J [pqdq C

This relationship is illustrated in Fig. 4-1. The output of this agricultural crop is initially determined by the intersection of the demand curve, D = p(q) with marginal cost, MC0 = dC/dq. It seems reasonable to suppose that an "improvement" in a crop will reduce the cost, and, specifically, the marginal cost, of growing it. Thus, I show the change in 6 from 0O to d\ shifting marginal cost down from MC0 to MC\. This new intersection of supply and demand results in quantity produced shifting from c/0 = q(0Q) to qi = q{0\).

Figure 4-1. Welfare changes induced by genetic improvement

Now the nature of the change in welfare induced by the improvement in 6 depends on the magnitude of that change. I have drawn the "before" and "after" marginal cost functions as straight lines, so part of the welfare change can be thought of as a "cost reduction" effect, and measured by the parallelogram abed in the figure. The remainder of the welfare change can be thought of as an "output" effect, and measured by the triangle cde. In short, abed measures the reduction in cost of producing q0, while cde measures the benefits to consumers, net of incremental costs of production, of expanding output from q0toq\.

Clearly, different aspects of the welfare change are going to be important depending on the nature of the genetic improvement. At one extreme we might think of the search for a genetic improvement that is absolutely essential if the crop is to be grown at all. For example, if a disease threatens to wipe out the entire crop, it may be essential to find a gene that confers resistance. In this case the welfare gain arising from the discovery of the gene would be the entire area between D and MC\. On the other hand, if we're thinking of a situation in which plant breeders have already developed a relatively high-yielding variety, the welfare gain from finding a marginally better one will consist largely of the cost reduction effect, with the output effect being of the second order of importance.

In the examples considered in the next two sections, it seems that qualitative genetic attributes are likely to give rise to discrete improvements, and hence to situations in which welfare gains would combine cost reduction and output effects. Conversely, quantitative genetic improvements are more likely to give rise to incremental improvements, so welfare changes would be dominated by cost reduction effects. In short, then, we are likely to encounter a common but vexing problem in environmental valuation: comparing very unlikely, but potentially large effects with more likely but probably small effects.

2.1 Qualitative characteristics

The economic value of a genetic resource is related to the value of the expected outcome of a process of search for improved attributes with and without that particular genetic resource included in the set over which search is conducted. When we are considering single-gene qualitative characteristics, the probability distribution of outcomes is simple: a gene providing the required service is either available or it is not. More formally, the probability distribution function simplifies to a Bernoulli trial: The desired trait either is or is not present in the genome of a particular organism. Let us denote the probability with which the gene is found in a particular organism sampled asp, so it is not present with probability 1 -p.

To keep the analysis tractable, suppose that each of N organisms in a population may contain a crucial genetic attribute with the same, independent, probability p (see Rausser and Small, 2000, for an example in which different organisms contain the desired gene with different probabilities). If an organism contains the crucial gene, a payoff of R is realized. This payoff, R, could be related to social welfare as in the previous section. For some crops, R might be astronomical: Consider, for example, the costs society would bear were it impossible to grow wheat, maize, rice, or potatoes. If the desired gene is not found, let us normalize the payoff to zero. Let us suppose that there is a cost c of evaluating any particular organism to determine if it exhibits genetic resistance to a particular pest. Combining the probability, payoff, and cost considerations, the value of the "marginal organism" with respect to its expected contribution to the development of genetic resistance to a particular pest is

Heuristically, the value of the "marginal organism" is its expected value net of the cost of testing, pR - c, times the probability that the desired gene is not found among any of the N other organisms.

For fixed values of R and c, the maximum value v can take on is

(Simpson, Sedjo, and Reid, 1996).4 Clearly, this becomes a small number as N gets large. Eq. (4) results when it is assumed that the probability with which any particular organism contains the necessary gene just happens to be that which maximizes the value of the marginal organism. For values of p other than those that approximately maximize the value of the marginal organism, v would be smaller yet. The issue then concerns the magnitudes of the payoff to successful discovery, R, the cost of testing, c, the probability, and uncertainty concerning the probability, p, with which success occurs, and the number of organisms over which testing can occur.

It is difficult to say exactly how these considerations interact with one another. Any conjectures are necessarily controversial given the magnitudes of the uncertainties involved. Perhaps if, as suggested above, humanity were truly confronted with the loss of a widely grown staple crop such as wheat, maize, rice, or potatoes, the prospect of so calamitous a loss would translate into a substantial value for the "marginal" element of genetic diversity. Given the existing quantity of potential "solutions" to such challenges, however, the value of diversity may still not be great with respect to the potential to provide qualitative genetic traits even in important crops.

2.2 Quantitative characteristics

4 This expression is derived by differentiating Eq. (3) with respect to p, setting the result equal to zero, and using the approximation, (n + 1 )"/n" ~ e, where e is the base of the natural logarithm, approximately 2.718.

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