A Simple Model of Technological Research 



149 



analogously to equating derivatives to zero in calculus. Optimal 

 number of trials in version 1 will be n* satisfying 



(8.17) 

 where \ c — c(n) — c{n — 1 ).See also figure 8.3. 

 In version 2 the optimization problem is 



"?''[fx-''H 



and since £'(Ay) = if a? = 0, optimal n, rf, is simply 



/7*=1 ifc(l)< ^ 



A7*= Otherwise. 



In this version the number of trials in an experiment does not 

 affect the expected value of the outcome of the experiment. 



(8.16") 



(8.18) 



Figure 8.3: Optimal n. Version I 



