The simple model sketched out above shows how recharge research is important to induced innovation. It does not address very directly the matter of incentives for undertaking R&D. Nor does it address inter-industry or geographic spillovers.
As the section on plant breeding and agricultural research below will show, both problems are central for this field of research. Perhaps it is because of the severity of both problems that we observe them being addressed as effectively as they have been. Public sector agricultural research systems have been built in most countries of the world. These systems were among the earliest cases where governments recognized that the incentive systems (chiefly intellectual property rights (IPRs) systems) were not sufficient to bring forth adequate invention. Colleges of agriculture and mechanics (A&Ms) were originally designed to train agricultural and engineering practitioners. Agricultural experiment stations were developed to facilitate inventions (especially plant breeding), and extension systems were developed to diffuse these inventions.
Over the years these institutions were continuously in tension over the relative weights to place on extension, invention, and pre-invention or recharge science. Equation (12) describes recharge activity and shows the resource allocation rule for breeding (equation 13). Pre-breeding (recharge) activity is described by equation (15), and equation (16) gives a simple allocation rule. Finally equation (17) describes the genetic resource allocation-collection activities.
There is thus a consistent system of derived demands for the relevant activities - breeding, pre-breeding, evaluation of CGRs and collection of CGRs -sketched out in the model. Empirical estimates of these derived demand equations are hampered by the lack of adequate markets for CGRs.
The simple breeding model sketched out above does provide guidelines as to the derived demand for various types of research activities. (Incentives affect the supply of such activities.) The demand for plant breeding research producing a single trait for a particular location is based on equation (7). Each new invention has an incremental value expressed by its value of marginal product XV/n (see equation (10). The optimizing level of trait search is determined by equation (10). For multiple traits, each has a demand function and optimization is governed by equation (12). These expressions describe the demand for inventive effort given the search distribution.
In the section 'Multiple periods without recharge', the demand for search field narrowing activities is developed. Some search field narrowing (SFN) is a by-product of search, but some is competitive with search. The value of the marginal product of SFN activity is based on its effect on the marginal product of search.
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