ment theory—versions associated with the models of economists Arrow (1962), Nordhaus (1969), and Scherer (1972)—inventors, as a group, are implicitly assumed to be diverse, working on different and generally noncompeting things. Thus in the absence of redundant efforts that might occur if many groups worked on competing things, stronger patent protection results in a greater number of useful inventions.

Most articulations of the invention-inducement theory presume that an invention is used or sold by the firm that made the invention. However, Arrow (1962) and more recently Merges (1995) and Arora and others (1994) address the problem that an inventor has in selling an invention to someone else in the absence of legal property rights to it and have taken the position that strong property rights to an invention reduce the transaction costs of licensing it. Strong patents would then also serve the purpose of providing incentives to invent for parties who are limited in the extent to which they can use the invention themselves, by facilitating the sale of rights to an invention.

In most versions of the invention-inducement theory it is assumed, generally implicitly, that the social benefit of a particular invention is strictly its final use value; the social benefit of patent protection stems, therefore, from the additional invention induced by the prospect of a patent. And the social cost of a patent is the restriction on the use associated with the monopoly power lent by a patent. That formulation of the invention-inducement theory leads naturally to analysis of optimal patent ''strength,'' defined as duration (Nordhaus 1969; Scherer 1972), or breadth (Klemperer 1990), and the tradeoff between the amount of increased invention induced by greater patent strength and the increased costs to society associated with the stronger monopoly position of the patent holder (see also Gilbert and Shapiro 1990).

The issues of the consequences of greater patent duration or scope are more complicated if an invention is not only useful as is, but also provides the basis for second-generation inventions. Arrow especially called attention to the possibility that the principal use of some inventions is as input for further inventions (such as PCR, see Chapter 5). Van Dijk (1994) considers what he calls the height of a patent, by which he means the extent to which the patent controls later improvements and variations in the initial invention. Those considerations lead us to the development and commercialization theory, and prospect-development theory, which are discussed later.

We stress that the version of the invention-inducement theory that we have been considering up to now presumes that more inventive effort and more inventors mean more useful inventing. The theory takes on a different look if, instead, all inventors are assumed to be focused on the same set of paths to invention. This assumption gives rise to the "patent race models" of Loury (1979) and Dasgupta and Stiglitz (1980a) and, if the assumed common focus is on a broader but still limited "pool" of invention prospects, to the "overfishing" models of Barzel (1968) and Dasgupta and Stiglitz (1980b). Under either model, patents no

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