Abstract
This article analyzes the value of a product’s surplus attributable to intellectual property (IP, such as patents or trademarks) relative to the product’s overall value. In a complex production process, learning by doing allows a leading firm to gain some surplus without IP, and as the number of steps approaches infinity, the surplus attributable to IP approaches zero. The value of the same IP held for licensing purposes, rather than to protect a production monopoly, shows no such convergence to zero. The model is used to explain the empirically observed differences between the use patterns of IP in industries based on discrete products, where patents are typically used to maintain monopolies, versus industries based on complex products, where patents are primarily licensing tools. The result is also applied to the questions of evaluating arm’s length transfers, which are often used to move revenue to tax-discounted IP boxes, and for discussion of non-practicing entities.
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Notes
Prospectus of RPX Corp, http://www.sec.gov/Archives/edgar/data/1509432/000119312511124791/d424b4.htm
State aid decision for SA.46470 (2017/NN) — Netherlands, “Possible State aid in favour of Inter IKEA.” European Commission, Brussels, 18 December 2017, §165.
As r rises, e−rt decreases for all values of t. As Ln rises, p(t − Ln, s) decreases, by the assumption that p is increasing in its first term, and the area over which the integral is computed shrinks, reaching zero when Ln = Lp.
Proof that \(\partial ({\int \limits } p)/\partial s > 0\): uniform convergence allows us to write this derivative of an integral as the integral of a derivative:
$$ \begin{array}{@{}rcl@{}} \partial (\int p)/\partial s &=& {\int}_{L_{n}}^{L_{p}} \frac{\partial p}{\partial s}e^{-rt}dt\\ &=& {\int}_{L_{n}}^{L_{p}} \ln\left( \frac{t}{t+1}\right)\left( \frac{t}{t+1}\right)^{s} e^{-rt}dt \end{array} $$which is always negative for t,s > 0.
This can be formalized: consider a firm that uses k patentable components, each of which has at least a strictly positive chance 𝜖 of being independently invented. Then the likelihood of some patent being independently invented is 1 − (1 − 𝜖)k, which approaches one as k rises.
After a Supreme Court appeal [137 S. Ct. 429, 196 L. Ed. 2d 363 (2016)] and several retrials, the damages were reduced from the full product value of just over 1billionto539 million, including damages.
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Thanks to John Asker, Jennifer 8. Lee, Bill Morgan, Mike McDonald, Ryan Nunn, and Neviana Petkova for the discussion and commentary.
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Klemens, B. Attributing Value to Patents and Trademarks in Complex Production Chains. J Knowl Econ 12, 842–875 (2021). https://doi.org/10.1007/s13132-020-00629-1
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DOI: https://doi.org/10.1007/s13132-020-00629-1