A Simple Model of Technological Research 147 



Note that A;^ > always, since 



Ay =x ~z (8.10) 



/(x)is continuous and therefore 



Pr{Ay = Q)^Pr{z<y) = Pr{x<d) = Q (8.11) 



The expected value of the technology increment is 



E^(Ay)= t zh^(z)dz (8.12) 



f: 



[1 -FHz)] dz 



The first row of table 8.1 shows the expected value and the 

 variance of the technology increment in the exponential distribu- 

 tion. 



Table 8.1 : Expected Value and Variance of A>'. 

 the Exponential Distribution (« > 1) 



EJ^^y) Vatri^y) 



« , « J 



Version! Z 5^ 2 (^2 



/= 1 /= 1 



Version 2 1 1 



X \^n 



Note: E„(Ay) = VarjAy) = for « = 



Version 2: Often the conditions in the experiment station differ 

 substantially from those in the field. What seems to be the best in 

 the laboratory may not be so in practice. To incorporate some of 

 the uncertainty associated with the applicability of experimental 

 results together with an element of learning, assume that equa- 

 tion 8.9 holds, but that 



Ay=x-y (8.13) 



where 



n 



x=^ x./n. 

 /-I 



