy
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Patent Races 6
• Patent races raise the possibility that R&D investment can
either be excessive as well as insufficient
– The possibility that it can be excessive is shown when both firms
invest. Then, we either get no development (prob = 0.04); a
monopoly (prob = 0.32) or a duopoly (0.64)
– The expected operating profit in total is then: 0.32*$312.50 +
0.64*$277.56 = $277.64.
– The expected consumer surplus is: 0.32*156.25 + 0.64*277.78 =
$227.28.
– So, the total expected surplus net of lab costs when both invest
is:$277.64+227.28 – 2K  $505 – 2K.
– The expected surplus with just one lab is 0.8($312.50 + $156.25) –
K = $375 – K.
– Two labs are excessive if $375 – K > $505 – 2K, i.e., if K > $130
Chapter 23: Patents and Patent Policy
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Patent Races 7
• The reason that R&D can be excessive is wasteful
duplication. Each firm thinks only about its own potential
gain and not about the fact that if both are successful
(which is fairly likely given that the probability of a
successful lab is 0.8) they will hurt each other’s profit
• However, there can also be too little investment.
• This is because firms do not consider the increased
consumer surplus that successful development of a new
product will generate
Chapter 23: Patents and Patent Policy
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“Sleeping” Patents
• Most firms have many patents including some that they
never use. Similarly, many film studios buy the rights to
books and plays but never produce them.
• Instead, these patents and copyrights are left dormant or
sleeping. Why?
• The answer is that it is worth more to the incumbent
monopolist to make sure that a rival does not enter than it
is for the rival to acquire the patent or copyright and come
in as a duopolist.
Chapter 23: Patents and Patent Policy
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“Sleeping” Patents 2
• Consider a market with demand: P = 100 – Q .
– An incumbent monopolist with constant unit cost cI = $20
based on the firm’s unique technology
– There is an alternative technology with constant cost cA = $30
• Monopolist has a patent on the alternative process. It
can sell it to its rival or let it sleep. Which will it do?
– At existing low cost [cI = $20] technology, monopolist sets
price of $60, sells 40 units and earns profit of $1,600
Chapter 23: Patents and Patent Policy
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“Sleeping” Patents 3
• Suppose competition is Bertrand:
– If rival has patent and ability to produce at cA = $30, rival will
earn no profit because it can’t compete with cI = $20
– But rival’s presence will constrain monopolist to set P no
higher than $30—Profit will fall to $700
• CONCLUSION:
– If competition is Bertrand, the rival will not pay anything for it
and it is worth $1,600 - $700 = $900 to the monopolist
– Monopolist will let the alternative technology patent sleep
Chapter 23: Patents and Patent Policy
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Sleeping Patents 4
• What if competition is Cournot?
– Incumbent has cost cI = $20; Rival has cost cA = $30
– Duopoly outcome is:
• Incumbent output is 30; Rival output is 20
• Incumbent profit is $900; Rival profit is $400
– If rival has access to the alternative technology, incumbent
loses $1600 – $900 = $700 in profit
– Most rival gains is $400
• CONCLUSION:
– Again, it is worth more to the incumbent to keep the patent
on the alternative technology sleeping than it is to the rival
to buy it out
Chapter 23: Patents and Patent Policy
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Patent Licensing
• Incumbents will often prevent rival entrant access to
alternative, high cost technology and keep it sleeping.
• But firms may license the best, low-cost technology
• Why? There is a difference between keeping new
firms out versus competing with existing rivals.
• The profitability of licensing depends on
– Nature of competition
– Drastic versus non-drastic innovation
Chapter 23: Patents and Patent Policy
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Patent Licensing 2
• Consider previous example with demand: P = 100 – Q
– Imagine that we now start with 2 firms each with
constant marginal cost of cA = $30
– The Cournot equilibrium results in each firm producing
23.33 units
• Total Output is Q = 46.67
• Price is P = $53.333
• Profit to each firm is $272.222
Chapter 23: Patents and Patent Policy
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Patent Licensing 3
• Let one firm develop new technology with cost cI =
$20
– The new equilibrium has P = $50
– Low-cost firm produces 30 units; earns profit of $900
– High cost firms produces 20 units; earns profit of $400
• What happens if low cost firm licenses its technology to
high cost firm for a fee of (just under) $10 per unit.
– Market outcome is unchanged from the original equilibrium.
– High cost firm now produce at $20 per unit but also has to pay
(nearly) $10 in licensing fees.
– Effectively, the high-cost firm still has a unit cost of $30
– Low cost firm still earns $900 profit from production, BUT
 It also picks up $10*20 = $200 in licensing fees
 Licensing definitely pays off
Chapter 23: Patents and Patent Policy
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Patent Licensing 4
• Licensing will not happen under Bertrand competition
– If both firms have unit cost cA = $30, P = $30 & Q = 70
– If one firm obtains cA = $20, its best strategy is to sell 70 units
at $30 (or just under) and earn profit of $700
– No licensing can improve on this
 No incentive to license if competition is Bertrand
• Licensing will not happen if innovation is drastic
– Drastic innovation permits firm to act as an unconstrained
monopoly
– No licensing can improve on this maximum monopoly profit
 No incentive to license if innovation is drastic
Chapter 23: Patents and Patent Policy
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Patent Licensing 5
• When it does happen, licensing is good
–
–
–
–
It raises innovator’s profit
It thereby increases the incentive to innovate
It expands output and consumer surplus
CAUTIONARY NOTES:
• Cross-licensing agreements, e.g., I license your product you
license mine can promote collusion and exclusion
(foreclosure) of rivals
 licensing may not always be desirable
• More recently, as advance builds upon advance, users of a
technology must navigate a “patent thicket” requiring a
prohibitive number of complicated license agreements
 Licensing may not always be feasible
Chapter 23: Patents and Patent Policy
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Recent Patent Policy Developments
• In early 1980’s, effort to unify patent law and patent
rights led to centralization of US patent cases in Court
of Appeals for Federal Circuit (CAFC)
– Strong, pro-patent legal framework emerged
– Polaroid victory against Kodak accompanied not just by
fines but by requirement that Kodak shut down the patentinfringing production—VERY EXPENSIVE
– In wake of this enhanced protection of patent rights, firms
began to file many more patents
– Patent applications doubled and patent grants more than
doubled
Chapter 23: Patents and Patent Policy
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Recent Patent Policy Developments 2
• By 2005 fears that patent protection had gone too far
– Business method patents like Amazon’s one-click
– The Blackberry case
• Blackberry offered 1st wireless, e-mail device in 1998
• NTP won a patent on a wireless e-mail technology in 1990
– Never produced a single product
– Never applied for licensing
• NTP won a patent infringement suit in 2002
• After appeals and negotiation, entire Blackberry
system almost shut down in 2006
• US Supreme Court ruling in Teleflex case suggests
patent protection has been weakened
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry
• Patent awards per million $ of R&D doubled in the US
semiconductor industry in decade after CAFC emerged
as main patent court
• Why this increase?
– New patent law environment
– Or something else
• Need a model of patent process
– Think of number of patents p in a given time period as a
random variable
– What random process makes sense?
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry 2
• Hall and Ziedonis (2002) model patent output at a firm as
the result of a Poisson process
e   p
f  , p  
p!
• Mean or expected value of this process is 
• Model this mean over time as conditional on firm
characteristics and time
ln it  X it   
• Maximum Likelihood Estimation of this relationship using
data from 95 semiconductor firms over years 1979 to 1995
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry 3
• What are the Xit independent variables?
– X1t is ln R&D spending per employee
– X2t is 1,0 dummy = 1 if no R&D spending that year
– X3t is ln Firm Size (thousands of employees)
– X4t is ln Plant & Equipment per employee
– X5t is 1,0 dummy = 1 if new entrant after 1982
– X6t is 1,0 dummy = 1 if Texas Instruments
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry 4
• First three variables meant to capture output of patents as a
productive result from inputs with possible scale economies
• Plant and equipment tests the importance of the new, postCAFC environment. If this was important, firms with a lot
of capital per employee would start to patent a lot to avoid
getting “held up” in patent negotiations
• Entry dummy tests the hypothesis that new environment led
to entry of new, patent-dependent semiconductor firms
• Last variable captures well known aggressive patent policy
of Texas Instruments
• There are also time dummies for each year
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry 5
• Hall and Ziedonis (2002) results
Variable
Coefficient Std. Error
ln R&D per employee
0.190
(0.084)
No R&D dummy
-1.690
(– 0.830)
ln Firm Size
0.854
(0.032)
ln P& E per employee
0.601
(0.113)
New Entrant Dummy
0.491
(0.169)
TI Dummy
0.791
(0.111)
Chapter 23: Patents and Patent Policy
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Empirical Application: Patent Explosion in
US Semiconductor Industry 6
• First three show that patent output rises roughly
proportionally with firm size—no scale economies
• There is also clearly a Texas Instruments effect
• Most importantly
– Time dummies are significantly positive
 All semiconductor firms patented more in 1980’s
– Firms with lots of capital per worker patented a lot more
– New entrants patented a lot more
 Change in policy environment in 1980’s is responsible for
upsurge in semiconductor patenting.
1. Firms with capital at risk patented more to protect it
2. New kind of semiconductor firms with greater propensity
to patent entered the industry
Chapter 23: Patents and Patent Policy
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