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Patents and Patent Policy
Chapter 23: Patents and Patent Policy
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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 (cont.)
• 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
Quantity
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Optimal Patent Length (cont.)
• 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
• 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 (cont.)
• 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 (cont.)
• 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 (cont.)
• Insights of the Nordhaus model (cont.)
– point, this cost of dominates the increment to x.
T is finite.
– 2. Optimal patent length is shorter the more elastic is
demand
• The more elastic demand is, 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 large
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
– Broad patent protection has the advantage that it prevents minor
alterations on the original invention [Klemperer (1990)]
– Long patents may actually discourage innovation [Gallini (1992)].
• With short patents, rivals can afford to wait until patent expires
• If patents are long, rivals cannot wait but will try to invent around the
patent. The anticipation of this copycat activity may depress innovation
– Denicolo (1996) argues that optimal patent length and breadth
depends on market conditions—The more competitive an industry
the more long, narrow patents are desirable
– Unfortunately, while the Denicolo argument may be rational, 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 a new good
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?
• Example:
–
–
–
–
Assume two firms, BMI and ECN
Developing a new product for which Demand is 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
Chapter 23: Patents and Patent Policy
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Patent Races (cont.)
• 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
• 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 (cont.)
• 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. This
happens with probability 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. This
happens with probability, 0.8*0.2 = 0.16. The expected
operating profit is therefore $50.
– Both BMI and ECN are successful. In this case they each
earn duopoly operating profits of $138.89. This happens with
probability, 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
– This is shown in 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
Races (cont.)
invest in a lab. If both invested, at
invest in a lab. EvenPatent
a
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 (cont.)
• Patent races raise the possibility that R&D investment can
either be excessive or insufficient
– The possibility that it can be excessive is illustrated by the
outcome in which both firms invest. When both invest, 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 (cont.)
• 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.
• 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
Chapter 23: Patents and Patent Policy
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“Sleeping” Patents (cont.)
• The monopolist has a patent on the alternative process
and can either sell it to its rival or let it sleep. Which
will it do?
– With existing low cost [cI = $20] technology, monopolist sets
monopoly price of $60, sells 40 units and earns profit of
$1,600
• 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 (cont.)
• What if competition is Cournot?
• Duopoly outcome with Cournot if :
– Incumbent has cost cI = $20; Rival has cost cA = $30
– 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
losest $1600 – $900 = $700 in profit
• Most rival gains is $400
• So, as before, 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 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 (cont.)
• Consider our previous example with demand given by 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 producing23.33 units
• Total Output is Q = 46.67
• Price is P = $53.333
• Profit to each firm is $272.222
• Now assume one firm develops new technology with unit
cost cI = $20
• We already know that the new equilibrium has the lowcost firm producing 30 units, selling at price P = $50 and
earning profit of $900 while the high cost firms produces
20 units and earns profit of $400
Chapter 23: Patents and Patent Policy
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Patent Licensing (cont.)
• Now consider what happens if low cost firm licenses its
technology to high cost firm for a fee of (just under) $10 per
unit.
• This leaves the market outcome unchanged. The high cost
firm can 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
• Accordingly, P = $50 and Q = 50 still holds with Q split 30
and 20 between the low-cost high-cost firm, respectively
• What’s different
– Low cost firm still earns $900 in profit from its 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 (cont.)
• Licensing will not happen if competition were Bertrand
• When both firms have unit cost cA = $30, P = $30 & Q = 70
• When 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
– If it licenses for a fee of $10 per unit,
– the market price will still be $30
– The two firms will split the market as before the innovation, each
producing 35 units
– The innovating firm will earn $350 from its own production
– It will earn $350 from licensing
– Total profit is $700
•
No incentive to license if competition is Bertrand
Chapter 23: Patents and Patent Policy
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Patent Licensing (cont.)
• 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
• When it does happen, licensing is good
– It raises innovator’s profit
– It expands output and consumer surplus
• Firms may be reluctant to license though because
• Licensee may use license to develop expertise while waiting
for patent to expire
• Licensee may use license to reverse engineer and develop
alternative low-cost technology
• Restricting competition among different licensees may be
difficult
Chapter 23: Patents and Patent Policy
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