126 Agricultural Research and Productivity 



With our assumptions, profits will increase with w for low levels 

 of the shadow price and decrease for higher levels (figure 

 7.3). Let u and u be the lowest and the highest w values for which 

 7r(u') = 0.^ Production will take place by producers with 

 shadow prices on the range(i/jO. With time, experience accumu- 

 lates, production expands, and prices fall. In the innovation cycle 

 process, falling prices drive high-skilled (and wage) producers out, 

 while low-skilled producers benefit from experience and adopt 

 the innovation. 



To trace the innovation cycle, focus on the movement of the 

 boundaries, the break-even points w, u. For these points tt = 

 always. Differentiating 7.6 with respect to time, incorporating 

 rr (=d 7r/dt) = 0, and writing bg/du for 3g/3vv evaluated at w , 



. P'm{u,H) + Pq^ Q 



II — ^r {u = u, or u = u) (7.7) 



Put in words: for u and u 



market effect + learning effect 



bu 



For w, the (negative) market effect is stronger than the (positive) 

 learning effect and ^< 0, thus lK 0. With a learning effect 



stronger than market effect and ^> 0, iT< also. At the 



beginning of the diffusion process, w = vv^and w =0, until high- 

 skilled producers start to exit.^ 



5. When the diffusion process starts, profits are positive for the highest-skilled 

 operators, therefore set m = w;^ if 7r(w) = for w > w^. Similarly, set w = wq 

 if tt{w) = for w < wq. 



6. For ihc innovation cycle proper to exist, i.e. for the innovation to move from 

 high-skilled producers to low-skilled ones, the market effect at Ti has to be stronger 

 than the learning effect. If this is not the case, high-skilled producers will never 

 drop the new product. These alternative possibilities will be rcllecied in different 

 hnal distributions, as shown in the next section in the text. 



