The Process of an Innovation Cycle 



129 



The innovation cycle may continue until u =H'Q,but this is 

 not the only possibility. Several alternative final distributions of 

 producers, attained after the completion of the diffusion process, 

 can be distinguished. Four such cases are depicted in figure 7.4. 

 Case c is an innovation cycle as described above. In case a the de- 

 mand was highly elastic and skilled producers did not exit at all. In 

 cases b and ^the innovation cycle stopped at u >Wq . A necessary 

 condition for this is the existence of a worker effect [g(w,oo)< 1 ] 

 in the new product, so that low-skilled producers can never, not 

 even with maximal industry experience, master the profitable 

 production of this product. 



Further Dynamics 

 Total product of the industry is 



j; 



Q ^ I n'{w) qg(w,H) dw. 



(7.8) 



Taking time derivative of Q, incorporating 7.8, and making use of 

 H = Q, one gets 



q I n '(w) ^jT dw + Pq ^ 



0.= 



d8 



dfi 



n'( ii)g( u,H) ^ n'CuJgfuM) ^ 







(7.9) 



pV 



n'( ukC uM)^ n'(u)g(u.H)^' 





hi 



It can be shown that (p(Q,H) > 0. The solution to 7.9 is 



(2(0 = exp [((l){Q,H)ds + cl 



(7.10) 



with 



QiO) = exp (c). 



