If the industry is producing S at profit-maximising levels, then marginal cost equals marginal revenue and the difference in the first set of brackets is zero, yielding

5 For making intercountry assessments of the importance of imported PGRFAs, V-(/) can be re-expressed as Rj(l) = 1 - [(w. ")]/[(%■ )] Since (wj ), the ratio /?^(/)ranges from 0 for no dependency on set I to 1 for complete dependency on set I.

6 While noting that set / can be more generally conceived of as germplasm, it is defined as varieties for ease of exposition.

dn dN

which says that the increase in profits for a marginal increase in N equals the negative of the decrease in costs associated with a marginal increase in N. If we assume that research costs fall with increases in N, then dn/dN > 0 and profits increase with increases in N. If the seed industry were to be taxed for contributions to the benefit-sharing fund in the amount t(N), so that 71 = pfSjS - C(N, S) - t(N), where dt/dN> 0, then dn/dN would be positive only if -dc/dN> dt/dN. In other words, the marginal tax rate on N must be less than the decrease in marginal cost of N for breeding firms to benefit from increases in N. Similar analysis can be used evaluate the impacts of N and of t(N) on consumer and producer surplus (Cooper, 1998).7

Of course, Vj(I) is a function of the scope of PGRFAs included in / as well as the time period over which benefits are to be evaluated. For instance, is / the set of all varieties of wheat, or even all major crop species in existence at time j, or I is the set of varieties obtained by plant breeders from suppler countries in j. If it is the former, Vfl) will be enormous. Or is I measured at the gene level? With regards to the time dimension, in quantifying total benefits for the purpose of determining contributions to the benefit-sharing pool, is the present value of past benefits to be included in addition to current benefits? If so, how far back? While scope and time dimensions have not been set in the multilateral negotiations, some definitions have been discussed. For example, the African Region states that the contribution to the fund should be some percentage of "the value of the commodity produced using intellectual property rights [IPR] material..." (CGRFA, 1998), which is similar to a definition set out in a proposal by Malaysia. Since Intellectual Property Rights (IPR) for PGRFAs are a fairly recent concept, this definition addresses the time dimension as well as the scope of PGRFAs to be considered in determining benefits.

Even if/is precisely defined, a complicating factor in estimating (Wj \ I) is that the substitutability of other inputs for set I must be considered, given that (Wj \ I) in the case where some substitutability of inputs is possible will be higher than (Wj\ I) in which no other inputs can substitute for set I. Substitutability may be in the form of technological innovations. If advances in biotechnology make the availability of PGRFAs for plant breeding less necessary, then Vj(I) may decrease.

7 In the equation for dn/dN, it would be more accurate, but less eloquent, to explicitly consider the stochastic aspects of N with respect to producing new commercial varieties. If so, the expectation of the function is not the same as the function of the expectation. The point of the expression given in the text is to convey the essence of the valuation argument V(I) and to serve as a serviceable first approximation to the exact, but much more complicated, expression.

Because of substitution possibilities between PGRFAs, one would expect diminishing marginal benefits to be associated with adding another randomly chosen PGRFA to I. The more varieties are contained in /, the smaller the difference in V/I) with and without any randomly chosen variety. For example, if I is a set of PGRFAs currently in publicly owned gene banks, given that most of these accessions are never examined, then the market value portion of V/I) changes little when a randomly chosen PGRFA is added to the collection (though, as discussed in the next section, the value added to society may be greater). Also, if one wants to consider the value associated with I supplied from any one country i, or Vj{Ii), then the extent of geographic substitutability must be considered in estimating this value. The value V/Ij) will be higher the more PGRFAs in /, are also grown in other countries other than i, and higher the less easily varieties from other countries can substitute for varieties in /,.

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