[Submitted today in response to this call for papers. -MFM]
ABSTRACT
Thanks to the ubiquity and integration of digital computers, each consumer of a product or service now produces a digital stream of data. Bundled together, these streams of data record how particular products or services, including any patented features, are valued by actual consumers in different geographical regions and in different windows of time. Most relevant to patent royalty calculations are the histories of transactions for a particular product or service. These transactions eventually show up in financial statements, which permit top-down estimates of value, such as revenue or gross margins. But alternative metrics drawn from these streams, such as change in the frequency of transactions before and after the introduction of a patented feature, also permit bottom-up estimates of the value of patented features. Demand can also be estimated using metrics for customer engagement, such as the frequency and length of visits to a particular website or the conversion ratio of number of independent visits per completed transaction. In some cases, analyses of these data permit calculation of a more reliable lower bound for the marginal value of a patented feature to a complex product or service. More generally, time-frequency analyses of data on consumer behavior complement existing methods for calculating lost profits or reasonable royalties, and can help resolve questions about the marginal value a patented feature adds to a complex or highly integrated product or service.
The Damages Apportionment Problem for Complex Systems
Under 35 U.S.C. § 284, “[u]pon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.” Famously, the Southern District of New York laid out a “comprehensive list of [fifteen] evidentiary facts relevant, in general, to the determination of the amount of a reasonable royalty for a patent license” Georgia-Pacific Corp. v. U.S. Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970). The thirteenth in this list is “[t]he portion of the realizable profit that should be credited to the invention as distinguished from non-patented elements, the manufacturing process, business risks, or significant features or improvements added by the infringer.” Id.
When Georgia-Pacific was decided in 1970, Jimi Hendrix was still performing, the Internet was known only as ARPANET, and access to information about cutting edge research and development usually required national security clearance. Four decades later, instead of secrets about national defense leaking to the press through a former first lieutenant in the Marine Corps with high-level security clearance, an Australian hacker is leaking them to the Internet. Instead of a carefully choreographed ballet of contractors producing a 747, a globally distributed swarm of programmers continuously releases new features and combinations of features in an effort to attract a stable base of users. Consumers depend upon producers – producers who compete vigorously with each other to make the sales necessary for their own survival – to cooperate in the development and adoption of industry standards that are necessary for complex, integrated systems to exist at all. The Federal Circuit put it well in describing one of the most commercially successful productivity software products as “an enormously complex software program comprising hundreds, if not thousands or even more, features.” Lucent Technologies, Inc. v. Gateway, Inc., 580 F. 3d 1301, 1333 (Fed. Cir. 2009). The Federal Circuit found “it inconceivable to conclude, based on the present record, that the use of one small feature … constitutes a substantial portion of the value.” Id.
Most lawyers agree with the Federal Circuit that the base for calculating royalties should be discounted to adjust for the value that other features contribute to a product. Other features may include features themselves covered by other patents (not owned in common with a patent-in-suit), or features not easily protectable through patents (such as the durability of parts, precision of manufacturing tolerances, or the timely availability of the product or service at a requested order volume). Moreover, what feature or features were sufficient or necessary to the completion of a sale may vary from customer to customer, or even for the same customer over time. In most cases, it is indeed inconceivable that any single patented feature could be responsible for the entire revenue (much less profit) generated by a complex or highly integrated product or service.
On the other hand, the very fact that an infringer has chosen to implement a patented feature rather than a non-infringing alternative is strong evidence that the patented feature most likely contributes some finite value to the product or service. That value, in turn, is ultimately reflected in the revenue and profit generated by the sale of the complex product or service that includes the patented feature.
[Discussion of economic case for patents, focusing on the potential social benefit of granting property rights in easily appropriable innovations in markets with high barriers to entry. Exclusionary rights permit supracompetitive prices in proportion to inelasticity of demand for patented innovations. Thus, measuring inelasticity of demand is core problem for patent valuation in general, and for damages apportionment in particular.]
Measuring the Price Elasticity of Demand
The Federal Circuit has acknowledged that price elasticity is at the core of the problem of patent valuation. The opinion in Crystal Semiconductor v. Tritech Microelectronics, 246 F. 3d 1336 (2001) is particularly instructive, although it deals specifically with price erosion. In Crystal Semiconductor, the Federal Circuit explained the economic theory of price elasticity:
For example, if substitution of a product were impossible and the product were a necessity, elasticity of demand would be zero — meaning consumers would purchase the product at identical rates even when the price increases. This very rare type of market is called inelastic. On the other side of the spectrum, if any price increase would eradicate demand, elasticity of demand would be infinite — meaning consumers would decline to purchase another single product if the price increases by any amount. This very rare type of market is called perfectly elastic. Markets typically have an elasticity greater than zero and less than infinity.
Crystal Semiconductor, 246 F.3d at 1359 (italics added). In other words, the market value of a patented feature should be tied to its effect on price elasticity, and price elasticity can be estimated by reference to the relative rate of sales at different price levels. The Federal Circuit went on to rule that the patentee in Crystal Semiconductor had failed to show sufficient evidence of whether or how much the rate of sales would have declined as a result of a price increase. Id. at 1360-1. It is enough for my purposes, however, to note that the Crystal Semiconductor case provides a legal precedent for the use frequency-averaged measures of the value of patented innovations, such as relative rates of sales.
Top-Down Estimates from Time-Averaged Revenues and Profits
The approach to estimating price elasticity described in Crystal Semiconductor requires the use of revenue and profit figures, which would typically be derived from financial statements. Financial statements provide a highly compact summary of the entire history of transactions that occurred among a company and its many stakeholders, from the purchasing of capital equipment and parts from suppliers, to the payment of labor for design and assembly, to the actual payments of cash from customers for delivery of the final product. Thus, financial statements provide a good foundation for what I will call “top-down” estimates of the value of patented features.
[Discussion of the information architecture of financial statements: Income and cash-flow statement record time-integrated flow of revenue and expenses; balance sheet records snapshot in time of assets and liabilities. The information architecture of financial statements lends itself to optimization of time-averaged measures of efficiency in increasing sales, decreasing costs of sales. Trends in sales or costs of sales are visible only after two or more periods have elapsed.]
Top-down estimates of the value of patented innovations are most appropriate for valuation of products or services that are protected by a single patent. Top-down estimates provide only a ceiling on valuation when multiple patents cover each product or service sold in the transactions that ultimately result in the financial statements from which the top-down estimates are drawn.
Frequency-Averaged Measures of Productivity
Every time-averaged measure of profitability has a frequency-averaged counterpart. In practice, experienced investors and managers use both to develop a picture of the health of an organization. For example, in addition to gross margin – a time-averaged ratio of profit to revenue – experienced investors and managers also track inventory turnover – a frequency-averaged ratio of costs of goods sold to average inventory. A company with high gross margins but dropping inventory turnover is unlikely to maintain its margins going forward. Conversely, low margins with increasing inventory turnover signals that higher margins might be available in the future. [Discuss analogy to driving without a tachometer.]
Inside large corporations, managers don’t wait until the end of the quarter to spot trends in supply or demand for a particular good or service. Rather, managers monitor daily reports about order and inventory volume to ensure that the supply of products and services stays synchronized with customer demand.
Bottom-up Estimates from Frequency-Averaged Measures
The stream of data that management uses for frequency-averaged measures of productivity provides the basis for alternative, bottom-up estimates of demand for patented innovations. Bottom-up estimates derived from frequency-averaged measures are useful in valuing patents on innovations introduced as features of an existing product or service, or in valuing patents on products or services that are sold as a bundle with many other products or services. Bottom-up estimates may also be helpful in putting a more reliable floor on the minimum value of a patented innovation. A variety of techniques may be used to produce bottom-up estimates using frequency-averaged measures. I give two as examples: Fourier analysis of a time-series of transactions and A|B testing of a web service.
Sales of a particular product are recorded as a time-series of transactions, each of which is associated with a particular price. Within a particular window of time, one can count up the number of transactions and the total sales. The former is a frequency-integrated measure of sales, the latter the time-integrated measure of revenue. Focussing on the former, we can see how the frequency of sales changes within different same-width and different-width windows of time. Most relevant to patent valuation, we can look at how the frequency of sales changes before and after the introduction of a new patented feature. If frequency increases even as price is held constant or decreased, the patented feature probably increased the demand for the product or service.
Because frequencies change seasonally, many web services rely upon a more direct method for testing demand for a feature, called A|B testing. Using A|B testing, managers can watch how actual consumers interact in real-time with a web service that includes slightly different features. It is conceivable that A|B testing could be used in some cases to demonstrate that a patented feature is less desirable than an existing version of web service, effectively resolving some disputes that cannot be resolved using only top-down estimates of value. [Discussion of A|B testing, Google Analytics, Optimizely, &c.]
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