148 Afiriciil/ural Research and Produclivily 



Then 



E^iAy) = E(x)-y, (8.14) 



and 



Var^(A>') = Var(x)/«. (8.15) 



See table 8.1 for the expected value and the variance of the tech- 

 nology increment. 



Optimal Experimentation 



The outcome of an experiment in period / affects the yield and the 

 technology level in periods ^ + 1, and so on. To consider optimal 

 experimentation, i.e. the optimal level of n, we observe that in 

 both version 1 and version 2 E (Ay) is independent of the value 

 of >'. Consequently, an increment of >' in one period will not affect 

 the increments in the following periods. This property is due to 

 the learning process that enables, by assumption, the search to be 

 restricted to better than available technologies (equation 8.9). The 

 expected economic value of an experiment in period t is therefore 



oJin^J^ o/' E[Ay(t)] 

 k = t 

 where Ay is technology increment at (. The cost associated with 

 Ay(t) is c[n(t - 1)] incurred at the beginning of the period 

 over which search takes place. 



Without loss of generality, assume that the system starts at the 

 point / = (the beginning of the period i = 1). Since future y 

 values will be independent of the state of the system — the tech- 

 nology level y— the problem of optimal /7 is a single period prob- 

 lem: maximize for each period independently the returns to 

 search net of cost. Formally, 



ma.x\y E(Ay) - c(«)l (8.16) 



where Ay is the technology increment when / = 0. In version 1 



To find optimal n we look for the smallest first differences, 



