Why Switching Costs Are Irrelevant to Patent Holdup

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:

R_1A = R_1P = 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

R_2A ≥ R_2P

However, our analysis is not affected if R_2A < R_2P.

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 C_2P < C_2A. 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 C_2P > C_2A. 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

r_maxA =  (R₁ – C₁) – (R_2A – C_2A)

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 = R_2P – C_2P, where C_2P = 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 > R_2P – C_2P, that is, if r < R₁ – (R_2P – C_2P).  And D prefers to switch rather than to abandon if R_2P – C_2P > 0, that is, if R_2P > C_2P, which is to say (intuitively) if using the alternative still would be profitable ex post.

Define r_H, the holdup royalty, as the difference between the maximum ex post and ex ante royalty:

r_H ≡ r_maxP – r_maxA

If switching is preferable to abandoning, then

r_H = [R₁ – (R_2P – C_2P)] – [(R₁ – C₁) – (R_2A – C_2A)] = C₁ + [(R_2A – C_2A) – (R_2P – C_2P)]

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 (R_2A – C_2A) and (R_2P – C_2P) are bounded from below at zero. If (R_2P – C_2P) < 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 (R_2A – C_2A) < 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 ≡ [(R_2A – C_2A) – (R_2P – C_2P)]

Then

r_H = 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  R_2A = R_2P and C_2A = C_2P, and so ΔP₂ = 0. In that case:

r_H = 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, R_2A > R_2P and C_2A = C_2P. For standards it is likely that R_2A > R_2P, and it is at least plausible that C_2A = C_2P for some standards. In that case:

r_H = C₁ + [R_2A – R_2P]

Again, switching costs, C_2P, 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 δ_12A ≡ P_1A – P_2A, 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: δ_12P ≡ P_1P – P_2P. 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:

r_H = δ_12P – δ_12A

Once the cost of implementing 1 is sunk, P_1P = R₁

r_H = [(R₁ – (R_2P – C_2P)] –  [(R₁ – C₁) –  (R_2A – C_2A)]

    = 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 C_2A < C_2P so that differential costs contribute to the differential profit, we suspect that differential revenues are generally characteristic of standards. Normally, R_2A > R_2P because the value of a non-standard technology is much lower than the value of the same technology if it were the standard.

In summary, switching costs as such are irrelevant to hold up. Second, it is differential profits which are important. Third, differential revenue is likely to be an important contributor to differential profits in the standards context, and it may well be generally more important differential cost, so switching costs are doubly irrelevant. 

* 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."