The Process of an hi nova lion Cycle 131 



N = n'iiT) u - n'(u)u. (7.12) 



In cases a and b in figure 7.4 



^ = -'^ [P'QQg(M,H) +Pq ^Q]. (7.13) 



du 



N is positive since the learning effect is stronger than the market 

 effect (see equation 7.7). But yv can actually increase as u—^wq if 

 n'(w)is high for low values of w (as assumed in figures 7.2, 7.4), 

 reflecting higher concentration of producers in the lower-skilled 

 groups. One can expect a general sigmoidal form of A^in time in 

 cases b and d , with entry rates increasing at the beginning of the 

 process and then starting to decline as the skilled producers exit, 

 not necessarily converging asymptotically to zero. 



On theoretical grounds these results are inconsistent with the 

 common observations that exhibit logistic time patterns. The 

 reason may be the neglect, in the present model, of the imitation 

 component (Mansfield 1961), i.e. a factor linking the rate of adop- 

 tion to the ratio of the number of potential adopters to those who 

 had already adopted. This implies the assumption that the diffu- 

 sion process is affected by the intensity of interactions between 

 these two groups.^ But on practical ground this inconsistency 

 should not be exaggerated. With errors in observations and in the 

 behavior of producers, who make their decisions according to 

 next season's expected prices, the judgment between the alterna- 

 tive models is not easy. Observations generated by a theoretical 

 time pattern, as in figure 7.5, can look consistent with a logistic 

 function. In empirical work such a function may be most suitable 

 for summarizing the diffusion information (see below). 



Remarks 



The profits made by the first adopters can justifiably be regarded 

 as rent to innovativeness. Whether the final producers of the new 



7. The crucial assumption in the present model in this respect is that experi- 

 ence diffuses freely (all firms have the same //). Imitation can be introduced into 

 the model by making learning by nonadopters a function of the ratio of adopters 

 to total number of producers. 



