The propensity to patent with differentiated products.

• Author: Harter, John F.R.
• Position: Communications

1. Introduction

   It has been noted in the literature [5; 8; 9], and observation readily confirms, that not all inventions are patented. There are, of course, several explanations for why a firm might not actually patent all of its innovations including the ideas that a patent would give information on profitability to non-inventors, that some inventions might not satisfy the novelty requirement [6; 10], or that a patent would give information to non-inventors on the production of the invention. Horstmann, MacDonald, and Slivinski [3] utilized the first explanation in providing a theoretical framework for why the propensity to patent--the proportion of innovations which actually are patented--is somewhere between zero and one. This paper will utilize the last explanation in offering a complementary framework.

   Economically, a patent system is justified for three basic reasons: it rewards the inventor, creating an incentive to invent [7]; it allows for the development of inventions into marketable innovations by defining the property rights over the inventions, lessening the need for secrecy in outside contracting [4]; and it entails the full disclosure of an invention such that someone "skilled in the art" could understand and duplicate it. It is this disclosure which is intended to be one of the main positives that counters the negative of artificially-created market power for the inventor since it allows for a faster diffusion of the new idea. This implies that a non-innovating firm would have little or no need of reverse-engineering the product, making imitation easier. In exchange for this information, the government guarantees the inventor certain property rights over that invention. It is then up to the inventor to decide if gaining those rights is worth letting that information become known. This paper tries to model this trade-off using a differentiated-products model. It is found that the firm will patent if the follower will not use that information, and that the firm might or might not patent if the follower will use the information in order to imitate. Simply put, some inventors will patent, and some will not. Thus, a propensity to patent is obtained between zero and one.

   It is assumed that innovation has already occurred for one of the firms. The question at hand is whether or not the inventor will patent, and the answer will depend on the non-innovator's intentions. Except for indifference, the inventing firm will know for certain if it will patent. However, neither firm knew a priori which would be the innovator and which firm would not (whether a patent is applied for also depends on the equilibrium being played if there are multiple equilibria).

   The purpose of this paper is to examine the patenting decision of a firm when a patent would allow non-inventors to learn more about how the product is made, potentially hurting the profits of the inventor. While this is a sub-game of a larger, differentiated-products game which would include the choices of product varieties by the firms, the patent issue must first be addressed and is an interesting topic on its own. The result here is a framework for explaining a propensity to patent between zero and one which acts as a complement to Horstmann, MacDonald, and Slivinski.

   The rest of the paper is organized as follows: section II describes the basic model; the patenting decision of the innovating firm is discussed in section III; and section IV concludes.

2. Basic Model

   The model is an adaptation of that found in Harter [2]. This paper, however, adds the option of imitation to the non-innovator's choices and includes a patent system. A patent will block off a segment of the market around the invention from further entry, but will make imitation less costly. Thus, this is a fencepost patent system, not a signpost system [11].

   The two risk-neutral, profit-maximizing firms, A and B, have simultaneously chosen product varieties which are described by locations on the unit interval and have begun R&D. The product variety chosen by firm A is described by the location a, and that chosen by B is described by b.

   The R&D process is location-specific, and is represented by a known, Poisson discovery process with a hazard rate denoted by h. Each firm faces a fixed cost, F, and a flow cost, z, to R&D, both of which are assumed to be strictly positive. Once a firm invents, it innovates immediately, producing the invented good at a constant marginal cost which, for simplicity, is assumed to be zero. The firm does not innovate again. The original innovator is a monopolist in this class of goods unless and until the non-innovator has also innovated.

   The innovating firm has the option of patenting its invention immediately after the successful completion of R&D. The patent is assumed to be of infinite length and to force any subsequent innovations to be farther than w from the location characterizing the...