## Model of Firm Intellectual Property Strategy

This section examines a firm's ex ante decision problem to apply for any form of IPRs through patents or to keep a trade secret. For the purposes of this exercise, we abstract from the differences between PVPA and utility patent property rights, but it is the differences in rules that will drive the value of IPRs with respect to trade secrets.

Let there be two firms (i and j) competing in a market to produce a seed to sell to a set of farmers. The firms can choose between keeping a trade secret and seeking

IPRs, i.e. a patent, on their technology. It is assumed that both the symmetric firms have a piece of R&D output that they wish to either patent or keep as a trade secret. The probability of success in the patent application process is independent for each firm. As a result, the probability of success of a patent application from firm i does not impact the probability of success of firm j. If both the firms are approved for a patent, they share the total monopoly rent equally. If they both keep trade secrets, they still share the market rent equally. The profit from a patent and a trade secret will differ due to differences in their costs and benefits, which are described below. When one chooses a patent and the other a secret, the majority of the rent accrues to the patent-holder.

In matrix form, the model can be given as

Firm j

Firm i

where ni{pt,pt} are the monopoly returns from firm i having a patent and sharing the market with firm j, and n{s,s} are the returns from both firms that are keeping a trade secret. When one firm chooses a patent and the other a trade secret, they have asymmetric returns ni {s,pt}, p {s,pt}, which provides monopoly returns to the firm that owns a patent, whereas the trade secret owner receives zero returns.

There are two interesting Nash equilibria from the perspective of the empirical evidence presented: the two diagonal elements of the matrix (trade secret/ trade secret) and (patent/patent). Given the very low returns for trade secret owners on the off-diagonal, these are also the least likely equilibria given reasonable parameterization of the other values. The trade secret/trade secret equilibrium characterizes an industry such as the plant or seed industry in the period before the advent of the PVPA, whereas the patent/patent equilibrium characterizes an industry such as the biotechnology part of the plant or seed industry in the last decade. Whether the equilibrium is at trade secret/trade secret or patent/patent, it will be a function of the relative value and costs of patents versus trade secrets.

The elements of the value of property rights are determined by the strength of the property rights, their enforceability and the length of time that they hold sway. Thus, a trade secret is only as valuable as the firm's ability to keep it a secret, and a patent's value is only as good as the firm's ability to enforce it. In addition, decisions to choose IPRs will be in part driven by how long they can be enforced, whereas decisions to keep trade secrets will be a function of the expected length of time before a rival can legally steal, copy or reverse-engineer the technology. Also relevant to the value of IP is the speed of technological change in the industry. In industries with rapid change, such as in software, the effective length of IPP is bounded by the length of time before the product becomes obsolete, which may be as short as 2 years. Thus, one is more likely to see the trade secret/trade secret equilibrium in industries with high levels of technological change.

The elements of the costs of IP and trade secrets to a firm come from two elements: (i) the probability that the information in the technology will be revealed;

and (ii) the cost of obtaining the IPRs. We focus primarily on the first cost as being the most important to the outcome of the firm's choices. Each type of property right will have its own probability of being revealed to a rival. Patents, because of their public disclosure, necessarily reveal some of the technology, although a part of that revelation is protected. PVPCs, in addition to having the same level of public revelation as PUPs, allow further public disclosure of the technology to rivals by having a research exemption.

This theory suggests the following relationship between the features of the IP and the technology as well as the equilibrium outcomes likely to be observed in the market:

High revelation loss probabilities in IP - When there are high probabilities of revelation losses in patenting, firms are more likely to keep trade secrets than apply for IPRs. Thus, under the PVPC-only regime the trade secret equilibrium is more likely than under the PUP regime.

Timing - A longer shelf-life for a technology is likely to lead to greater reliance on patents than on trade secrets. Thus, we can expect more trade secrets in corn than in soybeans.

Probability of losing a trade secret - As the probability of losing a trade secret goes up, firms are more likely to choose IP. Thus, for seeds in which hybrids do not exist such as soybeans and wheat, one is more likely to see the use of IPRs than in seeds such as corn, in which hybrids are possible.

These predictions are considered in the next section using empirical evidence from firm choices of IP in the plant and seed industry with a particular focus on corn and soybean IPRs.

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