The Process of an Innovation Cycle 123 



Since w is a one-to-one function of £, it will be convenient to 

 substitute w for E and write the knowledge function as 



(7.4) 



^>0 ^<0 



lim Hr = 0. 



With these restrictions, equation 7.2 is a two-stage production 

 function: in the first, skills and experience are combined in a 

 "well-behaved" production function to create a knowledge com- 

 ponent that is combined, in the second stage, with the physical 

 process to produce the final product. 



This specification is not limited to the new product under con- 

 sideration; other products were also new in the near or remote 

 past. Writing g(w,<x) for knowledge with maximal amount of 

 learning, two general classes of products can be distinguished 

 (figure 7.1). In the first (perhaps wheat-growing) gi(w,oo)^ \^ 

 given enough experience, all producers will possess the same 

 level of knowledge specific to the production of this product. Ex- 

 perience completely substitutes for previously acquired skills. In 

 the second (radio manufacturing, say), g2('^,°°) < 1 for some 

 range of w. Here a "worker effect" exists in the production of the 

 product. The assumption of complementarity between skills and 

 other factors in a technologically stagnant economy, introduced 

 earlier, implies the existence of a "worker effect" in at least some 

 of the firm's products. 



