124 Agriciiliiiral Research and Productivity 



The Industry is competitive and faces a downward sloping de- 

 mand curve for the new product with the price 



P = P(Q) 



(7.5) 

 P' <0. 



Producers in the industry can be ordered by skills (shadow price 

 of own labor). Let n(w)be the number of producers with shadow 

 price of h' or less. The cumulative function n is nondecreasing; 

 assume it to be differentiable (figure 7.2). If Wq is the lowest in the 

 industry and w^ the highest, then /?(\v'q)=0, and«(w;^)is the total 

 number of producers in the industry. The function n'{\v)(^dn/ 

 dw)\s the frequency distribution of producers. The particular 

 form depicted in figure 7.2 (and figure 7.4), in which //' is 

 diminishing with vv, implies greater concentration of producers in 

 the lower-skill range. 



Profits and Final Distributions 



Producers will generally adopt the new product if it is profitable, 

 and will increase production if profits increase. But to concentrate 

 on the main theme of the model and to reduce mathematical 

 complexity, it is assumed that the new product, if produced at all, 

 is produced by all firms with identical amounts, L,v, of physical 

 inputs. Let 



q=fd,v)'\. (7.6) 



be the output of a firm for which g(w,H) = 1, i.e. a firm with max- 

 imum knowledge. Assume further that the introduction of the 

 new product does not alter h', the shadow price in the other lines 

 of activity of the firm, then profits above alternative costs in the 

 new product in firm / are 



TT. = Pq g(Wi,H) -WjL - V. 



The firm will produce only if profits are positive 



Qi = Q g(w..H) TT. > 



q. = TT. < 0. 



