The calculations reported in Table 4-1 indicate that, as expected, the elasticity of expected welfare in the number of potential parent organisms declines in the number of potential parents, keeping the elasticity of demand fixed, and in the elasticity of demand, keeping the number of potential parents fixed. As the elasticity I have reported is the percentage change in welfare resulting from a 1% change in the number of potential parents, the change in welfare resulting from a small change in the absolute number of potential parents would be small indeed in most of the instances I have reported. While it would be difficult to estimate the total welfare derived from the consumption of something like teak wood, the results I have reported suggest that the incremental value of additional genetic resources would be modest.
This conclusion should be qualified in a number of ways. First, I have been assuming that consumer surplus is measured under uncompensated demand curves. As is well known, this approach is valid when income effects are not important. While this may not be too unreasonable of an assumption in discussing the demand for teak wood, it would be more questionable when applied to, for example, rice or wheat. Staple crops may claim large shares of income, at least when they become rare. Clearly, the stakes rise as the scope of use increases. Martin Weitzman (2000) has recently done interesting work in which he considers the tradeoffs between, on the one hand, maintaining a diversity of organisms to protect against the failure of each type of crop and, on the other, the opportunity costs of growing varieties anticipated to be less productive. The general issue he identifies—the desire to prevent very low probability but also very catastrophic outcomes—is important, but difficult to resolve.
Another major omission of the approach I have taken here concerns the treatment of dynamic considerations. One could make the approach I have illustrated dynamic by supposing that, in every period, breeders must identify a variety that best suits a set of conditions that have completely changed since the previous round of selection occurred. It may, in fact, be the case that this complete-change-in-circumstances scenario leads to the highest estimate of value for the "marginal potential parent": it would seem that, to the extent that selection continues to occur for the same traits over time, a finite upper bound would eventually be approached. More generally, however, each new generation of propagated organisms would comprise a new random draw from the gene pool. Thus, one might, in a more complex analysis, want to consider not only the direct benefits of genetic diversity in terms of producing superior varieties for immediate cultivation, but also for producing varieties that might in turn produce still other varieties.
This leads me to the final consideration that I will address here. I have supposed that the process of selection involves the identification of the single "best" individual, and that unlimited numbers of identical individuals can be replicated exactly from this source. In practice, selective breeding typically involves the identification of a group of individuals and the attributes of their offspring reflect only imperfectly those of the parents. The analysis I have presented here can be extended to consider selection of a set of parent organisms and to incorporate imperfect heritability of attributes.10 Results are compromised somewhat by the practical necessity of abstracting from Jensen's inequality in order to maintain tractability (results are much more easily derived by supposing each offspring organism exhibits the attribute at the mean level). Given the other imprécisions inherent in the analysis, however, this does not seem to be a major impediment to deriving illustrative results of the type I have illustrated here.
I might note in closing that the model I have sketched is becoming dated by advances in biotechnology. I have supposed that the only way to generate improved commercial varieties is to identify promising "packages of genes" in the form of parent organisms. As the process of agricultural improvement comes to rely more and more on the insertion of favorable individual genes, the search for superior quantitative characteristics may come more and more to resemble that for favorable qualitative characteristics. Moreover, the ability to transplant genes even between different species (and sometimes higher phylogenetic taxa) may imply that genetic resources are becoming less and less scarce with respect to particular crop improvement applications and, hence, of lower economic value.
10 A formula commonly encountered in quantitative genetics (see, e.g., Falconer and MacKay, 1996), holds that
where n® is the mean of the original population from which selection occurs, // the mean of the selected population (where selection is accomplished by choosing all those individuals for which the observed value of some attribute exceeds a certain level; in other words, fj,s is the mean conditional on the observed attribute exceeding the selection criterion), /f is the mean of the offspring of the selected parents, and h2 is heritability, a measure of the correlation between parent and offspring attributes.
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