1 30 Agriculniral Research and Productivity 



Equation 7.9 in its present form is applicable when the innova- 

 tion cycle proceeds, with some producers beginning and others 

 dropping the production of the new product. At the beginning of 

 the process, before the exit of the skilled producers, or always in 

 cases a and b in figure 7.4, u = h)^ in the integral in equation 7.9, 

 and other terms involving u vanish (since u*',^ = 0). 



When u = Wq in case a, or in all other cases when movement 

 of producers in or out stops, Q will continue to grow as a result of 

 learning at the rate 



until ^^ vanishes. (Q can be expected to have discontinuities, 



and Q "kinks," where producers start or stop to exist, and, strictly 

 speaking, the integral in 7.10 is calculated between such discon- 

 tinuities.) 



Unlike other diffusion models proposed (Mansfield 1961, 

 Nelson 1968), the present one does not yield a logistic time pat- 

 tern, although in some cases an S-shaped function can be 



expected. Eventually Q approaches zero as time passes and 



vTj -^ for all levels of w. When the process starts, P' will, in 



many cases, be comparatively low due to shifts in short-run de- 

 mand with growing familiarity of the market to the new product, 

 and Q can be expected to grow approximately in proportion to Q 

 (particularly so long as u = vv^). These two effects may be ex- 

 pected to generate an S-shaped time pattern of production. 



Although production of the new product can be expected to 

 taper off asymptotically as experience accumulates, this will not 

 be the general pattern with respect to the number of producers, 

 particularly not in cases a and c. Let the number of producers be 



N = n{u) - n{u). (7.11) 



Then 



