Today's post is jointly authored by Norman Siebrasse and Thomas Cotter.
Over the past several months, the two of us have
been working on a paper titled The Value
of the Standard, which proposes a new theoretical
framework for calculating FRAND royalties.
In the course of working on the paper, we’ve noticed that, in
the standards context, the terms “sunk costs” and “switching costs” are often
used more or less interchangeably as phenomena that give rise to patent holdup.
This is a bit odd. In the general economic literature on holdup, “sunk costs”
refers to transaction-specific investments that have been made by one of the
parties. Holdup occurs when the other party tries to charge a higher price than
it would have been able to before those sunk costs were incurred. In this
sense, sunk costs were necessarily incurred in the past; a party cannot be held
up for costs that it has not yet incurred. “Switching costs” on the other hand,
imply costs that would take place in the future, to switch to an alternative,
non-standard technology. For example, consider the statement that “If the patented technology is adopted after the
standard issues and the adopting firm and consumers make investments that are
specific to the standard, the cost of switching to the alternative technology
is prohibitively expensive” (Gilbert, Deal or No Deal, 77 Antitrust LJ 855, 862
(2011)). The first phrase of this sentence
clearly refers to sunk costs – which is to say, transaction-specific
investments – while the second phrase refers to the cost of switching to the
alternative technology, which is evidently a future cost. We therefore thought
it might be useful to analyze, as precisely as possible, the relationship
between sunk costs and switching costs in order to better evaluate the extent
to which the royalty that an implementer might agree to ex post under the
threat of an injunction will exceed the value of the patented technology over the
best alternative.
Our basic point is that switching costs as such –
the ex post cost of implementing the alternative – are not in themselves
relevant, even though in the standards context they can be very high. The
amount that is subject to holdup is sunk costs plus the opportunity cost of
selecting the infringing technology over a noninfringing alternative. Moreover,
while our discussion was prompted by the standards context, both sunk costs and
switching costs arise outside that context as well, and accordingly our discussion
is general.
We will define Technology 1 as the technology which
is in fact initially adopted, and Technology 2 as the next best available
technology. The revenue from a technology is R and the cost of implementing the
technology is C. Costs and revenues may change after Technology 1 is adopted.
This will be indicated by the subscript “A” for ex ante costs / revenues and
“P” for ex post costs / revenues. We will assume all expectations are accurate;
changes in revenues and costs after Technology 1 is adopted are real changes,
not due to new information. Because Technology 1 is actually adopted and
expectations are accurate, it follows that:
R1A = R1P = R1
In general both the cost and revenue associated with
Technology 2 may change ex post. For example, in the standards context, the
expected revenue from Technology 2 conditional on its having been initially
adopted as the standard might have been very high, but very low or even zero if
in fact a particular implementer adopts it only after 1 has become the
standard. It seems very unlikely that the expected revenue from 2 would go up
ex post, so in general
R2A ≥ R2P
However,
our analysis is not affected if R2A < R2P.
In general, the cost of implementing Technology 2
might go up or down. The cost of implementing Technologies 1 and 2 might
include some costs that are common to both, such as training personnel in a
general field of technology, which would need to be incurred to implement Technology
2 on its own, but do not need to be incurred a second time if Technology 2 is
adopted after Technology 1 is first adopted, in which case C2P < C2A.
On the other hand, complementary components might have been designed in light
of 1, and redesigning them to function with 2 might be more expensive than it
would have been to design them to function with 2 in the first place, in which
case C2P > C2A. Further, in cases where the costs and
revenues associated with the best alternative change, it is possible that one
technology is the best alternative ex ante and a different technology is best
ex post. The term Technology 2 refers to the technology that is the best
alternative at any given point in time, and is not necessarily always the same
technology.
The maximum royalty, r, that can be extracted ex
ante as the value of Technology 1 is its incremental ex ante value over Technology
2
rmaxA =
(R1 – C1) – (R2A – C2A)
Now consider implementer D’s options if D adopts Technology
1, the patent on Technology 1 is found to be valid and infringed, and the court
enjoins D’s further use. If D is
enjoined, it has three options:
Option 1: Abandon 1 and exit the market. D’s future payoff (i.e., ignoring the sunk
costs, which may affect D’s decision ex ante but not D’s decision ex post) = 0.
Option 2: Switch from 1 to 2
: D’s future payoff = R2P – C2P,
where C2P = the cost of implementing (2), that is, the switching
costs.
Option 3: Pay a post-injunction royalty for the use of
1: D’s future payoff = R1 – r.
Given
these options, D prefers to pay rather than to abandon if R1 – r
> 0, that is, as long as r < R1. D prefers to pay rather than to switch if R1
– r > R2P – C2P, that is, if r < R1 – (R2P
– C2P). And D prefers to
switch rather than to abandon if R2P – C2P > 0, that
is, if R2P > C2P, which is to say (intuitively) if
using the alternative still would be profitable ex post.
Define rH, the holdup royalty, as the
difference between the maximum ex post and ex ante royalty:
rH ≡ rmaxP – rmaxA
If switching is preferable to abandoning, then
rH = [R1 – (R2P – C2P)]
– [(R1 – C1) – (R2A – C2A)] = C1
+ [(R2A – C2A) – (R2P – C2P)]
That
is, the holdup royalty is equal to the sunk costs associated with Technology 1,
plus the difference between the ex ante and ex post payoffs associated with
Technology 2: the “differential profit” of 2. A caveat is that both the terms (R2A
– C2A) and (R2P – C2P) are bounded from below
at zero. If (R2P – C2P) < 0,, 2 is not
profitable ex post, abandoning is preferable to switching, and D will pay up to
R1 to continue using 1, for a profit of 0 going forward. Similarly,
if (R2A – C2A) < 0, then the alternative to Technology
1 is not to enter the market at all, and so R1 – C1
defines the ex ante value of the invention.
To simplify this equation, define “differential
profit” of Technology 2:
ΔP2 ≡ [(R2A – C2A)
– (R2P – C2P)]
Then
rH = C1 + ΔP2
This
means that switching costs per se are irrelevant to holdup, in the sense that
they cannot be extracted by a patentee with an injunction. It is only differential switching costs – the
difference between the ex ante and ex post cost of adopting 2 – or more
precisely, the differential profit of 2, ΔP2, that is relevant.
Now consider the special case when Technology 2 is
entirely unrelated to Technology 1, so that the costs and revenues associated
with 2 will not change when 1 is adopted; 2 is simply an outside option, which
implies that R2A = R2P
and C2A = C2P, and so ΔP2 = 0. In that case:
rH = C1
This verifies that when the alternative is an
outside option, our model reduces to the standard point that opportunism allows
the patentee to extract sunk costs associated with the technology. But it also
raises our main point. The cost of implementing Technology 2 might be very
substantial, and that cost is no different from switching costs in the
standards context. Whether the cost is that of switching to a different
standard technology, or to an entirely different undertaking in an unrelated
area, it is still the cost of the next best alternative. Yet it is not relevant
to holdup, and no one has ever supposed it is. When we talk about holdup in the
traditional context, such as Riles v
Shell Oil, 298 F.3d 1302 (Fed. Cir. 2002), no one ever says that the
patentee can hold up the user for the cost of switching to a different
technology. The reason that these “switching costs” drop out is that they are
considered both ex post and ex ante. It is true that by licensing ex post, the
user will avoid the cost of adopting the alternative technology; but that is
also true if the user licenses ex ante. The notion that the user can be held up
for switching costs reflects ex post thinking.
Now consider the case where Technology 2 is related,
in the sense that the costs and/or revenues associated with Technology 2 change
when 1 is adopted. This will often be the case with standards.
First consider the simpler case when the cost of
implementing 2 is not affected by whether 1 is adopted, but revenue is
affected: that is, R2A > R2P and C2A = C2P.
For standards it is likely that R2A > R2P, and it is
at least plausible that C2A = C2P for some standards. In
that case:
rH = C1 + [R2A – R2P]
Again,
switching costs, C2P, are not zero – indeed they may be very large –
but they are nonetheless irrelevant to holdup, for the reasons just discussed.
Thus, in the standards context, it is not switching
costs that can be extracted in addition to sunk costs, it is differential
profit.
The reason that it is only differential profits that
are relevant is that both ex ante and ex post, the profitability of the best
alternative disciplines the amount the patentee can charge. When these are the
same, they drop out. But when they are different, the difference between the ex
post and ex ante profitability adds to the amount the patentee can charge.
To understand why, it is perhaps helpful to approach
the derivation from a different angle. The differential profit discussed above,
ΔP, is the difference in profitability of a given technology at two different
points in time (ex ante and ex post). Now let us focus instead on the difference
in profitability between the two different technologies at a given point in
time.
Define comparative differential profit, δ12
≡ P1 – P2
We are accustomed to thinking of the true value of a
technology as being its ex ante profitability over the next best available
technology: in our notation, this is δ12A ≡ P1A – P2A,
But from the perspective of a user, the value of a technology at any given time,
and consequently the maximum royalty that can be charged, is always its profitability over the best
alternative. Ex post, the value of a licence to Technology 1 is its
differential profitability over Technology 2: δ12P ≡ P1P
– P2P. The holdup royalty is the difference in the value of the
technology to the user (which is not necessarily the same
as the true value of the technology), ex ante versus ex post. That is:
rH = δ12P – δ12A
Once the cost of implementing 1 is sunk, P1P
= R1
rH = [(R1 – (R2P –
C2P)] – [(R1 – C1)
– (R2A – C2A)]
= C1 + ΔP2
That is, sunk costs holdup really represents holdup
due to the differential profitability of Technology 1 ex ante and ex post. The
differential profitability of Technology 2 represents a separate source of
holdup. The profitability of Technology 2 is relevant because the threat of
switching to Technology 2 disciplines the amount that can be extracted by the
patentee; it is not the absolute profitability that can be extracted, either ex
ante or ex post, but only the profitability related to the alternative. The
sunk costs holdup related to Technology 1 arises because the profitability of
Technology 1 from the user’s perspective changes once costs are sunk; the
profitability increases, because the costs no longer have to be incurred. Similarly,
if the profitability of Technology 2 changes, the disciplining value of the
user’s threat to switch also changes. We will refer to the term that captures
this, ΔP2, as opportunity cost holdup: .the reduction in the
profitability of Technology 2 ex post is the opportunity cost of not having
chosen Technology 2 ex ante.
While there
are no doubt cases where C2A < C2P so that
differential costs contribute to the differential profit, we suspect that
differential revenues are generally characteristic of standards. Normally, R2A
> R2P because the value of a non-standard technology is
much lower than the value of the same technology if it were the standard.
Similarly, the joint report of
the U.S. Dep’t of Justice & Fed. Trade Comm’n, Antitrust Enforcement and
Intellectual Property Rights: Promoting Innovation and Competition 28 (2007)
states at 28 that "Generally, the greater the cost of switching to an
alternative standard, the more an IP holder can charge for a license." And
the Report of the Fed. Trade Comm’n, The Evolving IP Marketplace: Aligning
Patent Notice and Remedies with Competition (2011) at 5, stating that "At
the time a manufacturer faces an infringement allegation, switching to an
alternative technology may be very expensive if it has sunk costs in production
using the patented technology. That may be true even if choosing the
alternative earlier would have entailed little additional cost. If so, the
patentee can use the threat of an injunction to obtain royalties covering not
only the market value of the patented invention, but also a portion of the
costs that the infringer would incur if it were enjoined and had to switch.
This higher royalty based on switching costs is called the “hold-up” value of the
patent. Patent hold-up can overcompensate patentees, raise prices to consumers
who lose the benefits of competition among technologies, and deter innovation
by manufacturers facing the risk of hold-up."