A Simple Model of Technological Research 143 



From 1890 or so to 1939 a breeding program based on stage 2 

 methodology was pursued. From 1902 to 1912 the station released 

 ten commercially important varieties; from 1912 to 1939, only 

 five (three of minor importance). In 1929, a stage 2 interspecific 

 hybridization program was introduced. This program released 

 fourteen commercial varieties between 1929 and 1939. During 

 the period 1929-39, when both programs were being utilized, the 

 ratio of commercial varietal discovery to seedlings brought to the 

 final testing stage was 1:1800 for the first five stage 3 varieties, 

 1:2700 for the next nine, and only 1:13,000 for the stage 2 

 program. This evidence bears out the predictions of the model. 

 The formal model suggested here is first set forth as a process of 

 applied technological research. Supporting scientific discoveries 

 are viewed as "shifters" of the mean and variance of the distribu- 

 tion of potential discoveries. The model is economic. Research is 

 a costly process and discoveries have economic value. The objec- 

 tive of the managers of the system is to maximize the present 

 value of future income net of the costs of research. 



Applied Technological Research 



The scientist (scientific team) is assumed to be presented with a 

 given distribution of outcomes whose parameters he cannot 

 directly affect. His work is limited to testing, no basic research is 

 undertaken. To be concrete, imagine a research project aimed at 

 increasing the yield of a crop. To simplify, assume that net in- 

 come is in direct proportion to yield. The work on the project is 

 composed of a succession of experiments. In control theoretic 

 language, the state of the system is the yield at any point in time, 

 the results of the experiments are the transition equations- 

 changing the yield level. The control variable is the number of 

 trials in an experiment— the number of drawings from a random 

 distribution. 



Since the transition equation is a random process, the state vari- 

 able also is random, but other sources of randomness and uncer- 

 tainty, such as weather effects, are disregarded. 



At any period / an experiment composed of n^ trials is con- 

 ducted. Define the following variables: 



