150 A^riculiiiral Research and Procluctivily 



Optimal Variance (Version 2) 



Basic research, in the present framework, may shift the mean of 

 the distribution searched or open new distributions to study. The 

 importance of work aimed at increasing the variance of tech- 

 nologies available for experimentation is not always duly appreci- 

 ated. A common practice in agronomic research, for example, is to 

 subject seeds or plants at the reproductive stage of their life cycle 

 to radiation. This results in increased rates of mutations, of which 

 many will be without economic value. However, some may turn 

 out to have superior traits (Sigurbjbrnsson 1971). The Rice 

 Research Institute in the Philippines collected 15,000 varieties of 

 rice to be used in its search for superior genetic stock; similar 

 research procedures are to be found in other technological fields, 

 e.g. organic chemistry, where a large variety of compounds with 

 similar characteristics is produced. 



The effectiveness of variance-increasing research is due to the 

 fact that the expected value of the largest observation in a sample 

 is an increasing function of the variance of the population 

 sampled. To incorporate, in the present framework, variance-in- 

 creasing research, assume that the parameter X can be decreased 

 over time by research work. This variable X is a parameter of 

 both the mean and the variance. The choice of the exponential 

 distribution in the present exposition precluded the possibility of 

 the analysis of pure variance-increasing techniques. 



It may be reasonably assumed that the cost of modifying the 

 variance is an increasing function of both the rate of its change 

 and the existing variance. It will also be convenient to replace ~, 

 the variance parameter, by 7 . Denote now the cost of search by 

 Cj («)and the cost of variance modifying work by C2(A7, 7), 

 where y{t) = 7(0) + ^l^h ^li.^)^ and C2( ) is convex in A7 

 and 7 so that Cj [A7,7] = for A7 = and 



9c2 3c2 



3A7 ' 87 



8C2^ 8C2^ 



8A72 ' 3A7, 87 



>0 



(8.19) 



>0. 



